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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 65 Vsebina - Contents
Vsebina - Contents
Strojniški vestnik - Journal of Mechanical Engineering
letnik - volume 53, (2007), številka - number 2
Ljubljana, februar - February 2007
ISSN 0039-2480
Izhaja mesečno - Published monthly
Razprave                                                                    Papers
Floody S. E., Arenas, J. P., de Espindola J. J.:         Floody S. E., Arenas, J. P., de Espindola J. J.: Modelling
Modeliranje sestavov kovine in elastomerov                  Metal-Elastomer Composite Structures Using
z uporabo postopka končnih elementov         66             a Finite-Element-Method Approach
Kušar J., Duhovnik J., Tomaževič R., Starbek M.:         Kušar J., Duhovnik J., Tomaževič R., Starbek M.:
Ugotavljanje in vrednotenje potreb kupcev                  Finding and Evaluating Customers' Needs in
v postopku razvoja izdelka                           78             the Product-Development Process
Džijan L, Virag Z., Kozmar H.: Vpliv pravokotnosti        Džijan L, Virag Z, Kozmar H.: The Influence of Grid
mreže na konvergenco programa SIMPLE za                  Orthogonality on the Convergence of the SEVIPLE
reševanje Navier-Stokes-ovih enačb             105            Algorithm for Solving Navier-Stokes Equations
Cvetkovič D., Radakovič D.: Matematični modeli Cvetkovič D., Radakovič D.: Mathematical Models dinamike helikopterskega letenja                  114            of Helicopter Flight Dynamics
Cvrk S., Dukič Z., Rodič M.: Določanje vijačnih        Cvrk S., Dukič Z, Rodič M.: Determining the Propulsion
lastnosti motorja z merilnimi lističi in osebnim                  Characteristics of an Engine Under the
računalnikom v ustaljenih razmerah plovbe                   Conditions of a Standard Sailing Regime by
ladje                                                          127            Means of Strain Gauges and a Personal Computer
Petrovič P.: Uporaba zvočne jakosti in preizkusne Petrovič P.: The Application of a Sound-Intensity načinovne analize za določitev hrupa                  Analysis and an Experimental Modal
dizelskega motorja                                                       Analysis for Determining the Noise Emissions
140            of a Diesel Engine
Poročila                                                                     Reports
Gotlih K., Janežič L:  IFToMM - Mednarodna         Gotlih K., Janežič L: IFToMM - The International
federacija za promocijo znanosti o mehanizmih                  Federation for the Promotion of Mechanism
in strojih                                                    149             and Machine Science
Strokovna literatura                                                   Professional Literature
Iz revij                                                                  151 From Journals
Osebne vesti                                                               Personal Events
Doktorat in diplome                                               154 Doctor’s and Diploma Degrees
Navodila avtorjem                                                 155 Instructions for Authors


Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
UDK - UDC 678.033:519.61/.64
Izvirni znanstveni članek - Original scientific paper (1.01)
Modeliranje sestavov kovine in elastomerov z uporabo postopka
končnih elementov
Modelling Metal-Elastomer Composite Structures Using a Finite-Element-Method
Approach
Sergio E. Floody1 - Jorge P. Arenas2 - José J. de Espuntola3 ('Technical University of Chile; 2Austral University of Chile; Tederai University of Santa Caterina, Brasil)
Sestavi kovine in elastomerov so pomembno orodje za zmanjšanje mehanskih nihanj. Pri upogibu nihajoči sestav lahko dušimo z dodatkom primerne plasti dušilnega materiala, na primer elastomera, kjer je plast izpostavljena ciklični deformaciji in na ta način tudi izgubi energije. Vendar pa prisotnost elastomera pomeni, da je sestav odvisen od frekvence, zaradi tega težko natančno napovedujemo, saj je težko izračunati rešitev ustreznega problema lastnih vrednosti. V prispevku je predstavljena metodologija za modeliranje sestavov kovine in elastomerov z uporabo metode končnih elementov. V nadaljevanju je obravnavana računska metoda določitve približne rešitve frekvenčno odvisnega problema lastnih vrednosti. Številčne rezultate vztrajnosti smo primerjali z rezultati preizkusa običajnega “sendvič" sestava grede. Metodo smo razširili na model in tako optimirali Stockbridgove dušilnike, ki so uporabljeni za dušenje zračnih nihanj dejanskega električnega daljnovoda. Namesto uglasitve dušilnika na neko določeno frekvenco, smo z uporabo genetskih algoritmov določili ciljno fukcijo in optimirali fizikalne izmere dušilnika. S takim postopkom smo analizirali celoten problem brez uporabe modalnega pristopa napetost-energija, kar pomeni, da ta tako modeliranje zadosti načelu vzorčnosti. Metoda je uporabna kot orodje za načrtovanje in modeliranje sestavov kovine in elastomerov. © 2007 Strojniški vestnik. Vse pravice pridržane.
(Ključne besede: kompoziti kovine - elastomeri, modeliranje strukture, metode končnih elementov, dušilniki vibracij)
Metal-elastomer composite structures are an important tool for the reduction of mechanical vibrations. A structure that vibrates in flexure can be damped by the appropriate addition of a layer of damping material, for example, an elastomer, where the layer undergoes cyclic strain and thereby dissipates energy. However, the presence of the elastomer means that the structure is frequency dependent, which is a difficult case for obtaining accurate predictions since the solution of the corresponding eigenvalue problem is hard to compute. In this paper a methodology for modelling metal-elastomer composite structures using a finite-element approach is presented. In addition, a calculation scheme to approximate the solution of the frequency-dependent eigenvalue problem is discussed. The numerical results for the inertness were compared with the experimental results for a classic composite sandwich beam. The method is extended to model and optimise Stockbridge absorbers used to suppress the aeolian vibrations of an actual electrical transmission line. Instead of tuning the absorber to some particular frequency, an objective function is defined and the physical dimensions of the absorber are optimised by means of a genetic algorithm. In this approach, the complete problem is analysed without using the modal strain-energy approach, implying that this modelling satisfies the causality principle. The method appears to be useful as a tool for designing and modelling metal-elastomer composite structures.
© 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: metal elastomer composite, structure modelling, finite element methods, Stockbridge dumpers)
0 INTRODUCTION
Metal-elastomer composite structures are an important tool for the reduction of mechanical vibra-
tions. A structure that vibrates in flexure can be damped by the appropriate addition of a layer of damping material. As the whole system vibrates, the layer undergoes cyclic strain and thereby dissipates
66
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
energy. Since the first successful modelling of a metal-elastomer composite presented by Ross et al. [1], considerable attention has been paid to the prediction of the dynamic behaviour of such structures. For many years, the finite element method has been used for modelling structures, and several of its applications have been shown to be quite accurate. Soni [2] has presented a finite element analysis of viscoelastically damped sandwich beams, which uses a combination of shell elements and three dimensional solids for the viscoelastic part. Another approach is to use shell elements with spring elements to model the elastomer [3]. This methodology has been shown to increase the speed of the calculations of the stiffness and mass matrices. Lumsdaine et al. [4] have reported a method using multi-layer elements, which has been proven to be very accurate. Although the modelling using three dimensional solid elements is the most complete alternative to solve this kind of problem, sometimes the computational cost of formulating and solving the equations can become prohibitive.
The viscoelastic materials of greatest practical interest for damping applications are plastics and elastomers. An elastomer is a soft substance that exhibits thermo-viscoelastic behaviour. Viscoelastic materials possess both elastic and viscous properties. For a purely elastic material, all the energy stored in a sample during loading is returned when the load is removed. Furthermore, the displacement of the sample responds immediately, and in-phase, to the cyclic load. Conversely, for a purely viscous material, no energy is returned after the load is removed. The input stress is lost to pure damping as the vibration energy is transferred to internal heat energy. All the materials that do not fall into one of the above extreme classifications are called viscoelastic materials. Some of the energy stored in a viscoelastic system is recovered upon removal of the load, and the remaining energy is dissipated by the material in the form of heat.
In a metal-viscoelastic-metal structure, the bending of the composite produces not only bending and extensional strains in all three layers, but also shears, primarily of the middle (viscoelastic) layer. The shear-strain energy storage tends to dominate the damping action of the constrained viscoelastic layers. Many practical applications operate on the principle of constrained layer damping. The shear forces in the constrained viscoelastic layer cause the energy of the vibration to be converted into heat.
Undamped metal structures normally have a very low loss factor, typically in the range 0.001 to 0.01. Using a viscoelastic layer can increase this loss factor. This means that the amplitude of the resonant vibration when the structure is subjected to structure-borne sound or vibration will be much lower than for an undamped structure. A reduced amplitude of vibration means less radiation of sound, and also a reduced risk of fatigue failure [5].
A characteristic of viscoelastic materials is that their Young’s modulus is a complex quantity, having both a real and imaginary component. Furthermore, this complex modulus varies as a function of many parameters, the most important of which are the frequency and temperature of a given application. Consequently, this results in a corresponding eigenvalue problem in which the stiffness matrix depends on both the frequency and the temperature. The moduli typically take on relatively high values at low temperatures and/or high frequencies but take on comparatively small values at high temperatures and/or low frequencies. It is therefore necessary to establish an accurate understanding of the influence of these parameters in order to design effective damping treatments.
In general, the vibration analysis of a system that is frequency independent can be accurately achieved by classical techniques. It is much more difficult to obtain accurate predictions when the equations of motion are frequency dependent. This is because the solution of the corresponding eigenvalue problem is difficult to compute. Methods based on the modal strain energy have been used to approximate the solution of the problem [2]. However, they are not accurate when the frequency and temperature ranges are increased, and when they include the transition region, where the variations of the dissipation and the stiffness of the viscoelastic material are quite pronounced. The greatest loss factors occur in the transition region at intermediate frequencies and temperatures. On the other hand, some of the assumptions used by these methods do not fit the principle of causality for physical systems [6].
The final aim of this paper is to present a methodology to model metal-elastomer composite structures by using a finite-element approach. The method was experimentally tested for a classic composite sandwich beam. Then, an application to model and optimise a Stockbridge absorber used to suppress the aeolian vibrations of an electrical transmission line is presented.
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                   67
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
1 THEORY
The theory of finite element methods has been clearly presented by several authors ([7] to [9]), so it will not be repeated here. However, a method to avoid inverting matrices of a large size will be discussed in this section, since it is quite useful to speed up the numerical solution.
As a result of the modelling using finite elements of a metal-elastomer structure, a frequency-dependent equation of motion is obtained. The equations of motion as a function of frequency for a forced multi-degree-of-freedom system and its associated eigenvalue problem can be written as:
and
[-n2M+K (n,r)]q (n,r) = f(ß)        (i),
K(n,r)<p(n,r) = o-(n,r) M<p(n,r)      (2),
where Q is the angular frequency, T is a fixed temperature, M is the mass matrix, K(Q,7) is the stiffness matrix, q(Q,7) is the modal displacement vector, f(Q) is the vector of external forces, <p( Q,7) is an eigenvector associated with the vibration modes, and dß,T) is an eigenvalue associated with a natural frequency.
In general, a direct solution of Eq (2) will involve an expensive and inefficient method because of the large size of the matrices. Therefore, a proposed algorithm to simplify the task can be summarized as: 1) Solve the eigenvalue problem of order n for an arbitrary fixed frequency QQ, and for a value of temperature T, given by:
K{Ci0,T)<?{Ci0,T) = a{Cl0,T)M<?{Ci0,T)    (3)
Now, the modal matrix 0>0 has the following properties:
and
®oM®0=I„
<DjK(n0,r)<D0=s0
(4),
where the superscript T denotes the transpose, I is the «x« identity matrix, and 20=diag(cr0) is a diagonal matrix of eigenvalues.
2) Let <D0 be an «x h truncated matrix of the n eigenvectors associated with the minor eigenvalues ( h < n). For a frequency Q. * QQ, the following product is calculated:
®K(n,r)<i>=L(n,r)
(6),
where the matrix Z(Q,7) is not necessarily diagonal, but it is an n x n matrix. Then, the new eigenvalue problem can be stated as:
s(n,r)»|/(n,r) = /i(n,r)\|/(n,r)        (7),
xPT (Q,T )'Y(Q, T ) = lii                       (8),
and
xPT(Ci,T)l,(Ci,T)xe(Ci,T) = A(Ci,T)          (9),
where Mß,T) and v|/(Q,7) are the eigenvalue and eigenvector, respectively, lh is the hx» identity matrix, W(Çl,T) is a modal matrix, and A(Q,7)=tr(/l(Q,7)) is a trace matrix of eigenvalues. The new eigenvalue problem is still frequency dependent, but it is a problem of smaller size and consequently requires less computation time. 3) Consider the following transformation of coordinates:
q(n,r) = *0r(n,r)
(10),
and
"'                     "'                (U)"
Substituting Eq. (10) and (11) into Eq. (1), and pre-multiplying by rô0T(n,r)l   gives
[-n%+A(n,r)]p (n,r) = [e0i,(n,r)]rf (n) (12).
Thus, the nodal displacement vector is given by:
q (n,r) = e0w(n,T )[-n2ii + a(q,t ) ]"' [ô0T(Q,r)]r f (fi)
(13).
Therefore, the receptance matrix is obtained from Eq. (13) as:
a(n,r) = e0,p(n,r)[-n2i.+A(n,r) J1 [o"P(n,r)T
(14).
Defining the matrix product S (n, r) = ®0T (n, r), Eq. (14) can be re-written as:
(5),        a(n,r) = s(n,r)[-n%+A(n,r)]~Isr(n,:r) (i5);
where Z(Q,7) = A(Q,7) for all Q and J. Consequently, the inertness matrix is:
-ci2a(ci,T ) = -f22s(fî,r)[-f22i. + A(n,r)]_1 ST (Cl,T )
(16).
Then, the corresponding elements of the receptance matrix a(Q,7) are:

(17),
68                                                        F/ootfy L E. - Arenas J. P. - de Espindola J. J.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
where s is an element of the matrix S(Q,7), and \(Sl,T) = crt(Q,7).
Therefore, the nxn matrix T,(Q.,T) can be assumed to be a projection of the stiffness matrix into an approximated subspace of the space formed by the real eigenvectors. So the quality of the approximation depends on the subspace, or span {<p01... ç0}.
An important detail for stating the problem of Eq. (1) is the construction of the stiffness matrix K(Q,7). This construction can be done by using the finite element method for each frequency. If K(Q,7) is a matrix of large size, it can be computed for several frequencies by means of a Taylor series expansion in the neighbourhood of a transition frequency Q(as:
M   If (m) (Ç)     T\
K(n,r) = X      [, j(n-n,)"      (18),
where
KwfiT
d'KQJ
dfT
(19).
It is then relatively easy to compute the derivatives K(m)(Wt,T) since only the elementary stiffness matrices of the viscoelastic part are frequency dependent, while the derivatives of the stiffness matrices of the metal part are not. The use of M=3 for the series expansions shows that the results are quite exact for a narrow frequency band in the neighbourhood of a transition frequency.
2 RESULTS
2.1 Composite Sandwich-Beam
The first example of the application of the theory presented above is a simple clamped-free composite sandwich beam. This kind of structure is commonly used as a study object. The sandwich beam is made of two metal layers of steel 1020 and a viscoelastic core made of DYAD 601 material (Soundcoat Co.). The viscoelastic core was attached in between the metal layers by means of an epoxic-
structural adhesive. The properties of this viscoelastic material were presented in reference [10]. The beam was 211.85 mm long and 11.97 mm wide. The thickness of each metal layer was 2.14 mm and the thickness of the viscoelastic core was 0.5 mm. All the dimensions of the sandwich composite beam are in accordance to the requirements of the ASTM E 756-98 standard [11].
The composite sandwich beam was divided into 114 two-dimensional Lagrangian solid elements on a plane state of stress. Along the beam 19 elements were selected at equal intervals and each layer was divided into two elements, resulting in a total of 507 nodes, having two degrees of freedom at each node, so «=1014 for this application. The above parameters of the structure were selected because they assured the determination of the first four modes and the modal damping produced by the shear deformation of the core.
An experimental set-up was devised to perform a dynamic test to measure the frequency response of the beam. The beam was excited using a magnetic actuator (B&K MM0002). The signal fed to the actuator was a chirp excitation between 0 to 1600 Hz, i.e., a sine wave of linearly increasing frequency, and amplified by a power amplifier (B&K 2706). The response of the beam was measured by a small accelerometer (B&K 4375). The signals were analysed using a two-channel FFT analyser (HP 3567A). The experimental set-up was placed inside a chamber in which the temperature could be controlled in the range between -30 and 60°C. The precision of the chamber was ±1°C. The excitation was applied at 59.64 mm from the clamped edge, which corresponds to node 143 in the finite element mesh, and the response was measured at 37.95 mm from the clamped edge, which corresponds to node 91 in the finite element mesh (see Fig. 1).
Computation of the inertness was developed for different temperatures ranging between -30 and 60°C, and they were compared with the results obtained experimentally. In the computation n =50 was used for the theory presented in Section 1. Figures 2
Excitation (143)
h—,										
										
										
bl—1—1—1—										
Fig. 1. Finite element model for the clamped-free sandwich composite beam
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                   69
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
to 4 show the results of the inertness for three different temperatures.
From the results the effect on the natural frequencies caused by the increase in stiffness of the elastomer in the transition region (-100C < T < 200C) can be seen. In fact, in this region, the value of the fourth natural frequency increased so much that it fell out of the frequency range of the measurement. There is reasonable agreement between the numerical and experimental results for the inertness frequency responses presented in Figures 2 to 4, although it is observed that the numerical results seem to underpredict the natural frequencies when compared with those obtained from the experimental set-up. The differences are on average about 6%. Nevertheless, the differences between the numerical and experimental approaches can be due to imperfections in the experimental fixture, the small size of the structure under test, the contribution of the off-resonant modes, and the measurement uncertainty produced by the environment inside the chamber. The effect of the chamber should be more pronounced in the transition region, where small variations of temperature will cause large variations on the elastic properties of the elastomer. The value of the humidity inside the chamber was not accurately controlled during the experiment. This fact was reflected as noise in the measured inertness frequency-response curves, as seen in Figures 2 to 4.
2.2 Stockbridge Dynamic Vibration Absorber
In this section the theory will be applied to a more complicated case, i.e., a Stockbridge dynamic
vibration absorber. The vibration absorber will be viscoelastically modified in order to increase the dissipation of vibrational energy.
A dynamic vibration absorber, also called a vibration neutralizer, is a device or structure (secondary system) that is attached to another device (primary system) to reduce vibration levels. It acts on the primary system by applying reaction forces and dissipating vibration energy. Vortex-induced or aeolian vibrations of overhead electrical transmission lines, also referred to as conductors, are very common and can lead to fatigue damage. These vibrations are usually caused by winds ranging in velocity from 1 to 7 m/s and can occur at frequencies from 3 to 150 Hz with peak-to-peak displacement amplitudes of up to one conductor diameter. In conventional transmission line systems, one or more Stockbridge absorbers may be attached to a conductor in an effort to suppress the aeolian vibrations ([12] and [13]).
The classic theory introduced by den Hartog [14] for a viscous vibration absorber, called MCK, and their extensions to a viscoelastic absorber, presented by Snowdon [15], are difficult to apply. This is because for complex mechanical systems many modes can contribute to the total response of the primary system. Interesting methods to optimise dynamic vibration absorbers have been presented by Brennan and co-workers ([16] to [19]). Kidner and Brennan [17] used a multi-degree-of-freedom beam neutralizer with piezoceramic patches as active elements, and they analysed the improvement on the performance of the absorber considering the rigid
600          800          1000
Frequency, Hz
1600
Fig. 2. Comparison of the experimental and numerical results for the inertance frequency response
of the beam at -30 °C
70
Floody S. E. - Arenas J. P. - de Espindola J. J.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
100
80
60
0u 40
"D
O)
I 20
(TS
t
s    o
-20 -40
-60
.... FEM --- Exp
200
400
600    800    1000 Frequency, Hz
1200
1400
1600
Fig. 3. Comparison of the experimental and numerical results for the inertness frequency response
of the beam at 10 °C
100
600    800    1000 Frequency, Hz
1600
Fig. 4. Comparison of the experimental and numerical results for the inertness frequency response
of the beam at 60 °C
body mode and the first mode of the beam in their analysis. Brennan and Dayou [18] used an equivalent damper to represent the dynamic stiffness of the absorber assuming a very low damping. Then, they were able to model the problem without adding degrees of freedom, but by using all the modes of the primary structure. More recently, an experimental verification of the optimum tuning method has been presented [19]. An interesting finding is that the absorber can be as effective as active control in reducing the global vibration of the structure. On the other hand, Espindola and Silva [20] introduced the concept of generalized equivalent quantities. The basic idea of their technique is to transform the mechanical impedance of the absorber’s coupling point to the primary system, into generalized
quantities of mass and damping that are frequency dependent. Using the generalized quantities it is possible to formulate the compound equations of motion simply in terms of the generalized coordinates of the primary system. After the equations are written in the principal coordinates, and retaining those that correspond to the frequency band of interest (where the problem of high response residua), the computations are made in a modal subspace, which includes just a minimum number of equations.
2.3 Finite-Element Model for the Secondary System
In simple terms a Stockbridge absorber is composed of a mass at the centre, two attached
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                   71
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
sandwich (metal-elastomer-metal) beams, and two attached tuning masses, as shown in Figure 5. The mass at the centre is attached to the primary system. The finite element method is used to model the absorber’s behaviour. The corresponding eigenvalue problem, which is frequency dependent, can be solved using the technique presented in Section 1. The finite element model of the absorber is shown in Figure 5. Now, for a fixed temperature the equations of motion for the secondary system are:
Mü + K(n)u = f(0
(20).
After modification of the order of rows and columns in order to appropriately place the control node, as shown in Figure 5, we can define:
u=[%,<i2'--;<in-i>y ] T = [<i<y ] T        (21), f(0 = [o>o,-,o>/(0]2'= [o>/(0]r       (22),
K4(Q) is an lxl stiffness submatrix, u is the total displacement vector, q is the displacement vector without considering the control node, y is the displacement of the control node, and/(0 is the force applied to the absorber by the primary system. Now, in the frequency domain, Eq. (23) can be expressed as the system of equations: [-n2M! + Kt(n)]Q(n)+[-n2M2 + K2(n)] Y(n) = o
[-n2M3 + k3 (n)]Q(n) + [-n2M4 + k4 (n)] Y(n) = F(n)
(24).
After solving Eq. (24), we obtain the dynamic stiffness of the system as:
K(ci)=^^ = x4 (Ci) - x3 (n)x-1 (n)x2 (ci) (25),
Y(C1)
where:
X!. (CI) = -Q2M,. + K, (CI), for i=1, ... , 4        (26).
M,	M2	q	+	Ki(n)  K2(n)	q		0
M3	M4	y		K3(n) K4(n)	y		fit)
and then Eq. (20) can be written in partitioned matrix form as:
(23),
where M, is an «-lx«-l mass submatrix, JVL is an n-lxl mass submatrix, ^ is an lxw-l mass submatrix, MA is an lxl mass submatrix, K,(Q) is an «-lx«-l stiffness submatrix, K(Q) is an „-lxl stiffness submatrix, K^Q) is an lxw-l stiffness submatrix,
t
Now, the inverse of Xl can be computed approximately by using Eq. (15), as:
Xj-1 (n) = [-n2Mj + Kj(n) ]"' s s(n)[-n2L + A(n)]-1 sT (n)
(27).
From the dynamic stiffness we can obtain the dynamic impedance
K (Q)
Z(C1)
jQ.
where 7= 4^1, and the apparent mass
f(D
yd) *
(28),
Detail of restrictions
Detail of control node
			>	Tuning mass                  Jfc/'										\*												
														\		Central mass										
																										
																										
																										
							r																			
							v						V													
																										
															1  ¦  1											
													:     ? 1													
																										
			1																							
Viscoelastic
Mets I
Fig. 5. Finite element model for the Stockbridge dynamic vibration absorber
72
Floody S. E. - Arenas J. P. - de Espindola J. J.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
M(SI)
K(SI)
(29).
Consequently, the equivalent damping and equivalent mass are
Cc,(n) = «{z(n)}
and
meq (n) = M{ M (n) }
(30)
(31),
respectively.
Then, the model of the absorber is replaced by an equivalent mechanical system composed of an equivalent mass connected to the primary system and an equivalent damper connected to the ground, where both are frequency dependent. In this way there are new physical degrees of freedom in the mechanical system, but there are no new degrees of freedom in the model. This formulation is equivalent to the simple model of a Stockbridge absorber, which makes use of the Euler-Lagrange equations.
2.4 Optimisation of the Stockbridge Absorber
Now, the secondary system (Stockbridge absorber) is attached to a primary system (electrical transmission line) resulting in a compound system. In order to optimise the physical dimensions of the absorber, an objective function has to be proposed. Here, the objective function will be defined from the maximum absolute values of the principal coordinate functions of the compound system. Assuming that the primary system has a very low and almost constant hysteretic damping, the equations of motion for the primary system in the frequency domain are:
[-Si2Mpr+Kpr]qpr(Si) = f(Si)          (32),
where M is the mass matrix of the primary system, K is the complex stiffness matrix of the primary system, q (Q) is the displacement vector of generalized coordinates, and f(Q) is the force vector. Using the theory of the equivalent generalized quantities [20], the compound system can be modelled as:
[-a2 [Mpr + M„(n)] + jSiCeq(Si) + Kpr]qpr(a) = f (fi)
(33),
where M (Q) is the equivalent mass matrix and C (Q) is the equivalent damping matrix.
If p absorbers are attached to the primary system, at the generalized physical coordinates qk1,
qk2, ... , qkp, the equivalent generalized mass and damping matrices are:
M„(n)
"0	0
0	^(^)1 •••
0	0
0	0
0	0
0	0
0	0
0	0
m(   ) eq          kp 0	0 0
(34),
and
c„(n)
"0	0	0	0
0	C.Ä1    -	0	0
0	0	0	0
0	0	 c^(Q.)kp	0
0	0	0	0
(35),
respectively.
Using the transformation:
qpr(fi) = <DprPpr(D)                  (36),
where 0> is the matrix of the eigenvectors associated with the'eigenvalues of the primary system in the frequency band of interest, and ppr is the vector of the principal coordinates of the primary system, Eq. (33) can be written as:
[-n2[i+M,(n)]+ync,(fi)+spr]Ppr(fi) = n(n)
(37), where M(Q)=<I> TM (Q)<t , C(Q)=<t TC (Q)<t ,
A-     '        pr        of-     '    pr       A-              pr      eq-          pr
n(Q)=* rf(Q), and Z =0 TC O =tr(o) is a trace matrix of eigenvalues of the primary system. Consequently:
ppr (Si) = [-SI2 [ I + M, (Si) ] + JSICA (Si) + Lpr J1 n(n)
(38),
and the receptance matrix can be calculated by:
o(n) = <Dpr [-SI2 [ I + M, (Si) ] + JSICA (Si) + Lpr J1 <bTpr
(39).
Then, in order to solve the optimisation problem it is possible to define an objective function 7 as the modulus of a vector formed by the maximum absolute values of the generalized principal coordinates of the primary system [20]. This can be expressed by the equation:
/W
max
a < si < si
p(*,")
(40),
where Q1 and Q2 are the lower and upper limits of the frequency band of interest, respectively, x is a design vector of project variables to optimise, and i=1,..., N, where iVis the total number of degrees of freedom of the primary system.
2
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                   73
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
Fig. 6. Definitions of the physical dimensions to optimise for the Stockbridge absorber
The project variables to optimise are the physical dimensions of the absorber. Therefore, the design vector is defined as:
x = [l1,l2,l3,h1,h2,h3,h4,t]
(41),
where the elements of x are the physical dimensions shown in Fig. 6. The constraint functions are defined for each element of x as:
xf < x < xf
(42),
where xL and xu are the lower and upper limits for each element, respectively. For the force vector, a unit force at each excitation point of the primary system can be used, i.e., f=[1,1,...,1,1]r.
A numerical example was performed for a real compound system. A total of four Stockbridge absorbers were attached to the primary system. In this example of a Stockbridge absorber the two sandwich beams are designed from two metal layers of steel 1020 and a viscoelastic core DYAD 601 (Soundcoat Co.). The finite element model of the absorber is shown in Fig. 5. The beams were divided into 114 elements. For the length and thickness of the core, 19 and 2 elements were used, respectively. This choice was found appropriate for both, representing efficiently the internal shear and determining the first four modes in the frequency band used. The mass at the centre was divided into 32 elements and the tuning masses were divided into 24 elements each. This choice is because the mechanical purposes of the masses do not require high discretization. All the elements are two-dimen-
sional lagrangian and quadratic solids, of nine nodes, and they are in a plane state of stress. This gives a total of 308 elements, 1319 nodes, and a total of n=2638 degrees of freedom. For simplicity, the temperature is assumed to be a constant.
The primary system considered was an ACRS partridge cable, 30.2 m long, clamped at both extremes and subjected to a tension of 9000 N. The cable was divided into 81 equally spaced elements. The central masses of the absorbers were attached at nodes 5, 35, 46, and 76 of the cable. These positions were selected in order to be far from the nodes of the cable, allowing the absorbers to control a large number of modes of the primary structure. Figure 7 shows the physical model of the compound system and its corresponding generalized equivalent quantities model.
Since the finite elements were in a plane state of stress, t does not change a lot during the optimisation process, so it was fixed at a value of 10 mm. The lower and upper limits for each xi were chosen such that: 1) the weight and size of the absorbers should not be excessive, and 2) the thickness of the elastomer should be small in order to have shear deformation from the vibration of the sandwich beams. The frequency range used to optimise the Stockbridge absorber was 40 to 60 Hz. The temperature was fixed at 10OC. Because of its nature, the objective function has a large number of local minima so a genetic algorithm was used to perform the optimisation. The theory and applications of the genetic algorithms in optimisation problems
74                                                        Floody S. E. - Arenas J. P. - de Espindola J. J.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
Table 1. Results of the optimisation of the physical dimensions for the Stockbridge absorbers
a)
n
Xi
h                   0                 200
1000 h                  0                 200
Xi
mm
h1                    0
A3                       0
A4                       0                      400
Xi
mm
100
Ä2___________0___________10___________2.013
xi optimised mm
10.321
210.002 30.024
10.096
5                    2.000
30.102
10.000
ACSR Cable
JZ
Q_
_D
Nolle 5
Node 35
Q_

