let. - vol. 47 C2001D št. - no. "7 STROJNIŠKI VESTNIK JOURNAL OF MECHANICAL ENGINEERING Iptimizacijski postopek v procesu zasnove zobnikov Optimisation Feature in Gear Design Procedure Model in simuliranje delovanja odprtega hladilnega postopka brez uporabe CFC Design and Simulation of a CFC-Free Open Air-Conditioning System Analiza delovnega postopka pri praktičnem pouku s poudarkom na projektni nalogi An Analysis of the Working Process in Practical Classes with the Accent on the Project Task Toplotne izgube v tla pri stavbah glede na standard SIST EN ISO 1 33"70 - poenostavljena metoda izračuna Heat Losses to the Ground According to the SIST EN ISO 1 33~7D Standard - a Simplified Calculation Method 0000020059576 © Strojni{ki vestnik 47(2001)7,285 Mese~nik ISSN 0039-2480 © Journal of Mechanical Engineering 47(2001)7,285 Published monthly ISSN 0039-2480 Vsebina Contents Strojni{ki vestnik - Journal of Mechanical Engineering letnik - volume 47, (2001), {tevilka - number 7 Razprave Ulaga, S., Flašker, J., Zafošnik, B., Ciglarič, I.: Optimizacijski postopek v procesu zasnove zobnikov 286 Stritih, U., Može, M., Novak, P.: Model in simuliranje delovanja odprtega hladilnega postopka brez uporabe CFC 300 Fošnarič, S.: Analiza delovnega postopka pri praktičnem pouku s poudarkom na projektni nalogi 313 Černe, B., Medved, S.: Toplotne izgube v tla pri stavbah glede na standard SIST EN ISO 13370 - poenostavljena metoda izračuna 325 Strokovna literatura 336 Osebne vesti 337 Navodila avtorjem 339 Papers Ulaga, S., Flašker, J., Zafošnik, B., Ciglarič, I.: Optimisation Feature in Gear Design Procedure Stritih, U., Može, M., Novak, P.: Design and Simulation of a CFC-Free Open Air-Conditioning System Fošnarič, S.: An Analysis of the Working Process in Practical Classes with the Accent on the Project Task Černe, B., Medved, S.: Heat Losses to the Ground According to the SIST EN ISO 13370 Standard - a Simplified Calculation Method Professional Literature Personal Events Instructions for Authors stran 285 glTMDDC © Strojni{ki vestnik 47(2001)7,286-299 © Journal of Mechanical Engineering 47(2001)7,286-299 ISSN 0039-2480 ISSN 0039-2480 UDK 621.833:531.43/539.62:519.61/.64 UDC 621.833:531.43/539.62:519.61/.64 Izvirni znanstveni ~lanek (1.01) Original scientific paper (1.01) Optimizacijski postopek v procesu zasnove zobnikov Optimisation Feature in Gear Design Procedure Samo Ulaga - Jo`e Fla{ker - Bo{tjan Zafo{nik - Iztok Ciglari~ V prispevku je opisano orodje za optimiranje geometrijske oblike zob kot dodatek k splošnim postopkom zasnove zobnikov. Algoritem omogoča zmanjšanje in enakomerno porazdelitev obrabe in jamičenja zob v ubiru. V postopku optimiranja upoštevamo dva glavna parametra, ki sta odvisna od geometrijske oblike zob: kontaktne napetosti in relativno drsenje. Oba sta odvisna od oblike kontaktne površine, ki pa je v veliki meri odvisna od koeficientov premikov profila. Če želimo doseči čim večjo življenjsko dobo zobnikov, moramo poiskati optimalne vrednosti koeficientov premikov profila, z upoštevanjem vseh preostalih robnih pogojev, ki so predpisani za zasnovo zobnikov. Uporabljen je algoritem adaptivnega izboljšanja mreže. V nadaljevanju prispevka je preverjena oblika zob, dobljena po predlaganem postopku. Prav tako so primerjane in ocenjene drsne razmere za obe obliki zob. Prikazana je možnost uporabe MKE v postopku snovanja zobnikov. Za izračun kontaktnih napetosti je uporabljen algoritem z metodo Lagrangeovih množiteljev po metodi končnih elementov, kontaktne površine pa so dodatno opisane s parametričnimi zlepki. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: zasnove zobnikov, dresenje relativno, optimiranje, problemi kontaktni) In this paper a tooth-geometry optimisation feature is proposed, which is to be added to the general gear-design procedure, so as to provide reduced and equally distributed wear and pitting of mating gear-teeth flanks. Two principal geometry-dependent parameters are considered for the optimisation purposes: contact stress and relative sliding. Both depend on the geometry of the contacting surfaces, which is mainly influenced by the addendum modification coefficient. To maximise the service life of the gear pair, optimum values of this coefficient have to be chosen, in order to satisfy prescribed criteria for specific sliding and Hertz pressure while all the design boundary conditions are fulfilled. An adaptive-grid-refinement algorithm procedure is applied and the gear-flank geometry resulting from the optimisation algorithm is subsequently analysed. The sliding circumstances are compared and evaluated. A FEM contact algorithm using the Lagrange multiplier method and a spline-based geometry definition is applied to calculate the contact stress distribution patterns and to show the applicability of the computational methods to the general gear design. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: gear design, relative sliding, optimization, contact problems) 0 UVOD Kontakt dveh zobnih bokov v ubiru je mogoče obravnavati kot neprilegajoč kotalno-drsni kontakt s trenjem [1], kakor je prikazano na sliki 1. Kotaljenje je vir normalnih napetosti v zobu, drsenje s trenjem pa povzroča strižne napetosti. Če je prekoračena trdnost materiala, se lahko pojavijo poškodbe površine zoba, kar ima za posledico skrajšanje dobe trajanja ali celo zlom zoba. Relativno drsenje se med ubiranjem zobnih bokov (sl. 1), pojavi kot posledica naslednjega: zaradi kotaljenja prideta točki P1 in P2 v kontakt v točki A - začetek ubiranja, medtem 0 INTRODUCTION The contact of two mating teeth flanks can be described as a non-conforming, rolling-sliding contact with friction, [1], as shown in Figure 1. Due to the rolling, the gears are subject to normal stresses, while the frictional sliding produces shear stresses. Exceeding the material’s stiffness can result in damage to the contacting surfaces, and as a result, the service life of the gear pair may be seriously affected or, in the extreme case, the material could fail. During the mating process, adjacent gear-tooth flanks are subject to relative sliding (Fig. 1) for the following reasons: the rolling of the mating gears, points P1 and P2 are brought into contact at point A VH^tTPsDDIK stran 286 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature Gnan zobnik Driven gear a1 P1. A^B P1' Xv Ubirnica Contact line Pogonski zobnik Driving gear Sl. 1. Kotalno-drsni kontakt zobnikov Fig. 1. Rolling-sliding contact of gears ko prideta točki P1’ in P’ v kontakt v točki B na ubirnici. Posledično bo del zobnega boka 1 v kontaktu z delom protiboka l2. Zaradi različnih dolžin se pojavi relativno drsenje, zaradi česar se obrabi krajši del zobnega boka v kontaktu. V uporabi so metode za analizo razmer med ubiranjem. Najbolj so razširjene različne metode, ki jih predlagajo standardi (DIN, ISO, AGMA). V prispevku je predlagan algoritem za optimiranje obrabe zobnih bokov kot dodatek k postopku zasnove zobnikov, ki ga predlaga standard DIN3990 [2]. V standardnih metodah običajno najprej izberemo parametre, kakor so modul, medosna razdalja in število zob, ki določajo ustrezno vsoto koeficientov premikov profilov (PP) po ISO112/1 [3]. Izračunana vsota je nato porazdeljena med zobnik in pastorek, kakor to predlaga DIN3992 [4]. Na ta način dosežemo navidezno sorazmerno upogibno nosilnost zob, drsne hitrosti in relativno drsenje. Fazi določanja geometrijske oblike zob sledi natančna določitev nosilnosti. Izračunane vrednosti napetosti nato primerjamo z dovoljenimi vrednostmi za izbran material pastorka in zobnika. V prispevku je, z namenom zmanjšati obrabo in jamičenje zobnih bokov, običajnemu postopku dodan algoritem za optimiranje oblike zobnih bokov (sl. 2). Obravnavana je soodvisnost PP, relativnega drsenja in Hertz-ovega tlaka v primeru evolventne valjaste zobniške dvojice. Definiran je nelinearen problem, z namenom poiskati najboljšo rešitev glede optimalne porazdelitve PP za izbrano zobniško dvojico. Definicija omogoča minimizacijo in optimalno porazdelitev relativnega drsenja glave in korena ISO112/1 [3] zob v ubiranju in posledično zmanjšanje obrabe. Upoštevani so običajni robni pogoji, ki veljajo pri običajnih postopkih zasnove zobnikov: normalne in — the beginning of engagement; while points P1’ and P2’ come into contact with each other at the engagement point B. Consequently, a flank section l1 will be in contact with contacting the adjacent flank section l2. Due to a difference in their lengths, relative sliding occurs, causing increased wear of the shorter section of the mating flanks. Different methods are available to analyse the contact circumstances during gear meshing, methods suggested by different standards (DIN, ISO, AGMA) are widely used. In this paper a general gear- design procedure, suggested by the DIN3990 standard [2], is examined and some wear optimisation features are suggested. When using the