Nude 46
IL
_C
Node 76
mtJi(Ll)
meJQ)
mtq(Li)
m„{€i)
h)
e^fi)
^(L1)
Ces(fi)
Cei(Q)
Fig. 7. Diagram of the compound system (cable plus Stockbridge absorbers): a) the physical model and
b) its generalized equivalent quantities model
were explained in detail in the literature [21] to [23]. The numerical results of the optimisation process are presented in Table 1.
Figure 8 shows the results of the receptance at the mid point of the cable, when no absorber is attached, and when the absorbers are attached to the cable before and after the optimisation process. It can be seen that after their dimensions were optimised, the Stockbridge absorbers reduced the vibration level of the cable in a very effective way. Most of the peak values of the receptance frequency response were attenuated and for the peak value at around 60 Hz an attenuation of 30 dB was achieved after the optimisation.
3 CONCLUSIONS
The modelling of a metal-elastomer composite structure based on a finite element method has been presented. In addition, a methodology to reduce the computation time when dealing with frequency dependent matrices has proven to give good approximate results. It has to be noted that the precision of the approximation presented in Section 1
depends on the subspace. The factors that determine the behaviour of the algorithm are: a) the dimension h of the subspace (a larger value of the dimension will produce a better approximation), and b) the variation of the complex shear modulus of the viscoelastic material with both frequency and temperature. It can be expected that in the transition zone the errors will be increased. As a result, the distance between the subspace generated by the truncated modal matrix e0 and the space generated by the modal matrix F is increased. Obviously, this implies that the initial frequency Q0 plays an important role in the computations since the difference between K(Q0,7) and K(Q,7) increases with the change of temperature. However, it can be concluded that the method used in this work seems to be quite efficient when compared to the subspace iteration method [8] and the Lanczos method [25], since these require the calculation of the inverse of the stiffness matrix for each iteration. In addition, a theory to determine the generalized equivalent quantities for a Stockbridge dynamic absorber has been presented. The use of these quantities does not add more degrees of freedom to the primary system and the
t
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                     75
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
-90
Q. (D
without absorber
with absorber
with optimized absorber
"T--------------------r~
50            60            70
Frequency, Hz
Fig. 8. Comparison of receptance frequency responses at the mid point of the primary system, with and
without an optimised Stockbridge absorber
theory could be extended to other kinds of absorbers. Moreover, the use of generalized equivalent quantities allows one to define an objective function of the maximum absolute values of the principal coordinates of the primary structure. This objective function is independent of the geometry of the primary system and it is dependent on its modal parameters. The application of the method to Stockbridge absorbers used to suppress the aeolian vibrations of a real electrical transmission line shows that the
reduction in the response of up to eleven modes is achieved after the dimensions of the absorbers are optimised using a genetic algorithm. The optimisation process can be quite slow when compared to other techniques reported in the literature [18] and [19]; however, the results presented in this work seem to be encouraging. Further work will be conducted regarding the computational costs and detuning of the absorber due to the presence of temperature changes in the elastomer layer.
4 REFERENCES
[1]    Ross D., E.E. Ungar, E.M. Kerwin Jr. (1959) Damping of plate flexural vibrations by means of viscoelastic laminate structural damping, in Structural Damping, ASME, New York, pp. 49-88. Soni, M.L. (1980) Finite element analysis of viscoelastically damped sandwich structures, in Proc. of 51st Shock and Vibration Symposium, San Diego, pp. 97-109.
Mignery, L. (1995) Vibration analysis of metal/polymer/metal components, in Proc. of ASME Design Engineering Technical Conferences, Vol. 3 (C), Boston, pp. 23-33.
Lumsdaine, A., R.A. Scott (1995) Shape optimisation of unconstrained beam and plate damping layers, in Proc. of ASME Design Engineering Technical Conferences, Vol. 3 (C), Boston, pp. 15-22. Ungar, E.E. (1998) Vibration isolation and damping, Chapter 55 in Handbook of Acoustics (Edited by M.J. Crocker), John Wiley and Sons, New York.
Crandall, S.H. (1991) The hysteretic damping model in vibration theory. Proc. of the Institute of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 205(1), pp. 23-28. Hughes, T.J.R. (2000) The finite element method, Dover, New York. Bathe, K.J. (1995) Finite elements procedures, Prentice-Hall, New York.
Petyt, M. (1990) Introduction to finite element vibration analysis, Cambridge University Press, Cambridge.
[10] Espindola, J.J., CA. Bavastri (1997) Reduction of vibration in complex structures with viscoelastic neu-tralizers - a generalized approach and a physical realization, in Proc. of ASME Design Engineering Technical Conferences, Sacramento (CD-Rom).
[2]
[3]
[4]
[5]
[6]
[7] [8] [9]
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Floody S. E. - Arenas J. P. - de Espindola J. J.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 66-77
[11] ASTM E 756-98 (1998) Standard test method for measuring vibration-damping properties of materials, ASTM, New York.
[12] Vecchiarelli, J., I.G. Currie, D. G. Havard (2000) Computational analysis of aeolian conductor vibration with a Stockbridge-type damper. J. of Fluids and Structures 14(4), pp. 489-509.
[13] Richardson, A.S. (1996) Performance requirements for vibration dampers. Electric Power Systems Re-search 36(1), pp. 21-28.
[14] den Hartog, J.P. (1956) Mechanical vibrations, McGraw-Hill, New York, 1956.
[15] Snowdon, J.C. (1966) Vibration of cantilever beams to which dynamic absorbers are attached. J. of the Acoust. Soc. Am. 39(5), pp. 878-886.
[16] Brennan, M.J. (1998) Control of flexural waves on a beam using a tunable vibration neutraliser. J. Sound and Vib. 222(3), pp. 389-407.
[17] Kidner, M., M.J. Brennan (1999) Improving the performance of a vibration neutraliser by actively removing damping. J. Sound and Vib. 221(4), pp. 587-606.
[18] Brennan, M.J., J. Dayou (2000) Global control of vibration using a tunable vibration neutralizer. J. Sound and Vib. 232(3), pp. 585-600.
[19] Dayou, J., M.J. Brennan (2003) Experimental verification of the optimal tuning of a tunable vibration neutralizer for global vibration control. Appl. Acoustics 64(3), pp. 311-323.
[20] Espindola, J.J., H.P. Silva (1992) Modal reduction of vibrations by dynamic neutralizers: a general approach, in Proc. Tenth International Modal Analysis Conference, San Diego, pp. 1367-1373.
[21] Espindola, J.J., S.E. Floody (2001) Optimal design of Stockbridge dynamic vibration neutralizer viscoelastically modified applying the finite element method, in Proc. 9th International Symposium on Dynamic Problems of Mechanics, Florianópolis, pp. 507-513.
[22] Rechenberg, I. (1993) Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution (Evolution strategy: optimization of technical systems by means of principles of biological evolution), Fromman-Holzboog, Stuttgart.
[23] Hung, S.L., H. Adeli (1994) A parallel genetic/neural network learning algorithm for MIMD shared memory machines. IEEE Transactions Neural Networks 5(6), pp. 900-909.
[24] Espindola, J.J., CA. Bavastri (1999) Optimum conceptual design of viscoelastic dynamic vibration neutralizer for low frequency complex structures, in Proc. Int. Symposium on Dynamic Problems in Mechanic and Mechatronic, Günzburg, pp. 251—259.
[25] Lanczos, C. (1950) An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal of Research of the National Bureau of Standards 45(4), pp. 255-281.
Authors’ Addresses: Prof. Dr. Sergio E. Floody Univ. Tecnologica de Chile Brown Norte 290 Santiago, Chile s.floody@utecnologica.cl
Prof. Dr. Jorge P. Arenas Institute of Acoustics Univ. Austral de Chile PO Box 567, Valdivia, Chile jparenas@uach.cl
Prof. Dr. José J. de Espindola Dept. Mechanical Engineering Univ. Federal de Santa Caterina Florianópolis, SC 80040-900, Brasil espindol@mbox1.ufsc.br
Odprto za diskusijo: 1 leto Open for discussion: 1 year
Modeliranje sestavov kovine in elastomerov - Modelling Metal-Elastomer Composite Structures                   77
Prejeto:                                                                Sprejeto:
1.2.2006                                                                25.10.2006
Received:                                                             Accepted:
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
UDK - UDC 658.512.2
Izvirni znanstveni članek - Original scientific paper (1.01)
Ugotavljanje in vrednotenje potreb kupcev v postopku razvoja
izdelka
Finding and Evaluating Customers' Needs in the Product-Development Process
Janez Kušar1 - Jože Duhovnik1 - Rok Tomaževič2 - Marko Starbek1 ('Fakulteta za strojništvo, Ljubljana; 2CIMOS d.d., Koper)
Podjetja današnjih dni se soočajo z novimi izzivi. Imamo opravka z globalizacijo poslovanja in lokalizacijo delovanja, standardizacijo in individualizacijo izdelkov, zahtevnim kupcem in močno konkurenco. V prispevku so prikazane faze razvoja funkcij kakovosti (RFK - QFD) postopka sprejemanja izdelka in podano mesto pridobivanja, sestavljanja in vrednotenja potreb kupcev izdelka. Podrobno so opisani viri pridobivanja informacij o potrebah kupcev, predstavljene so metode pridobivanja, sestavljanja in vrednotenja podatkov o potrebah kupcev izdelka ter prikazan postopek razvoja izdelka. Podani so rezultati preizkusa predlagane metodologije upoštevanja glasu kupcev v postopku razvoja izdelka Vario Flow podjetja, ki se ukvarja s proizvodnjo in prodajo medicinske opreme za domači in tuji trg. © 2007 Strojniški vestnik. Vse pravice pridržane.
(Ključne besede: razvoj izdelka, razvoj funkcij kakvosti (RFK), potrebe kupcev, odločitveni postopki, hiša kakovosti)
Today's companies are facing new challenges: global business and local operation, the standardization and individualization of products, and demanding customers and fierce competition. This paper presents the phases of quality functions deployment (QFD) during a new-product development process along with the method for obtaining, structuring and evaluating customer needs. A full description of the information resources for obtaining the data on customer needs is given, and the methods for obtaining, structuring and evaluating the data on customer needs are presented. The QFD process of new-product development is described. We present the results of testing the proposed methodology, taking into account the voice of the customer, in the process of developing a new Vario Flow product in a company that produces and sells medical equipment on domestic and foreign markets. © 2007 Journal of Mechanical Engineering. All rights reserved.
(Keywords: product development, quality function deployment (QFD), customer needs, decision making, house of quality)
0 UVOD                                                                    0 INTRODUCTION
Za današnjega kupca izdelkov lahko trdimo, da je “kralj”, saj je pripravljen kupiti le izdelke, ki zadovoljujejo njegove potrebe in zahteve. Podjetje želi doseči krajši čas razvoja izdelka, manjše stroške, vrhunsko kakovost izdelka ter končno zadovoljstvo kupcev izdelka. Da bi podjetje doseglo postavljene cilje, mora že med razvojem izdelka upoštevati potrebe in zahteve kupcev izdelka. Znano je, da se izdelek razvija v postopku, ki se prične z abstraktnim razmišljanjem in konča s končnim izdelkom. Izkušnje kažejo, da je treba v tem miselnem in stvarnem postopku razvoja izdelka upoštevati glas kupcev (potrebe in zahteve), če
Today, we can maintain that the customer is “king” as he or she will only buy products that satisfy his or her needs and wants. Every company wants to achieve shorter product-development times, lower costs, higher quality of the product, and, finally, the satisfaction of its customers. In order to achieve the set goals, the company has to take into account the customers’ wants and needs during the new-product development process. It is well known that the new-product development process starts with an abstract idea and ends with the physical realization of the product. Experience has shown that in this mental and physical product-development process the voice
71

Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
želimo, da bo izdelek lahko tekmoval na globalnem tržišču.
Razvoj funkcij kakovosti ([1] do [3]) je edini, na kupca usmerjeni postopek razvoja izdelka, pri čemer je “glas kupca” izhodiščna točka vseh dejavnosti. RFK vpraša: “Kaj potrebuje in zahteva kupec” in spremeni njegova pričakovanja v značilke izdelka [4]. Razvoj funkcij kakovosti strmi za tem, da se izdelek tako definira, razvije, konstruira, izdela, dobavi in vgradi, da se ne izpolni le želja kupca, ampak da so želje celo več ko izpolnjene. Metoda razvoja funkcij kakovosti rabi za preoblikovanje potreb in zahtev kupcev v zmožnosti podjetja ter za vključitev vseh oddelkov oziroma služb podjetja za izpolnitev naročila.
Metoda RFK je igra vprašanj in odgovorov z dvema osnovnima vprašanjema:
•  KAJ pričakujejo kupci izdelka,
•  KAKO podjetje izpolni potrebe kupcev.
Metoda RFK spremlja postopek razvoja izdelka od faze razmišljanja pa do faze uporabe izdelka, pri tem pa je “hiša razvoja funkcij kakovosti izdelka” (si. 1) namenjena dokumentiranju miselnih in načrtnih rezultatov.
of the customer (his or her needs and wants) has to be taken into account in order to ensure that a globally competitive product will be produced.
Quality functions deployment (QFD) ([1] to [3]) is the only customer-oriented product-development method where the “voice of the customer” is the starting point of all activities. QFD starts with the question: “What does the customer need and want?” and transforms the customers’ expectations into the product’s features [4]. The goal of the QFD method is to define, develop, design, manufacture, supply and install the product in such a way that the customers’ wishes are over-fulfilled rather than simply “just” fulfilled. The QFD method allows the transformation of the customers’ needs and wants into the company’s potentials and the engagement of all its departments to serve the customers.
The QFD method is a game of questions and answers with two basic questions:
•  WHAT do customers expect from the product?
•  HOW can the producer fulfill the customer needs?
The QFD method is used throughout the product-development process: from the first abstract concept to the use of the product. The “product’s quality-functions-deployment house” (Figure 1) is used to record the mental and planned results.
KAJ želijo kupci (potrebe, zahteve)
WHAT do customers wish (needs, wants)
KAKO izpolni podjetje želje kupcev
HOW can the company fulfil the customer needs
Stopnja podpore KAJ-ev KAKO-jem
Level of WHATs' support to HOWs
TRG / MARKET
KOLIKO želi podjetje s
KAKO-ji doseči      \7
HOW MUCH does the
company wish to achive
with HOWs
ZAKAJ
izboljšati (primerjava s konkurenco)
WHY
improve
(comparision with
competition)
>
IZHOD - pomembni in kritični KAKO-ji
OUTPUT - important and critical HOWs
SI. 1. Hiša razvoja funkcij kakovosti izdelka Fig. 1. Products quality-functions-deployment house
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
79
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
	KAKO / HOW Značilke izdelka / Product characteristics
KAJ WHAT	1. HIŠA NAČRTOVANJE IZDELKA 1st HOUSE PRODUCT PLANNING
	KAKO / HOW Značilke sklopov, sest. delov / Component characteristics
KAJ WHAT	2. HIŠA NAČRTOVANJE SKLOPOV SESTAVNIH DELOV 2nd HOUSE COMPONENT PLANNING
	KAKO / HOW Značilke postopkov Process characteristics
KAJ WHAT	3. HIŠA NAČRTOVANJE POSTOPKOV 3rd HOUSE PROCESS PLANNING
	KAKO / HOW Značilke proizvodnje Production characteristics
KAJ WHAT	4. HIŠA NAČRTOVANJE PROIZVODNJE 4th HOUSE PRODUCTION PLANNING
Sl. 2. Postopek sprejemanja izdelka na osnovi RFK Fig. 2. QFD process of new-product development
Postopek razvoja izdelka na osnovi RFK poteka kaskadno in se opiše s štirimi hišami razvoja funkcij kakovosti (si. 2) in to [4]:
•  hišo razvoja funkcij kakovosti izdelka
•  hišo razvoja funkcij kakovosti sklopov oziroma sestavnih delov izdelka,
•  hišo razvoja funkcij kakovosti postopka in
•  hišo razvoja funkcij kakovosti proizvodnje.
Kakor prikazuje slika 2 se postopek razvoja izdelka na osnovi RFK prične s pridobivanjem, sestavljanjem in vrednotenjem potreb kupcev izdelka - rezultat je vektor ugotovljenih potreb kupcev izdelka, ki pomeni vhodni podatek hiše načrtovanja izdelka.
Da bi lahko pri sprejemanju izdelka upoštevali glas oz. potrebe kupcev, je le-te treba pridobiti in raziskati z namenom, da bi razumeli ter vedeli, kako bodo upoštevane.
Slika 3 prikazuje osnutek pridobivanja, sestavljanja in vrednotenja potreb kupcev izdelka.
V nadaljevanju bodo prikazani postopek in metode pridobivanja, sestavljanja in vrednotenja podatkov o potrebah kupcev, kar je temelj za uspešno izvedbo postopka razvoja izdelka oziroma za uspeh izdelka na trgu.
The QFD process of new-product development is carried out in cascades and can be described with four QFD houses (Fig. 2) [4]:
•  the product’s quality-functions-deployment house
•  the product’s component quality-functions-deployment house
•  the process quality-functions-deployment house
•  the manufacturing quality-functions-deployment house.
As presented in Figure 2, the QFD process of new-product development starts by obtaining, structuring and evaluating the customer needs, which represent the input data for the product planning house.
In order to take into account the customer needs during new-product development, they must be identified and analyzed beforehand, so that they can be properly understood and fulfilled.
Figure 3 presents the concept of obtaining, structuring and evaluating the data on customer needs.
In the text that follows, the procedure and methods for obtaining, structuring and evaluating customer needs are presented. These are the basis for the successful execution of the product-development process or for the success of the product on the market.
80
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
ANALIZA TRGA
»GLAS KUPCEV«
MARKET ANALYSIS
^VOICE OF THE CUSTOMERS^
-&
DDD DDD DDD
Metode vrednotenja podatkov Methods for data evaluation
O
I VEKTOR POTREB KUPCEV IZDELKA I      CUSTOMERS' NEEDS VECTOR
^1
viri glasu kupcev
voice of customers sources
pridobivanje podatkov o potrebah kupcev obtaining of customers' needs data
urejanje podatkov o potrebah kupcev structuring of customers' needs data
vrednotenje podatkov o potrebah kupcev evaluation of customers' needs data
vhodni podatek hiše načrtovanja izdelka input data for the product plannig house
Sl. 3. Osnutek zbiranja, urejanja in vrednotenja potreb kupcev izdelka Fig. 3. The concept of obtaining, structuring and evaluating customer needs
1 VIRI GLASU KUPCEV
1 SOURCES OF THE CUSTOMERS’ VOICE
Glas kupcev je pojem, s katerim se opišejo izrečene in neizrečene potrebe ter zahteve kupcev in je kot tak potreben za zagon postopka razvoja izdelka ([5] in [6]). Potreba kupca pomeni izjavo kupca o koristi, ki bi mu jo lahko prinesel izdelek ali storitev ([1] in [7]). Kupci želijo svoje potrebe in želje zadovoljiti z izbiro izdelkov ali storitev, ki to najbolje izpolnjujejo.
Kupci pa pogosto izražajo svoje potrebe z izjavami, ki govorijo o tem, kako bi lahko te potrebe zadovoljili, te izjave pa se imenujejo kupčeve zahteve [8], ki se prepoznajo kot nekaj zahtevanega, nekaj, o čemer se ne da pogajati.
Poznani so trije glavni viri pridobivanja informacij o glasu kupca, in to so ([3] in [9]):
•  zunanji kupci,
•  notranji kupci in
•  podatki o izdelkih in postopkih.
The voice of the customers is a concept that describes the uttered and unuttered customers’ wants and needs; as such it must exist in order to start the new-product development process ([5] and [6]). A customer need is a description, in the customer’s own words, of the benefit to be fulfilled by the product or service ([1] and [7]). Customers would like to satisfy their needs and wishes by selecting products or services that best fulfill them.
Customers often express their needs using statements that describe how these needs could be fulfilled and these statements are called “customer requirements” [8], which are considered as something required, something that is non-negotiable.
There are three major sources for obtaining information on the voice of the customer ([3] and [9]):
•  external customers,
•  internal customers,
•  information on products and processes.
1.1 Zunanji kupci
Zunanji kupci so kupci, ki so zunaj podjetja in govorijo drugačen jezik kakor proizvajalec izdelka. Po pregledu literature ([1], [3], [6] in [7]) lahko ugotovimo, da se zunanji kupci delijo v več kategorij in podkategorij, glede na to, od koga
1.1 External customers
External customers are the customers outside the company. They speak a different language than the company that manufactures the product. A survey of the reference works ([1], [3], [6] and [7]) reveals that external customers fall into several categories and
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ZUNANJI KUPCI EXTERNAL CUSTOMERS J
KUPUJEJO ARE BUYING
SO THEY ARE
Uporabniki izdelkov Product users
Ljudje z vplivom na nakupe drugih ljudi
People influencing other people in the process of purchasing
Ljudje, ki sprejemajo končne denarne odločitve
People making the final financial decisions
Kupujejo naše	^	Zadovoljni Satisfied
izdelke	<c	
Buying our products	^>	Nezadovoljni Dissatisfied
		
Kupujejo izdelke konkurence	^	Bivši naši kupci Our former customers
	<c	
Buying the competitive products	^	Stalni kupci konkurence Regular customers of the competition
Sl. 4. Pregled zunanjih kupcev Fig. 4. The overview of external customers
kupujejo izdelke in kakšno vlogo imajo v oskrbovalni verigi. Slika 4 prikazuje delitev zunanjih kupcev.
1.2 Notranji kupci
Notranji kupci ([1], [3], [6] in [7]) so kupci, ki so v podjetju, njihov jezik se gotovo razlikuje od jezika zunanjih kupcev. Notranji kupci imajo svoje poglede na določene probleme v postopku razvoja izdelka, zato je treba ločevati njihov glas od glasu zunanjih kupcev. Glas notranjih kupcev lahko pomembno prispeva k izboljšanju postopka razvoja izdelka, saj je v njihovem interesu, da izboljšajo sam postopek razvoja izdelka, katerega del so, ter tako prispevajo k zadovoljevanju potreb zunanjih kupcev. Slika 5 prinaša pregled notranjih kupcev.
1.3 Podatki o izdelkih in postopkih
Podatki o izdelkih in postopkih pomembno pomagajo pri ugotavljanju potreb kupcev, tako zunanjih kakor tudi notranjih.
Slika 6 prikazuje pregled podatkov o izdelkih in postopkih.
sub-categories, depending on who they buy the products from and their role in the supply chain. Figure 4 presents the categories of external customers.
1.2 Internal customers
Internal customers ([1], [3], [6] and [7]) are customers who are from the company, and most certainly use a different language than the external customers. Internal customers have a unique perspective on specific problems in the product-and-process development, and that is why their voice must be distinguished from the voice of external customers. The voice of the internal customers can contribute significantly to the product-and-process development, as it is very important for them to improve the product development they are part of. In this way they contribute to satisfying the needs of external customers. Figure 5 gives an overview of internal customers.
1.3 Information on products and processes
Information on products and processes is very helpful for discovering the needs of the customers, both the internal and external ones.
Figure 6 shows an overview of the information on products and processes.
2 METODE PRIDOBIVANJA IN POSTOPEK
UREJANJA PODATKOV O POTREBAH
KUPCEV
2 METHODS FOR OBTAINING THE CUSTOMER NEEDS AND THE PROCEDURE FOR STRUCTURING THESE DATA
Analizirane in ocenjene so bile različne metode pridobivanja in postopki sestavljanja podatkov o potrebah kupcev ([7] do [12]), rezultat tega dela je predlog za prakso najprimernejših metod pridobivanja in sestavljanja podatkov o potrebah kupcev.
Several methods for obtaining customer needs and the procedures for structuring these data were analyzed and reviewed ([7] to [12]). The result is a suggestion for using the most suitable methods for obtaining and structuring the data on customer needs.
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NOTRANJI KUPCI
INTERNAL CUSTOMERS
Inženirji podjetja Company engineers
Oblikovalci izdelka Product designers
Vodje projektov Project managers
Naši dobavitelji Our suppliers
Ostali zaposleni v podjetju
Other company employees
VPLIVAJO NA INFLUENCE
Izboljšanje lastnosti izdelka
Improving the product features
Kakovost izdelka Product quality
Sestavljivost in razstavljivost izdelka Product assemblability and disassemblability
Proizvodljivost izdelka Product manufacturability
Zanesljivost izdelka Product reliability
Enostavnost izdelka Product simplicity
Združljivost izdelka Product compatibility
Prilagodljivost izdelka Product flexibility
Druge lastnosti Other features
Delovne postaje Workstations
Informacijska orodja Information tools
Modernizacija tehnologij Technology modernization
Integracija orodij Integration of tools
Ostala orodja Other tools
Prilagodljivost Flexibility
Metodologija Methodology
Avtomatizacija Automation
Metode za hitro dostavo na trg Methods to improve the time-to-market
Drugo Other
Sl. 5. Pregled notranjih kupcev Fig. 5. The overview of internal customers
2.1 Metode pridobivanja podatkov o potrebah kupcev
2.1 Methods for obtaining the data on customer needs
Za pridobivanje podatkov o potrebah kupcev imajo prednost naslednje metode:
•  metoda žariščne skupine,
•  metoda izvedbe intervjuja
•  metoda pripomb in pritožb kupcev in
•  metoda soočanja idej.
When obtaining the data on customer needs preference is given to the following methods:
•  the focus-group method,
•  interviews,
•  the customer-remarks-and-complaints method,
•  brainstorming.
2.1.1 Metoda žariščne skupine
2.1.1 Focus-group method
Metoda žariščne skupine je metoda, pri kateri izbrana skupina kupcev razpravlja o vprašanjih, ki jih poda moderator. Razprava nastane tako, da vsak član skupine poda svoje poglede na določen
The focus-group method uses a selected group of customers who discuss questions posed by a moderator. The discussion is initiated so that each group member first expresses his/her opinion on a particular
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Sl. 6. Podatki o izdelkih in postopkih Fig. 6. Information on products and processes
problem, sliši mnenja drugih in nanje tudi odgovarja. S takim načinom razprave metoda žariščne skupine priskrbi kakovostne poglede majhnega števila ljudi. Moderator lahko razišče razloge, ki povzročajo nezadovoljstvo in lahko razpravlja o mogočih rešitvah določenih problemov. Običajno je v žariščni skupini od 6 dol2 ljudi, razprava pa traja dve do tri ure. Slika 7 prikazuje potek pridobivanja podatkov o potrebah kupcev po metodi žariščne skupine.
Da bi lahko s pomočjo žariščne skupine zagotovili ustvarjalno razpravo o določeni temi, je treba v skupino povabiti člane tirna s podobnimi interesi in znanji. Izkušnje so pokazale, da je pri tem treba paziti, da člani tirna niso v kakršnikoli ukazovalni hierarhiji.
Običajno se pri raziskovalnih projektih oblikuje več žariščnih skupin (zunanji in notranji kupci, razdeljeni po različnih delih), da se pridobijo različni pogledi na problem.
Razprava v žariščni skupini je sestavljena iz treh faz:
1.  faza: uvodna predstavitev
2. faza: razprava,
3. faza: sklep razprave.
Delo žariščne skupine vodi in usmerja moderator, ki prične z uvodno predstavitvijo, se
problem, then other participants comment on it and then further discussion of their opinions follows. In this way the discussion of the focus group provides a qualitative view of a small number of people. The moderator can search for reasons causing dissatisfaction and can discuss possible solutions for particular problems. Normally, there are 6 to 12 people in a discussion group, each discussion lasts for two to three hours. Figure 7 presents the course of obtaining the data on customer needs using the focus-group method.
To be able to provide a productive discussion on a particular subject, discussion members with similar interests and knowledge must be selected. Experience shows that care must be taken that the members are neither in a superior nor in a subordinate relationship with each other.
Normally, there are several focus groups formed in the research project (external and internal customers are grouped by different segments) with the goal of gathering different opinions on a problem.
The focus-group discussion is carried out in three phases:
•  phase 1: introduction,
•  phase 2: discussion,
•  phase 3: conclusion.
The focus-group work is directed by a moderator. He or she starts with an introduction by
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Člani žariščne skupine Focus group members J
(,
Začetek dela žariščne skupine Start of the focus group work
r\
(Moderator postavi odprto vprašanje članom žariščne skupine (na določeno temo) Moderator sets an open question to the members of the focus group (on a specific topic).
Spraševani odgovarjajo na vprašanje moderatola in reagirajo eden na
drugega in tako navajajo potrebe, želje, tehnične rešitve, značilke
delov, cilje, primerjalne vrednosti in ostalo
The customers answer the moderator's question, react to one another,
expressing their needs, wants, technical solutions, value
characteristics, goals, reference values and other things.
-Ne / No
Zapisovanje drugih izjav kupca o:
- tehničnih rešitvah in značilkah, značilkah vrednot, ciljih, primerjalnih vrednostih, ostalo.
Recording other statements of the customers:
- technical solutions and characterises! value caracteristics, goals, reference values, other things.
C
Da / Yes JL.
Sklep dela žariščne skupine End of the focus group work
3
Nadaljno spraševanje moderatola s ciljem odkriti skrite potrebe, ki jih skrivajo druge zapisane izjave kupcev:
- Zakaj si to želite?
- Kakšno korist bi imeli zaradi tega?
- To si želite zato, da bi lahko....?
Further questions from the moderator aimed to discover any hidden needs, included in the written statements of the customers:
- Why do you want that?
- What benefit do you expect from that?
- You want this in order to be able to...?
ao
Zvočno zapisovanje Audio recording
Slikanje Camera
Opazovalci Observers
SI. 7. Pridobivanje podatkov o potrebah kupcev z metodo žariščne skupine Fig. 7. Obtaining the data on customer needs using the focus-group method
predstavi in razloži namen žariščne skupine in vzrok za vabilo članom. Sledi seznanitev članov z osnovnimi pravili, nato pojasnitev namena zapisovanja in snemanja razgovorov ter zagotovitev zasebnosti sodelujočih.
Ko se člani tirna predstavijo, moderator začne voditi razpravo tako, da uporablja osnutek vprašanj, namenjenih raziskavi različnih pogledov na obravnavano temo. Moderatorjevo osnovno delo je, da obdrži skupino osredotočeno. Po obravnavi
presenting the focus group, its purpose and the reason why the members have been invited. Then the members are acquainted with the basic rules and explained the purpose of recording the discussion, and the discretion of the participating members is ensured.
Then the members participating in the discussion are introduced and the moderator starts the discussion by asking the initial questions in order to gather different views relating to the topic of the discussion. The moderator’s basic task is to keep the discussion group
Moderator
C
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določenega vprašanja lahko moderator raziskuje naprej, da bi dobil več informacij in postavlja izzivalna vprašanja, da izvabi več razprave.
Običajno se zahteva, da je moderator izvedenec na področju, ki ga skupina obravnava, in da pozna cilje študije. Njegov cilj je pomagati skupini, da ustvarjalno razpravlja o temi. Kakovost podatkov v žariščnih skupinah je močno odvisna od tega, kako učinkovito moderator postavlja vprašanja in kako dobro vzdržuje razpravo, osredotočeno na predmetu raziskave. Moderator mora delovati kot pospeševalec, nadzirati mora sodelovanje med njim in člani skupine, kakor tudi med samimi člani skupine. Nekaj članov žariščne skupine je običajno bolj zgovornih, preostali pa so bolj zadržani, zato mora moderator najti način, da utiša preveč zgovorne, da lahko tihi spregovorijo. Ko so vprašanja izčrpana, moderator konča delo skupine.
Razprava žariščnih skupin se običajno izvede v posebni sobi, po možnosti je ta soba urejena tako, da ima na eni strani posebno steno, skozi katero se vidi v sobo, iz nje pa ne. Za to steno so slikovne in zvočne snemalne naprave ter ljudje, ki opazujejo intervju, vendar nanj nimajo vpliva.
2.1.2 Intervju
Intervju je metoda za pridobivanje kakovostnih informacij, pri katerih obstaja dialog med spraševalcem in vprašanim. Omogoča pridobivanje podrobnih informacij o potrebah kupcev in razpoznavo kakršnihkoli inovativnih rešitev. Kakovost intervjuja se meri s številom zapisanih potreb.
Odvisno od področja in obsega projekta je treba izbrati kupce, ki bodo intervjuvani, določiti, kje bodo intervjuji potekali, kdo jih bo vodil in kakšne vrste vprašanja bodo postavljena.
Intervju v konferenčni sobi
Najbolj običajna oblika intervjuja za pridobivanje potreb kupcev je intervju v konferenčni sobi (slika 8). Pri intervjuju v konferenčni sobi se je treba zanesti na zmožnost odgovarjajočega, da prikliče v spomin stvari, ki so mu bile ali mu niso bile všeč pri izdelku in da poskuša navesti tiste stvari, ki jih je pogrešal.
Spraševalec mora imeti nekakšen vodnik intervjuja, ki deluje kot opomnik, katere teme spraševati med intervjujem.
focused. After a question has been generally discussed, the moderator can search further to get more information by using additional teaser questions.
Normally, it is necessary that the moderator is an expert in the field discussed by the group and is acquainted with the subject of the study. It is his or her goal to help the group create a productive discussion on the specified topic. The quality of the data in the focus group mostly depends on how efficiently the moderator is asking questions and focusing the entire group on the topic. The moderator must work as a promoter, controlling the interaction between himself/herself and the members as well as between the members themselves. Some members of the focus group are usually more eloquent, while others are more reserved, so the moderator has to find a way to silence the too eloquent people in order to make the quiet ones start speaking as well. When all the issues have been discussed, the moderator concludes the work of the focus group.
The focus group discussion is normally carried out in a special room. The room can have a special one-way see-through wall, behind which there can be video- and audio-recording equipment, as well as additional observers.
2.1.2 Interview
The interview is a method of gathering qualitative information through a dialog between the interviewer and the interviewee. It enables them to gather detailed information on customer needs and identify innovative solutions. The quality of the interview is measured by the number of recorded needs.
Depending on the area and the size of the project, the following must be selected: the customers to be interviewed, the locations where the interviews are to be carried out, the interviewers, and the type of questions asked.
Conference-room interview
The most common form of interview for obtaining customer needs is a conference-room interview (Figure 8). During a conference-room interview it is necessary to rely upon the ability of the interviewee to recall the things he or she liked or disliked about the product, and that he or she will try to mention the things he or she missed.
The interviewer has to have some sort of interview guide that serves as a checklist for the subjects to be asked about during the interview.
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Spraševalec Interviewer
*
HP
Spraševani kupec Interviewed customer
(j
Začetek intervjuja v konferenčni sobi Beginning of the conference room interview
ij
Spraševalec postavi odprto vprašanje
spraševanemu kupcu (na določeno temo)
Interviewer sets an open question to the interviewed
customer (on a specific topic).
Spraševani kupec odgovarja na vprašanje spraševalca, tako navaja potrebe, želje, tehnične rešitve, značilke delov, cilje, primerjalne
vrednosti in ostalo
The interviewed customer answers the interviewer's question,
expressing his/her needs, wants, technical solutions, part
characteristics, goals, reference values and other things.
-Ne / No
Zapisovanje drugih izjav kupca o:
- tehničnih rešitvah in značilkah, značilkah vrednot, ciljih, primerjalnih vrednostih, ostalo.
Recording other statements of the customers:
- technical solutions and characteristis\ value caracteristics, goals, reference values, other things.
C
Da / Yes
Sklep intervjuja v konferenčni sobi End of the conference room interview
}
Nadaljno spraševanje spraševalca s ciljem odkriti skrite potrebe, ki jih skrivajo druge zapisane izjave kupcev:
- Zakaj si to želite?
- Kakšno korist bi imeli zaradi tega?
- To si želite zato, da bi lahko....?
Further questions from the interviewer aimed to discover any hidden needs, included in the written statements of the customers:
- Why do you want that?
- What benefit do you expect from that?
- You want this in order to be able to...?
OQ
Zvočno zapisovanje Audio recording
Slikanje Camera
Opazovalci Observers
SI. 8. Intervju v konferenčni sobi Fig. 8. Conference-room interview
Intervjuji v konferenčnih sobah omogočajo dobro vodenje intervjujev in zato učinkovito izrabo časa.
The conference-room interviews make possible good time-planning and the efficient use of time.
Povezano poizvedovanje
Povezano poizvedovanje se izvaja na mestu uporabe izdelka (si. 9). Omogoča spraševanje med opazovanjem dejanske uporabe izdelka.
Povezano poizvedovanje se uporabi predvsem za boljše razumevanje okolja (vremenski
Contextual inquiry
A contextual inquiry is carried out at the location where the product is being used (Fig. 9). It allows the interview to be conducted during observation of the actual use of the product.
A contextual inquiry is used mostly for better understanding of the environment (weather, culture,
c
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
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Začetek povezanega poizvedovanja Beginning of the contextual inquiry
—

Poizvedovalec opazuje kupca pri uporabi izdelka. Iz povezave
uporabe izdelka ugotavlja kupčeve potrebe.
The inquirer observes the customer at using the product and
determines the customer's needs from the context of use.
Resnične potrebe kupca i Customer's real needs  I
Združno iskanje poizvedovalca in kupca tehničnih rešitev za izdelek
glede na potrebe kupca
The inquirer and customer join in finding technical solutions for the
product according to the customer's needs
Tehnične rešitve, značilke vrednot, ciljne
vrednosti
Technical characteristics, value
characteristics, target values, etc.
C
Zaključek povezanega poizvedovanja End of the contextual inquiry
Sl. 9. Povezano poizvedovanje Fig. 9. Contextual inquiry
Z>
vplivi, kultura okolja, vrednote), v katerem kupec uporablja izdelek. Povezano poizvedovanje pomeni partnerstvo kupca in spraševalca pri iskanju rešitev za ugotovljene potrebe kupca.
2.1.3 Pridobivanje potreb iz pritožb kupcev
Potrebe kupcev, ki se pridobijo iz baze podatkov o pritožbah kupcev so kakovostne informacije, ki se zaradi narave pridobivanja ne morejo posploševati na večjo populacijo. Pogosto se zgodi, da so ljudje, ki se pritožujejo, taki, da se pritožujejo iz navade, ali taki, ki so imeli posebej slabo izkušnjo, predvsem pa tisti, ki imajo čas, da se pritožujejo. Pritožbe kupcev pokažejo informacijo o vzrokih za nezadovoljstvo. Potrebe iz pritožb kupcev se uporabijo kot dopolnilo k potrebam kupcev, ki se pridobijo z intervjuji oz. žariščnimi skupinami.
Postopek ustvarjanja potreb kupcev iz pritožb kupcev obsega naslednje korake:
1.  korak: Naključna izbira dogovorjenega števila pritožb iz baze podatkov.
2. korak: Pritožbe je treba prevesti v pozitivne izraze in osnutke, ki pomenijo skrite potrebe kupcev,
values) where the customer uses the product. A contextual inquiry is a partnership between the customer and the inquirer during their search for a solution to the identified customer needs.
2.1.3 Obtaining the needs from customer complaints
Customer requirements, obtained from the customer-complaint database are qualitative data that cannot be generalized to a wider population because of the way they were obtained. It often happens that certain people complain out of a habit, or those who have had an especially bad experience, and particularly those who have time to complain. Customer complaints reveal the causes of dissatisfaction. The needs obtained from customer complaints can be used in addition to the customer needs obtained by interviews and focus groups.
The procedure for obtaining the customer needs from customer complaints consists of the following steps: Step 1: Random retrieval of a certain number of complaints from the database, Step 2: Translation of the complaints into positive expressions and concepts, which represent the hidden
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izražene s pritožbo.
3. korak: Prečistiti izraze potreb kupcev z odstranitvijo ponovitev.
4. korak: Označiti vsak izraz, dobljen iz pritožb kupcev.
5.  korak: Spojiti izraze pritožb kupcev z izrazi, pridobljenimi z drugimi metodami.
needs of the customers, expressed by the complaint, Step 3: Removal of duplicates, Step 4: Marking of each expression obtained from customer complaints,
Step 5: Combining customer complaints with the expressions obtained by other methods.
2.1.4. Metoda soočanja idej pridobivanja podatkov o potrebah notranjih kupcev
2.1.4 The brainstorming method for obtaining data on internal customer needs
Metoda soočanja idej je najbolj znana in najpogosteje uporabljena metoda ustvarjalnega pridobivanja podatkov o potrebah kupcev. Pri uporabi te metode je treba upoštevati štiri osnovna pravila:
1.    pravilo: Vsaka kritika ali vrednotenje zamisli je strogo prepovedana, saj zavira ustvarjalno mišljenje.
2.    pravilo: Zamisli drugih članov skupine so lahko prevzete in nadalje razvite.
3.    pravilo: Člani skupine naj čim bolj prožijo svojo fantazijo pri reševanju problema.
4.    pravilo: V kratkem času naj bo predlaganih čim več zamisli rešitve problema.
The brainstorming method is the most popular and the most widely used creative method for obtaining data on customer needs. When using this method, four basic rules should be taken into account: Rule 1: Any criticism or evaluation of ideas is strictly forbidden because it obstructs creative thinking. Rule 2: The ideas of other team members can be used and developed further.
Rule 3: Team members should activate their imagination as much as possible during problem solving. Rule 4: As many ideas as possible should be proposed in the shortest possible time.
2.2 Postopek sestavljanja podatkov o potrebah kupcev
2.2 Methods for structuring the data on customer needs
Sestavljanje podatkov o potrebah kupcev naj se izvede v naslednjem zaporedju korakov:
Structuring of the data on customer needs is carried out in the following sequence:
				Tabela podatkov o izdelkih in postopkih / Table of products and processes data																								
				ID št/ ID No.	E/I	Demografija kupcev/ Customer demographics		Izjava kupca/ Customer statement		Uporaba / Usage												Anali izja	zirana va/ lyzed ment	Potreba/ Značilka Need/ Characteristic		Vrsta potrebe/ značilke Type of need/ characteristic		
										Kdo/ Who		Kaj/ What		Kdaj/ When		Kje/ Where		Zakaj/ Why		Kako/ How		Ana state						
																												
		Tabela glasu notranjih kupcev / Table for the voice of the internal customers																										
																												
		ID št/ ID No.					Izjava kupca/		Uporaba / Usage														Potreba/ Značilka		Vrsta potrebe/ značilke			
			kupce Custo demogra			v/															izj Ana state	ava/						
						mer phics	statement		Kdo/ Who		Kaj/ What		Kdaj/ When		Kje/ Where		Zakaj/ Why		Kako/ How			lyzed ment	Need/ Characteristic		Type of need/ characteristic			
																												
Tabela glasu zunanjih kupcev / Table for the voice of the external customers																												
																												
ID Št/ ID No.						Izjava kupca/ Customer statement		Uporaba / Usage											Analizirana izjava/ Analyzed statement			Potreba/ Značilka Need/ Characteristic		Vrsta potrebe/ značilke Type of need/ characteristic				
	ku Cus demo		pcev/		s																							
			tomer graphic					Kdo/ Who	Kaj/ What		Kdaj/ When		Kje/ Where		Zakaj/ Why		Kako/ How											
																												
																												
																												
																												
																												
																												
																												
																												
																												
SI. 10. Izhodiščne preglednice glasu kupcev Fig. 10. Initial tables for the voice of the customers
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
89
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
1. korak: Oblikovanje izhodiščnih preglednic glasu kupcev,
2. korak: Oblikovanje sorodnostnega diagrama
3. korak: Oblikovanje drevesnega diagrama.
Step 1: Design of initial tables for the voices of the
customers
Step 2: Design of the affinity diagram,
Step 3: Design of the tree diagram.
1. korak: Oblikovanje izhodiščnih preglednic glasu kupcev
Z metodami za zbiranje podatkov se pridobijo najrazličnejše izjave kupcev, ki govorijo o njihovih problemih, priložnostih, zamislih, rešitvah, željah in potrebah.
Ločevanje resničnih potreb kupcev je prvi pogoj za sestavljanje potreb in ovrednotenje relativne pomembnosti potreb, ki naj se upoštevajo pri načrtovanju izdelka. Pri tem si tisti, ki analizirajo kakovostne podatke pomagajo z izhodiščnimi preglednicami glasu kupcev, v katere se vpišejo dobesedne izjave kupcev. Slika 10 prikazuje vsebino izhodiščnih preglednic glasu kupcev.
Stolpec z “razpoznavno številko” razpozna vir izjave kupca, npr. številka intervjuja, številka strani, številka vrstice ali datum intervjuja. Njegov namen je, da preskrbi povezavo nazaj do vira izjave za primer, ko želimo izvedeti nadaljnje informacije o izjavi.
Stolpec, ki obravnava “demografijo kupcev”, vsebuje informacije, to so starost, prihodki, poklic ali lokacija osebe, ki je preskrbela podatke.
Razdelek “uporaba” vsebuje informacije, ki opisujejo povezavo uporabe izdelka.
V stolpcu “analizirana izjava” se označi, ali gre za resnične potrebe kupcev, in/ali pa za možne tehnične rešitve in cilje.
Step 1: Design of initial tables for the voices of the customers
Using data-acquisition methods various statements of the customers are obtained, related to their problems, opportunities, ideas, solutions, wishes and needs.
The separation of real customer needs from other expressions is a precondition for structuring the needs and evaluating the relative relevance of needs that are taken into account when planning the product. Those who analyze the quantitative data use the initial tables of the voice of the customers, which are filled out with literal customer statements. Figure 10 presents the contents of the initial voice-of-the-customer tables.
The “ID” column identifies the source of the customer statement, e.g., interview number, page number, number of the line or the date of the interview. It is used for back-referencing the statements in case further information is required about the source.
The “Customer demographics” column contains the age, income, occupation and location of the customer.
The “Use” section describes the context of use of the product in detail.
The “Analyzed statement” marks whether the statement is a real customer need and/or a possible technical solution or goal.
2. korak: Oblikovanje sorodnostnega diagrama
V izhodiščnih preglednicah glasu kupcev zbrane potrebe se nadalje razvrstijo z uporabo sorodnostnega diagrama, to je orodja za hierarhično organizacijo kakovostnih informacij. Slika 11
Step 2: Design of the affinity diagram
The needs, collected in the initial tables of the voice of the customers are further classified using the affinity diagram – this is a tool for the hierarchical organization of qualitative information.
KAKOVOST IZDELKA / QUALITY OF THE PRODUCT
"^
ERGONOMIJA
- prijazno za uporabnika
- dostopnost
ERGONOMICS
- user friendly
- accessibility
;
'   r.
IZGLED
- sodobna oblika
- skladnost z okoljem
DESIGN
- contemporary design
- harmony with
surroundings
;
DELOVANJE
- enostavna uporaba
- dobro počutje
;
FUNCTIONALITY
- simple usage
- well-being
;
/v
VARNOST in                          SAFETY and
ZANESLJIVOST                     RELIABILITY
- brezhibno trajno delovanje   - lasting flawless operation
- varnost uporabnika               - user's safety
;                             ;
V.
^v
U

SI. 11. Načelo gradnje sorodnostnega diagrama za vrednoto “kakovost izdelka” Fig. 11. Principle of building the affinity diagram for the value of the quality
90
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
prikazuje načelo oblikovanja sorodnostnega diagrama načrtovanja izdelka. Hierarhija se začne sestavljati od spodaj navzgor.
V vrednoti “kakovost izdelka” so vse potrebe, ki so jih izrazili zunanji kupci, to so predvsem potrebe, ki se nanašajo na varnost, delovanje in videz izdelka.
Figure 11 presents the principle of affinity-diagram development for planning the product. The hierarchy is being built bottom-up.
“Quality of the product” contains all of the needs expressed by external customers, especially the needs related to the safety, functionality and aesthetics of the product.
3. korak: Oblikovanje drevesnega diagrama
Drevesni diagram tako kakor sorodnostni diagram sestavlja potrebe hierarhično. V nasprotju s sorodnostnim diagramom je drevesni diagram grajen od zgoraj navzdol oz. z leve v desno. V drevesnemu diagramu so prikazane osnovne, drugotne in ostale potrebe kupcev. Terciarne potrebe predstavljajo vhod v “hišo kakovosti” načrtovanega izdelka. Slika 12 prikazuje načelo gradnje drevesnega diagrama za vrednoto “kakovost izdelka”.
Step 3: Design of the tree diagram
In the tree diagram the needs are also structured in a hierarchical way. In contrast to the affinity diagram, the tree diagram is built from the top to the bottom (or from the left to the right). In the tree diagram the primary, secondary and tertiary customer needs are shown. Tertiary needs represent the entrance into the house of quality of the planned product. Figure 12 presents the principle of building the tree diagram for the value of the quality.
3 VREDNOTENJE PODATKOV O POTREBAH KUPCEV
3 EVALUATION OF THE DATA ON CUSTOMER NEEDS
Na podlagi podatkov o potrebah kupcev, sestavljenih v sorodnostnem oz. drevesnem diagramu, je treba izvesti še vrednotenje potreb, torej določiti pomembnost posameznih potreb kupcev.
Analiza in ocena razpoložljivih metod vrednotenja podatkov o potrebah kupcev ([5] in [13]) je pokazala, da je za vrednotenje podatkov najprimernejše “orodje” anketa, in to telefonska ali poštna.
_      OSNOVNE POTREBE
PRIMARY NEEDS
KAKOVOST IZDELKA QUALITY OF THE PRODUCT
On the basis of the data on customer needs, stored in the affinity and tree diagrams, it is necessary to evaluate the needs, and therefore to define the relevance of each customer need.
The analysis and appraisal of the available methods for evaluating the data on customer needs ([5] and [13]) has revealed that in order to evaluate the data on customer needs the most suitable tool is a survey (conducted either by phone or mail).
OSTALE POTREBE TERTIARY NEEDS
- prjazno do uporabnika / user friendly
- dostopnost / accessibility
- enostavna uporaba / simple usage
- dobro počutje / well-being
- sodobna oblika / contemporary design
- skladnost z okoljem / in harmony with surroundings
r- brezhibno trajno delovanje / lasting and flawless operaton - varnost uporabnika / user's safety
SI. 12. Načelo gradnje drevesnega diagrama za vrednoto “kakovost izdelka” Fig. 12. Principle of building the tree diagram for the value of the quality
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
V anketi je treba vzorec izbrati naključno, tako da ima vsaka oseba v populaciji merljivo verjetnost izbire, s tem se rezultati ankete zanesljivo preslikajo iz vzorca na večjo populacijo. Anketa se lahko izvede v državi, regiji ali občini.
Telefonske ankete so drage, običajni vir za vzorčenje pa so telefonski imeniki.
Poštne ankete terjajo manjše stroške, so pa zelo učinkovite takrat, ko so naslovljene na uporabnike določene skupine izdelkov in preskrbijo merljive podatke, ki se lahko posplošijo na celotno populacijo. Naslovno pismo poštne ankete mora razložiti vzroke za anketo in izraziti zagotovila o zaupnosti.
Da zagotovimo veliko odgovorov, priporočamo pri poštni anketi priporoča upoštevanje naslednjih pravil:
1. pravilo: Večkratni stiki, ki obsegajo:
o pošiljanje predhodnega poštnega naznanila o
anketi, o pošiljanje ankete vsem odgovarjajočim ob istem
času s spremnim besedilom, o pošiljanje opomnika z informacijo, da lahko
spraševani zahtevajo nadomestni vprašalnik, o pošiljanje zadnjega nadomestnega vprašalnika
s priporočeno pošto, o pošiljanje potrdila ali priznanja za sodelovanje v
anketi,
2. pravilo: Uporabiti natiskani papir in predstavniška pisma z logotipom in stično osebo,
3. pravilo: Vključitev ovojnice z znamko in naslovom za vrnitev ankete,
4. pravilo: Vključitev simboličnega darila s prvotnim ali naslednjim vprašalnikom kot spodbudo in znak spoštovanja.
Pri izvedbi ankete kupce zaprosimo, da posamezno potrebo ustrezno ovrednotijo. Za vrednotenje potreb kupcev je na voljo več metod ([14] in [15]), katerih značilnosti, prednosti in pomanjkljivosti so prikazane v preglednici 1.
Po opisani metodi pridobljene, sestavljene in vrednotene potrebe kupcev izdelka pomenijo vhodni podatek 1. hiše postopka razvoja izdelka z načinom RFK. Slika 13 prikazuje posplošeni model ugotavljanja in vrednotenja potreb kupcev.
4 PRIMER
Podjetje, ki izdeluje zdravstveno opremo, želi izboljšati konkurenčno zmožnost na domačem trgu in razširiti svojo ponudbo tudi na svetovni trg.
The sample for the survey should be selected randomly, so that each person in the population has a measurable probability of being selected and thus the survey results can be reliably extended to a larger population. The survey can be conducted in the state, region or municipality.
Phone surveys are expensive and the usual source for sampling is phone directories.
Mail surveys cost less; they are very effective when they are targeted to the users of a particular group of products and they provide measurable data that can be generalized to the whole population. The letter accompanying the mail survey should explain the reasons for the survey and give an assurance of confidentiality.
To ensure a high response rate, the following rules should be followed when conducting mail surveys: Rule no. 1: Multiple contacts should be used, including:
•  sending an announcement of the survey by mail,
•  sending the survey with a cover letter to all interviewees at the same time,
•  sending a reminder with contact details, enabling the interviewees to request a substitute survey
•  sending the last substitute survey with registered mail,
•  sending a letter or certificate as a symbol of appreciation for the cooperation.
Rule no. 2: Use printed paper and memos with letterheads and contact person details. Rule no. 3: Use stamped envelopes with printed return addresses.
Rule no. 4: Enclose a symbolic gift with the first or subsequent surveys to recognize the efforts of the interviewees and to thank them,
When conducting a survey, the customers are requested to evaluate each individual need. There are several methods available to evaluate the customer needs ([14] and [15]). Their characteristics, advantages and drawbacks are presented in Table 1.
With the described methods obtained, structured and evaluated customer needs represent the input data for the 1st QFD house of new-product development. Figure 13 shows a general model for obtaining and evaluating customer needs.
4 CASE STUDY
A company that produces medical equipment wishes to improve its competitiveness on the domestic market and to offer its products to the global market.
92
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
METODA VREDNOTENJA/ EVALUATION METHOD	OPIS METODE / DESCRIPTION OF THE METHOD	PREDNOSTI METODE / ADVANTAGES OF THE METHOD	SLABOSTI METODE/ DISADVANTAGES OF THE METHOD
Neposredna ocenitev potreb kupcev/ Direct evaluation of customer needs	Kupce se prosi, da ovrednotijo pomembnost vsake potrebe z lestvico, ki jo navaja anketa. Najbolj pomembne potrebe naj bi bile ocenjene z visokimi števili, medtem, ko naj bi bile potrebe z majhno pomembnostjo ocenjene z nizkimi števili. / The customers are asked to evaluate the relevance of every need on a scale, given by the survey. The most important needs should be marked with high scores while the less important needs should qet lower scores.	Metoda jeza kupce lahko razumljiva. / The method is easily comprehensible to the customers.	Kupci težijo k temu, da ocenijo vse potrebe kot zelo pomembne. To naredijo predvsem zato, ker jim ni potrebno primerjati potreb med seboj. / The customers tend to mark all needs as very important because they do not have to compare the needs with each other
Razvrstitev potreb kupcev po pomembnosti / Sorting customer needs by relevance	Kupce se naprosi, da razvrstijo potrebe iz seznama od najbolj pomembne do najmanj pomembne. / The customers are requested to sort the needs on the list from the most important need to the least important one.	Metoda jeza kupce lahko razumljiva. Kupci morajo narediti tudi nekaj primerjalnih odločitev. / The method is easily comprehensible to the customers. They must also make some comparative decisions.	Metoda je težka za izvedbo, kadar je potrebno razvrstiti več kot deset potreb. / This method is difficult to carry out when more than ten needs have to be evaluated.
Kombinirana metoda razvrstitve pomembnosti in dodeljevanja točk potrebam kupcev/ Combined method of sorting by relevance and assigning points to the needs	Pri tej metodi kupci potrebe najprej razvrstijo po padajočem vrstnem redu pomembnosti, nato tem potrebam dodajo števila s 100 številčne lestvice. Najvišje število dajo najpomembnejši potrebi in najmanjše število najmanj pomembni potrebi. / In this method the customers first sort the needs by relevance in descending order. Then they assign numbers from a 100 point scale to the needs, giving the highest number to the most important need and the smallest number to the least important need.	Metoda je lahko razumljiva. Kupci naredijo primerjalne odločitve že pri določanju vrstnega reda potreb, zato lažje dodajo različne vrednosti potrebam s 100 številčne lestvice./ The method is easily comprehensible to the customers. The customers already make comparative decisions when selecting the order of needs and can easily assign values from the 100 point scale to different needs.	Metoda je težka za izvedbo, kadar je potrebno razvrstiti več kot deset potreb. / This method is difficult to carry out when more than ten needs have to be evaluated.
Dodeljevanje 100 točk med vse potrebe ku pcev / Assigning 100 points among all customer needs	Pri tej metodi je potrebno razdeliti 100 točk med potrebe kupcev iz seznama. / In this method, 100 points are distributed to the customer needs on the list.	Kupci morajo pri razdeljevanju točk sprejemati primerjalne odločitve in relativno primerjati potrebe med seboj. / The customers must make comparative decisions when assigning points and compare the needs relatively.	Ker se od odgovarjajočih zahteva velika pozornost, odgovarjajoči porabijo veliko časa za razdeljevanje točk med potrebe, posebej, če je teh potreb 10 ali ve< As the attention required from the interviewees is very high, a lot ottime is necessary to assign the points to the needs, especially if there are more than ten needs.
Priorizacijski model 1-2-3 / Prioritization model 1-2-3	Priorizacijski model 1-2-3 je metoda, kjer kupci najprej določijo za njih najpomembnejšo potrebo, kasneje določijo druga mesta potrebam, za katere menijo, da so po pomembnosti za najpomembnejšo potrebo. Ostalim potrebam pripišejo tretja mesta. Analitiki kasneje pripišejo najpomembnejši potrebi za posameznega kupca 5 točk, potrebam, uvrščenim na drugo mesto, 3 točke in tretje uvrščenim potrebam 1 točko. Vsote točk za vsako potrebo so osnova za določanje relativne pomembnosti potreb. / The prioritization model 1-2-3 is a method where customers first determine the needs they find most important. Then they select the second most important needs. The remaining needs are considered as the third most important. The analysts assign 5 points to the most important need of the customer, 3 points to the second most important needs and 1 point to the third most important needs. The sum of points for each need is the basis for determining the relative relevance of the needs.	Metoda je lahka za razumevanje in hitra za izpolnjevanje. / The method is easy to comprehend and quick to fill in.	Kadar je potrebno obravnavati večje število potreb je metoda zamudna. / The method is slow when a large number of needs have to be dealt with.
Metoda primerjave parov potreb kupcev / Couple comparison method	Pri metodi primerjave parov se primerjata po dve potrebi, glede na direktno primerjavo se da prednost eni od obeh potreb. Potreba, ki je imela največkrat prednost glede na ostale potrebe, je po rangu najvišje, to pomeni, daje najpomembnejša. Potrebe se uredijo v obliki matrike, ugotovitve primerjave parov pa se vnašajo v odgovarjajoča polja matrike. / In the couple comparison method, two needs are directly compared in order to determine the more important one. The need which was selected in favor of others most of the times, is ranked the highest, i.e., the most important need. The needs are sorted in matrix form and the results of comparisons are entered in the appropriate fields of the matrix.	Možnost pridobitve relativnih pomembnosti potreb. / The possibility to acquire relative relevance of needs.	Možnost nedoslednih sodb. Kadar je potrebno obravnavati večje število potreb je metoda zamudna. / The possibility of inconsistent judgments. Time-consuming when a lot of needs have to be evaluated.
Analitični hierarhični pristop / Analytical hierarchic approach	Analitični hierarhični pristop uporablja primerjavo parov potreb samo med sorodnimi potrebami v drevesu in tako ustvarja lestvico razmerij pomembnosti. Najprej se ugotovijo pomembnosti potreb na višjih nivojih, nato pa pomembnosti potreb po posameznih skupinah na nižjih nivojih. Pare primerjamo z ocenami od 1 do 9. / The analytical hierarchic approach uses the couple comparison of needs only among related needs in the tree, creating a scale of relevance relations. Firstly, the relevance of needs on higher levels is determined, followed by the relevance of needs by individual groups on lower levels. The couples are compared by using marks from 1 to 9.	Možnost pridobitve relativnih pomembnosti potreb. Najbolj natančna metoda. / The possibility to acquire relative relevance of needs. The most accurate method.	Kadar je potrebno obravnavati večje število potreb je metoda zamudna. / The method is slow when a large number of needs must be dealt with.
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
(      cm
Zunanji kupci .External customers!
¦O      ^
Notranji kupci Internal customers
Podatki o izdelkih in postopkih
Data on products and processes
Metode za zajemanje kakovostnih podatkov o potrebah kupcev Methods for the acquisition of qualitative data on customer needs
Žariščne skupine:     Focus groups of:
- zunanjih kupcev     - external customers
- notranjih kupcev     - internal customers
Povezano poizvedovanje Contextual inquiry
Intervjuji v konferenčni sobi Conference room interview
Soočanje idej kupcev Brainstorming with customers
I
Izhodiščne tabele glasu kupcev
Initial voice of the customer tables
Sorodnostni diagram potreb Affinity diagram of needs
Drevesni diagram potreb Tree diagram of needs
Vrednotenje podatkov o potrebah kupcev Evaluation of data on customer needs
Telefonska anketa Telephone survey
Poštna anketa Postal survey

KAKO / HOW f
NACRTOVANJE IZDELKA 1st HOUSE PRODUCT PLANNING
KAKO / HOW
NA 2 RT A SKLOPOV, SEST
2nd HOUSE COMPONENT PLANNING
KAKO / HOW
NARTOVANJE
POSTOPKOV
3rd HOUSE
PROCESS
PLANNING
KAKO / HOW
NACRTOVANJE PROIZVODNJE
4th HOUSE PRODUCTION
PLANNING
RFK/QFD
SI. 13. Posplošeni model ugotavljanja in vrednotenja potreb kupcev Fig. 13. A general model for obtaining and evaluating customer needs
Vodstvo podjetja se je odločilo, da za izdelek Vario Flow (si. 14), ki se uporablja v zdravstvu kot pripomoček pri posegih, ugotovi potrebe kupcev in kasneje z uporabo metodologije RFK te potrebe v kar največji meri upošteva pri sprejemanju nove različice izdelka ([16] in [17]).
V nadaljevanju je prikazan postopek pridobivanja, sestavljanja in vrednotenja potreb
The company management has decided that it will establish the customer needs for the Vario Flow product (Fig. 14 – it is used in medicine as an aid in surgery), and later on, using the QFD methodology, consider these needs in the development of a new version of the product ([16] and [17]).
In the text that follows, the procedure for obtaining, structuring and evaluating the needs of



94
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
Sl. 14. Vario Flow Fig. 14. Vario Flow
kupcev izdelka Vario Flow ter oblikovanja vhodnega vektorja KAJ hiše razvoja funkcij kakovosti izdelka.
Za izvedbo naloge je vodstvo podjetja izbralo projektni način in imenovalo projektni tim v sestavi:
• Moderator: Inženir načrtovanja kakovosti, ker dobro pozna metodologijo RFK in izdelek Vario Flow, . Člani tima: o razvojni inženir, ker pozna konstrukcijske zahteve
izdelka, o zdravnik, ker uporablja izdelek pri posegih o oblikovalec, ker je odgovoren za obliko
izdelka, o član vodstva, ker je odgovoren za povezovanje projektne skupine z vodstvom podjetja in pozna kupce, o inženir načrtovalec proizvodnih postopkov ker pozna tehnološke postopke izdelave izdelka, o proizvodni inženir, ker pozna možnosti in omejitve izdelave v podjetju.
4.1 Viri glasu kupcev za izdelek Vario Flow
Projektna skupina je ugotovila, da so za izdelek Vario Flow na voljo naslednji viri glasu kupcev:
Vario Flow customers and the establishment of the input WHAT vector for the house of QFD of the product is presented.
In order to accomplish the task, the company management selected the project approach and appointed a project team consisting of:
•  Moderator: quality-planning engineer - because he knows well the QFD methodology and the Vario Flow product,
•  Team members:
o development engineer - because he knows the
design requirements of the product, o physician - because he uses the product in
surgical procedures, o designer - because he is responsible for the
design of the product, o managing board member - because he is responsible
for connecting the project team with the company
management and he knows the customers, o production process planning engineer -
because he knows the production processes, o production engineer - because he knows the
possibilities and limitations of manufacturing in
the company.
4.1 Sources of the customers’ voice for the Vario Flow product
The project team established that the following sources for the customers’ voice for the Vario Flow product are available:
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
95
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
Zunanji kupci (zdravniki, ki opravljajo endoskopske posege; inštrumentarke, ki sodelujejo pri posegih, ter zastopniki vodstva podjetja).
Notranji kupci (inženirji, odgovorni za razvoj izdelka, postopkov, kakovosti; dobavitelji sestavnih delov in materialov; vzdrževalci, ki skrbijo za nemoteno delovanje izdelka). Podatki o izdelkih in postopkih (podatki o opravljenih vzdrževalnih posegih, pripombah in pritožbah kupcev).
External customers (physicians who perform endoscopies, scrub nurses who participate in surgery and representatives of the company management). Internal customers (engineers responsible for the development of the product, the processes, the quality; the suppliers of components and materials; the maintenance crew that is responsible for normal operation of the product). Product and process data (data on performed maintenance works, customer remarks and complaints).
4.2 Pridobivanje podatkov o potrebah kupcev izdelka Vario Flow
4.2 Obtaining the data on customer needs for the Vario Flow product
Za pridobitev podatkov o potrebah kupcev je projektna skupina izbrala metodo intervjujev, in to v obliki:
•  intervjujev v konferenčni sobi in
•  povezanega poizvedovanja.
Za prvo obliko intervjujev se je projektna skupina odločila zaradi lažjega časovnega usklajevanja udeležencev intervjuja. Intervjuja se je udeležilo 10 oseb različnih profilov: zdravniki, inštrumentarke, inženirji, vzdrževalci, predstavniki vodstev podjetij. Udeleženci so vnaprej dobili okvirna vprašanja, da so se lahko ustrezno pripravili.
S pomočjo intervjuja je bilo zbranih 35 potreb kupcev, in sicer:
•  posebne zahteve za laparaskopijo, artroskopijo...
•  stabilnost sistema
•  nadzor kakovosti
•  majhni proizvodni stroški
•  majhni garancijski stroški
•  majhni stroški posegov
•  zahteva za prave dobavitelje in kooperante
•  oblika za dobro mobilnost sistema
•  primernost videza za zdravstveno okolje
•  neodvisnost od vira energije
•  varnost za bolnika
•  varnost naprave
•  zanesljivo delovanje
•  vzdržljivost naprave
•  varnost delovanja
•  varnost izdelka in odgovornost za posledice
•  izboljšanje napak človeškega dejavnika
•  varnost za uporabnika in odgovornost za posledice
•  hiter prenos
•  varen prenos
•  preprosto vzdrževanje
•  preprosta in hitra montaža/demontaža
In order to obtain the data on customer needs the project team selected the following forms of interviews:
•  conference-room interviews
•  contextual inquiry.
The project team selected the first form of interview because of the easier time management of the interviewees. The interviewees were 10 people of various profiles: physicians, scrub nurses, engineers, maintenance personnel and company management representatives. The participants were given general questions in advance so that they could prepare properly.
35 customer needs were identified by the interview:
•  Special requirements for laparoscopy, arthroscopy, etc.
•  Stability of the system
•  Quality control
•  Low production costs
•  Low warranty costs
•  Low operating costs
•  Requirement for suitable suppliers and cooperators
•  Good system mobility design
•  Aesthetical suitability for medical environment
•  Independence of energy source
•  Patient’s safety
•  Device’s safety
•  Reliable operation
•  Durability of the device
•  Safety of operation
•  Safety of the product and responsibility for consequences
•  Improvement of human-factor errors
•  Safety for the user and responsibility for the consequences
•  Fast transport
•  Safe transport
•  Simple maintenance
•  Simple and quick assembly/disassembly






96
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
•  lahka izvedljivost
•  pravočasnost (JIT)
•  prilagodljivost delovnega okolja
•  metodologija načrtovanja
•  avtomatizacija
•  vrednostni sistem
•  izboljšanje organizacije/vodenja
•  izobraževanje in izpopolnjevanje zaposlenih
•  delovna postaja
•  informacijsko vodenje
•  zahteve skupin
•  integracija
•  orodje za odzivnost
Povezano poizvedovanje je bilo namenjeno spoznavanju postopka uporabe izdelka v kirurški dvorani.
V razgovoru z uporabniki je bilo oblikovanih še nadaljnjih 14 potreb kupcev, in sicer:
•  dobra vidljivost v polju posegov
•  nastavitev tlaka kirurgu in/ali inštrumentarki
•  dobra vidnost informacije o stanju tlaka v sistemu
•  dobra vidnost informacije o stanju pomanjkanja v sistemu
•  hitra menjava tekočine
•  večja ločljivost prikazovalnika
•  omogoča dostop v notranjost telesa
•  zvezna nastavitev tlaka
•  segrevanje vode
•  po menjavi vode upoštevanje prejšnjega stanja tlaka
•  prednastavljanje vrednosti tlaka
•  nadzor količine vode v sistemu
•  opozorila stanja zbiralnika
•  opozorila o kritičnih stanjih sistema
Skupno je bilo torej oblikovanih 49 zahtev kupcev.
4.3 Sestavljanje podatkov o potrebah kupcev izdelka Vario Flow
Projektna skupina je izvedla sestavljanje podatkov o potrebah kupcev v treh korakih:
1. korak: Oblikovanje izhodiščnih preglednic glasu kupcev
Izhodiščne preglednice glasu kupcev izdelka Vario Flow (si. 15) so bile oblikovane posebej za zunanje in notranje kupce ter glede na podatke o izdelkih in postopkih.
V preglednici zunanjih kupcev je navedenih 21 potreb, v preglednici notranjih kupcev 26 in v preglednici podatkov o izdelkih in postopkih dve
•  Simple manufacturability
•  JIT (just in time)
•  Flexibility of the operating environment
•  Planning methodology
•  Automation
•  Value system
•  Improvement of organization/management
•  Training of employees
•  Workstation
•  IT management
•  Requirements of teams
•  Integration
•  Tool for response
The purpose of the contextual inquiry was to get acquainted with the use of the product in the operating theater.
Another 14 customer needs were identified during the discussions with users:
•  Good visibility in the surgical field
•  Operator and/or scrub nurse can set the pressure
•  System pressure is clearly visible
•  System deficit is clearly visible
•  Quick exchange of fluid
•  Higher display resolution
•  Interior of the body should be accessible
•  Continuous set of pressure
•  Heating of water
•  Following water change, the previous pressure is taken into account
•  Pressure can be pre-set
•  Control of amount of water in the system
•  Battery status warnings
•  Critical system state warnings
Altogether there were 49 customer requirements formed.
4.3 Structuring the data on customer needs for the Vario Flow product
The project team carried out the structuring of data on customer needs in three steps:
Step 1: Forming the initial tables of the voice of the customers
Initial tables of the voice of the customers of the Vario Flow product (Figure 15) were formed especially for external and internal customers and according to the data on products and processes.
The table of external customers contains 21 needs, the table of internal customers contains 26 needs, and the table on the product and process
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
97
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PREGLEDNICA GLASU ZUNANJIH KUPCEV / TABLE FOR THE VOICE OF THE EXTERNAL CUSTOMERS											
Id. št./ ID No.	Demografija kupcev Customer demography	Izjava kupca Customer statement	UPORABA/USE						Analizirana izjava Analyzed statement	Potreba/ značilka Need/feature	Vrsta potrebe/ značilke Type of need/ feature
			Kdo Who	Kaj What	Kdaj When	Kje Where	Zakaj Why	Kako How			
1.	Zdravniki Physicians	Omogoča dostop v notranjost telesa Interior of the body is accessible	Kirurg Surgeon		Med celotnim posegom During entire surqery	Operacijska dvorana Operation theatre	Za nemoteno delo For uninterrupted work		Omoqocen dostop v notranjost telesa med poseqom I nterior of the body is accessible	Kakovost Quality	Delovanje Functionality
2.	Zdravniki Physicians	Dobra vidljivost v polju posega Good visibility in the surgical field	Kirurg Surgeon		Med celotnim posegom During entire surqery	Operacijska dvorana Operation theatre	Za nemoteno delo For uninterrupted work	Z endoskopom With endoscope	Dobra vidljivost v polju poseqa Good visibility in the surqical field	Kakovost Quality	Delovanje Functionality
3.	Zdravniki Physicians	Zvezna nastavitev tlaka Continuous set of pressure	Kirurg Surgeon	Dobra vidljivost Good visibility	Med celotnim posegom During entire surqery	Operacijska dvorana Operation theatre	Za nemoteno delo For uninterrupted work		Nastavitev tlaka mora biti zvezna Pressure should be set continuously	Kakovost Quality	Delovanje Functionality
4.	Zdravniki, inštrumentarke Physicians, scrub nurses	Nadzor količine vode v sistemu Control of water amount in the system	Kirurg in in strum. Surgeon and scrub nurse	Prava količina vode The right amount of water	Med celotnim poseqom Durinq entire surqery	Operacijska dvorana Operation theatre	Varnost bolnika Safety of the patient	Kontrolna naprav; Control device	Kontrola količine vode v napravi Control of water amount in the device	Kakovost Quality	Varnost Safety
											
21.											
											