standardised procedure, gear-pair parameters such as module, centre distance and number of teeth are initially defined, and then the accompanying sum of the addendum modification coefficients (AMC), as defined in ISO112/1 [3], is calculated. Its distribution between the pinion and the gear is suggested by DIN3992 [4]. Following the above recommendation, pseudo-proportional bending-load capacity, sliding velocity and relative sliding are assured. The exact bending- and contact-load capacity evaluation follows the geometry definition phase. The calculated values are compared with the allowed values for the pinion and gear material. In the present paper, a gear-teeth-geometry optimisation algorithm is added to the above gear-design procedure in order to reduce the abrasion wear and pitting of mating gear-teeth flanks (Figure 2). The interdependency of the AMC, the specific sliding and the Hertz pressure is analysed for the case of an involute cylindrical gear pair. A non-linear programming problem is defined in order to find the best solution by means of the optimum AMC distribution values for the selected gear pair. This definition enables minimisation and equal distribution of the relative sliding for the addendum and dedendum flank ISO112/1 [3] of the mating gear teeth, and as a result, minimises the wear of the gear pair. Normal and bending stresses are constrained to gfin^OtJJlMISCSD 01-7 stran 287 |^BSSITIMIGC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature z1 = 16 mn= 4,5 mm a = 91,5 mm z2 = 24 x1+x2 = 0,353 b = 14 mm Običajen postopek Standard procedure Verifikacija(MKE) Verification (FEM) Sl. 2. Način reševanja Fig. 2. Solution approach upogibne napetosti znotraj dovoljenih vrednosti, prav tako tudi debelina zoba, stopnja ubiranja in spodrezanje. Optimalna rešitev je določena z uporabo globalnih metod optimiranja. Napetosti, izračunane z običajnim postopkom so primerjane z vrednostmi, dobljenimi po metodi končnih elementov (MKE). 1 TEORETIČNE OSNOVE 1.1 Drsenje Kakor je navedeno v različni strokovni literaturi [5], se pojavi relativno drsenje v kontaktnih točkah vzdolž ubirnice zaradi različne dolžine kontaktnih površin vrha in korena zob v ubiranju. Od kinematskega pola C, kjer se drsenje teoretično ne pojavlja, se razlika obodnih hitrosti vT1 in vT2 v kontaktnih točkah veča proti zunanjim točkam ubiranja A in E (sl. 3). Relativno drsenje pomeni razmerje med relativno obodno hitrostjo zobnih bokov v ubiranju in obodno hitrostjo določenega zobnega boka: V1 remain within the prescribed values, and other design criteria such as gear-tooth thickness, contact ratio and tooth interference are also considered. An optimum distribution is found using global optimisation methods. Stresses calculated by conventional methods are compared to the numerical solution obtained by the finite-element method (FEM). 1 THEORETICAL BACKGROUND 1.1 Sliding As a consequence of the different lengths of the addendum and the dedendum flanks (Fig. 1), relative sliding occurs in the contact points along the transverse path of contact Niemann et al. [5]. From the pitch point C, where sliding is theoretically zero, the difference between the tangential velocities vT1 and vT2 at the contacting points increases towards the external points of the engagement A and E respectively (Fig. 3). Specific sliding represents the ratio between the relative tangential velocity and the tangential velocity of the particular gear-tooth flank: V2 (1) v izbrani kontaktni točki Y, kakor prikazuje slika 3. V enačbi (1) pomenita vT1 in vT2 obodne hitrosti pastorka in zobnika. Obodno hitrost izračunamo kot: at the particular contacting point Y, as shown in Fig. 3. In (1), vT1 and vT2 are the tangential velocity of the pinion and gear, respectively. The tangential velocity is calculated as: vT1 =w1 N1Y vT2 =w2 N2Y (2), kjer sta w1 in w2 kotni hitrosti, N1Y in N2Y pa sta razdalji med N oziroma N2 in trenutno ubirno točko Y. Specifično drsenje imamo lahko za merilo abrazivne where w1 and w2 are angular velocities and N1Y and N2Y are distances between the engagement point Y and the points N1 and N2, respectively. The specific VBgfFMK stran 288 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature O, Sl. 3. Razmere pri ubiranju Fig. 3. Mating circumstances obrabe [6]. Kot optimalno porazdelitev relativnega drsenja vzdolž kontaktnih površin se šteje stanje, ko je izpolnjen pogoj iz enačbe (3). Takšna porazdelitev, razen na