PREGLEDNICA GLASU NOTRANJIH KUPCEV / TABLE FOR THE VOICE OF THE INTERNAL CUSTOMERS											
Id. št./ ID No.	Demografija kupcev Customer demography	Izjava kupca Customer statement	UPORABA/USE						Analizirana izjava Analyzed statement	Potreba/ značilka Need/feature	Vrsta potrebe/ značilke Type of need/ feature
			Kdo Who	Kaj What	Kdaj When	Kje Where	Zakaj Why	Kako How			
22.	Nadzorni inženirji Inspection engineers	Varnost za bolnika Safety of the patient		3repreČit. poškodb Prevention of n juries	Med poseqom Durinq surqery	Op. dvorana Operation theatre		Varnost, sistem Safety system	Zaqotovljena varnost pacienta Ensured safety of the patient	Kakovost Quality	Varnost Safety
23.	Razvojni inženir Development engineer	Zanesljivo delovanje Reliable operation		Preprečitev zastojev Prevention of deadlocks	Med poseqom Durinq surqery	Operacijska dvorana Operation theatre	Nemoteno delovanje Undisturbed operation	Konstrukcijska rešitev Desiqn solution	Izboljšanje konstrukcijske rešitve Desiqn solution improvement	Kakovost Quality	Zanesljivost Reliability
24.	Razvojni inženir Development engineer	Vzdržljivost naprave Device durability			Vsaj dve leti At least 2 years		Brezhibno delovanje Perfect operation	Konstrukcijska rešitev Desiqn solution	Vzdržljivost naprave Device durability		Zanesljivost Reliability
25.	Razvojni inženir Development engineer	Varnost delovanja Safety of operation		Preprečitev zastojev Prevention of deadlocks	Med poseqom Durinq surqery	Operacijska dvorana Operation theatre	Da ne pride do poškodb To prevent injuries	Konstrukcijska rešitev Desiqn solution	Varnost delovanja izdelka in odqovornost za posledice Safety of operation and responsibility for consequences	Kakovost Quality	Zanesljivost Reliability
											
47.											
											
PODATKI O IZDELKIH IN PROCESIH / PRODUCT AND PROCESS DATA											
Id. št./ ID No.	Demografija kupcev Customer demography	Izjava kupca Customer statement	UPORABA/USE						Analizirana izjava Analyzed statement	Potreba/ značilka Need/feature	Vrsta potrebe/ značilke Type of need/ feature
			Kdo Who	Kaj What	Kdaj When	Kje Where	Zakaj Why	Kako How			
1.	Vzdrževalna služb; Maintenance service	Hitra menjava tekočine Quick exchange of fluid	Inštru me ntarka Scrub nurse		Pred in med poseqom Before and durinq surqery	Na izdelku On the product	Nemotena oskrba s tekočino Uninterrupted fluid supply	Ročno Manual	Enostavna menjava tekočine Simple exchanqe of fluid	Kakovost Quality	Delovanje Functionality
2.	Zdravniki Physicians	Premajhen prikazovalnik Too small a display	Zdravnik Physician	Premajhna ločljivost Insufficient resolution	Vied poseqom durinq surqery	Na izdelku On the product	Da ne pride do napak To prevent errors		Zaqotoviti večjo ločljivost prikazovalnika To ensure hiqher display resolution	Kakovost Quality	Delovanje Functionality
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
KAKOVOST IZDELKA »VARIO FLOW«    /    QUALITY OF »VARIO FLOW« PRODUCT
ERGONOMIJA; ERGONOMICS                                                     ^
Dobra vidljivost v polju posega / Good visibility in the surgical field Omogoča nastavitev tlaka kirurgu in/ali inštrumentarki / Operator and/
or scrub nurse can set the pressure Dobra vidnost informacije o stanju tlaka v sistemu / System pressure
is clearly visible Dobra vidnost informacije o stanju v sistemu / System deficit is clearly
visible Hitra menjava tekočine / Quick exchange of fluid Večja ločljivost displeja / Higher display resolution
/delovanje ; functionality
Omogoča dostop v notranjost telesa / Interior of the body should be
accessible Zvezna nastavitev tlaka / Continuous set of pressure Segrevanje vode / Heating of water Po menjavi vode upoštevanje prejšnjega stanja tlaka / Following
water change, the previous pressure is taken into account Prednastavljanje vrednosti tlaka / Pressure can be pre-set Posebne zahteve za laparaskopijo, artroskopijo... / Special
requirements for laparoscopy, arthroscopy... Stabilnost sistema / Stability of the system Nadzor kakovosti / Quality control
STROŠKI / COSTS                                                                       ^
Nizki proizvodni stroški / Low production costs Nizki garancijski stroški / Low warranty costs Nizki stroški delovanja / Low operation costs Zahteva za prave dobavitelje in kooperante / Requirement for suitable V   suppliers and cooperators                                                             ,
Izgled / design
- Oblika za dobro premičnost sistema / Good system mobility design
- Primernost izgleda za zdravstveno okolje / Aesthetical suitability for
medical environment
VARNOST in ZANESLJIVOST / SAFETY and RELIABILITY
Nadzor količine vode v sistemu / Control of water amount in the system
Neodvisnost od vira energije / Independence of energy source
Opozorila stanja baterije / Battery status warnings
Varnost za pacienta / Patients safety
Opozorila o kritičnih stanjih sistema / Critical system state warnings
Varnost naprave / Device's safety
Zanesljivo delovanje / Reliable operation
Vzdržljivost naprave / Durability of the device
Varnost delovanja / Safety of operation
Varnost izdelka in odgovornost za posledice / Safety of the product
and responsibility for consequences Izboljšanje napak človeškega faktorja / Improvement of human factor
errors Varnost za uporabnika in odgovornost za posledice / Safety for user
and responsibility for consequences
DRUGE ZMOŽNOSTI / OTHER ABILITIES
Hiter prenos / Fast transport
Varen prenos / Safe transport
Enostavno vzdrževanje / Simple maintenance
Enostavna in hitra montaža/demontaža / Simple and quick assembly/
disassembly Lahka izdelavnost / Simple manufacturability pravočasnost (JIT) / JIT - just in time Prilagodljivost delovnega okolja / Flexibility of operating environment Metodologija načrtovanja / Planning methodology Avtomatizacija / Automatization Vrednostni sistem / Value system Izboljšanje organizacije/upravljanja / Improvement of organization/
management
Izobraževanje in izpopolnjevanje zaposlenih / Training of employees Delovna postaja / Workstation Informacijsko upravljanje / IT management Zahteve skupin / Requirements of teams Integracija / Integration -Orodje za odzivnost / Tool for response
Sl. 16. Sorodnostni diagram za vrednoto kakovost izdelka Vario Flow Fig. 16. Affinity diagram for the value of the quality of the Vario Flow product
potrebi. Za vsako potrebo so v preglednicah navedeni podatki: prepoznavna številka potrebe, demografija kupca, izjava kupca, uporaba potrebe (kdo, kaj, kdaj, kje, zakaj, kako), analiza izjave ter vrsta potrebe oz. značilke.
data contains 2 needs. For each need the table contains the following data: ID number of the need, customer demography, customer statement, use of the need (who, what, when, where, why, how), analyzed statement and the type of need or characteristics.
2. korak: Oblikovanje sorodnostnega diagrama izdelka Vario Flow
Na podlagi podatkov, zbranih v izhodiščnih preglednicah kupcev, je projektna skupina lahko oblikovala sorodnostni diagram za vrednoto kakovost izdelka Vario Flow. Zahteve kupcev je razdelila na šest skupin in vsaki potrebi, zapisani v izhodiščni preglednici glasu kupcev, priredil pripadnost v eno skupino potreb. Sorodnostni diagram za vrednoto kakovost izdelka Vario Flow je prikazan na sliki 16.
Step 2: Forming the affinity diagram for the Vario Flow product
On the basis of the data collected in the source tables of customers the project team formed the affinity diagram for the value of quality of the Vario Flow product. Customer needs were divided into six groups and each need, written in the source table for the voice of the customers, was assigned to one group of needs. The affinity diagram for the value of quality of the Vario Flow product is presented in Figure 16.
3. korak: Oblikovanje drevesnega diagrama izdelka Vario Flow
V drevesnem diagramu za vrednoto kakovost je projektna skupina, podobno kot v sorodnostnem diagramu potrebe kupcev uredila hierarhično,
Step 3: Forming the tree diagram for the Vario Flow product
In the tree diagram for the value of quality the customer needs are arranged hierarchically (similar to the affinity diagram), divided into primary,
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
99
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
OSNOVNE POTREBE PRIMARY NEEDS
DRUGOTNE POTREBE
SECONDARY NEEDS
t
OSTALE POTREBE
TERTIARY NEEDS
KAKOVOST IZDELKA »VARIO FLOW«
QUALITY OF »VARIO FLOW« PRODUCT
ERGONOMIJA ERGONOMICS
DELOVANJE FUNCTIONALITY
Dobra vidljivost v polju posega / Good visibility in the surgical field
- Omogoča nastavitev tlaka kirurgu in/ali inštrumentarki / Operator and/or scrub nurse
can set the pressure
- Dobra vidnost informacije o stanju tlaka v sistemu / System pressure is clearly visible
- Dobra vidnost informacije o stanju v sistemu / System deficit is clearly visible
- Hitra menjava tekočine / Quick exchange of fluid
-Večja ločljivost displeja / Higher display resolution_____________________________
-Omogoča dostop v notranjost telesa / Interior of the body should be accessible        "
- Zvezna nastavitev tlaka / Continuous set of pressure
- Segrevanje vode / Heating of water
- Po menjavi vode upoštevanje prejšnjega stanja tlaka / Following water change, the
previous pressure is taken into account
- Prednastavljanje vrednosti tlaka / Pressure can be pre-set
- Posebne zahteve za laparaskopijo, artroskopijo... / Special requirements for
laparoscopy, arthroscopy...
- Stabilnost sistema / Stability of the system -Nadzor kakovosti / Quality control
STROŠKI COSTS
IZGLED DESIGN
VARNOST in ZANESLJIVOST
SAFETY and RELIABILITY
DRUGE ZMOZNOSTll OTHER ABILITIES   f
Nizki proizvodni stroški / Low production costs Nizki garancijski stroški / Low warranty costs Nizki stroški delovanja / Low operation costs Zahteva za prave dobavitelje in kooperante / Requirement for suitable suppliers and cooperators
Oblika za dobro premičnost sistema / Good system mobility design Primernost izgleda za zdravstveno okolje / Aesthetical suitability for medical environment___________________________________________________
'Nadzor količine vode v sistemu / Control of water amount in the system Neodvisnost od vira energije / Independence of energy source Opozorila stanja baterije / Battery status warnings Varnost za pacienta / Patient's safety
Opozorila o kritičnih stanjih sistema / Critical system state warnings Varnost naprave / Device's safety Zanesljivo delovanje / Reliable operation Vzdržljivost naprave / Durability of the device Varnost delovanja / Safety of operation Varnost izdelka in odgovornost za posledice / Safety of the product and responsibility
for consequences Izboljšanje napak človeškega faktorja / Improvement of human factor errors Varnost za uporabnika in odgovornost za posledice / Safety for user and responsibility
for consequences
f- Hiter prenos / Fast transport -Varen prenos / Safe transport
- Enostavno vzdrževanje / Simple maintenance
- Enostavna in hitra montaža/demontaža / Simple and quick assembly/disassembly
- Lahka izdelavnost / Simple manufacturability
- pravočasnost (JIT) / JIT - just in time
- Prilagodljivost delovnega okolja / Flexibility of operating environment
- Metodologija načrtovanja / Planning methodology
- Avtomatizacija / Automatization
- Vrednostni sistem / Value system
- Izboljšanje organizacije/upravljanja / Improvement of organization/management
- Izobraževanje in izpopolnjevanje zaposlenih / Training of employees -Delovna postaja / Workstation
- Informacijsko upravljanje/ IT management
- Zahteve skupin / Requirements of teams
- Integracija / Integration
-Orodje za odzivnost / Tool for response
Sl. 17. Drevesni diagram za vrednoto kakovost izdelka Vario Flow Fig. 17. Tree diagram for the value of quality of the Vario Flow product
razdeljene na osnovne, drugotne in ostale potrebe. Drevesni diagram za vrednoto “kakovost izdelka” Vario Flow je prikazan na sliki 17.
secondary and tertiary needs. The tree diagram for the value of quality of the Vario Flow product is shown in Figure 17.
4.4 Vrednotenje podatkov o potrebah kupcev izdelka Vario Flow
4.4 Evaluation of the data on customer needs for the Vario Flow product
Skupina se je odločila za izvedbo poštne ankete. Izdelan je bil anketni list, v katerem so bile
The team decided to use the postal survey. A survey form was composed where the primary, sec-
100
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
navedene osnovne, drugotne in ostale potrebe kupcev, in poslan v ocenitev 50-tim naključno izbranim možnim kupcem izdelka Vario Flow.
V predpisanem roku je prispelo 38 izpolnjenih anketnih listov, v katerih so kupci izdelka Vario Flow določili za njih najpomembnejšo potrebo, manj pomembne in končno zelo malo pomembne potrebe. Projektna skupina je kasneje z uporabo PREDNOSTNEGA MODELA 1-2-3 najpomembnejši potrebi posameznega kupca (prvo mesto) pripisala 5 točk malo pomembnim potrebam, uvrščenim na drugo mesto, 3 točke in potrebam, uvrščenim na tretje mesto, 1 točko.
S seštevanjem točk pomembnosti potreb, navedenih v vseh 38 izpolnjenih anketnih listih, je projektna skupina končno prišla do rezultatov o absolutni in relativni pomembnosti posamezne potrebe, kar prikazuje preglednica 2.
V preglednici 2 pridobljene, sestavljene in vrednotene potrebe kupcev predstavljajo vhodni podatek 1. hiše (načrtovanje izdelka) - postopka sprejemanja izdelka. Slika 18 prikazuje model ugotavljanja in vrednotenja potreb kupcev izdelka Vario Flow.
ondary and tertiary customer needs were stated and it was sent for evaluation to 50 randomly selected potential customers of the Vario Flow product.
Up to the due date, 38 survey responses were received; in these, Vario Flow customers stated what in their opinion were the most important, less important and least important needs. After that the project team, using the “PRORITY MODEL 1-2-3”, assigned 5 points to the most important feature of a particular need, less important needs were assigned 3 points and the least important features were assigned 1 point.
By summing up the points obtained from all 38 surveys the project team finally obtained the results on the absolute and relative relevance of a particular need, as presented in Table 2.
The customer needs, obtained, structured and evaluated in Table 2, are the input data for the first – product planning house – the development process. Figure 18 shows a model for obtaining and evaluating the customer needs of the Vario Flow product.
5 SKLEPI
5 CONCLUSIONS
Podjetje ne more priti do konkurenčnega izdelka, če že v fazo sprejemanja izdelka ne vključi tistega osebka, ki bo izdelek uporabljal oziroma imel od njega korist, torej kupca izdelka.
Pravočasno vključevanje kupcev v postopek sprejemanja izdelka daje kupcu možnost, da z
A company cannot produce a competitive product unless the client (end user) takes part in the development process.
If the clients take part in the new-product development process early enough, then the client (by expressing his or her needs) can influence the
Preglednica 2. Absolutna in relativna pomembnost dela potreb kupcev izdelka Vario Flow Table 2. Absolute and relative relevance of customer needs for the Vario Flow product
ID ŠT.
ID NO
POTREBE KUPCEV / CUSTOMERS’ NEEDS
Absolutna pomembnost (število točk)
Relativna pomembnost
Relative Absolute relevance    relevance (number of points)             [%]
1.
4. 5.
;
Dobra vidljivost v polju posega /
Good visibility in the surgical field
Omogoča nastavitev tlaka kirurgu in/ali inštrumentarki /
Surgeon and/or scrub nurse can set the pressure
Dobra vidnost informacije o stanju tlaka v sistemu /
System pressure is clearly visible
Dobra vidnost informacije o stanju v sistemu /
System deficit is clearly visible
Hitra menjava tekočine / Quick exchange of fluid
;
149                      2,8
190                      3,5
143                      2,7
135                      2,5
151                      2,8
;
;
48.     Integracija / Integration
49.     Orodje za odzivnost / Tool for response
VSOTA / TOTAL
69                       1,3
63_____________1,2
5370___________100,0
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
Zunanji kupci External customers
Notranji kupci Internal customers
Metode za zajemanje kakovostnih podatkov o potrebah kupcev Methods for the acquisition of qualitative data on customer needs
Intervjuji v konferenčni sobi Conference room interview
Povezano poizvedovanje Contextual inquiry
J
Podatki o izdelkih in postopkih
Data on products and processes
Tabela podatkov o IZDELKIH in POSTOPKIH Table of PRODUCTS and PROCESSES data
Tabela glasu NOTRANJIH KUPCEV Table for the voice of the INTERNAL CUSTOMERS
Tabela glasu ZUNANJIH KUPCEV Table for the voice of the EXTERNAL CUSTOMERS
SORODNOSTNI diagram potreb kupcev AFFINITY diagram of customers' needs
DREVESNI diagram potreb kupcev TREE diagram of customers' needs
Sl. 18. Model ugotavljanja in vrednotenja potreb kupcev izdelka Vario Flow Fig. 18. Model for obtaining and evaluating the customer needs of the Vario Flow product
izražanjem svojih potreb vpliva na definiranje izdelka in celotni postopek sprejemanja izdelka.
Dosedanje raziskave upoštevanja potreb oziroma zahtev kupcev izdelka v postopku sprejemanja izdelka so se nanašale na oblikovanje modela ugotavljanja, sestavljanja in vrednotenja potreb oziroma zahtev kupcev izdelka glede na kakovost izdelka. V primeru izdelka Vario Flow je bilo prepoznanih 21 potreb zunanjih kupcev, 26 potreb notranjih kupcev in 2 potrebi o izdelku in
concept of the product and the whole product-development process.
Past researches that analyzed the customers’ needs or demands in the new-product development process were related only to the development of the model for obtaining, structuring and evaluating the customers needs as to the quality of the product. In the case of the Vario Flow product, there were identified 21 needs of external customers, 26 needs of internal customers and 2 needs on product and pro-
102
Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
postopkih, torej skupaj 49 potreb oziroma zahtev        cesses. There are 49 needs or customer demands
kupcev, ki pomenijo izhodiščni podatek za razvoj        together, which represent the source data for the
delovanja kakovosti izdelka na sonovi RFK ([3] in        quality functions deployment (QFD) process [3, 16].
[16]). Pri ugotavljanju pomembnosti potreb izdelka        The obtaining of the importance of the needs of the
Vario Flow z ABC analizo [18] se je izkazalo, da je        Vario Flow product with ABC analysis [18] shows
nadpovprečno pomembnih 12 potreb, povprečno        that there are 12 needs with high importance, 16 with
pomembnih 16 in manj pomembnih 21 potreb. V        average importance and 21 less important needs.
postopku razvoja izdelka, bo torej treba posebej paziti        Special attention should be given to fulfilling the
na izpolnitev nadpovprečno pomembnih zahtev in        high-importance needs in the process of product
med njimi najbolj na izpolnitev zahteve o “možni        development, and from these needs, in particular for
nastavitvi tlaka”.                                                         “Possible pressure setting”.
Nadaljnje raziskave upoštevanja glasu                  Further research on the influence of the voice
kupcev bodo usmerjene na ugotavljanje potreb za        of the customers will be focused on establishing the
izboljšanje ne samo kakovosti temveč tudi drugih        needs for the improvement of not only the quality
lastnosti in vrednot izdelka, npr. preprostost,        but other features as well, such as simplicity, ease of
sestavljivost, možnost ponovne uporabe , odzivnost,        assembly, recyclability, responsibility, costs, etc.,
stroški itn., ki jih izražajo predvsem notranji kupci in        which are expressed mostly by internal customers
so izhodiščni podatek za sočasni razvoj funkcij         and which represent the source data for concurrent
kakovosti [12].                                                            functions deployment [12].
6 LITERATURA 6 REFERENCES
[I]    Cohen, L. (1995) Quality function deployment - How to Make QFD Work for You, Addison Wesley Longman, Inc.
[2]    Prasad, B. (1998) Review of QFD and related deployment techniques, Journal of Manufacturing Systems,
Society of Manufacturing Engineers, May/June, Dearborn, MI. [3]    Prasad, B. (1996) Concurrent engineering fundamentals: integrated product and process organization.
Vol. I, New Jersey, Prentice Hall. [4]   Mazur, G. (1997) Voice of customer analysis: A modern system of front-end QFD tools, with case studies.
Proceedings of AQC 1997. Orlando. May 5-7, [5]    Crow, K. (2004) Voice of the customer investigation. DRM Associates, http://www.npd-solutions.com/
drm.html, October 2, 2004 [6]    Crow, K (2004) Voice of the customer. DRM Associates, http://www.npd-solutions.com/drm.html, October
2, 2004 [7]   Hauser, R.J. (2004) Note on the voice of the customer. http://ocw.mit.edu/OcwWeb/Sloan-School-of-
Management/15-810Spring2004/Readings/, October 10, 2004 [8]    Klein, B. (2004) Customer requirements - optional or required? Applied Marketing Science, Inc., http://
www.ams-inc.com/newsletter/voices014.pdf, October 10, 2004 [9]    Crow, K. Focus groups, DRM Associates, http://www.npd-solutions.com/drm.html, October 2, 2004 [10] Crow, K. »Customer interviews«, DRM associates, http://www.npd-solutions.com/drm.html, October 2,
2004
[II]  Schlicksupp, H. (1977) Kreative Ideenfindung in der Unternehmung. Watter de Gruyter, Berlin New York. [12] Prasad, B. (1997) Concurrent engineering fundamentals: integrated product development. Vol. II, New
Jersey, Prentice Hall. [13] Daetz, D., B. Barnard and R. Norman (1995) Customer integration: The QFD leader’s guide for decision
making, John Wiley and Sons, USA. [14] Terninko, J. (1997) Step by step QFD: customer-driven product design, St. Lucie Press, Boca Raton, FL.
USA [15] Saaty, TL (1994) Fundamentals of decision making and priority theory with the analytic hierarchy process.,
Pittsburgh, PA: RWS Publications
Ugotavljanje in vrednotenje potreb kupcev - Finding and Evaluating Customers' Needs                       103
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 78-104
[16] Tomaževič, R., J. Kušar, M. Starbek, L. Savnik (2004) Introduction of concurrent function deployment method into CE organization in SMEs. Proceeding of The 11th ISPE International Conference on Concurrent Engineering , Beijing.
[17] Duhovnik, J., M. Starbek, S.N. Dwivedi, B. Prasad (2001) Development of new products in small companies, Concurrent Engineering: Research and Applications Volume 9, Number 3, September 2001.
[18] Starbek M., Petrišič J., Kušar J.(2001): Extended ABC analysis, Strojarstvo, Volume 42, Number 3,4
Naslova avtorjev: doc. dr. Janez Kušar
prof. dr. Jože Duhovnik prof. dr. Marko Starbek Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana janez.kusar@fs.uni-lj.si joze.duhovnik@fs.uni-lj.si marko.starbek@fs.uni-lj.si
Authors’ Addresses: Doc. Dr. Janez Kušar
Prof. Dr. Jože Duhovnik
Prof. Dr. Marko Starbek
University of Ljubljana
Faculty of Mechanical Eng.
Aškerčeva 6
1000 Ljubljana, Slovenia
janez.kusar@fs.uni-lj.si
joze.duhovnik@fs.uni-lj.si
marko.starbek@fs.uni-lj.si
Rok Tomaževič CIMOS d.d.
Marežganskega upora 2 6000 Koper
Rok Tomaževič CIMOS d.d.
Marežganskega upora 2 6000 Koper, Slovenia
Prejeto: Received:
31.8.2005
Sprejeto: Accepted:
25.10.2006
Odprto za diskusijo: 1 leto Open for discussion: 1 year
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Kušar J. - Duhovnik J. - Tomaževič R. - Starbek M.
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 105-113
UDK - UDC 519.65:004.021
Kratki znanstveni prispevek - Short scientific paper (1.03)
Vpliv pravokotnosti mreže na konvergenco programa SIMPLE za reševanje Navier-Stokes-ovih enačb
The Influence of Grid Orthogonality on the Convergence of the SIMPLE Algorithm
for Solving Navier-Stokes Equations
Ivo Džijan - Zdravko Virag - Hrvoje Kozmar (University of Zagreb, Croatia)
Razvili smo metodo končnih volumnov za reševanje Navier-Stokesovih enačb na lokalno pravokotni nestrukturirani mreži z uporabo algoritma SIMPLE. Razvito metodo smo primerjali s podobno metodo na strukturirani, ne nujno pravokotni mreži, v členih pretekle konvergence in obsegu pod-relaksacijskih faktorjev, pri katerih se metodi približujeta. Kadar je strukturirana mreža pravokotna, sta stopnji približevanja obeh metod podobni. V primerih, kadar strukturirana mreža ni pravokotna, se pokaže prednost predlagane metode pri lokalno pravokotni mreži v razmerah pretekle konvergence. V teh primerih je obseg pod-relaksacijskih faktorjev, pri katerih je predlagana metoda zadovoljivo konvergentna, mnogo večji kot pri metodi na nepravokotni mreži. © 2007 Strojniški vestnik. Vse pravice pridržane.
(Ključne besede: Navier-Stokesove enačbe, metode končnih volumnov, algoritmi SIMPLE, nestrukturirane mreže)
A finite-volume method for solving the Navier-Stokes equations on a locally orthogonal unstructured grid using the SIMPLE algorithm has been developed. The developed method was compared with a similar method on a structured, not necessarily orthogonal grid, in terms of convergence history and the range of under-relaxation factors in which the methods converge. When the structured grid is orthogonal, the convergence rates of the two methods are similar. For the cases when the structured grid is non-orthogonal, the superiority of the proposed method on the locally orthogonal grid is demonstrated in terms of convergence history. In these cases, the range of under-relaxation factors in which the proposed method shows satisfactory convergence is much wider than for the method on the non-orthogonal grid. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: Navier-Stokes equations, finite volume methods, SIMPLE algorithm, unstructured grid)
0 INTRODUCTION
The rapid development of computers has brought about rapid developments in the field of computational fluid dynamics. Calculation domains are now more complex, which increases the need to use an unstructured grid for their discretization. Finite volume methods are widely applied for solving fluid flow problems. Initially, these methods were used on structured staggered grids. Nowadays they are used on unstructured collocated grids, on which segregate algorithms with the pressure-based approach are applied for incompressible flows. The most popular algorithm based on pressure correction is the SIMPLE (Semi-Implicit Method for the Pressure-
Linked Equation) algorithm, Caretto et al. [1] and Patankar and Spalding [2]. In the pressure-velocity correction relation the effects coming from velocity corrections in neighboring nodes on the pressure correction in the central node are neglected. The consequence of this neglecting is the overestima-tion of the pressure correction, which can cause the divergence of the numerical process. To ensure the stability of the numerical process, the under-relax-ation factor for the pressure is introduced. The optimal value of this factor cannot be estimated in advance since it depends on the grid’s characteristics and the nature of the problem.
The SIMPLE algorithm is originally defined on a staggered grid where the pressure is calculated