obrabo, ugodno vpliva tudi na hrupnost zobniškega para: sliding may be considered as a measure of the abrasive wear [6]. It is regarded as the optimum distribution of relative sliding along the mating-teeth flanks to reduce their wear when the condition stated in (3) is achieved. It also has a beneficial effect on noise reduction. V =V 1A 2E 1.2 Hertzov tlak V =V 1E 2A 1.2 Hertz pressure (3). V primeru kontakta dveh teles, lahko uporabimo Hertzovo [7] teorijo, kadar so izpolnjeni naslednji pogoji: - kontaktne površine so zvezne in neprilegajoče, - vsako telo v stiku je moč obravnavati kot elastičen polprostor, - majhne deformacije, znotraj linearne teorije elastičnosti, - ni trenja med površinami v kontaktu. Ko so zgornji pogoji izpolnjeni, pričakujemo eliptično porazdelitev napetosti, kakor je prikazana na sliki 4. Kontaktno področje je majhno v primerjavi z velikostjo teles. Napetosti v kontaktnem področju niso bistveno odvisne od oblike telesa daleč stran od področja stika. Za izračun največjih napetosti so na When two bodies are brought into contact and the following restrictions are fulfilled, Hertz [7] theory may be applied: - surfaces are continuous and nonconforming, - each solid can be considered as an elastic half-space, - the strains are small and within the linear range of elasticity, - the surfaces are frictionless. An elliptical distribution of the normal stresses, as shown in Figure 4, is expected. The contact region becomes an area that is small in comparison with the dimensions of the contacting bodies. The stresses in the region of contact are not essentially dependent upon the shape of the contacting bodies away from the contact region. Their maxi- gfin^OtJJlMISCSD 01-7 stran 289 |^BSSITIMIGC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature Sl. 4. Hertzova porazdelitev napetosti Fig. 4. Hertz pressure distribution voljo preprosti izrazi. V primeru, da sta v kontaktu telesi iz različnih materialov, je treba izračunati nadomestni modul elastičnosti: mum value can be calculated using simple formulae. In the case of solids made of two different materials, an equivalent modulus of elasticity has to be defined: E 2 [E E (4). V primeru kontakta dveh zobnih bokov izračunamo največje napetosti kot: When applied to analyse the line-contact circumstances of the mating gear-teeth flanks, the maximum normal stress can be calculated as: s H max E F 0 E F (5), kjer pomenijo: E - Youngov modul, Fb - normalno silo where E isYoung’s modulus, Fb is the normal force na zobni bok, b - širino zob, v - Poissonovo število. on the tooth flank, b represents the face width and v Povprečni polmer ukrivljenosti r v trenutni točki is Poisson’s ratio. The mean radius of curvature, r, at ubiranja Y, izračunamo po enačbi: the engagement point Y, is calculated as: 11 1 Širino konatktnega področja izračunamo kot: rr r 1Y 2Y The width of the contact area is defined as: bH 32(1-v2)FbP TIE b (6). (7). 1.3 Koeficient premika profila Evolventno ozobje je, v nasprotju od cikloidnega, neobčutljivo na spremembo medosne razdalje. Sprememba medosne razdalje povzroči samo spremembo ubirnega kota. Da ohranimo zvezno in enolično prenašanje krožnega gibanja in zagotovimo predpisano obodno ohlapnost, je treba prilagoditi obliko zobnega profila. Slednje dosežemo s t.i. premikom profila. Izraz pomeni premik referenčnega profila orodja med izdelavo ozobja, in sicer za vrednost x . m, kjer m pomeni normalni modul, x pa imenujemo koeficient premika profila (ISO112/1[3]). Za dano zobniško dvojico ob izbrani medosni razdalji in modulu izračunamo ustrezno vsoto PP. Vsaka sprememba PP pomeni spremembo oblike profila zob. Spremenijo se tudi lastnosti zobnikov v ubiru, kakor so prekrivanje zobnih bokov, ukrivljenost 1.3 Addendum modification coefficient Unlike cycloid gear pairs, involute gears are insensitive to changes in centre distance. It only causes an alteration of the pressure angle. To preserve the continuous and uniform transformation of rotary motion, and to retain the prescribed circumferential backlash of the gear teeth, it is necessary to adjust the profile geometry of the teeth. This can be achieved by an addendum modification. It is understood as the tool reference profile shift during the manufacture of the toothed gear by an . amount x m, where m represents a normal module and x is termed the addendum modification coefficient, as defined in ISO112/1 [3]. For the particular gear pair at the prescribed centre