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in the cell centre and the velocity components are calculated on the cell faces. On a collocated grid, the pressure field and velocity components are calculated in the cell centre. The application of the SIMPLE algorithm on a collocated grid started with Rhie and Chow [3].
The grid non-orthogonality is one of the factors that increases the number of iterations of the SIMPLE algorithm. If the connecting line of two neighboring nodes is not perpendicular to the cell face, some terms that appear due to non-orthogonality are usually neglected. This is the case with the CAFFA public-domain computer code [4]. It is believed that this neglecting slows down the rate of convergence of the numerical method. Therefore, the modification of the finite volume method on an unstructured locally orthogonal grid is proposed. The rate of convergence of the SIMPLE algorithm on that grid will be compared with the rate of convergence on a structured, not necessarily orthogonal grid.
1 MATHEMATICAL MODEL AND NUMERICAL PROCEDURE
The mathematical model of steady, laminar, incompressible fluid flow with constant viscosity and without mass forces is adopted. The model is described with the following Navier-Stokes equations:
d
OX
(pVj) = 0
d t                 dp          d v.
------I/7V.V,. ) =-----— + JU--------
ôx                    dx        ôxôx
(1) (2)
Fig. 1. A part of calculation domain and a typical cell of locally-orthogonal unstructured grid
where p, v., p, ju and x. are the fluid density, velocity, pressure, 'viscosity and coordinates, respectively. These equations will be numerically solved on an unstructured locally orthogonal grid. A part of such a computational grid is shown in Fig. 1.
The main nodes, C and N, at which the velocity and pressure fields are calculated, are placed within their respective cells. The connecting line CN is perpendicular to the cell face and the nodes C and N are at an equal distance from an auxiliary node n, which enables a simple formulation of the high-order interpolation. It is clear that such a grid is possible in every 2D case, because the cell vertex a in Fig. 1 is the circumcenter of the triangle formed by the nodes C, M and K. Such a grid generator is described by Džijan [5], which includes a grid-smoothing procedure that forces the main nodes to be close to the cell centroids and the auxiliary nodes to be close to the cell-face centroids.
Discretization of the equations starts with integrating over the cell volume V, according to Fig. 1. By using the Gauss theorem and the mean-value theorem, the integrated governing equations take the form:
m
L [F]  =0                       (3)
Fv\
mA
cV.
dx
-V
dp
dx
mA
dv
dx
(4)
where F = p A v. «. = p A vn is the mass flow through the cell face and J, = F vt n - juA (dv, / dXj ) n «y. is the momentum flux through the cell face. A and « are the cell-face area and its outward normal vector, V is the cell volume, while k denotes the cell-face index and m is the number of cell faces on the considered volume. The scope of the differencing schemes is to define the velocity v;|n and its normal derivatives at the auxiliary node n in terms of velocity values at the main nodes. Since the adopted grid is locally orthogonal, these values are defined by using only the values at nodes C and N. A blending scheme of the central differencing scheme (CDS) and of the first-order upwind differencing scheme (UDS) is used in the CAFFA computer code. Therefore, the same scheme will also be used in the proposed method. In the case of the locally orthogonal grid, the diffusion part of the flux vector is modeled with the following equation:
Jd
-mA
dvi dx
-mA
-mA
2s
(5).
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 105-113
In the case of a non-orthogonal grid, an additional term appears. In the CAFFA computer code this term is implemented by using the deferred correction approach, i.e., by using the velocity values from the previous iteration.
In the first-order UDS, the convective flux is modelled by:
F viC   for F>0 F viN    for F<0
(6),
and in the CDS (for the case when the node n lies in the middle of the CN connection line) by:
•^1MC+4N )
(7).
By introducing the mixing factor g, the final expression for the momentum flux is:
T        t1        \   rUDS   ,        xCDS   ,     xd
(8)
where, for g = 0 the result is the UDS, and for g = 1 the CDS.
Introducing the expressions for the fluxes into (4) results in:
where:
E[aN^|N_
max) -F,0]
-V
dp
dx
mA 2s
m
aC = Xk]
+ bi        (9)
(10), (11)
and
b^r\l\12Fvi] -E[max(-*,0)]\lC + E[max(-*,0)v.Nî}
L"              "                      "                (12).
It is obvious that all the terms coming from
the CDS are treated as a deferred correction, the same
as in the CAFFA code.
To reduce the possibility that the numerical process diverges, this equation is under-relaxed in the following form:

dx
u     aCvi\C L>,+---------
(13) which was proposed by Patankar [6]. The last term on the right-hand side is calculated from the previous iteration, and auv is the under-relaxation factor for the velocity.
According to Rhie and Chow [3], the mass flow through the cell face is defined as follows:
F = pAvn=pA{vn)-pA
{n}	dp dn	(dp	n]
(14)
where the line above a symbol indicates the linear interpolation between the values at nodes C and N, as follows:
( v ) = — (v.I   +V.I
h
and
Udp
2{dn
dp dn
(15), (16)
(17). C       CNy In the case of a locally orthogonal grid, the normal derivative of the pressure is defined by using the CDS, as follows:
K
dp dn
pC
2s
(18).
In the CAFFA code, where the grid is non-orthogonal, additional terms emerge and are treated explicitly by using the values from the previous iteration.
Solving the momentum equation with a given pressure field/?* results in the velocity field v *, and the mass flow F, which does not necessarily satisfy the continuity equation. For that reason, the velocity corrections v ’ and the corresponding F’ and pressure corrections ' are searched, so that the corrected velocity field v. = v.* + v ’ and corrected mass flow F = F + F’ satisfy the continuity equation. According to Equation (14), the corrected mass flow is approximated as follows:
F= *EäK
2s ^an
PC
F -<  Ä-fC
(19).
Introducing the corrected mass flows in the continuity equation (3) results in the following equation for the pressure correction:
where
and
m                                 i
"c/'c-IKK]   =b"'
aC   =Z[flN
m
bp'=-np
k
(20)
(21)
(22).
The solving of this equation results in the pressure-correction field. Therefore, the pressure
Vpliv pravokotnosti mreže - The Influence of Grid Orthogonality
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field is corrected using the following equation:
pC = p*C+app'C                     (23)
where a is the under-relaxation factor for the pressure. The velocities in the main nodes are corrected as follows:
viC =vi C
aC dXj
(24).
The gradients of the physical values in the main nodes are calculated using the Gauss formula as follows:
dx
1v±WA
2>    k=1
(25)
where f can stand for vi, p or p’.
The steps in the SIMPLE algorithm for solving the Navier-Stokes equations can be summarized as follows:
1.   Guess the pressure field p* and the velocity field vi.
2.   Solve the momentum equation (13) to obtain vi*.
3.   Solve the p’ equation (20). Correct the pressure according to (23), correct the velocity according to (24) and the mass flow according to (19).
4.   Treat the corrected pressure as p* and return to Step 2. Repeat the whole procedure until a converged solution is obtained.
The converged solution is obtained when the normalized residuals for the continuity and momentum equations become smaller than some small number, e. In this paper e = 10-6 was used. The residual for the continuity equation is:
R
M   ,_
and the residual for the momentum is:
*,=z
LMn]V
(26)
(27).
In the above expressions, l denotes the cell index and M the total number of cells. The values of the variables in the above formula are from the current iteration, and the coefficients are prepared for the next iteration. The following residuals are usually normalized: the mass residuals with the inlet mass-flow rate and the residuals for the momentum equation with the inlet momentum flow rate.
2 RESULTS
The described numerical method is implemented in the FVM computer code. In this code the
residuals are defined and normalized in the same way as in the CAFFA code. The rate of convergence of the described method and of the method used in the CAFFA code will be compared by varying the grid’s non-orthogonality and the differencing scheme. Also, the range of under-relaxation factors in which the numerical procedure converges will be analyzed.
2.1 Laminar flow in a lid-driven cavity with inclined side walls
In this test the 2D laminar fluid flow is calculated in a closed cavity whose lid is moving in a tangential direction with velocity v Peric [7]. The Reynolds number based on the side length a is Re = p.v .a/'u= 1000. The calculation is performed for different inclination angles of the side walls, /?= 90°, 67.5° and 45°. In this problem the residuals defined by (26) and (27) are not normalized.
Fig. 2 shows the qualitative picture of the streamlines for ß= 90° and 45°. It is obvious that the initially assumed constant-velocity field will be very different from the final solution.
The problem is solved using the CAFFA numerical code on structured grids of size 40x40 cells, and with the FVM code on unstructured grids with approximately 1600 cells. Fig. 3 a shows a part of the unstructured grid for ß= 45° that is used in the FVM code. The borders of the finite volumes are presented, and the main nodes are marked. Fig. 3 b shows a part of the geometric grid for the same case, which is used in the CAFFA code. The displayed lines connect the main nodes at which the pressure and velocity fields are calculated.
In the SIMPLE algorithm, two under-relaxation factors should be given. The rate of convergence depends on the values of these two factors. Their optimal values are not known in advance, so that the described problem will be solved for a range of under-relaxation factors by varying a from 0.5 to 0.95 with a step of 0.025, and a from 0.1 to 0.6 with a step of 0.1. The comparison criteria will be the number of iterations needed for the residuals to fall below s= 106.
In the CAFFA and FVM codes different solvers for linear algebraic equations are used. For this reason, a sufficient number of inner iterations is given at every iterative step to be sure that the systems are solved equally well in both codes.
Fig. 4 shows the numbers of outer iterations N required to reduce the residual levels to s as a function of the under-relaxation factors a   and a,
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a)
b)
Fig. 2. Streamlines in laminar flow in a lid-driven cavity a) b = 90°, b) b = 45°
	f/	// / /
		// / /, J / / / /
		///////
		///////
		//////// ///////// ////////
	j// /	
	////////////	
	// / / /	////////
	//////	////////
	//////,	'///////.
	v / / / / /	////////
JY	//////	////////
/z//////////////,		
/////////////////		
// / /	//////	////////
// / / /	//////	'////////
/////,	'/////	////////.
//////	//////	////////
/////////////		////////
a)                                                              b)
Fig. 3. A part of the grid for the lid-driven cavity problem for b = 45° a) FVM, b) CAFFA
1000 800 600 400 200
1000
800
600

400
200
0.5        0.6        0.7        0.8        0.9
0.5        0.6        0.7        0.8        0.9
<uv                                                                             a uv
a)                                                              b)
Fig. 4. Required number of outer iterations to reduce residual levels to e = 10-6 for the lid-driven cavity
problem for b = 90° (UDS) a) FVM, b) CAFFA
for b = 90°. In this case, the grids for both codes are orthogonal, and the achieved results are almost identical. This confirms the equivalent implementation of the SIMPLE algorithm in both codes.
Fig. 5 shows Ne for two algorithms for b = 45°. The SIMPLE algorithm in the CAFFA code converges in that situation only in the case that a = 0.1, and only for small a   < 0.7. Ne is considerably

v

v





Vpliv pravokotnosti mreže - The Influence of Grid Orthogonality
109
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 105-113
1000
800
600

400
200
1000
800
600

400
200
0.5        0.6        0.7        0.8        0.9
a
a)

0.5       0.6       0.7       0.8       0.9 a
uv
b)
Fig. 5. Number of outer iterations required to reduce the residual levels to e — IO'6 for the lid-driven cavity problem for b = 45° (UDS) a) FVM, b) CAFFA
larger than for the FVM code, which is a consequence of the grid’s non-orthogonality.
Fig. 6 shows N for two algorithms for b = 67.5°. In the FVM code, the necessary number of iterations has not significantly changed compared with the two previous cases. In the CAFFA code, the range of under-relaxation factors in which the algorithm converges is narrower than for b = 90°, and wider than for b = 45°. For the same combination of under-relaxation factors, N increases with the in-crease of the grid’s non-orthogonality.
Fig. 7 a shows the convergence histories (the greatest of three residuals versus the number of iterations A) of two methods for b = 90°, 67.5° and 45°, at a corresponding optimum combination of under-relaxation factors and by using the UDS. It is obvious that the convergence history on a locally
1000
800
600 400
200
orthogonal grid is unaffected by b, unlike the case of a non-orthogonal grid. It is worth noting that this comparison is valid for optimum values of under-relaxation factors that are unknown prior to the calculation. The clear advantage of the locally orthogonal grid over the non-orthogonal one can be read from Figs 4 to 6, from which one can conclude that the convergence history on this grid is slightly changed by a relatively large deviation from the optimum combination of under-relaxation factors, which is not the case for the non-orthogonal grid.
Fig. 7 b shows the convergence histories of two methods for b = 90° and 45°, at a corresponding optimum combination of under-relaxation factors and by using the CDS. The optimum values of the under-relaxation factors are the same as for the UDS. The rate of convergence slows down by switching from
1000
800
600

400
200
0.6
0.7       0.8 a
uv
0.9
0.7       0.8 a
uv
 a a)                                                              b)
Fig. 6. Number of outer iterations required to reduce the residual levels to e — IO'6 for the lid-driven cavity problem for b = 67.5° (UDS) a) FVM, b) CAFFA
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101 100 10-1 10-2
10-4 10-5 10-6 0

FVM,     p =90° FVM,     p = 67.5°
FVM,     p =45°
CAFFA, p =90°
¦- CAFFA, p =67.5°
--------CAFFA, p =45°

200
N
400
600
a)

101 100 10-1 10-2
d10-3
10-4 10-5
10-6 0"

\\	o
	-------------FVM,     p =45°
\	
	------------CAFFA, p =45°
\\	
\ \	
: \ \	
\	
-       ,         ,         ,         1    \\V.....X	
200
N
400
600
it
b)

Fig. 7. Convergence histories for the SIMPLE algorithm in the FVM and CAFFA codes for the lid-driven
cavity problems a) UDS, b) CDS scheme
the UDS to the CDS, which can be explained with the implementation of the CDS by using the deferred correction approach. Again, for ß= 90° the convergence history of the two methods is practically the same. For ß = 45° the convergence history of the method on a non-orthogonal grid is considerably slowed down due to the addition of the deferred correction on the non-orthogonality effects.
2.2 Laminar flow in a curved channel
The example of laminar flow in a curved channel where the grid is in some parts orthogonal and in some parts non-orthogonal is chosen. This is the usual case in practical applications of this method.

Fig. 8. Streamlines for laminar flow in a curved channel
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														-T--
														
			t. .	-• •!§&	/•Ai.		'•T		¦#	,	-#	,	,	•
														•
				* 35^»y			\*      *		•	•	•	•	•	•
														•
				-•iP$v:										
				• ^j-ryiZ										
			fclzi-											
														
				f*Jm^iJm\* •										
				^w^\,l# •										
					,[									
--T+jTiViS-AY"				r«I3Z • •										
														
														
														
														
														
														
														
a)                                                                    b)
Fig. 9. A part of the computational grid for the curved-channel problem a) FVM, b) CAFFA
Vpliv pravokotnosti mreže - The Influence of Grid Orthogonality
111
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 105-113
300
200

100
300
200

100
	r\   1
	--------------a= 0.2 p --------------  a =0.3 p
	l
*v	
^                                                     1	
	
0.5
0.6
0.7
a                                                           a
uv                                                                                                           uv
a)                                                              b)
Fig. 10. Number of outer iterations required to reduce the residual levels to e
channel problem (UDS) a) FVM, b) CAFFA
0.8
0.9

10-6 for the curved-
Fig. 8 shows the calculation domain and the streamlines for this problem. Obviously, the final flow pattern is significantly different from the one that can be reasonably guessed at the beginning of the calculation.
Fig. 9 shows the part of the calculation area discretized with a locally orthogonal grid for the FVM            ^
and a structured grid for the CAFFA codes. The grid for the CAFFA code is non-orthogonal, and partially smoothed in the corners. In the straight parts of the channel this grid is orthogonal. The grid for the FVM code has 1180 finite volumes and the grid dimensions for the CAFFA code are 20x60 finite volumes. The uniform profile of the normal velocity v is given at the inlet. At the outlet boundary, the standard assumption of a zero velocity gradient is applied. The other boundaries are impermeable walls. The Reynolds number based on the normal velocity v and the inlet width a is Re = r.v a/m = 200.
Fig. 10 shows N for the SIMPLE algorithm on a locally orthogonal grid. The range of good values of the under-relaxation factors is wider than in the case of the non-orthogonal grid. For the non-orthogonal grid, N increases considerably for small changes of the under-relaxation factors with respect        1)
to their optimum values.
Fig. 11 shows the convergence histories for two methods for a corresponding optimum combina-        2)
tion of under-relaxation factors by using the UDS and the CDS. The advantage of the method on the locally orthogonal grid is obvious. The effects of the deferred correction approach in the CDS are superimposed on the effects of the grid’s non-orthogonality.
102
101I
100 10-1
 10-2 10-3 10-4 10-5
10-6 0
FVM, FVM,
UDS CDS
CAFFA, UDS CAFFA, CDS
TY
\*
AA
100
200 N
300
400
Fig. 11. Convergence histories for the SIMPLE
algorithm in the FVM and CAFFA codes for the
curved-channel problem (UDS and CDS)
3 CONCLUSIONS
From the comparison of the two methods in the selected test problems, the following conclusions can be drawn:
The results obtained by the FVM and CAFFA codes are nearly the same when both grids are orthogonal.
The method on a locally orthogonal grid implemented in the FVM code requires a smaller number of iterations than the method on a nonorthogonal grid implemented in the CAFFA code, when using corresponding optimum combinations of under-relaxation factors.
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 105-113
3)  The range of under-relaxation factors for             vance, and that they take different values from
which the method converges is narrowing             problem to problem.
with the increase of the grid’s non-        4) The application of the CDS based on the de-orthogonality. This is a serious drawback, if             ferred correction approach increases the required we know that the optimum values of the un-             number of iterations. This effect is superimposed der-relaxation factors are not known in ad-             on the effects of the grid’s non-orthogonality.
4 LITERATURE
[1] Caretto, L.S., A.D. Gosman, S.V. Patankar und D.B. Spalding (1972) Two calculation procedures for steady
three-dimensional flows with recirculation. Proceedings of Third International Conference on Numerical
Methods in Fluid Dynamics, Paris. [2] Patankar, S.V., D.B. Spalding (1972) A calculation procedure for heat, mass, and momentum transfer in three
dimensional parabolic flows. Int. J. Heat Mass Transfer, 15(1972), pp. 1787-1806. [3] Rhie, CM., W.L. Chow (1983) A numerical study of the turbulent flow past an isolated airfoil with trailing
edge separation. AIAA J., 21(1983), pp. 1525-1532. [4] Ferzinger, J. H., M. Peric (1996) Computational methods for fluid dynamics. Springer-Verlag, New York. [5] Džijan, I. (2004) Numerical method for fluid flow analysis on unstructured grid (in Croatian), PhD. Thesis.
University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb. [6] Patankar, S.V (1980) Numerical heat transfer and fluid flow. McGraw-Hill, New York. [7] Peric, M. (1990) Analysis of pressure-velocity coupling on nonorthogonal grids. Numerical Heat Transfer,
Part B; 17(1990), pp 63-82.
Authors’ Addresses:
Doc. Dr. Ivo Džijan
Prof. Dr. Zdravko Virag
Dr. Hrvoje Kozmar
University of Zagreb
Faculty of Mechanical Engineering and
Naval Architecture
I. Lučiča 5
HR-10000 Zagreb, Croatia
ivo.dzijan@fsb.hr
zdravko.virag@fsb.hr
hrvoje.kozmar@fsb.hr
Prejeto:                                                                Sprejeto:                                                        Odprto za diskusijo: 1 leto
6.4.2006                                                                22.6.2006
Received:                                                             Accepted:                                                      Open for discussion: 1 year
Vpliv pravokotnosti mreže - The Influence of Grid Orthogonality
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UDK - UDC 629.735.4:533.6
Strokovni članek - Speciality paper (1.04)
Matematični modeli dinamike helikopterskega letenja
Mathematical Models of Helicopter Flight Dynamics
Dragan Cvetkovič1 - Duško Radakovič2 ('University "Union", Serbia; Federal Bureau for Measures and Precious Metals, Serbia)
Helikopter se razlikuje od drugih prometno transportnih sredstev, ne le po svoji sestavi temveč tudi po možnostih svojega gibanja. Helikopter se lahko premika navpično, lahko lebdi v zraku, lahko se vrti na istem mestu, lahko se premika naprej in v stran, a lahko tudi kombinira vse te premike. Zaradi tega sta modeliranje in testiranje dinamike helikopterja zelo zapleten problem. Trenutno se problemi dinamike helikopterskega letenja v glavnem rešujejo z uporabo sodobnih računalnikov. Čeprav so za mnoge zahtevne probleme računalniki neizogibni, ne omogočajo razumevanja fizikalne plati problema. Na srečo je veliko problemov v zvezi s helikopterji mogoče analizirati brez preveč zapletenih izračunov in navadno je mogoče priti do preproste formule. Čeprav niso ustrezne za preračune, te formule, pri konstrukciji helikopterja, omogočajo zadovoljivo interpretacijo potrebnih aerodinamičnih in dinamičnih pojavov. Helikopter spada v skupino zračnih sistemov in njegovo tradicionalno modeliranje se deli na: a) prostorsko geometrijo in kinematiko in na b) dinamiko togega telesa in dinamiko zraka, skozi katerega se giblje. V zadnjem času, so se razvili naslednji modeli: c) elastični model, odvisen od aerodinamičnih sil, d) model pogonskega sistema, e) model hidravličnih in drugih izvršilnikov za aerodinamično krmiljenje, ß model obnašanja pilota, g) model sistema navigacije in h) model problema vodenja. Matematični model, opisan v tem prispevku, se nanaša na a) in b).
© 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: helikopterji, dinamika letenja, matematični modeli)
The helicopter is a specific form of traffic-transportation, not just in terms of its structure but also in terms of its possibilities for motion. The helicopter can move vertically, hover in the air, turn around, move forward and move laterally, and it can also perform combinations of these movements. As a result, modeling and testing helicopter dynamics is a very complex problem. The problems in helicopter flight dynamics are mostly solved with the aid of modern computers. Though inevitably, with many complex problems, computers do not make it possible to understand the physical nature of the problem. Fortunately, many problems related to helicopters can be analyzed without overly complex calculus, and usually it is possible to obtain simple formulae. Though not suitable for calculus, these formulae, when designing the helicopter, enable a satisfactory interpretation of the required aerodynamic and dynamic phenomena. The helicopter belongs to the group of aerospace systems and its traditional modeling may be divided into: a) three-dimensional (space) geometry and kinematics, and b) rigid-body dynamics and the fluid dynamics through which it moves. Recently, the following models were developed: c) the elasticity model in intersubordinance with a fluid, d) the propulsion system model, e) the hydraulic model and other actuators that achieve aerodynamic control, ß the pilot-behavior model, g) the navigation-system model, and h) the beacon-problem model. The mathematical model described in this paper is related to a) and b). © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: helicopters, flight dynamics, mathematical models)
1 GIBANJE ROTORSKIH KRAKOV                                    1 MOTION OF ROTOR BLADES
Da bi razumeli dinamiko letenja helikopterja in določili dinamične momente in sile, ki delujejo na helikopter, je nujno potrebno najprej raziskati
To understand the flight dynamics of helicopters and determine the dynamic moments and forces that act upon the helicopter, it is a necessity to pre-investigate
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gibanje nosilnih krakov rotorja. Iz velikega števila različnih helikopterjev smo izbrali helikopter z enim rotorjem, katerega kraki so povezani na glavo rotorja s členkom, okoli katerega se prosto gibljejo. Treba je povedati, da so kraki trdno povezani z glavo rotorja.
1.1 Enačbe mahanja kraka
Krake rotorja vzamemo kot togo telo. Vodoravni členek je na razdalji eR od osi vrtenja. Kotna hitrost gredi je Q=konst, a krak maha s kotno hitrostjo dßdt. Vzdolžna os kraka je vzporedna vztrajnostni osi kraka in gre skozi členek(sl. 1).
Na sliki 1 je R dolžina kraka, kot #je položaj kraka. Po zapletenih preračunih, dobimo enačbe gibanja krakov:
1.2 Enačbe zaostajanja kraka
Predpostavimo, da je />0 in da se krak giblje naprej glede na navpični členek za kot zaostajanja L Navpični členek je na razdalji eR od osi vretena. Koordinatni sistem postavimo enako kot v prejšnjem primeru. Slika 2 prikazuje poenostavljeno skico za določanje zaostajanja kraka.
Iz tega izhaja enačba zaostajanja kraka:
the motion of the supporting rotor blades. From a vast number of different types of helicopters, we chose the single-rotor helicopter that has its blades coupled with the main rotor by a hinge about which they can move freely. It should be noted that there are also rotors that have the blade connected in a fixed manner to the hub.
1.1 Equations of blade flapping
Rotor blades are regarded as a rigid body. The horizontal hinge is placed at a length eR from the rotation axis. The shaft rotates at an angular speed W=const, and the blade flappers at an angular speed of db/dt. The axis that passes through the blade is parallel to the axis of inertia of the blade and passes through the hinge (Fig. 1).
In Figure 1, R represents the length of the blade, b represents the flapping angle of the blade. Following some complex calculus, the equations for blade flapping are obtained:
(1)
(2)
(3).
1.2 Equations of blade throwback
It is assumed that b=0 and that the blade is moving forward in relation to the vertical hinge by the throwback angle amount x. The vertical hinge is placed at a distance eR from the shaft axis. The coordinate system is positioned as in the previous case. Figure 2 presents a simplified scheme for determining the blade throwback.
From this the equation for blade throwback follows:
Jxy0Q cosß + Jx(-ß)Q. sinß = 0 -2 JyQ.ß sinß = Mz
Sl. 1. Prikaz mahanja kraka Fig. 1. Explanatory drawing for blade flapping
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Sl. 2. Prikaz zaostajanja kraka Fig. 2. Explanatory scheme for blade throwback
x +W2e x -2 W b b =Mz /Jz &&                                                                          &
(4)
Če je kot med položajem kraka in smerjo letenja y=Q.t, sledi:
d2Ç
If the azimuth angle is described as y=Wt, then it follows that:
dy2
+ s C-2ß
db      Mz
1.3 Enačba vzpenjanja kraka
Vzemimo, da sta kota mahanja in zaostajanja enaka nič. Korak kraka je kot med tetivo profila kraka in ravnino glave rotorja, označen kot 9k. Na sliki 3 vidimo koordinatni sistem, povezan s krakom.
Enačbe gibanja kraka okoli vzdolžne osi so:
dy     JzW2
1.3 Equation of blade climb
(5)
It is assumed that the flapping and the throwback angles are equal to zero. The blade step is the angle between the blade cross-section chord and the plane of the hub, designated as qk. Figure 3 shows the coordinate system attached to the blade.
The equations of blade motion about the longitudinal axis are:
qk +W2 qk = Mx /Jx &&
-2 Jz W q&k sinqk = Mz J   W q& cosq - J   q& cosq =0
(6) (7) (8)
Sl. 3. Koordinatni sistem na profilu kraka Fig. 3. Coordinate system at the blade cross-section
2 ROTORSKE SILE
2 ROTOR FORCES
Za projekcijo sil lahko uporabimo naslednje osi: os v smeri vlečne sile rotorja, os rotorskega diska, ki je pravokotna na ravnino rotorja, to je na ravnino, kjer ležijo konci krakov in os gredi.
Ko izberemo eno izmed teh osi, bosta preostali dve osi v koordinatnem sistemu pravokotni nanjo, usmerjeni bočno, oziroma proti repu helikopterja. Običajno se komponenta sile v smeri izbrane osi
To project the forces the following axes may be used: the control axis, the rotor disc axis (which is normal to the rotor plane, i.e., to the plane on which the blade tips reside), and the shaft axis.
Once the axis is chosen, the remaining axes of the coordinate system will be normal to it and pointed laterally, i.e., to the tail of the helicopter. The force component along the chosen axis is normally referred
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imenuje vlečna sila, komponenta sile proti repu se imenuje süa H, a komponenta sile, usmerjena bočno, se imenuje sila Y. Če komponente sile označimo brez indeksiranja, menimo da se nanašajo na os v smeri včene sile. Indekse “D” in “5" uporabljamo, če se komponente nanašajo na os rotorja oziroma na os pogonske gredi.
Ker sta kota mahanja in zaostajanja ponavadi majhna (do 10°), lahko napišemo:
to as the tow force, the force component pointed towards the tail is called the H force, and the force component pointed laterally is said to be the Y force. If the force components are designated without subscripts, it is assumed that they are determined relative to the control axis, whereas the subscripts "L>" and “S” are used when they relate to the rotor axis, i.e., the shaft axis.
Since the flutter and mount angles are usually small (to 10°), a relation between these components can be obtained:
2.1 Vzdolžno ravnotežje sil
2.1 Longitudinal equilibrium of forces
Kot 5, je vzdolžna amplituda ciklične                  Angle Bx is the longitudinal amplitude of a cyclic
spremembe koraka kraka; kot au je kot med gredjo in        change in the blade step; angle au is the angle be-
osjo rotorskega diska. Po obsežnih izračunih dobimo        tween the shaft and the axis of the rotor disc. After
izraz za vzdolžno amplirudo ciklične spremembe        extensive calculus the expression for the longitudinal
koraka kraka:                                                               amplitude of cyclic change in the blade step is obtained:
M  -G-fR + H-hR + Ms-a1
B1
T-hR + M
(9)
Za e=0, lahko vzamemo da je Ms=0 in Mf=0. Ker je T=G, sledi:
For e=0, we can say that Ms=0 and Mf=0, and since T=G, it follows that:
B=_l + K 1       hG
D             f      M
— cost- —H------
G               h    GhR
(10) (11)
Za enačbo (10) imamo preprosto fizikalno                   Equation (10) has  a simple physical
pojasnilo: amplituda vzdolžnega cikličnega krmiljenja interpretation: the amplitude of the longitudinal krakov mora imeti tako vrednost, da postavi smer cyclic control must have such a value in order to rezultirajoče sile rotorja skozi masno središče.                position the direction of the resultant rotor force
through the center of mass.
Vodoravna os Horizontal axis
SI. 4. Skica vzdolžnega ravnotežja sil Fig. 4. Drawing for determining the longitudinal equilibrium of forces
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2.2 Prečno ravnotežje sil
2.2 Lateral equilibrium of forces
Kot A, pomeni amplitudo prečne ciklične spremembe koraka kraka rotorja:
Angle A1 represents the amplitude of lateral cyclic change in the blade step of the supporting helicopter rotor:
G-W + Ms-b1+Trhfl
G-hR + M
(12)
Če vrednost A, uvrstimo v ustrezne enačbe, dobimo vrednost köta f ki določa lego trupa.
By replacing the value A, in the corresponding equations, we obtain the value Of angle f which determines the position of the fuselage.
Tt | G-fR + Ms-b1+Tt-htR G            G-hR + M
(13)
SI. 5. Skica prečnega ravnotežja sil Fig. 5. Drawing for determining the lateral equilibrium of forces
Če je M=0 in h=h, kar pogosto lahko
vzamemo, sledi:
If M=0 and h=h, which can often be assumed, it follows that:
f1 , h
kar pomeni, da je glava rotorja navpično nad masnim        which means the rotor hub is positioned vertically
središčem. Vse vrednosti izračunanih kotov so tako        above the center of mass. All the values of these
imenovane uravnovešene vrednosti.                             determined angles are the so-called trimmed values.
3 NELINEARNI MATEMATIČNI MODEL DINAMIKE LETENJA
3 NON-LINEAR MATHEMATICAL MODEL OF THE FLIGHT DYNAMICS
Matematično modeliranje helikopterskega gibanja je izredno zahtevna naloga in zato je nujno privzeti številne predpostavke in približke. Za analizo dinamičnih značilnosti helikopterja ni nujno treba, razen v izjemnih primerih, poznati gibanja
Mathematical modeling of a helicopter’s motion is a very complex task and, therefore, it is necessary to introduce a series of assumptions and approximations. Knowledge of the motion of the individual helicopter blades is not necessary for investigating the dynamic
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posameznih krakov. Za definiranje sil in momentov pri motenem letu je dovolj opazovati rotor kot celoto. Zaradi velikega števila različnih helikopterjev, v tem prispevku analiziramo helikopter z enim samim rotorjem, katerega kraki so s členki pritrjeni na glavo rotorja. Kakor je že bilo rečeno, je helikopter zmožen različnih gibanj in bi zato bilo zelo težko narediti matematični model za kombinacijo vseh gibanj. Vzeli bomo, da je helikopter vzletel in da leti premočrtno. Komponente hitrosti helikopterja pri nominalni vrednosti in premočrtnem letenju so: W, W in W. Koti spremembe smeri % nagiba ^in vzpenjanja éz veljajo dokler so velikosti motenj v dovoljenih mejah. Na sliki 6 je predstavljena shema helikopterja s premičnim koordinatnim sistemom, vezanim na njegovo masno središče, a na sliki 7 je blokovni diagram helikopterja.
Po uvedbi nekoliko predpostavk, na primer da:
•  je masa helikopterja konstantna,
•  je helikopter togo telo,
•  ravnina xz simetrijska ravnina,
•  so kotni prirastki A ^ A6>, A0 majhni in tako dalje;
pridemo do nelinearnega matematičnega modela z odkloni v obliki:
characteristics of the helicopter, except in a special case, but rather for defining the forces and moments in a disturbed flight it is sufficient to view the rotor as a whole. Because of the large number of different helicopters, in this paper a single-rotor helicopter that has its blades connected to the hub by hinges was studied. As mentioned before, the helicopter can perform different movements and it would be very difficult to make a mathematical model that would combine all those movements. It is assumed that the helicopter is airborne and in straightforward flight. It is necessary that the helicopter, during its straightforward flight, has the following velocity components, Wx, Wy, and Wz, at nominal values, and the angle of turn y, the angle of roll f, and the angle of climb q, as long as the intensity of disturbance is within permitted limits. Figure
6 presents a schematic of the helicopter with a floating coordinate system tied to its center of mass, and Figure
7 presents a helicopter block diagram. After introducing a series of assumptions,
such as:
•  the helicopter mass is a constant value,
•  the helicopter is a rigid body,
•  the 0xz is a plane of symmetry,
•  the angle increments DY, Dq, Df are too small, and so on,
we come to a non-linear mathematical model with deviations in the form:
Sl. 6. Shema helikopterja Fig. 6. Schematic of helicopter
Sl. 7. Blokovni diagram helikopterja Fig. 7. Helicopter block diagram
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d(AWr)     ir,                  .         x    .
^—i  = -[f1(AWx,AWz,Aß,u1,u2)- mgcosr )A0 dt        mL    v                            7
d(AW)      lr     /                           x
dt         mL    v                            7
i----Z = A#
dt
d(A0)     i                        ...
 jv     x       z       z            l    l'
dt       J
d(AWy)     \v    f           ,
^        = —\fAAWA0,Aiy,ui,u4) + WzNmAiy + mgcosTA0 + mgsmTAii
dt        mL    y
d(A^)
d(D f&)
dt
D f&
dt       J
-[/5 ( Wy,A<f>,Aifs,u3,u4 ) +JxzAif/ d(Ay
d(D y&)= 1 dt        J
dt
D y&
-[f6 (kWy,AeAY,u„u4 ) +JxzA(j>
(14) (15)
(16) (17)
(18) (19)
(20)
(21)
(22)
Kjer so:
•  u=AB1 - amplituda ponovitvene spremembe koraka v vzdolžni smeri (za vzdolžno gibanje),
•  u=A0Q- sprememba skupnega koraka kraka rotorja helikopterja (za vzdolžno gibanje),
Where:
u1=DB1 – the amplitude of the cyclic change in step in the longitudinal direction (in terms of longitudinal motion), u 2=Dq 0 – the change of the collective step of the helicopter rotor blade (in terms of longitudinal motion),
SI. 8. Shema prečnega gibanja Fig. 8. Schematic for lateral motion
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•  u=AAl - amplituda ponovitvene spremembe koraka v prečni smeri (za prečno gibanje) in
•  u=A0t - sprememba skupnega koraka repnega
rotorja (za prečno gibanje).
Shematska diagrama predstavljamo na slikah 8 in 9.
SI. 9. Shema vzdolžnega gibanja Fig. 9. Schematic for longitudinal motion
•  u=AAx - the amplitude of the cyclic change in step in the lateral direction (in terms of lateral motion),
•  u=A0t - the change of the collective step of the tail rotor (in terms of lateral motion).
Schematic diagrams are presented in Figures 8 and 9.
4 LINEARIZIRAMMATEMATIČNI MODEL DINAMIKE LETENJA
4 LINEARIZED MATHEMATICAL MODEL OF THE FLIGHT DYNAMICS
Dokazano je, da v tehniki lahko uporabimo s sprejemljivo natančnostjo linearizirane matematične modele pod pogojem, da imajo fizikalne veličine majhna odstopanja od nominalnih vrednosti. Nelinearni matematični model dinamike letenja helikopterja ni primeren za določanje splošnih rešitev v analitični obliki, čeprav se problem rešuje s sodobno računalniško tehnologijo.
Zaradi sprejetih predpostavk bodo izstopne vrednosti, vstopne vrednosti in vektor stanja tako za vzdolžno kakor za prečno gibanje:
In technical applications it has been shown that, with an acceptable accuracy, linearized mathematical models may be used under the condition that the deviations of the physical quantities from their nominal values are small. A nonlinear mathematical model of the helicopter’s flight dynamics is inadequate for finding general solutions in an analytical form, even though the problem is solved with the aid of modern computer technology.
The outcome of the adopted presumptions is that the output values, input values, and the vector of state for both the longitudinal and lateral motion will be:
X = (X1...X9
x=(x...x
u = [u ...u
(23) (24) (25)
Vektorska enačba stanja za linearizirani matematični model z brezrazsežnimi veličinami, odstopanji, to je veličinami stanja, je enačba (26). Enačba izstopnih veličin je (27).
The vector equation of state for the linearized mathematical model with non-dimensional quantities, deviations, i.e., the quantities of state, is shown in Equation (26). Equation (27) presents the output values.
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X
a 11	a 12	a 13	a 14	0	0	0	0
a 21	a 22	a 23	a 24	0	0	0	0
0	0	0	1	0	0	0	0
a 41	a 42	a 43	a 44	0	0	0	0
0	0	0	0	a 55	a 56	0	a 58
0	0	0	0	0	0	1	0
0	0	0	0	a 75	0	a 77	0
0	0	0	0	0	0	0	0
0	0	0	0	a	0	a	0
x +
0    0
X
100000000 010000000 001000000 000010000
00000      1      000
[000000100
X
0    0
00
(26)
(27)
Čeprav so tukaj prikazana v skupni matrici, je treba poudariti, da so vzdolžna in prečna gibanja ločena, ker je to bil eden izmed pogojev za izpeljavo tega matematičnega modela. V enačbah (26) in (27), so enačbe za vzdolžno gibanje predstavljene v prvih štirih vrsticah matrike, medtem ko preostalih pet vrstic pomeni enačbo stanja in enačbo prečnega gibanja. V enačbi (26) uporabljamo naslednje označbe:
In addition to the way this is presented, in the form of a common matrix, it should also be noted that the longitudinal and lateral motions are separated, because this was the condition for deriving this mathematical model. In Equations 26 and 27, the equations for the longitudinal motion are presented within the first four rows of the matrice, while the remaining five rows present the equation of state and the equation of lateral motion. The designations used in Equation 26 are:
C*
1-i/ij,
a
a
12
a
13
a 59 =W*
a23 = -mc sin t        a24 = WxN+zq      a5 a41 =mu + mivzu       a42 =mw+ m^zw      a4
01        Z                   ö9        X                  ö9        Z
-mc cos Z"       O14 = x          a21 = zu
= y v     a56 =mccosT     a58 = mc sin = -milmc sin z   a44 = mq + m. I Wm + zq b   =mz   +m         b   =mz   +m
11             B 1                                          1                                              0                                               0                                                11                                              0                 0
K=yA          K=ys,       K={lA+nAh/h) C*     K={le,+ne,h/h)c*      K={ne,+le,h/h)c*
a75={nX/h H)   C*        a77={lp+npi*z/h)   C*            a95={nv+lX/h)   C*        a97={np+lpL/h)   C*
a99={nr+lrixz/iz) C*        b93 ={nA + lAixz/iz) C*  a79={lr+nrixz/ix) C*
Na slikah 10 in 11 so predstavljene sheme lineariziranega matematičnega modela v vzdolžnem in prečnem gibanju.
5 REZULTATI PROGRAMA
Figures 10 and 11 present schematics of the linearized mathematical model in a longitudinal and lateral motion.
5 PROGRAM RESULTS
Program je testiran na primeru helikopterja z enim samim rotorjem, ki ima krake členkasto vpete na glavo rotorja. Helikopter je opisan z naslednjimi vstopnimi podatki: teža helikopterja G=45042N, količnik pokritja rotorja 5=0,058, polmer rotorja fl=8, lm, koeficient višine glave rotorja A=0,25, količnik upora (5=0,013, število krakov glavnega rotorja b=4, masa kraka m=79,6kg, količnik napredovanja rotorja
The program was tested on the example of a single-rotor helicopter for which the main rotor blades are tied to the hub over hinges. The helicopter is described by the following input data: helicopter weight, G=45042N; rotor abundance degree, 5=0.058; rotor radius, tf=8. lm; hub height coefficient, Ä=0.25; drag coefficient, (5=0.013; number of blades of the main rotor, b=4; blade mass, m=79.6kg; rotor
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SI. 10. Shema lineariziranega matematičnega modela pri vzdolžnem gibanju Fig. 10. Schematic of a linearized mathematical model when in longitudinal motion
SI. 11. Shema lineariziranega matematičnega modela pri prečnem gibanju Fig. 11. Schematic of linearized mathematical model when in lateral motion
/y=0,3, vzgonski gradient profila a=5,65 l/rad, hitrost konca kraka Qtf=208m/s, masno središče kraka x je na 45% radija kraka R, oddaljenost členka kraka'od gredi pa je 0,04R, gostota zraka na višini letenja (100m) /7=1,215 kg/m3. Za vzdolžno gibanje je matematični model v vektorski obliki:
X
		X = A
-0,0509	0,1323	-0,0734
0,1216	-1,2525	0
0	0	0
6,512	12,1	0
operating mode coefficient, m=0.3; gradient of lift, a=5.65; velocity of blade top, WR=208m/s; distance of blade mass center coefficient, xg=0.45; distance of hinge from shaft, eR=0.04R; and air density at flight altitude (100m), r=1.215 kg/m3. For longitudinal motion the mathematical model in vector form is: X +b u
0,00263
0,3
1
-0,844
X
X2 X,
x
x+
0,1344	0,066
0,3578	-0,9477
0	0
-28,329	17,88
Matematični modeli dinamike helikopterskega letenja - Mathematical Models of Helicopter Flight Dynamics       123
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 114-126
Enačba izstopnih veličin je:
X
"1	0	0	0"
0	1	0	0
0	0	1	0
0	0	0	1
The equation at the exit is: X      kjer je/where is      Xi
Matrika A linearizkanega modela helikopterja za prečno gibanje je:
X
i2
X
i3
Matrix A of the linearized model of the helicopter for lateral motion is:
-0,15125   0,0734        0        0     0,3 0             0            10       0
-64,42         0        -2,948   0    1,378
0             0            0        0       1
55,297         0        0,413     0    -1,64
X = A X + B u
X = yX5    X6    X7    X8    X9 J
u = \u     u 1
6 SKLEPI
6 CONCLUSIONS
Da bi bil matematični model dinamike helikopterskega letenja, strogo določen, bi moral biti sestavljen iz sistema nelinearnih, neustaljenih, parcialnih diferencialnih enačb. Da bi te enačbe poenostavili, smo vzeli nekaj predpostavk. Zanemarili smo elastične lastnosti helikopterja, da bi helikopter analizirali kot togo telo in tako eliminirali razpršitev parameterov. Poleg tega smo zanemarili porabo goriva in s tem neustaljenost, ki bi se pojavila zaradi časovne spremembe mase helikopterja.
Glede na to, da ima helikopter šest prostostnih stopenj, smo zaradi poenostavitve vzeli, da se gibanje da ločiti na vzdolžno in prečno gibanje in da se ta gibanja analizirajo posamično. Povdarimo, da se matematični model helikopterja nanaša na helikoptersko premočrtno gibanje s hitrostjo W. Matematični model, ki bi obsegal vsa gibanja helikopterja, vključno z vzletom in pristankom, bi bil veliko bolj zapleten. Vpliv resonance in vibracije se prav tako zanemari. Zaostajanje kraka se tukaj tudi ne upošteva, ker drugače kotna hitrost kraka v ravnini rotacije ne bi bila več nespremenljiva. Ločene analize posamičnih gibanj krakov so velika poenostavitev, zato ker obstaja velika medsebojna odvisnost med gibanji kraka. Če bi ta gibanja ne bili ločili, bi bilo nujno analizirati stabilnost vseh gibanj kraka.
Postavljanje koordinatnega začetka v vztrajnostno središče omogoča odstranitev nekaterih vztrajnostnih momentov, tako da se
The flight dynamics mathematical model of a helicopter that would be strictly determined would comprise a system of non-linear, non-stationary, partial differential equations. To simplify these equations we introduce a number of assumptions. Ignored are the elastic characteristics of the helicopter so the helicopter can be thought as a rigid body and, in this way, the dispersal of parameters is eliminated. Also, fuel consumption is disregarded and so is the non-stationarity due to the temporal change in helicopter mass being eliminated.
Because the helicopter has six degrees of freedom, for simplification it is assumed that the motion can be separated into longitudinal and lateral motions and that they can be investigated independently. It should be noted that the mathematical model of the helicopter relates to the helicopter’s forward motion at velocity W. A mathematical model that would incorporate all the motions of a helicopter, all together with takeoff and landing, would be far too complicated. The influence of resonance and vibration is also ignored. The blade throughback is also ignored in this paper, because if this was not the case the blade-angle velocity in the plane of rotation would no longer be constant. A separate study of the individual motions of blades is a great simplification, because there is an interdependency of all the blade motions. If the motions are not separated, then it is necessary to analyze the stability of all the motions of the blade.
The choice of the coordinate origin in the center of inertia makes it possible to eliminate certain moments of inertia so the Euler equations can be
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 114-126
Eulerjeve enačbe lahko poenostavijo. Opazovanje         simplified. Viewing the rotor as a whole eliminates
rotorja kot celote odstrani potrebo po preučevanju        the need for investigating the motion of an individual
posameznih gibanj krakov. V tem je v veliko pomoč        blade. This is made much simpler by the introduction
uvajanje osi rotorskega diska in osi v smeri vlečne        of the rotor disc axis and the control axis. sile rotorja.                                                                            The determination of the aerodynamic
Določanje aerodinamičnih odvodov je        derivatives is related to a series of approximations.
povezano z vrsto približkov. Treba je poudariti, da        It should be noted that, besides assumptions in the
poleg predpostavk pri modeliranju, uporabljamo        modeling, mathematical simplifications were also
tudi matematične poenostavitve (na primer,        made (for example, omitting small values in the
izpuščanje zanemarljivo majhnih vrednosti iz        equations) which could not have been derived in
enačb), ki jih ni mogoče prikazati v obliki        the form of an assumption due to their meaning,
predpostavke, ker je njihov pomen tesno povezan        which is tightly related to a specific equation. z določeno enačbo.                                                               It is possible to determine projections of the
Kot izstopne značilnosti je mogoče določiti        position vector with respect to the non-moveable
projekcije vektorja lege v nepremičnem koordinatnem        coordinate system tied to Earth instead of using
sistemu, povezanem s tlemi namesto projekcij hitrosti        projections of the helicopter’s velocity with respect
helikopterja v premičnem koordinatnem sistemu. Ta        to a moveable coordinate system such as the exit
problem bi se rešil s projiciranjem hitrosti helikopterja        characteristics. Projecting the helicopter velocity
na nepremični koordinatni sistem, nakar bi se        onto a non-moveable coordinate system and then
integrirale projekcije hitrosti po času z začetnimi        integrating the velocity projections over time with
pogoji.                                                                       the initial conditions may solve this problem.
Nadaljnja analiza matematičnega modela se                  A further analysis of the mathematical model
lahko usmeri na raziskovanje dinamičnih in        can be made in order to investigate the dynamic and
statičnih lastnosti in na določanje primernega        static properties, and to determine the control that
krmarjenja, ki bi helikopterju zagotovilo zahtevano        would guarantee the object to execute the required
dinamično obnašanje.                                                 dynamic behavior.
8 LITERATURA 8 REFERENCES
[I]    W. Z. Stepniewski (1984) Rotary-wing aerodynamics, New York. [2]   M. Nenadovič (1987) OAK - Elise i propeleri, Beograd.
[3]    M. Nenadovič (1978) OAK - Aeroprofili -1, deo, Beograd.
[4]    M. Nenadovič (1977) OAK - Opšti deo, Beograd.
[5]    M. Nenadovič (1982) Osnovi projektovanja i konstruisanja helikoptera, Beograd.
[6]    A. R. S. Bromwell (1976) Helicopter dynamics, London.
[7]    W. Johnson (1980) Helicopter theory, London.
[8]    G. Saundres (1972) Teorija leta helikoptera [prevod sa engleskog], Beograd.
[9]    Gesov & Myers (1952) Aerodynamics of the helicopter, New York.
[10]  A. K. Martinova (1973) Teorija nesuščego vinta, Moskva.
[II]  M. L. Mil’ (1973) Vertoljoti, Moskva.
Matematični modeli dinamike helikopterskega letenja - Mathematical Models of Helicopter Flight Dynamics       125
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Naslova avtorjev: Dragan Cvetkovič Univerza "Union" Fakulteta računalniških znanosti Knez Mihailova 6/VI 11000 Beograd, Srbija
Authors’ addresses: Dragan Cvetkovič University "Union" Faculty of Computer Science Knez Mihailova St. 6/VI 11000 Belgrade, Serbia
Duško Radakovič Zvezni zavod za mere in dragocene metale Mike Alasa 14 11000 Beograd, Srbija
Duško Radakovič Federal Bureau for Measures and Precious Metals Mike Alasa St. 14 11000 Belgrade, Serbia
Prejeto: Received:
27.2.2006
Sprejeto: Accepted:
22.6.2006
Odprto za diskusijo: 1 leto Open for discussion: 1 year
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 127-139 UDK - UDC 629.5.026:539.371 Strokovni članek - Speciality paper (1.04)
Določanje vijačnih lastnosti motorja z merilnimi lističi in osebnim računalnikom v ustaljenih razmerah plovbe ladje
Determining the Propulsion Characteristics of an Engine Under the Conditions of a Standard Sailing Regime by Means of Strain Gauges and a Personal Computer
Sead Cvrk - Zdravko Dukič - Milorad Rodič (Mornarica SČG, Črna Gora; Navy SCG, Montenegro)
V tem prispevku je z uporabo merilnih lističev in osebnega računalnika, z nedotikalno metodo, opisan postopek merjenja elastične deformacije osi ladijskega vijaka. Na podlagi znanega prečnega prereza in vrste materiala osi ladijskega vijaka, je določen vrtilni moment. Z znano frekvenco osi, kotno hitrostjo in vrtilnim momentom je mogoče določiti delež koristne moči, ki se prenaša od motorja do ladijskega vijaka. Vsa uporabljena oprema pri preizkusih, tako strojna kakor programska oprema, je bila izdelana v podjetju ''HOTTINGER BALDVIN MESSTEHNIK'' (HBM), Darmstadt, Nemčija. Preizkus je potekal na ladji Mornarice Srbije in Črne Gore pri ustaljeni plovbi. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: ladijski motorji, dizelski motorji, vijačne lastnosti, merilni listič)
This paper describes the process of measuring a propeller shaft's elastic deformation by means of a non-contact method, strain gauges and a PC. By using the known cross-section as well as the propeller shaft's material type the torque was determined. Knowing the shaft frequency, that is the radial velocity and the torque, it is possible to determine the effective power transmitted from the engine to the propeller. The equipment, i.e., the hardware and the software, was produced by HOTTINGER BALDWIN MESSTEHNIK (HBM), Darmstadt, from the Federal Republic of Germany. The experiment was carried out on a ship belonging to the Navy of Serbia and Montenegro under the conditions of a standard sailing regime. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: ship diesel engines, propulsion systems characteristics, strain gauges)
0 UVOD                                                              0 INTRODUCTION
Moč ladijskega motorja se v času njegove uporabe stalno spreminja, odvisno od priključenega porabnika. Pri potisku ladje z ladijskima vijakom z nepremičnimi krili, je koristna moč na ladijskem vijaku, odvisna od števila vrtljajev in geometrijskih lastnosti ladijskega vijaka. Pri nespremenljivem premeru in koraku ladijskega vijaka, je upor ladijskega vijaka, ki ga premaguje motor, sorazmeren kvadratu števila vrtljajev ladijskega vijaka.
Delež koristne moči motorja na ladijskem vijaku se lahko izrazi v odvisnosti od vrtilnega momenta, ki se prenaša od ročične osi prek spojke na ladijski vijak, ta se vrti s kotno hitrostjo w.
During the exploitation of a diesel engine, the changes of engine power always depend on connected devices. When a ship is propelled by a screw, the power that the engine delivers to the fixed thread screw depends on the number of turns and the geometrical characteristics of the screw. When the screw diameter and the thread are fixed, the resistance of the propeller, which is suppressed by the engine, is proportional to the square of the number of revolutions.
= V«2                                                            (1).
The effective power that an engine transmits to the screw can be expressed by the torque that the clump transfers from the crankshaft to the screw, while it revolves at angular velocity w.
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P=M-a
(2).
V primeru, ko motor poganja ladijski vijak z določenim korakom kril, bo moč motorja, ki jo absorbira ladijski vijak pri različnih vrtljajih [1]:
In the case when the engine drives the fixed thread screw, the power of the engine that the screw absorbs, at different numbers of revolutions, is [1]:
P =M-a> = k0 -n-------= t -n
30
(3).
Enačba (3) pove, da se moč motorja spreminja po kubni paraboli v odvisnosti od spremembe števila vrtljajev ladijskega vijaka. Krivulja se imenuje vijačna lastnost motorja (si. 1, krivulja 1).
Pri uporabi ladijskega motorja je zelo pomembno določiti preneseno moč na ladijski vijak pri vseh vrtljajih. Na podlagi posnete vijačne lastnosti se da določiti, v katerem režimu motor deluje v področju možnih vrtljajev, oziroma ali deluje po proračunski lastnosti vrtilnega momenta pri plovbi, lastnosti vrtilnega momenta pri plovbi s “težkim ladijskim vijakom”, ali po lastnosti vrtilnega momenta pri plovbi z “lahkim ladijskim vijakom”.
V ladijskih razmerah običajno nimamo na voljo opreme za merjenje vrtilnega momenta motorja (ali njegove moči) in potisne sile ladijskega vijaka. Zato je v takšnih razmerah nujno treba izvajati neposredni nadzor trupa ladje, ladijskega vijaka in motorja.
Posadki ladje, ki upravlja pogonski sestav, znatno pomaga pri rešitvi takšne naloge uporaba ustreznih metod nadzora posameznih delov pogonskega sestava ladje, posebno pa nadzor delovanja glavnih potisnih motorjev.
Ena od učinkovitih metod, s katero se lahko meri vrtilni moment in tako tudi prenesena moč na
It is evident from Equation (3) that the power of the engine changes with cube parable, which depends on the number of screw revolutions. This curve is called the “screw characteristic of the engine’’ (Fig. 1, curve 1).
When an engine is used aboard a ship, it is very important to determine the power that the screw absorbs at different numbers of propeller revolutions, ranging from the minimum to the maximum. By using the transcribed characteristics we can determine the regime in which the engine is working at different numbers of propeller revolutions, i.e., whether it works with the forecast characteristic of the screw moment, the characteristic of the screw moment while sailing with a “hard propeller” or the characteristic of the screw moment while sailing with a “light propeller”.
Ships usually do not have instruments for measuring the torque (engine power) propeller lifting, and so in this case it is necessary to perform direct control of the hull, the propeller and the engine.
To the members of the crew working in the engine room, using an appropriate method to control the functioning and condition of some of the elements in the engine room, especially of the main propulsion engine, can provide considerable help while executing this task.
One of the effective methods by which we can measure the torque and the power that the en-
SI. 1. Vijačna in zunanja lastnost motorja Fig. 1. The screw characteristic and the outer characteristic of the engine
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 127-139
ladijski vijak, je metoda z uporabo merilnih lističev in osebnega računalnika.
1 UPORABA MERILMH LISTIČEV
gine transmits to the propeller is a method based on strain gauges and a personal computer.
1 APPLICATION OF THE STRAIN GAUGES
Merilne lističe sta odkrila leta 1938 E.E. Simons in A.C. Ruge iz Kalifornije, ZDA, neodvisno drug od drugega. Prva tovarna za industrijsko izdelavo merilnih lističev je bila zgrajena leta 1941 v Baldwin-Southwark, ZDA. V Evropi je leta 1952 podjetje "HOTTINGER BALDVIN MESSTECHNIK" (HBM) iz Darmstadta, Nemčija začelo izdelovati uporovne merilne lističe. Uporaba merilnih lističev je danes že zelo razširjena, unčinkovito se uporabljajo za analizo napetosti v konstrukcijah. Merilni lističi se lahko uporabljajo tudi za statična, navidezno statična in dinamična merjenja na konstrukcijah ali pa tudi na delih strojev.
Ko govorimo o merjenju pomikov in napetosti, se merilni lističi uporabljajo v področju elastičnih deformacij po Hookeovem zakonu. Merilni listič pomeni prevodnik določenega upora in je postavljen na površini merjenega predmeta. Vsaka deformacija merjenega predmeta, zaradi njegove obremenitve, povzroči sorazmerno deformacijo merilnega lističa, kar omogoča merjenje sprememb upora merilnega lističa.
V neobremenjenem stanju je upor merilnega lističa R0, ko pa se obremeni, je po deformaciji R + AR [2]:
Strain gauges were discovered in 1938 by E.E. Simons and A.C. Ruge (working independently of each other in California, USA). The first company to begin the industrial production of strain gauges was founded in 1941 (Baldwin-Southwark, USA). In Europe, “HOTTINGER BALDWIN MESSTECHNIK’’ (HBM) from Darmstadt, Germany, began producing foil strain gauges in 1952. The use of strain gauges is widespread, and they can be used for the analysis of a stress measurement in a construction. Strain gauges can be used for static, quasi-static and dynamic measurements on constructions and machine parts.
When measuring dilatation and strain, strain gauges are used in the area of elastic deformations, according to Hooke’s law. The strain gauge represents a conductor of defined resistance, fastened to the surface of a measuring object. Each deformation of the measuring object, due to stress, causes a certain deformation of the strain gauge and changes its electrical resistance.
During a no-load state the strain gauge’s resistance is R0, and during a load state, i.e., after the deformation, it will be R0 + DR [2].
R0
P-lo
A
4-p-lo
(4).
Skupna sprememba upora po deformaciji in spremembi mikrostrukture sestavnih materialov merilnega lističa je:
The total change of resistance, due to the deformation, and the change of the microstructure of the strain-gauge material is:
dR R0
•(1 + v) +
dr
(5).
^___
Dl
G
<-
l+ Dl
¦>
Sl. 2. Deformacija predmeta ob obremenitvi Fig. 2. Deformation of an object during a load state
Določanje vijačnih lastnosti motorja - Determining the Propulsion Characteristics of an Engine                129
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Odvisnost med mehanično deformacijo in                  The relationship between the mechanical
spremembo upora na merilnem lističu za raznovrstne        deformation and the strain gauge’s electrical resist-
prevodne materiale je omejena z občutljivostjo        ance for different conductors is determined from the
merilnega trakuA;[2].                                                    strain gauge’s response k[2].
AR    AR
L = 4t = —                                                     (6).
A/       e
l0
Za nekatere zlitine, ki se uporabljajo pri                  k is different for each alloy that is used for
izdelavi vlaken v merilnem lističu je občutljivost k        making the strain gauges. The strain gauge should
tudi drugačna. Merilni listič naj bi spreminjal upor le        change its resistance only due to the stress in the
zaradi napora v aktivni smeri (smer, v kateri se meri).        active direction (the direction of the measurement).
Če je merilni listič obremenjen v svoji dejavni smeri,        If the strain gauge is loaded in its active direction,
je občutljivost {k - količnik) definirana kot:                    then the strain gauge’s response is defined as:
AR
R                                                                     (7).
ki= —
Če je merilni listič obremenjen v prečni smeri,      e'           If the strain gauge is loaded in a transverse
je ^-količnik izražen kot:                                               direction, then the appropriate k factor is defined as:
AR
If                                                          (8).
h=—
Razmerje teh dveh količnikov določa prečno                  The ratio of these two factors is defined as
občutljivost:                                                               the cross response:
1 = T                                                                             (9).
Ta učinek se zmanjša z uporabo uporovnih merilnih lističev s prečnim odebelenjem omrežja. Odvisno od vrste merilnega lističa ter dolžine omrežja je prečna občutljivost 9<0,01 do 0,02. Merilni lističi se na splošno uporabljajo za merjenje deformacij do 3000 |im/m. Največje podaljšanje merilnega lističa je odvisno od konstrukcije in materiala ter znaša od ± 2 cm/m do 15 cm/m. V primera velikih deformacij, merilni lističi prikazujejo nelinearne lastnosti, ki niso zanemarljive.
Merilni listič pritrdimo na testiram predmet z lepljenjem, z uporabo različnih vezivnih materialov, kar terja zelo veliko natančnost. Električna vezava merilnih lističev se izvaja v obliki Wheatstonovega mostiča. Wheatstonov mostič se lahko uporabi za merjenje upora, in to:
-  za merjenje  absolutne  vrednosti upora  s primerjanjem znanega upora,
-  za merjenje relativne spremembe električnega upora.
Ta način vezave merilnih lističev omogoča merjenje spremembe upora z zelo veliko natančnostjo, v mejah od 107 do 10 14 Q/Q. Merilni lističi so določeni upori, ki se povezujejo od R do R   kakor
This effect is reduced by the use of a foil strain gauge with transversal wire thickening. The cross response is between q<0.01 to 0.02, depending on the strain-gauge type and the length of its grid. Strain gauges are normally used for measuring deformations up to 3000 |im/m. The maximum deformation of a strain gauge, which depends on its design and material, ranges from ±2 cm/m to 15 cm/m. In the case of extensive deformations, strain gauges show nonlinear characteristics that cannot be neglected.
The strain gauge is glued to the object of investigation using different binding materials, and it requires maximum attention. The electrical connection of the strain gauges is performed in the shape of a Wheatstone bridge. The Wheatstone bridge can be used for the resistance measurement, i.e.:
-  for measurement of an absolute value of resistance by comparing it with a known resistance,
-  for measurement of the relative alterations of resistance.
Strain gauges connected in this way provide a measurement of resistance alterations, ranging from 107 to 104 Q/Q, with a high accuracy. Strain gauges represent specific resistors, which
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4   Vs
SI. 3.  Wheatstonov mostiček Fig. 3. The Wheatstone bridge
je narisano na sliki 3. Točki 2 in 3 se povezujeta z
are connected from R1 to R4 as shown in Figure 3.
virom električne napetosti Vs, bodisi z enosmernim        At points 2 and 3 there is the supply voltage Vs
ali z izmeničnim električnim tokom. V točkah 1 in 4 dobimo izhodno električno napetost Vo, ki izraža vrednost merjenega signala.
Načelo delovanja Wheatstonoevega mostiča se lahko predstavi s sliko 4.
Predvidevamo lahko, da je upor vira električnega toka RG zanemarljiv ter da je notranji upor naprave za merjenje izhodnega električnega toka zelo velik. Električne napetosti Vt in V4 lahko izračunamo z uporabo znanih uporov RpR2, R3, R4 in K.
with alternating or direct current. At points 1 and 4 there is the output voltage V0, that represents the measurement signal.
The basic functioning principles of the Wheatstone bridge can be explained with Figure 4.
It is supposed that the resistance of the source RG is negligible, and that the inner resistance of the instrument for the measurement of the output voltage is infinite. If the resistances R1, R2, R3, R4 and Vs are known, voltages V1 and V4 can be calculated:
R
R3+R4
(10) (11).
Razlika električnih napetosti K, in K, je izhodna električna napetost V0:
V=V
The difference between V1 and V4 represents the output voltage V0:
R
R4
K1 -\- iL     it3 + R4
(12).
R1
R2
V1 V4                 R 4
~14 -   ^
\    ,    Vo    v    ||
I    *          *     I       I     R3
3------------------
SI. 4. Načelo delovanja Wheatstonovega mosta Fig. 4. The first principles of the Wheatstone bridge
1
2
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Neuravnoteženost mostiča je določena kot relativna izhodna električna napetost:
Obstajata dva primera uravnoteženosti mostiča:
-  upori upornikov so v mostiču enaki (RI = R2 = R3 =
R4 ),
-  razmerje uporov v obeh polovicah mostiča je enako (Rj/ R^ R4 / R3 ).
V obeh primerih, ko je vrednost električnih napetosti V0 / Vs = 0, je mostič uravnotežen. Če se vrednosti uporov v mostiču Rr..R4 spremenijo za določeno razliko AR, mostič ni uravnotežen, pojavi se določena izhodna električna napetost V0. V tem primeru je relativna izhodna električna napetost:
When the bridge is not balanced it is defined as the relative output voltage.
R4 -                                                                   (13).
R3 +R4
There are two cases when the bridge is balanced:
-  the electrical resistances of the bridge are equal (R1= R 2 = R 3 = R 4),
-  the proportion of the electrical resistance on both sides of the bridge is equal (R1 /R2=R4 /R3).
In both cases V0 /VS =0, and the bridge is balanced. If the electrical resistances in the bridge, R1...R4, change their values by DR, the bridge is not balanced, and there is a certain output voltage, V0. In this case the relative output voltage is:
R +DR
R3 + AR3 + R4 + AR4
(14).
Ko je AR « R, se lahko relativna izhodna električna napetost izrazi tudi:
Because of fact that DRi << Ri, the relative output voltage can be expressed as:
AR3    AR4
R3          R4
(15).
Če pa je AR /R = jfce, je relativna izhodna
 i        i                i
električna napetost:
Vs     4V
Izhodna električna napetost z mostiča je torej funkcija:
-  električne napetosti napajanja mostiča V,
-  ^-koeficienta merilnega lističa in
-  deformacije ali spremembe električne napetosti v vejah Sl do s4.
Considering DRi /Ri = kei, the relative output voltage is:
+L3-L4)
(16).
The output voltage V0 is a function of:
-  the input voltage of the bridge Vs,
-  the k strain-gauge factor,
-  the deformation or change of voltage in the bridge’s branches e1 to e4.
2 OPIS IN REZULTATI PREIZKUSA
2 DESCRIPTION AND RESULTS OF THE EXPERIMENT
Preizkus je izvajan v ustaljenih razmerah plovbe ladje. Pojem ustaljene razmere plovbe pomeni, da ladja pluje v določeni smeri in v mirnem morju. Eksperimentalno določanje vijačne lastnosti dvotaktnega ladijskega dizelskega motorja, z merilnimi lističi in osebnim računalnikom, z nedotikalno metodo smo izvedli na ladji Mornarice Črne Gore. Dolžina ladje je 96,5 m, širina 12,5m in standardni izpodriv 1470 ton. Vgrez ladje na premcu je 2790 mm, na krmi pa 3240 mm. Ladjo poganjajo dva glavna dizelska motorja in ena plinska turbina prek lastnih pogonskih osi. Na koncu vsake pogonske osi je trikrilni ladijski vijak z
The experiment was carried out under the standard sailing-regime conditions of a navy vessel. The standard sailing regime means that the ship is sailing on a given course and still at sea. The experimental determination of the screw characteristics of a two-stroke naval diesel engine by means of strain gauges and a personal computer, a no-contact method, was performed on a Serbian and Montenegrin Navy vessel. The length of the ship was 96.5 m, the width 12.5 m, and the standard displacement 1470 t. The drift on the prow was 2.79 m; the drift on the stern was 3.24 m. The ship is pro-
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nepremičnimi krili. Dizelski motorji so vrstni, vsak s po devet valji v dveh vrstah v navpičnem bloku. Motor je vrste 68B in je dvotaktni z močjo 5880 kW. Rabi dizelsko gorivo DS in olje SAE-50. Pri izvajanju preizkusa sta ladjo poganjala dva motorja, plinska turbina pa ni bila uporabljena. Os plinske turbine se je pri tem vrtela prosto. Položaj ladje, s katere se je začelo snemanje vijačne lastnosti je azimut pravi oo =047 °, oddaljenost d=0,3 M na otok Mamula. Smer plovbe ladje v času preizkusa je bila K=136o. Morje je bilo 0 dolpo Beaufortovi lestvici stanja morja, temperatura zraka 12 °C, barometrski pritisk 1005 mbarov, veter jugovzhodni 3 vozli, relativna vlažnost 68 % in temperatura morja 14 °C.
Merjenje je bilo izvedeno s postavljanjem merilnih lističev in merilne opreme na pogonsko os levega ladijskega vijaka. Mesto postavljanja merilnega lističa na osi je bilo med spojko motorja in odrivnega ležaja.
Del pogonske osi ladijskega vijaka, kjer so bili pritrjeni merilni lističi, je bilo v obliki obročastega prečnega prereza velikosti 260/80 mm. Pogonska os ladijskega vijaka je iz litega jekla z modulom elastičnosti E = 215 MPa.
Shematski prikaz postavljanja in vezave merilne naprave je prikazan na sliki 5. Na pogonsko os ladijskega vijaka sta bila pritrjena dva para merilnih lističev tipa “XY21-6/350” povezana v Wheatstonov mostič. Lističi so bili postavljeni pod kotom 180° drug na drugega. Napajanje merilnih lističev je izvajano z enosmernim električnim tokom 9 V. Merilni signal Wheatstonovega mostiča je potekal do predajnika in čez predajno anteno do sprejemnika merilnega signala. Vir električne energije, oddajnik in antena so bili postavljeni na obročasti disk iz plastične snovi, da bi izločili motnje, vse skupaj pa pritrjeno na pogonsko os ladijskega vijaka. Na pogonsko os ladijskega vijaka je bil pritrjen tudi temni listič s svetlim lističem čez njega, za registriranje števila vrtljajev pogonske osi ladijskega vijaka. Na pogonski osi ladijskega vijaka je bil na določenem razmiku postavljen sprejemnik merilnega signala in bralnik števila vrtljajev.
Sprejemnik merilnega signala in pretvornik števila vrtljajev sta bila povezana z elektronsko merilno napravo “SPIDER-8”, ki je bila povezana z osebnim računalnikom. Programska oprema, ki omogoča merjenje in obdelovanje izmerjenih podatkov, se imenuje “CATMAN 3.0”. Vsa ta oprema, strojna in programska je izdelana v podjetju “HOTTINGER BALDWIN MESSTECHNIK” (HBM), Darmstadt, Nemčija.
Računalniški program “CATMAN 3.0” deluje v delovnem sistemu MS Windows in omogoča
pelled by two diesel engines and one gas turbine via independent propeller shafts. On each shaft there are three bladed propellers with fixed blades. The diesel engines are linear, placed in two rows with nine cylinders each, and in a vertical block. The type of engine is a 68B, two stroke, with a rated power of 5880 kW. The engine uses diesel fuel, and SAE 50 motor oil. When the experiment was performed the ship was propelled by two diesel engines, and though the gas turbine was not used its shaft rotated freely. The position of the ship when the propeller characteristic was recorded was: azimuth real oo =047, distance from Mamula island d=0.3 M. The course was K =136. The sea conditions were 0 to 1, air temperature t=12°C, pressure p=1005 mbar, wind SE, 3 knots, humidity 68%, sea temperature 14°C.
The measurement was performed by placing the strain gauges and the measuring equipment on the left shaft, between the clutch and the thrust bearing.
The strain gauges were placed on a shaft with an annular cross-section of 260/80 mm. The shafts were made of forged steel with elastic modulus E=215 MPa.
A schematic review of installing and connecting the measuring equipment is shown in Figure 5. Two pairs of strain gauges, type “XY21-6/350”, were placed on the shaft and connected in the Wheatstone bridge. The strain gauges were installed at an angle of 1800. The strain-gauge circuit feed was a DC voltage of 9V The measuring signal from the Wheatstone bridge was carried to the emitter, and through an aerial delivered to the receiver. The circuit feed, emitter and antenna were placed on an annular disk (that has to be made of plastic to eliminate the backset) that was installed on the shaft. A dark ribbon with a light ribbon over it was also put all around the shaft to provide a measurement of the number of revolutions. Near the shaft, at a certain distance, a receiver and a transducer of the number of revolutions were installed.
The receiver and the transducer were linked to an electronic measuring device named “SPIDER8”; the “SPIDER-8” was linked to a personal computer. The software that makes possible the measurement and data processing is “CATMAN 3.0”. The hardware and software were produced by “HOTTINGER BALDWIN MESSTECHNIK” (HBM), Darmstadt, Germany.
“CATMAN 3.0” is software designed to work with MS Windows. It allows the user to focus his or
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23   4   5    67
1 - pogonska os ladijskega vijaka, 2 - merilni lističi, 3 - el. prevodniki, 4 - vir el. energije, 5 - antena, 6 - obročast nosilnik, 7 - motor, 8 - osebni računalnik, 9 - oddajnik merilnega signala, 10 - sprejemnik merilnega signala, 11 -“SPIDER-8”, 12 - pretvornik števila vrtljajev osi ladijskega vijaka
1 – propeller shaft; 2 – strain gauge; 3 – conductors; 4 – power supply; 5 – antenna; 6 –annular disc; 7 – engine; 8 – personal computer; 9 – emitter; 10 – receiver; 11 – “SPI-DER-8”; 12 – transducer
Sl. 5. Shematski prikaz postavitve in povezave merilne opreme Fig. 5. Diagrammatic view of the installation and the connections of the measuring equipment
uporabniku popolno koncentracijo za merjenje. “CATMAN 3.0” je namenjen za uporabo interaktivne ali avtomatične merilne programske opreme, prav tako pa ga je mogoče uporabljati kot podlago za razvoj posebnih uporab [3].
“SPIDER-8” je elektronska merilna naprava za merjenje fizikalnih spremenljivk, to so delo, moč, pritisk, pospešek, hitrost ali temperatura. Prek osebnega računalnika je povezan na tiskalnik. Sinhronizacija se izvaja s pomočjo programske opreme in upravljanjem prek računalnika. Ima štiri digitalne ojačevalnike, ki delujejo na frekvenci 4,8 kHz in 8 kanalov oštevilčenih od 0 do 3 in od 4 do 7. Vsak kanal deluje z lastnim analogno-digitalnim (A/D) pretvornikom, ki dovoljuje merilne hitrosti od l/s do 9600/s, kar zagotavlja popolno pokritost obsega mehaničnih merilnih opravil [4].
Merilni lističi, ki so uporabljeni pri merjenju deformacije pogonske osi ladijskega vijaka, so posebne serije Y, vrste XY21-6/350, izdelani iz dveh lističev, tako da oblikujejo dvojico merilnih lističev. Notranji upor merilnih lističev je 350 W, a njihova občutljivost je k = 2,07. Največja napetost električnega toka v merilnem lističu je 19 V. Videz merilnega lističa je prikazan na sliki 6.
Izmere merilnega lističa na sliki 6 so: a=6 mm, b=7,8 mm, b2=10 mm, c=17,5 mm in d=12,7 mm.
her attention primarily on the tasks of measuring. “CATMAN” is designed to work with interactive or automatic measuring software, but it can also be used as a matrix for special applications [3].
The “SPIDER-8” is an electrical measuring device for the measurement of changeable physical values like strain, force, pressure, acceleration and temperature. It is linked to a personal computer through the printer connection. All the adjustments of the device are performed by the software, i.e., by a personal computer. There are four digital amplifiers that work with a frequency of 4.8 kHz, and eight channels numbered from 0 to 3 and from 4 to 7. Each channel works with a separate analogue to digital converter (A/D) that allows a measuring rate from 1/ s to 9600/s, which means that it covers the complete range of mechanical measuring tasks [4].
The strain gauges that were used for the shaft deformation measurement are from a specially shaped series Y, type XY21-6/350, made from two gauges that form the strain-gauge pair. The strain-gauge resistance is 350 W, and the sensitivity is k=2.07. The maximum voltage of the strain gauge is 19V. For details see Figure 6.
The dimensions of the strain gauge according to Figure 6 are as follows: a=6 mm, b1=7.8 mm, b =10 mm, c=17.5 mm and d=12.7 mm.
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a		
<	f—tH —|	—   b2cl
	~*?........4L	
		
SI. 6. Videz merilnega lističa XY2l-6/350 Fig.6. Strain gauge XY21-6/350
Za začetek postopka merjenja moramo v program “CATMAN” vnesti vse podatke, ki prikazujejo lastnosti pogonske osi ladijskega vijaka:
-  modul elastičnosti E,
-  strižni modul G,
-  Poissonov količnik/,
-  odpornostni moment prečnega prereza osi W,
-  torzijski moment Md.
V program je bilo še nujno treba vnesti podatke o sinhronizaciji merilne opreme po metodi kretnice. Pri takšni metodi sinhronizacije in glede na uporabljeno vrsto merilnih lističev, vrednost izstopne napetosti električnega toka mostiča 2 mV/V ustreza vrednosti deformacije merilnega lističa 1000 um/m, kar se mora upoštevati pri določanju torzijskega momenta.
Odpornostni moment za obročasti prečni prerez se določa z enačbo [5]:
To start the measurement it is necessary to input the following initial shaft data in the “CATMAN” program:
-  coefficient of elasticity, E (elastic modulus),
-  shear modulus, G,
-  Poisson’s coefficient,
-  moment of drag shaft’s cross-section, W,
-  moment of torsion, Md.
Besides this data it is also necessary to input the calibration data of the measuring equipment. The “shunt’’ calibration method was applied in this case. With this method of calibration, considering the type of strain gauge used, a strain-gauge deformation of 1000 um/m corresponds to a bridge output voltage of 2 mV/V, which must be taken into consideration when determining the moment of torsion.
The polar drag moment for an annular cross-section is defined as [5]:
W
Strižni modul se določa z enačbo [5]:
D4-d4
---------------7t
16-D
The shear modulus is defined [5]:
E
2- 1 + v)
(17).
(18).
Za jeklo je vrednost v= 0,3. Torzijski moment se določi [2]:
M
1
For steel v= 0.3.
The moment of torsion is [2]:
¦W-G-s
(19),
s. pomeni izmerjeno vrednost deformacije osi.
Moč, ki jo motor oddaja ladijskemu vijaku preko osi, znaša [1]:
ei represents the measured shaft-deformation value. The power that the engine delivers to the screw through the propeller shaft is [1]:
P = M-a>
(20).
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Vrednost moči se vnese kot začetni podatek v program “CATMAN", ki v vsakem trenutku omogoča določanje moči, ki jo motor odda osi vijaka. Menjava vrednosti oddane moči motorja se lahko spremlja stalno v daljšem časovnem koraku ali pa v koraku nekaj sekund.
Tako je izvedeno merjenje vijačne lastnosti ladijskega motorja v celotnem obsegu vrtljajev ročične osi od 273 min ' do 602 min '. Moč je snemana na 9 delovnih točk, in to za vsako točko v 10 sekundnem časovnem koraku merjenja. V vsakem 10 sekundnem časovnem koraku je izmerjenih po 250 vrednosti. Izmerjeni rezultati so prikazani v preglednici 1.
Na sliki 7 je grafično prikazana sprememba moči za vsak vrtljaj ročične osi na podlagi izmerjene vrednosti deformacije osi ladijskega vijaka v 10-sekundnem časovnem koraku.
Za pridobitev vijačne lastnosti ladijskega motorja so uporabljene srednje izmerjene vrednosti moči v vsakem časovnem koraku. Vijačna značilka ladijskega dizelskega motorja je grafično prikazana na sliki 8 (krivulja 3).
Preglednica 1. Izmerjeni rezultati moči za posamezna števila vrtljajev osi motorja Table 1. Measured values of power for different numbers of shaft revolutions
We input the formula for power, as initial data, into the “CATMAN’’ program, thus providing the determination of the power that the engine transmits through the propeller shaft to the screw at any moment. The power change can be observed continuously during a long period or during a period of a few seconds, depending on the requirements.
In this way, the propeller characteristic for the engine, from a minimum number of crankshaft revolutions, 273 min-1, to 602 min-1, achieved under the given conditions, was recorded. The power was recorded at nine working points, at an interval of 10 seconds for each point. During each of these intervals 250 values were measured. The measured values are shown in Table 1.
Figure 7 illustrates the change of power, for each number of crankshaft revolutions, based on the measured values of propeller deformation during an interval of 10 seconds.
The mean values of the power at each interval were used to determine the screw characteristic. The screw characteristic of the diesel engine is illustrated in Figure 8 (curve 3).
n min-1
P
sr
kW
273           316           355           397           447           553           566           586           602
241,27
414,28
612,22
870,33
1283,98     2432,64
2587,33
2902,47
3088,79
3500

3000 I 2500 2000 1500 1000 i 500 0
y,—«>—;»=<;=<>
0   1   2   3   4   5   6   7   8   9101112 T [s]
602 min-1 586 min-1 566 min-1 553 min-1 447 min-1 397 min-1 355 min-1 316 min-1 273 min-1
SI. 7. Grafični prikaz spremembe moči dizelskega motorja v 10-sekundnem časovnem koraku pri številu
vrtljajev od 273 do 602 min-1 Fig. 7. The change of diesel engine power during a 10-second interval for numbers of revolutions
ranging from 273 min-1 to 602 min-1


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SI. 8. Grafični prikaz vijačne značilke ladijskega motorja Fig. 8. The screw characteristic (curve 3)
Na sliki 8 je predstavljena zgornja mejna                  Figure 8 shows the upper engine-power limit
vijačna značilka motorja (krivulja 1) in vijačna        (curve 1) and the screw characteristics for driving
značilka pri vožnji "naprej" (krivulja 2), ki ji je dal        “ahead” (curve 2), given in the manufacturer’s manual
proizvajalec v navodilu za uporabo motorja 68B,         for the engine type 68B. These curves are based on the
narisane pa so na podlagi izidov testiranja motorjev        results achieved during an investigation of a diesel en-
po vgradnji na novi ladji [6]. Pri testiranju sta ladjo        gine aboard a ship, after it was built. During the investi-
poganjala dva dizelska motorja, plinska turbina pa        gation the ship was propelled by two diesel engines,
je mirovala, pri čemer se je vrtela samo os ladijskega        without a gas turbine, although its shaft rotated freely.
vijaka.                                                                                  As you can see in Figure 8, it is obvious that
Na sliki 8 je vidno, da se z merilnimi lističi        the screw characteristic transcribed with the use of
izmerjena vijačna značilka znatno razlikuje od vijačne        the strain gauges is different from the screw charac-
značilke proizvajalca v navodilu ter predstavlja delo        teristic given in the manual by the manufacturer, and
motorja pri "težkem ladijskem vijaku". Razlaga je        represents an engine working in the ‘’hard propeller’’
lahko naslednja:                                                          regime. We can find the explanation in the following:
- ladja ni bila na popravilu 4 leta ter so podvodni        - Because the ship was not at dock for four years
deli trupa in ladijski vijak ‘’obrasli", kar pomeni           the underwater parts of the ship were “overgrown”
velik upor pri premikanju ladje.                                      and this represents a large resistance to the movement of the ship.
3 SKLEP                                                               3 CONCLUSION
Z metodo  snemanja vijačne  značilke                   The experimental data acquired by this method
pridobljeni eksperimentalni podatki na dejanski ladji        of transcribing the screw characteristic, on a concrete
so pokazali, da ladijski motor deluje po krivulji        ship, show that the engine is working in the “hard
“težkega ladijskega vijaka”, kar nam pove, da ladja        propeller characteristic”, and  that this ship cannot
ne more razviti take hitrosti plovbe kakor ladja s čistim        achieve the same speed as a ship whose underwater
podvodnim delom. Da bi se dosegla nujna hitrost        part and propellers are clean. To achieve the neces-
ladje, bi bilo treba povečati število vrtljajev motorja,        sary speed the number of engine revolutions must be
to pa ima za posledico preobremenitev motorja. Iz        increased, which would cause the engine to be over-
diagrama je razvidno, da je že na 600 min ' vrtljajev        loaded. The transcribed screw characteristic shows
ročične osi, krivulja bližja zunanji mejni značilki        that at 600 crankshaft revolutions per minute the curve
motorja, to pomeni da so vsi parametri delovnega        is nearing the outer boundary of the engine’s charac-
postopka blizu zgornjih meja. Ugotovimo lahko, da        teristics, i.e., all the parameters of the process are near
motor ne more delati na načrtovanem številu vrtljajev        their upper limits. This means that the engine is not
(n = 900 min '), ladja pa ne more doseči načrtovane        able to work with the projected number of revolutions
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hitrosti oziroma delo vsega pogonskega sestava je negospodarno.
Kakor vse znane metode, ima tudi ta svoje dobre in slabe strani. Dobre strani te metode so:
-  merilni lističi in pretvorniki po načelu merilnih lističev so zelo majhnih mas, kar pomeni, da nimajo vztrajnosti,
-  merilni lističi ne delujejo na testiram predmet,
-  merilni lističi so se pokazali kot zelo uporabni za dolgotrajna dinamična testiranja z velikim številom ponovitev (delo motorja),
-  zaznavala po načelu merilnih lističev delujejo na zelo nizkih in zelo visokih tlakih (od 107 mbar do 10000 bar),
-  glede na zgornje mejne frekvence nimajo omejitev, kar pomeni, če so merilni lističi pravilno postavljeni, sprejemajo vse dinamične spremembe na testiranem predmetu,
-  ko so merilni lističi postavljeni na predmetu, se lahko po testiranju zaščitijo s posebno gumijasto zaščito in se nato lahko ponovno uporabijo.
Slabe strani metode so:
-  največje še dovoljene temperature za uporabo merilnih lističev so do 350 °C,
-  merilni listič je občutljiv na parazitske obremenitve,
-  merilni lističi so občutljivi na vlago, zato jih je treba obvezno zaščititi s posebno gumijasto zaščito.
Povzamemo lahko, da se metoda z merilnimi lističi uspešno uporablja za nadzor trupa ladje in ladijskega vijaka ter nadzor ustreznosti vgrajenih ladijskih vijakov za dejansko ladjo oziroma ladijski motor.
(nn=900 min-1), and the ship is not able to achieve its projected velocity, and that the work of the propulsion complex is not economic.
Like other known methods, this one has both advantages and disadvantages. The advantages of this method:
-  Strain gauges and strain-gauge transducers are very light, which means that there is no inertia.
-  Strain gauges have no influence on the object of the investigation.
-  Strain gauges proved to be very convenient for long-term dynamic investigations of a large number of cycles (in this case engine work).
-  Strain-gauge transducers can endure both low and high pressures (from 10-7 mbar to 10000 bar).
-  There are no upper frequency limits, so if they are properly installed, strain gauges can record all the dynamic changes of the object of the investigation.
-  Once the gauges are installed on an object they can be protected with a special rubber band, so the measurement can be repeated, when required, even after a long period of time.
The disadvantages of this method:
-  Strain gauges can be used up to a maximum temperature of 3500C, except for special strain-gauge transducers, which can stand higher temperatures;
-  Strain gauges are sensitive to so-called parasite stress;
-  Strain gauges are sensitive to moisture, so it is necessary to protect them with a special rubber.
The conclusion is that we can use this method successfully to check the condition of the hull and the screw, as well as to determine whether the screw is suitable for the particular hull and engine.
	4 OZNAKE		
	4 INDEX		
vrtilni moment	M	I\m	torque
stalnica	K		constant
število vrtljajev	n	min1	number of revolutions
nominalno število vrtljajev	n	min1	number of revolutions-nominal
moč	P	kW	power
koristna moč	P	kW	effective power
nominalna koristna moč	P	kW	effective power-nominal
kotna hitrost	w	S"1	angular velocity
azimut dejanski	w	O	real azimuth
Ludolfovo število	p		Ludolf’s number
stalnica	K		constant
dejanska smer	K	O	real course
električna upornost	R	W	electric resistance
specifična upornost materiala	r	WmmVn	specific resistance of material
138
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 127-139
dolžina	/	rrm	length
premer	d	nm	diameter
površina	A	mm2	surface
relativno podaljšanje	e	mm/m	relative extension
relativno podaljšanje vzdolžno	e	mm/m	relative along extension
relativno podaljšanje prečno	e	mm/m	relative across extension
Poissonov količnik	n		Poisson’s coefficient
faktor občutljivosti	k		factor of sensitivity
prečna občutljivost	q		across sensitivity
električna napetost izhodna	V	V	outgoing voltage
električna napetost vhodna	V	V	voltage supply
odpornostni moment prereza	W	mm3	polar moment of cross section resistance
premer	D	nm	diameter
strižni modul	G	kPa	shear modulus
modul elastičnosti	E	kPa	elastic modulus
torzijski moment	M	Nm	moment of torsion
čas	T	s	time
	5 LITERATURA		
	5 LITERATURE		
[1]
[2]
[3] [4] [5] [6]
Gitis V.J., Bondarenko V.L., Jefimov T.P., Poljakov J.G., Čurbanov B.M. (1973) Teorijske osnove eksploatacije
brodskih dizel motora (prevod s ruskog), SSNO Beograd.
Hoffmann K. (1989) An Introduction to measurements using strain gages, Hottinger Baldwin Messtechnik
GmbH, Darmstadt.
CATMAN 3.0 32-bit measurement technique software for MS-Windows 95/98 WL {1999) HBM Darmstadt.
Spider8-the friendly alternative for PC-based measurements (1997) HBM Darmstadt.
Raškovič D. (1990) Otpornost materijala, Gradevinska knjiga Beograd.
Dizel motor 68B, Uputstvo za eksploataciju-prevod (1985) SSNO Beograd.
Naslov avtorjev: mag. Sead Cvrk
mag. ZdravkoDukič mag. Milorad Rodič Mornarica SČG Ul. Maršala Tita 2 85000 Bar, Črna Gora cvrk@cg.yu zdravko.djukic@cg.yu roda@cg.yu
Authors’ Address: Mag. Sead Cvrk
Mag. Zdravko Dukič
Mag. Milorad Rodič
Navy SCG
St. Maršala Tita 2
85000 Bar, Crna Gora
cvrk@cg.yu
zdravko.djukic@cg.yu
roda@cg.yu
Prejeto: Received:
30.3.2006
Sprejeto: Accepted:
22.6.2006
Odprto za diskusijo: 1 leto Open for discussion: 1 year
Določanje vijačnih lastnosti motorja - Determining the Propulsion Characteristics of an Engine                139
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UDK - UDC 621.436:534.83
Strokovni članek - Speciality paper (1.04)
Uporaba zvočne jakosti in preizkusne načinovne analize za določitev hrupa dizelskega motorja
The Application of a Sound-Intensity Analysis and an Experimental Modal Analysis for Determining the Noise Emissions of a Diesel Engine
Predrag Petrovič (Institute “Kirilo Savie", Serbia)
Motor z notranjim zgorevanjem predstavlja večkratno vzbujan vir vibracij in hrupa, ki izvira iz sestavov, katerih delovna energija se spremeni v energijo zvočnega valovanja. Energija, ki jo absorbira sestav motorja, vzbuja lastna nihanja večjih motornih delov (blok motorja, zbiralnik olja, glava valja itn.), skozi katerih površine  seva zvok.
Za določitev stopnje zvočne emisije v posameznih delih motorja pri različnih hitrostih delovanja so bile narejene podrobne analize v podjetju "Industrija motora Rakovica" iz Beograda, z uporabo preizkusne načinovne analize in zvočne jakosti. V tem pomenu je bila ugotovljena povezava med lastno frekvenco in emitiranim zvokom na posameznih zunanjih površinah motorja.
Del rezultatov, dobljenih med temi raziskavami, je predstavljen v tem prispevku. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: dizelski motorji, emisija hrupa, zvočna jakost, načinovna analiza)
The internal combustion engine represents a multi-exciting source of vibration and noise that originates from its assemblies, and whose energy of operation is transformed into sound-wave energy. The energy absorbed in the engine's structure excites the natural modal oscillations of the larger engine parts (cylinder block, oil sump, cylinder head, etc.), through whose surfaces the sound is radiated.
To determine the level of emitted sound in individual areas of the engine at various running speeds, detailed research was carried out at Industrija motora Rakovica of Belgrade using experimental modal analyses and sound-intensity measurements. In this way a correlation was made between the natural modal frequencies and the emitted sound from particular external areas of the diesel engine.
Some of the results obtained in the course of these investigations are presented in this paper. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: diesel engine, noise emissions, sound intensity, modal analysis)
0 UVOD                                                                     0 INTRODUCTION
Raziskovalno delo pri pojavu nastajanja zvoka v motorjih z notranjim zgorevanjem poteka v več smereh. Prva obsega zgorevalni postopek, vključno s plinskim tokom skozi dovod in izpuh. Druga smer v razvoju se nanaša na moteče pojave, kakršni so udarci, drsenje, resonance gibljivih delov, npr. kolenasta gred, bati in podobno. Tretja skupina pokriva raziskave sestavne togosti in dušenja (blok, glava, zbiralnik ita.). Pogon odmične gredi, pomožni mehanizmi in agregati predstavljajo še eno skupino ali smer raziskovalnega dela na področju hrupa motorjev.
Research work on the way noise is generated by internal combustion engines can be conducted in several directions. The first involves the combustion processes, including the gas flow during inlet and exhaust. The second direction of research relates to disturbance processes, such as the impacts, the sliding, and the resonance of the moving parts, e.g., the crankshaft and the pistons. The third group covers research on structure stiffness and damping (block, head, sump, etc.). The timing gear, auxiliary mechanisms and aggregates represent another group or course of research work in the field of engine noise.
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 140-148
Področje raziskav v tem prispevku je pojav nastanka hrupa v sestavu motorja, ki ga povzročajo premični deli, na primer kolenasta gred z batnim mehanizmom.
Raziskave so bile narejene pri podjetju "Industrija motora Rakovica" na S54 visokem štirivaljnem dizelskem motorju. Namen teh raziskav je bila sprememba v konstrukcijskih rešitvah osnov razvitega mehanizma nastanka zvoka, da bi zmanjšali stopnjo hrupa.
1 SPEKTER HRUPA, KI GA USTVARJA MOTORNI SESTAV
1.1 Izvir zvoka
Slika la) prikazuje sestav motorja, ki je namenjen tem raziskavam. Sestoji iz bloka motorja, kolenaste gredi z vztrajnikom, štiribatnim mehanizmom in oljnim zbiralnikom z mazalno črpalko.
Sestav poganja električni motor s spremenljivo kotno hitrostjo. Vseeno je mogoče simulirati delovni pojav in nastanek hrupa v področju motorja. Udarne sile se povečujejo s povečevanjem kotne hitrosti in večanjem zračnosti. Med delovnim postopkom se sile povečajo zaradi tlaka zgorevalnega plina. Vendar je hkrati sunek med zračnostmi na splošno odvisen od vztrajnosti, ki postane bolj intenzivna zaradi vibracij kolenaste gredi. Zaradi lastnih vibracij se kolenasta gred elastično deformira s povečanjem moči teh sunkov.
Pojav nastanka zvočnih valov, povzročen s sunki v ležajih in podobnimi motnjami, je zapleten. Lahko ga razdelimo v naslednje faze:
1.   Primarni zvočni val nastane pri točki sunka z neposrednim stikom bližnjih površin. Ta zvok se širi skozi okolišni prostor v motorju, še posebej v zbiralniku olja. Tu se ojači z resonanco in prodre skozi zbiralnik olja in blok motorja v okolico (si. la).
2.   Iz točke sunka se energija prenese na zunanje površine bloka in zbiralnika olja. Prenos poteka z elastičnimi deformacijami, ki se širijo kot valovi. Ko val doseže zunanje površine, se energija prenese na okolico kot zvočni valovi (si. lb).
3.   Valovi elastičnih deformacij vzbujajo lastne (modalne) vibracije. Načinovne vibracije bloka motorja     in     oljnega     zbiralnika     so
The scope of the research in this work is the noise-generation process in the engine structure, caused by the moving parts, i.e., the crankshaft with the piston mechanism.
The research was carried out at Industrija motora Rakovica of Belgrade on a S54 high 4-cylinder diesel engine. The aim of the research was to make modifications to the design solutions on the basis of the developed mechanism of noise generation in order to reduce the noise levels.
1 THE NOISE SPECTRUM GENERATED BY ENGINE ASSEMBLIES
1.1 Noise excitation
Figure la shows the engine assembly that was the subject of these examinations. It consists of an engine block, a crankshaft with a flywheel, four piston mechanisms, and an oil sump with a lubrication pump.
The assembly is operated by an electric motor with a variable angular speed. Nevertheless, it is possible to simulate the operation process and the noise generation in this engine area. Impact forces increase with the angular speed and with the clearance magnitude. During the working process, because of the combustion gas pressure, the forces are increased, but the impact within the clearances generally depends on the inertia, which becomes more intensive due to crankshaft vibrations as well. Because of its own vibrations, the crankshaft elastically deforms with the increase in the intensity of these impacts.
The process of sound-wave generation, caused by the impacts in the bearings and by similar disturbances, is complex. It can be divided into the following stages:
1.   Primary sound waves occur at the point of impact in the direct contact of contiguous surfaces. This sound spreads through the enclosed space in the engine, especially in the oil sump. Here, it is amplified by the resonance and penetrates through the engine sump and block walls into the environment (Fig. 1a).
2.   From the impact point, energy is transmitted to the external surfaces of the block and the sump. The transmission is carried out by means of elastic deformations spreading as waves. When a wave reaches the external surfaces, the energy is transmitted to the surroundings as sound waves (Fig. 1b).
3.   The waves of elastic deformation excite the engine parts' natural (modal) vibrations. The modal vibrations of the engine block and the oil sump are the most
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a)
b)
c)
Sl. 1. Sestav testnega motorja in pojav nastanka hrupa: a) sunek v reži ročičnega Maja in primarno
nastajanje hrupa, b) sunek v reži Menaste gredi in nastanek valov v elastični sestavi motorja,
c) lastna nihanja motorja in drugotno nastajanje hrupa
Fig. 1. The tested engine assembly and the process of noise generation: a) impact in the clearance of the
connecting-rod bearing and the primary noise generation, b) impact in the clearance of the crankshaft
bearing and the wave generation in the elastic structure of the engine, c) natural vibrations of the
engine structure and secondary noise generation
najpomembnejše. Ta dva dela imata velike površine, ki oddajajo zvok in sta v neposrednem stiku z okolico. Tako se oddajajo zvočni valovi s frekvenco, ki je enaka njihovi lastni frekvenci sten teh delov. Slika 1c) prikazuje vibracije in zvok nastale na ta način.
important. These parts have large surfaces to emit the sound and are in direct contact with the surroundings. In this way, sound waves are emitted, the frequencies of which are equal to the individual frequencies of the walls of these parts. Figure 1c, designates the vibration and sound generated in this way.
1.2 Meritve hrupa ločenih motornih sestavov
1.2 Measurement of the noise of a separate engine assembly
Motorni sestavi s slike 1 so bili preizkušeni v brezodmevnem prostoru. Pogon je bil izveden iz sosednjega prostora z uporabo električnega motorja s spremenljivo kotno hitrostjo. V brezodmevnem prostoru je bil tlak merjen 1 m stran od testnega predmeta.
Slika 2 prikazuje spekter hrupa v različnih preizkusnih razmerah. Na sliki 2a) sta primerjana spektra hrupa oddana iz motornih sestavov (sl. 1) pri dveh hitrostih vrtenja. Slika 2b) vsebuje primerjavo spektrov hrupa, ki ga oddaja sestav motorja (črta 1), spekter hrupa, ki ga oddaja celoten od zunaj gnan motor (črta 2) in spekter hrupa avtomobilskega motorja z zgorevanjem pri polni obremenitvi (črta 3). Na podlagi primerjav zapisanih spektrov lahko naredimo naslednje sklepe.
The engine assembly shown in Figure 1 was tested in an anechoic chamber. The propulsion was effected from an adjacent room by means of an electric motor with variable angular speed. In the anechoic chamber, the acoustic pressure was measured at a distance of 1 m from the tested object.
Figure 2 illustrates the noise spectra for different experimental conditions. In Figure 2a is a comparison of the noise spectrums emitted by the engine assembly (Fig.1) for two rotation speeds. Figure 2b contains a comparison of the noise spectra emitted by the engine assembly (line 1), the noise spectra emitted by the complete externally operated engine without combustion (line 2), and the noise spectra of the automotive engine with combustion under full-load conditions (line 3). On the basis of the comparison of the spectra of registered noise, the following conclusions can be drawn.
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a)                                                                                       b)
Sl. 2. Spektri hrupa: a) motorni sestav, predstavljen na sliki 1, b) celoten od zunaj gnan motor v
primerjavi s spektrom hrupa motornega sestava (1 s slike a) in avtomobilski motor z zgorevanjem pod
polno obremenitvijo (3)
Fig. 2. The noise spectra of: a) the engine assembly presented in Fig. 1, b) the complete engine driven
externally (2) in comparison with the noise spectrum of the engine assembly (1 - from Fig.a) and the
noise spectrum of the automotive engine with combustion under full-load conditions (3)
1.   Spekter hrupa, ki ga oddajata kolenasta gred in batni mehanizem v bloku motorja, je razdeljen v dva ločena pasova. V nizkofrekvenčnem območju se frekvenca visokih stopenj hrupa ujema s frekvenco sunka v glavnem ležaju. V visoko frekvenčnem področju se frekvenca hrupa približno ujema z lastno frekvenco kosa. Nizkofrekvenčni pas predstavlja vsiljeni del spektra, visokofrekvenčni pa lastni del spektra.
2.   S povečanjem kotne hitrosti (iz 1000 na 4200 vrt/min) se frekvenca sunka poveča, kar lahko vidimo na vsiljenem delu spektra: najvišja raven zvočnega tlaka je pri 2000 vrt/min v oktavi od 63Hz in v 125Hz pri 3000 vrt/min (sl. 2a). Oblika lastnega dela spektra ni spremenjena, ker lastna frekvenca delov motorja ni odvisna od frekvence vzbujanja.
3.   Oblika spektra hrupa (črta - sl. 2b) dobljena z motornim sestavom, predstavljenim na sliki 1, je enaka kakor spekter hrupa v celoti zunanje gnanega motorja (črta 2 - sl. 2b). Kaže, da so vztrajnostne sile in sile zaradi sunka v reži v glavnem ležaju najpomembnejše motnje, ki
1.   The spectrum of noise emitted by the assembly of the crankshaft and the piston mechanism in the engine block is divided into two separated bands. In the low-frequency range the frequency of the high noise levels is approximately the same as the frequencies of impact in the main bearings. In the high-frequency band, the noise frequency is approximately the same as with the parts' natural frequencies. The band of lower frequencies represents a forced part of the spectrum, and that of the higher frequencies represents a natural part.
2.   With an increase in the angular speed (from 1000 to 4200 rpm.) the frequency of the impacts increases, which can be seen in the forced part of the spectrum: the highest level of sound pressure is at 2000 rpm in the octave of 63 Hz, and in the 125 Hz range at 3000 rpm (Fig. 2a). As a result, the shape of the natural part of the spectrum is not changed, because the frequency of the engine parts' natural vibrations does not depend upon the frequency of excitation.
3.   The shape of the noise spectrum (line - Fig. 2b) generated by the engine assembly presented in Figure 1 is the same as the noise spectrum of the complete engine driven externally (line 2 - Fig. 2b). It shows that the inertial forces and the impact forces
Uporaba zvočne jakosti - The Application of a Sound-Intensity Analysis
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povzročajo hrup. Oddajanje tega hrupa je odvisno od frekvence in dušilnih lastnosti bloka, zbiralnika in podobnih motornih delov. Stopnja hrupa celotnega motorja je odvečna energija, zapravljena z udarci v celotni strukturi in s utripanjem tlaka. 4. Stopnja hrupa celotnega zunanje gnanega motorja je nekoliko manjša od hrupa avtomobilskega motorja pod polno obremenitvijo (črta 3 - sl. 2b). Med zgorevanjem so sunki v režah dušeni. V primerjavi z od zunaj gnanim motorjem je absorbirana energija v sestavi motorja razsipana.
2.1 Vzbujane frekvence
V frekvenčnem spektru posnetega hrupa (sl. 2), so zvočne tlačne stopnje povečane pri prvih treh oktavah (31,5; 63 in 125 Hz) z namenom, da se najvišja stopnja premakne na višjo oktavo (iz 63 na 125 Hz) s povečanjem vzbujane frekvence. Frekvenca najvišjih stopenj hrupa v vsiljenem delu spektra se ujema z vzbujano frekvenco.
V  vseh spektrih je najnižja zvočna tlačna stopnja pri oktavi s srednjo frekvenco 500Hz. Ta oktava jasno ločuje vsiljeni del spektra od vzbujanega. Zato so ti spektri zelo značilni. V drugih mehanskih sistemih se delno prekrivajo ali so oddaljeni drug od drugega , kar jih naredi neprimerne za primerjavo.
2.2 Lastne frekvence
V  frekvenčnih spektrih oddanega hrupa, prikazanih na sliki 2, se območje nad 1000 Hz ne spremeni ne po legi ne po obliki. Spreminja se samo velikost zvočnega tlaka. To dokazuje, da so zvočni valovi v tem delu spektra posledica lastnih nihanj delov motorja. Da bi to izboljšali, so bile narejene obširne raziskave, še posebno na bloku in zbiralniku. Modalno testiranje je bilo izvedeno s sunkovitim vzbujanjem in merjenjem vibracij kot odziva.
Primerjava je narejena med odzivom v obliki pospeška (a) in vzbujanja v obliki sile (F), dobljene z množenjem mase kladiva in njegovega pospeška ob udarcu. Slika 3 kaže frekvenčni spekter, dobljen na ta
in the clearances in the main bearings are the most important disturbances causing the structural noise. The emission of this noise depends on the frequency and the damping characteristics of the block, the sump and similar engine parts. The noise level of the complete engine is higher because of the energy absorbed by impacts in the complete engine structure and by the pressure pulsation. 4. The noise level of the complete engine, driven externally, is somewhat higher than the noise level of the automotive engine under full-load conditions (line 3 - Fig. 2b). During the combustion, the clearance impacts and the parts' inertial forces are dumped. In comparison with the engine driven externally, the absorbed energy in the engine structure is distressed.
2.1 Exciting frequencies
In the frequency spectra of registered noise (Fig.2), the sound-pressure levels are increased for the first three octaves (31.5, 63 and 125Hz) with the tendency that the highest level moves to the higher octaves (from 63 to125Hz) with the increase of the impact frequency. The frequency of the highest noise level in the forced part of the spectra coincides with the impact frequency.
In all the spectra the lowest acoustic pressure level is in the octave with a mean frequency at 500Hz. This octave clearly separates the forced part of the spectrum from the natural. Therefore, these spectra are very characteristic. In other mechanical systems they partially coincide or are distant from one another, which makes them unsuitable for a comparison.
2.2 Natural frequencies
In the frequency spectra of the emitted noise shown in Figure 2, the area above 1000 Hz does not change its position or its shape during the change of operating conditions; only the magnitude of the acoustic pressure changes. This proves that the sound waves in this area of the spectrum occur due to the natural oscillation of the engine parts. In order to improve this, comprehensive examinations of the natural vibrations of the engine parts were made, especially of the block and the sump. The modal testing was carried out by excitation with the method of impact and by measuring the vibrations as a response.
A comparison was made between the response expressed in terms of acceleration (a) and the excitation in terms of force (F), obtained by multiplying the hammer
2 FREKVENČNA ANALIZA                                          2 FREQUENCY ANALYSIS
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način. Razmerje med odgovorom in vzbujanjem je na ordinati a/F izraženo z m/Ns2 in s frekvenco na abscisi.
Blok motorja je bil vzbujen z načinovnim kladivom na podporah, kjer nalega kolenasta gred. To so mesta, kjer se pojavi vzbujanje v dejanskih obratovalnih okoliščinah. Odziv je bil merjen na bočni strani bloka. S premikanjem točke vzbujanja iz ležaja na ležaj in točke merjenja odziva, je bila največja intenzivnost odziva vedno na frekvenci 2800 Hz. Slika 3 prikazuje rezultat ene od teh meritev.
Zbiralnik olja je tankostenski z ojačitvenimi rebri. Vzbujanje je bilo izvedeno z udarci z načinovnim kladivom na prirobnico od povezave z blokom, hrup pa je bil merjen iz bočne strani. Dobljenih je bilo več frekvenc (sl. 3), pri katerih je bila stopnja odziva izredno velika. To so frekvence 2400, 3500 in 4600 Hz.
Vrhovi v visokofrekvenčnem področju spektra so sestavljeni iz lastnih frekvenc motornih delov. Poleg lastnih frekvenc bloka in zbiralnika so bile vsebovane še lastne frekvence kolenaste gredi, vztrajnika, ročic, oljne črpalke in drugih delov. Te frekvence so bile vključene tako, da se je po sunku iz cone sunka osnovni zvočni val razširil s frekvenco enako lastnim frekvencam delov, vpletenih v sunek neposredno. Vse te frekvence predstavljajo lastni del spektra enotskega zvočne tlačne stopnje od 1 do 8 kHz. Zato so potrebna dodatna testiranja, da bi podrobno preučili mehanizem izvira zvoka v strukturi tako zapletenega mehanskega sistema. To je analiza gibanja motilnih valov skozi dele motorja z uporabo metode končnih elementov, kar ni vsebovano v tem prispevku. Druga možnost je lociranje točk
mass and its acceleration at the impact. Figure 3 shows the frequency spectra obtained in this way. The response/excitation ratio is of the ordinate a/F, expressed in m/Ns2 and the frequency on the abscissa.
The engine block was excited by modal hammer impacts on the supports where the crankshaft lies. These are the locations where the excitation is introduced during real operating conditions, too. The response was measured from the lateral sides of the block. By displacing the excitation point from bearing to bearing and the point response measurement, the highest intensity response was always for the 2800 Hz frequency. Figure 3 shows the result of one of these measurements.
The oil sump has thin rib-stiffened walls. The excitation was carried out by striking a modal hammer on the flange from a connection with the block, and the response was measured from the lateral sides. Several frequencies were obtained (Fig. 3b), for which the response level was extraordinarily high. These frequencies were 2400, 3500 and 4600 Hz.
The peaks in the high-frequency part of the spectrum in Figure 2 consist of the engine parts' natural frequencies. Besides the block's and the sump's natural frequencies the frequencies of the crankshaft, the flywheel, the connecting rods, the oil pumps and other parts were also recorded. These frequencies were included in such a way that, after the impact from the zone of the stroke, primary sound waves spread with frequencies equal to the natural frequencies of the parts directly involved in the impact. All of these frequencies together represent the natural part of the spectrum of the unified sound-pressure level from 1 to 8 kHz. Therefore, additional testing is necessary in order to study in detail the mechanism of the origin of the sound in the structure of such a complex mechanical system, i.e., the analysis of the motion of disturbance waves through engine parts by applying the final-element method, which is not included in this work. Another
a)                                                                              b)
Sl. 3. Izbrani rezultati načinovnih testov: a) za blok motorja, b) za zbiralnik olja
Fig. 3. Selected modal test results: a) for engine block, b) for engine sump
Uporaba zvočne jakosti - The Application of a Sound-Intensity Analysis
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v prostoru, od koder so zvočni valovi ustreznih frekvenc.
3 ANALIZA LOKACIJ ZVOČNIH VIROV V MOTORNEM SESTAVU
possibility is to locate the points in space from where sound waves of corresponding frequencies come.
3 ANALYSIS OF THE LOCATION OF THE SOUND SOURCES IN THE ENGINE'S STRUCTURE
Za določitev prostorske razporeditve zvočnih valov ustreznih frekvenc, so bile izvedene meritve zvočne intenzivnosti celotnega motorja pri polnih obremenitvah. Meritve so bile narejene za vse oktave v frekvenčnem spektru in samo značilne so prikazane na sliki 4.
Slika 4 prikazuje porazdelitev zvočne jakosti za vsiljeni del spektra in točno za oktave s srednjo frekvenco območja pri 125 Hz in 250 Hz. Zvočna jakost je najvišja v oktavi s 125 Hz, največje vrednosti 110 dB (A) pa so sproščene v območju vrtenje kolenaste gredi.
Razpon najvišje zvočne jakosti se razprostira na desno stran. Ker je na tej strani vztrajnik, lahko predpostavimo, da so sunki v ležajih povečani zaradi večje mase. Jakost je večja v območju izpostavljenih delov oljnega zbiralnika. Lahko sklenemo, da so to zvočni valovi, ustvarjeni s sunkom, ki prodira skozi stene motornega zbiralnika.
4 SKLEP
In order to determine the spatial layout of the sources of sound waves of corresponding frequencies, the measurements of the sound intensity of the complete engine under full-load conditions were made. The measurements were made for all octaves in the frequency spectrum, but only the typical ones are shown in Figure 4. Figure 4 illustrates the sound-intensity maps for the forced part of the spectrum and precisely for octaves having the means of frequency range at 125 Hz and 250 Hz. The sound intensity is highest in the octave of 125 Hz, and the highest values of 110 dB(A) are found in the crankshaft's rotating area.
The range of the highest sound intensity spreads to the right-hand side. Since the flywheel is on that side, it may be supposed that the strokes in the bearings are amplified because of the increased mass. The intensity is higher in the area of the extended part of the sump. It can be concluded that these are the sound waves generated by the stroke, which penetrated through the engine sump's walls.
4 CONCLUSION
Veliko različnih preizkusov in analiz v zvezi s
strukturnim hrupom IMR S54 dizelskega motorja
ponuja naslednje ugotovitve:
1.   Stopnja mehanskega hrupa je blizu stopnji
celotnega hrupa motorja pri polni obremenitvi.
Our experiments and analyses concerning the structural noise of the IMR S54 diesel engine suggest the following:
1.  The level of mechanical noise is close to the total noise level of the engine under full-load
Sl. 4. Zvočni obrisi v vsiljenem delu spektra hrupa: a) oktava s srednjo frekvenco 125 Hz,
b) oktava s srednjo frekvenco 250 Hz
Fig. 4. Sound maps in the forced part of noise spectrum: a) octave with the mean frequency of 125 Hz,
b) octave with the mean frequency of 250 Hz
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Na razdalji 1 m, pri 4200 vrt/min je splošna stopnja mehanskega hrupa 104 dB(A), stopnja obremenjenega motorja med zgorevalnim postopkom pa je 105 dB(A). To kaže, da je delež mehanskega hrupa v celotnem hrupu pomemben. Če se poveča zračnost, se mehanska stopnja hrupa znatno poveča.
2.   Spekter mehanskega hrupa je razdeljen v del z vsiljenimi frekvencami (sunki) in del z lastnimi frekvencami delov motorja. Najvišja stopnja vsiljenega dela spektra je na oktavi s srednjo vrednostjo 125 Hz. Frekvenca najvišje stopnje hrupa se približno ujema s frekvenco sunkov v zračnosti glavnega ležaja.
3.   Za vse oktave v spektru je narejena porazdelitev zvoka po metodi zvočne jakosti. Te kažejo, da največja jakost hrupa prodira skozi območje kolenaste gredi. V tem območju se udarci dogajajo v zračnosti ležajev. V tem delu je togost stene najmanjša, zato se pojavijo ojačana lastna nihanja. Tam je zračni prostor v notranjem delu motorja. V tem prostoru se zračni hrup poveča in prehaja skozi sorazmerno tanke stene.
conditions. At a distance of 1 m, at 4200 rpm, the general level of mechanical noise is 104 dB(A), and that of the loaded engine during the combustion process is 105 dB(A). This suggests that the share of mechanical noise in the total noise is significant. When the clearances are increased, the mechanical noise level can increase considerably.
2.   The spectrum of the mechanical noise is divided into the part with forced frequencies (strokes) and the part with the engine parts' natural frequencies. The highest level is in the forced part of the spectra, for the octave with a medium frequency of 125Hz. The frequency of the highest noise level approximately coincides with the frequency of the strokes in the main-bearing clearances.
3.   For all octaves in the spectrum, sound maps are made using the sound-intensity method. They show that the highest noise-intensity penetrates from the crankshaft area. In this area, the impacts occur in the bearing clearances. In this area the wall stiffness is the lowest, and amplified individual vibrations occur. There is an air gap in the internal area of the engine. In this space, the air noise increases and passes through relatively thin walls.
4 LITERATURA 4 REFERENCES
[1] P. Petrovič (1996) Research on Diesel engine structural noise generation process, Dissertation, Faculty of
Mechanical Engineering, University of Belgrade, Yugoslavia. [2] M. Ognjanovič (1994) Wave energy movement in mechanical systems and vibration and noise emission,
Journal of Machine vibration, Vol. 3, No 1, 1994, pp 40-48. [3] P. Petrovič, M. Ognjanovič, S. Jankovič (1997) Research of generation of noise of Diesel engine components,
Inter-noise 97, August 1997, Budapest, Vol. 1, pp 231-234. [4] P. Petrovič, M. Ognjanovič (1997) Effect of nature of elastic disturbances on modal responses of Diesel
engine parts, International symposium Machines and mechanisms - ISMM 97, Faculty of Mechanical
Engineering, University of Belgrade, Yugoslavia, pp 239-296. [5] P. Petrovič, S. Jankovič   (1998) Experimental determination of dynamic disturbances of Diesel engine
structure, 31st ISATA, June 1998, Düsseldorf Germany, pp 381-386. [6] P. Petrovič (1996) Analysis of structural noise of Diesel engines by applying experimental modal analysis
and sound intensity, International Journal for Vehicle Mechanic Engines and Transportation systems,
Mobility & Vehicle Mechanics, Vol. 22 , No. 1,2, 1996. [7] Lj. Markovič, P. Petrovič (2005) Toxic parameters of unregulated Diesel-engine emission, 7th Conference
and exhibition- IAT 05, Innovative Automotive Technology, 21-22. April 2005, Bled, Slovenia. [8] A. Dowing (1989) Acoustically coupled combustion instabilities, Proceedings of the 13th International
Congress on Acoustics, Belgrade 1989, pp 91-106. [9] P. Petrovič, S. Jankovič, M. Ognjanovič (2000) Application of experimental modal analysis and sound
intensity in determining Diesel-engine noise emission,ISATA 2000, September 25-27 Dublin, Ireland.
Uporaba zvočne jakosti - The Application of a Sound-Intensity Analysis
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Avtorjev naslov:   dr. Petrovič Predrag
Institute “Kirilo Savič” Vojvode Stepe 51 11000 Beograd, Srbija mpm@eunet.yu
Author’s Address: Dr. Petrovič Predrag Institut “Kirilo Savič” Vojvode Stepe 51 11000 Belgrade, Serbia mpm@eunet.yu
Prejeto: Received:
23.5.2005
Sprejeto: Accepted:
23.2.2006
Odprto za diskusijo: 1 leto Open for discussion: 1 year
148
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 149-150 Poročila - Reports
Poročila - Reports
IFToMM - Mednarodna federacija za promocijo znanosti o mehanizmih in strojih -The International Federation for the Promotion of Mechanism and Machine Science
V Sloveniji deluje sekcija mednarodne organizacije IFToMM že od leta 1995 in namen
prispevka je predstavitev, prikaz organizacije    in    delovanje        IFToMM
IFToMM-a in možnosti za povezovanje ter objavljanje slovenskih raziskovalcev na srečanjih IFToMM po vsem svetu.
Dejavnost IFToMM je definirana s statutom [http://130.15.85.212/indexa.html]. Najširše jo opišemo kot znanost o mehanizmih in strojih s poudarkom na teoriji in praksi na področju oblike, gibanja, dinamike ter vodenja strojev, mehanizmov in njihovih elementov skupaj z industrijsko uporabo. Dejavnost IFToMM-a se razširja tudi na druga področja kot so: biomehanika in področja povezana z okoljskimi problemi. V polje obravnave sodijo tudi premene energij in informacij.
Prvi svetovni kongres o temi mehanizmov in strojev je bil septembra 1965 v Varni v Bolgariji. Bolgarska delegacija je v okviru kongresa predlagala ustanovitev IFToMM-a, the International Federation for the Theory of Machines and Mechanisms. Zamisel so sprejeli delegati na kongresu in tako je bi ustanovljen mednarodni koordinacijski komite za stroje in mehanizme z zastopniki iz dvajsetih držav.
Rezultat štiriletnega dela komiteja je bila ustanovna skupščina 27. septembra 1969 v Zakopanih na Poljskem v času drugega svetovnega kongresa za teorijo strojev in mehanizmov. Na tem srečanju je bila ustanovljena mednarodna federacija za teorijo strojev in mehanizmov ter sprejet statut organizacije.
Na ustanovni skupščini so bili navzoči zastopniki iz držav: Avstralije, Avstrije, Bolgarije, Čehoslovaške, Vzhodne Nemčije, Zvezne republike Nemčije, Madžarske, Indije, Italije, Nizozemske, Norveške, Poljske, Romunije, Velike Britanije, ZDA, ZSSR in Jugoslavije. Do leta 2003 ima IFToMM petinštirideset članic iz držav vsega sveta.
V obdobju od 1996 do 1999 je bila izvedena prenova vloge IFToMM-a glede na razvoj informacijske tehnologije. Prenova še traja, vendar je vidnih že nekaj rezultatov te prenove. Eden od predlogov se je navezoval na ime federacije.
Generalna skupščina je podprla spremembo izvirnega imena IFToMM in tako je od leta 2000 ime federacije IFToMM, the International Federation for the Promotion of Mechanism and Machine Science.
Trenutno v IFToMM deluje pet stalnih komisij za:
-  povezovanje - komunikacijo,
-  izobraževanje,
-  zgodovino znanosti o mehanizmih in strojih,
-  publikacije in
-  standardizacijo in terminologijo.
Ob stalnih komisijah je še trinajst tehničnih komitejev za:
-  računalniško kinematiko,
-  ozobja,
-  sisteme človek - stroj,
-  ročične in sledne mehanizme,
-  mehatroniko,
-  mikromehaniko,
-  dinamiko večmasnih sistemov,
-  nelinearna nihanja,
-  zanesljivost,
-  robotiko,
-  dinamiko rotorjev,
-  transportne mehanizme in
-  tribologijo.
IFToMM je organizator in soorganizator mnogih znanstvenih srečanj. Termini in seznami so sprotno objavljeni na spletni strani IFToMM-a. Izdaja ali pa soizdaja tudi štiri strokovne revije:
-  Mechanism and Machine Theory (http://www. elsevier.com/wps/find/journaldescription. cws_home/303/description#description),
-  Problems of Mechanics (http://pam.edu.ge/),
-  Journal of Gearing and Transmission (http:// sjf.stuba.sk/NEWDV/Journals/GAT.htm) in
-  Electronic Journal of Computational Kinematics (http://www-sop.inria.fr/coprin/EJCK/EJCK.html).
Najpomembnejši za vse člane IFToMM-a in raziskovalce, ki se ukvarjajo s teorijo strojev in mehanizmov, je vsekakor svetovni kongres, ki poteka vsaka štiri leta v eni od držav članic IFToMM-a.
Od prvega ustanovnega kongresa v Varni v Bolgariji leta 1965 so bili svetovni kongresi še v Zakopanih na Poljskem leta 1969, Kuparih v

149
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Jugoslaviji leta 1971, Newcastlu v Veliki Britaniji leta 1975, Montrealu v Kanadi leta 1979, New Delhiju v Indiji leta 1983, Sevilli v Španiji leta 1987, Pragi na Češkem leta 1991, Milanu v Italiji leta 1995, Oulu na Finskem leta 1999 in zadnji na Kitajskem v mestu Tianjin leta 2004.
Slovenski nacionalni komite je leta 1994 ustanovil prof. dr. Igor Janežič s Fakultete za strojništvo v Ljubljani.
Slovenija je postala polnopravna članica IFToMM leta 1995 v Milanu. Pred tem pa so slovenski raziskovalci in strokovnjaki sodelovali s svojimi prispevki preko Jugoslovanskega nacionalnega komiteja. Slovenski nacionalni komite je do junija 2004 vodil izr.prof.dr. Igor Janežič s Fakultete za strojništvo v Ljubljani. Od junija 2004 naprej za dobo štirih let pa slovenski nacionalni
komite vodi prof. dr. Karl Gotlih s Fakultete za strojništvo v Mariboru. V prvem obdobju se je delovanje slovenskega nacionalnega komiteja osredotočilo na priprave na udeležbo na svetovnem kongresu IFToMM. Slovenski delegati so bili navzoči skoraj na vseh kongresih in ob dejstvu, da se prispevki za kongres izbirajo po strogem postopku, je to za slovensko znanost na področju mehanizmov in strojev velik uspeh.
Naslednja svetovna konferenca IFToMM bo letos v Franciji v kraju Besançon. Razpisni postopek za prispevke na konferenci je že končan, vse informacije o svetovnem kongresu so na spletni strani kongresa: http://www.iftomm2007.com/.
prof.dr. Kari Gotlih prof.dr. Igor Janežič
150
Poročila - Reports
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 151-153 Strokovna literatura - Professional Literature
Strokovna literatura - Professional Literature
Iz revij - From Journals
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temperature daljnovodnih vodnikov Čretnik J., Gumprecht F.: In situ meritvi deležev kisika
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Valh D., Bratina B., Tovornik B.: Sprotno odkrivanje
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Slovenska znanost in industrija se povezujeta -Posvet o naprednih materialih 2006 na Institutu "Jožef Stefan"
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Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 151-153
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Kozmar H., Džijan L, Šavar M.: Jednolikost modela atmosferskoga graniČnoga sloja u zračnom tunelu
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2006,  3-4
Bijedič M., Durakovič H.: Dynamic model of the process of contact and convective paper drying
Raos P., Lucie M., Lesina P.: Ispitivanje propustnosti zavarenih spojeva na polipropilenskim cijevima za toplu i hladno vodu
ThyssenKrupp Techforum, Düsseldorf 2006, 1
Tamler H.W., Becker J.-U., Wunderlich R, Friedrich K.E, Rademacher P: TriBond® - hot-rolled clad strip customized steel composite material from coil
Lehmann U.: Environmentally sustainable recycling of acids for pickling of stainless steel
Klukowski C, Meier R.: Adaptive linear crash systems - intelligent materials for passenger car steering columns
Transactions of FAMENA, Zagreb 2006, 1
Turkalj G., Čehič Z., Brnič J.: A beam model for the buckling analysis of curved beam-type structures considering curvature effects
Alfirevič I., Skozrit I.: Linear, quadratic and cubic invariants of orthotopic elastic materials
Gruen F., Gódor L, Eichlseder W.: Tribological test engineering - comparison of component tests of sliding bearings with tribological model tests
2006, 2
Jasak H., Tukovič Ž.: Automatic mesh motion for the
unstructured finite volume method Pavazza R., Jovič S.: A comparison of approximate
analytical methods and the finite element
method in the analysis of short thin-walled
beams subjected to bending by couples KranjčevičL., Družeta S.,Čarija Z.: A balanced implicit
numerical scheme for one-dimensional open
channel flow equations Bijedič M., Neimarlija N.: Thermodynamic properties
of argon and xenon derived from the speed
of sound
Strokovna literatura - Professional Literature
153
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 154 Osebne vesti - Personal Events
Osebne vesti - Personal Events
Doktorat in diplome - Doctor’s and Diploma Degrees
DOKTORAT
Na Fakulteti za strojništvo Univerze v Mariboru je z uspehom zagovarjal svojo doktorsko disertacijo:
dne 16. januarja 2007: mag. Martin Volmajer, z naslovom: "Modeliranje dvofaznih tokov v vbrizgalni šobi" (mentorica: prof. dr. Breda Kegl).
S tem je navedeni kandidat dosegel akademsko stopnjo doktorja znanosti.
DIPLOMIRALI SO
Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva:
dne 1. februarja 2007: Blaž KLUN, Andraž REKELJ, Dejan ŠTRUS.
Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva:
dne 25. januarja 2007: Matjaž FRANC, David KOLAR, Andrej KOPUŠ AR.
*
Na Fakulteti za strojništvo Univerze v Ljubljani sta pridobila naziv diplomirani inženir strojništva:
dne 11. januarja 2007: Boštjan BARTOLJ, Marko NOVAKOVIČ.
Na Fakulteti za strojništvo Univerze v Mariboru je pridobil naziv diplomirani inženir strojništva:
dne 25. januarja 2007: Jože TIHEL.
154

Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 155-156 Navodila avtorjem - Instructions for Authors
Navodila avtorjem - Instructions for Authors
Članki morajo vsebovati:
-   naslov, povzetek, besedilo članka in podnaslove slik v slovenskem in angleškem jeziku,
-   dvojezične preglednice in slike (diagrami, risbe ali fotografije),
-   seznam literature in
-   podatke o avtorjih.
Strojniški vestnik izhaja od leta 1992 v dveh jezikih, tj. v slovenščini in angleščini, zato je obvezen prevod v angleščino. Obe besedili morata biti strokovno in jezikovno med seboj usklajeni. Članki naj bodo kratki in naj obsegajo približno 8 strani. Izjemoma so strokovni članki, na željo avtorja, lahko tudi samo v slovenščini, vsebovati pa morajo angleški povzetek.
Za članke iz tujine (v primeru, da so vsi avtorji tujci) morajo prevod v slovenščino priskrbeti avtorji. Prevajanje lahko proti plačilu organizira uredništvo. Če je članek ocenjen kot znanstveni, je lahko objavljen tudi samo v angleščini s slovenskim povzetkom, ki ga pripravi uredništvo.
Članek naj bo napisan v naslednji obliki:
-   Naslov, ki primerno opisuje vsebino članka.
-   Povzetek, ki naj bo skrajšana oblika članka in naj ne presega 250 besed. Povzetek mora vsebovati osnove jedro in cilje raziskave, uporabljeno metodologijo dela,povzetek rezulatov in osnovne sklepe.
-   Uvod, v katerem naj bo pregled novej šega stanja in zadostne informacije za razumevanje ter pregled rezultatov dela, predstavljenih v članku.
-   Teorija.
-   Eksperimentalni del, ki naj vsebuje podatke o postavitvi preskusa in metode, uporabljene pri pridobitvi rezultatov.
-   Rezultati, ki naj bodo jasno prikazani, po potrebi v obliki slik in preglednic.
-   Razprava, v kateri naj bodo prikazane povezave in posplošitve, uporabljene za pridobitev rezultatov. Prikazana naj bo tudi pomembnost rezultatov in primerjava s poprej objavljenimi deli. (Zaradi narave posameznih raziskav so lahko rezultati in razprava, za jasnost in preprostejše bralčevo razumevanje, združeni v eno poglavje.)
-   Sklepi, v katerih naj bo prikazan en ali več sklepov, ki izhajajo iz rezultatov in razprave.
-   Literatura, ki mora biti v besedilu oštevilčena zaporedno in označena z oglatimi oklepaji [1] ter na koncu članka zbrana v seznamu literature. Vse opombe naj bodo označene z uporabo dvignjene številke1.
Besedilo članka naj bo pripravljeno v urejevalnilku Microsoft Word. Članek nam dostavite v elektronski obliki.
Ne uporabljajte urejevalnika LaTeX, saj program, s katerim pripravljamo Strojniški vestnik, ne uporablja njegovega formata.
Enačbe naj bodo v besedilu postavljene v ločene vrstice in na desnem robu označene s tekočo številko v okroglih oklepajih
Papers submitted for publication should comprise:
-   Title, Abstract, Main Body of Text and Figure Captions in Slovene and English,
-   Bilingual Tables and Figures (graphs, drawings or photographs),
-   List of references and
-   Information about the authors.
Since 1992, the Journal of Mechanical Engineering has been published bilingually, in Slovenian and English. The two texts must be compatible both in terms of technical content and language. Papers should be as short as possible and should on average comprise 8 pages. In exceptional cases, at the request of the authors, speciality papers may be written only in Slovene, but must include an English abstract.
For papers from abroad (in case that none of authors is Slovene) authors should provide Slovenian translation. Translation could be organised by editorial, but the authors have to pay for it. If the paper is reviewed as scientific, it can be published only in English language with Slovenian abstract, that is prepared by the editorial board.
The paper should be written in the following format:
-   A Title, which adequately describes the content of the paper.
-   An Abstract, which should be viewed as a mini version of the paper and should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, the methodology employed, summarize the results and state the principal conclusions.
-   An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the paper to be understood and evaluated.
-   A Theory
-   An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results.
-   A Results section, which should clearly and concisely present the data using figures and tables where appropriate.
-   A Discussion section, which should describe the relationships and generalisations shown by the results and discuss the significance of the results making comparisons with previously published work. (Because of the nature of some studies it may be appropriate to combine the Results and Discussion sections into a single section to improve the clarity and make it easier for the reader.)
-   Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion.
-   References, which must be numbered consecutively in the text using square brackets [1] and collected together in a reference list at the end of the paper. Any footnotes should be indicated by the use of a superscript1.
Texts should be written in Microsoft Word format. Paper must be submitted in electronic version.
Do not use a LaTeX text editor, since this is not compatible with the publishing procedure of the Journal of Mechanical Engineering.
Equations should be on a separate line in the main body of the text and marked on the right-hand side of the page with numbers in round brackets.
VSEBINA ČLANKA                                                           THE FORMAT OF THE PAPER
OBLIKACLANKA                                                              THE LAYOUT OF THE TEXT

155
Strojniški vestnik - Journal of Mechanical Engineering 53(2007)2, 155-156
Enote in okrajšave
V besedilu, preglednicah in slikah uporabljajte le standardne označbe in okraj save SI. Simbole fizikalnih veličin v besedilu pišite poševno (kurzivno), (npr. v, T, n itn.). Simbole enot, ki sestojijo iz črk, pa pokončno (npr. ms1, K, min, mm itn.).
Vse okrajšave naj bodo, ko se prvič pojavijo, napisane v celoti v slovenskem jeziku, npr. časovno spremenljiva geometrija (ČSG).
Slike
Slike morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot si. 1, si. 2 itn. Posnete naj bodo v ločljivosti, primerni za tisk, v kateremkoli od razširjenih formatov, npr. BMP, JPG, GIF. Diagrami in risbe morajo biti pripravljeni v vektorskem formatu, npr. CDR, Al.
Pri označevanju osi v diagramih, kadar je le mogoče, uporabite označbe veličin (npr. t, v, m itn.), da ni potrebno dvojezično označevanje. V diagramih z več krivuljami, mora biti vsaka krivulja označena. Pomen oznake mora biti pojasnjen v podnapisu slike.
Vse označbe na slikah morajo biti dvojezične.
Preglednice
Preglednice morajo biti zaporedno oštevilčene in označene, v besedilu in podnaslovu, kot preglednica 1, preglednica 2 itn. V preglednicah ne uporabljajte izpisanih imen veličin, ampak samo ustrezne simbole, da se izognemo dvojezični podvojitvi imen. K fizikalnim veličinam, npr. t (pisano poševno), pripišite enote (pisano pokončno) v novo vrsto brez oklepajev.
Vsi podnaslovi preglednic morajo biti dvojezični.
Seznam literature
Vsa literatura mora biti navedena v seznamu na koncu članka v prikazani obliki po vrsti za revije, zbornike in knjige: [1] A. Wagner, I. Bajsič, M. Fajdiga (2004) Measurement of
the surface-temperature field in a fog lamp using
resistance-based temperature detectors, Stroj. vestn.
2(2004), pp. 72-79. [2] Vesenjak, M., Ren Z. (2003) Dinamična simulacija
deformiranja cestne varnostne ograje pri naletu vozila.
Kuhljevi dnevi ’03, Zreče, 25.-26. september 2003. [3] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente
- Tabellen, 16. Auflage. Vieweg Verlag, Wiesbaden.
SPREJEM ČLANKOV IN AVTORSKE PRAVICE
Uredništvo Strojniškega vestnika si pridržuje pravico do odločanja o sprejemu članka za objavo, strokovno oceno recenzentov in morebitnem predlogu za krajšanje ali izpopolnitev ter terminološke in jezikovne korekture.
Avtor mora predložiti pisno izjavo, da je besedilo njegovo izvirno delo in ni bilo v dani obliki še nikjer objavljeno. Z objavo preidejo avtorske pravice na Strojniški vestnik. Pri morebitnih kasnejših objavah mora biti SV naveden kot vir.
PLAČILO OBJAVE
Avtorji vseh prispevkov morajo za objavo plačati prispevek v višini 20,00 EUR na stiskano stran prispevka. Prispevek se zaračuna po sprejemu članka za objavo na seji Uredniškega odbora.
156
Units and abbreviations
Only standard SI symbols and abbreviations should be used in the text, tables and figures. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms1, K, min, mm, etc.).
All abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG).
Figures
Figures must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF, JPG. However, graphs and line drawings sholud be prepared as vector images, e.g. CDR, AI.
When labelling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimise the need to label the axes in two languages. Multi-curve graphs should have individual curves marked with a symbol, the meaning of the symbol should be explained in the figure caption.
All figure captions must be bilingual.
Tables
Tables must be cited in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. The use of names for quantities in tables should be avoided if possible: corresponding symbols are preferred to minimise the need to use both Slovenian and English names. In addition to the physical quantity, e.g. t (in italics), units (normal text), should be added in new line without brackets.
All table captions must be bilingual.
The list of references
References should be collected at the end of the paper in &e Mowing styles for journals, proceedings and books, respectively: [1] A. Wagner, I. Bajsič, M. Fajdiga (2004) Measurement of
the surface-temperature field in a fog lamp using
resistance-based temperature detectors, Stroj. vestn.
2(2004), pp. 72-79. [2] Vesenjak, M., Ren Z. (2003) Dinamična simulacija
deformiranja cestne varnostne ograje pri naletu vozila.
Kuhljevi dnevi ’03, Zreče, 25.-26. september 2003. [3] Muhs, D. et al. (2003) Roloff/Matek Maschinenelemente
- Tabellen, 16. Auflage. Vieweg Verlag, Wiesbaden.
ACCEPTANCE OF PAPERS AND COPYRIGHT
The Editorial Committee of the Journal of Mechanical Engineering reserves the right to decide whether a paper is acceptable for publication, obtain professional reviews for submitted papers, and if necessary, require changes to the content, length or language.
Authors must also enclose a written statement that the paper is original unpublished work, and not under consideration for publication elsewhere. On publication, copyright for the paper shall pass to the Journal of Mechanical Engineering. The JME must be stated as a source in all later publications.
PUBLICATION FEE
For all papers authors will be asked to pay a publication fee prior to the paper appearing in the journal. However, this fee only needs to be paid after the paper is accepted by the Editorial Board. The fee is €20.00 per printed paper page.