distance and module the corresponding pressure angle and the sum of the AMC are calculated. Any variation of the AMC results in a changed tooth profile. It also leads to changed properties of the mating gears, such as: meshing interference, tooth flank radii of VBgfFMK stran 290 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature zobnih bokov, ubirni kot, debelina korena zob, stopnja ubiranja, medosna razdalja, drsne hitrosti, [8]). Porazdelitev vsote PP, kakršno predlagajo različni standardni postopki za zasnovo zobnikov, ni vedno optimalna glede obrabe in jamičenja zobnih bokov. Izbrani koeficienti PP pa odločilno vplivajo na vsaj dva pomembna parametra obrabe zobnikov (sl. 5). Vrednosti največjih normalnih napetosti v kontaktnih točkah vzdolž ubirnice, izračunane po enačbi (5), so neposredno odvisne od polmera ukrivljenosti na mestu dotika, ta pa je funkcija PP. curvature, pressure angle, tooth root thickness, contact ratio, centre distance, sliding velocities, etc. (Beitz et al. [10]). The distribution of the sum of the AMC, as suggested by standardised gear-design procedures is not always optimum with respect to the abrasion wear and pitting of the mating gear flanks. The shape of the gear tooth following from the selected coefficient of the AMC directly influences at least two important parameters of gear wear (Fig. 5). The maximum value of the normal stress at the contact points along the contact line, calculated from (5), directly depends on the curvature of the contacting surfaces, which is the function of the AMC. 0&- 'A b C D E' Sl. 5. Soodvisnost parametrov Fig. 5. Parameter interdependence Razdalje NY, i = 1,2, uporabljene v enačbi (2) so neposredno odvisne od PP. Da bi zmanjšali obrabo, moramo relativno drsenje zmanjšati do najmanjših mogočih vrednosti, medtem ko morajo normalne napetosti ostati znotraj dovoljenih vrednosti. Optimalno porazdelitev PP lahko izračunamo z metodami nelinearnega programiranja. 2 NALOGA MATEMATIČNEGA PROGRAMIRANJA 2.1 Definicija Veliko nalog s področja optimalnega konstruiranja lahko zapišemo v obliki naloge nelinearnega matematičnega programiranja P, kakor je predlagal Arora v delu [9]: The distances NiY, i=1,2 used in (2) directly depend on the AMC. To reduce the wear of the gear pair, relative sliding has to be reduced to the smallest possible level, while normal stresses must remain below the permissible values. The optimum distribution can be calculated using non-linear programming methods. 2 NON-LINEAR PROGRAMMING PROBLEMS 2.1 Definition The optimum design can be formulated in the form of a non-linear programming problem P, as stated by Arora [9], which can generally be written as: min f(x),xeRk (8), in upoštevamo omejitve subject to gfin^OtJJIMISCSD 01-7 stran 291 |^BSSITIMIGC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature fi(x)<0,11,1 (11.1) (11.2) (11.3) (11.4) (11.5) (11.6) (11.7) (11.8) Omejitvi (11.1) in (11.2) zagotavljata, da sta največja normalna in upogibna napetost zob v ubiranju manjši od dovoljenih vrednosti konstrukcijskega materiala. Omejitvi (11.3) in (11.4) preprečujeta prekrivanje aktivnih delov zobnih bokov v ubiranju. Ustrezno debelino vrha zoba [10]: Constraints (11.1) and (11.2) ensure that the maximum calculated normal and bending stresses, respectively, are less than the permissible values for the particular material. Constraints (11.3) and (11.4) prevent interference of the active sections of the tooth flanks from occuring. In order to keep the thickness of the tooth tip greater than the permissible value [10]: grin^(afcflM]SCLD ^BSfiTTMlliC | stran 292 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature 0,4-m (12) zagotavljata omejitvi (11.5) in (11.6), upoštevani v formulacijo naloge. Omejitev (11.7) je upoštevana z namenom, da zagotovimo konstantno vsoto koeficientov profilnega premika in omejitev (11.8) z namenom, da zagotovimo stopnjo profilnega ubiranja manj ko 1,1. Izrazi, uporabljeni v (11), so dobro znani v literaturi [5], ki obravnava konstruiranje zobnikov. 2.2 Rešitev naloge Naloga nelinearnega matematičnega programiranja je rešena z uporabo globalne optimizacijske metode. Uporabljen je algoritem prilagodnega izboljševanja mreže (AGR), ki smo ga uvedli v okolju Mathematica [11]. Algoritem AGR spada med hevristične deterministične metode [12]. Načelo delovanja algoritma AGR je naslednje. Na definicijskem območju, na katerem je rešitev, ustvarimo n začetnih točk na enakih medsebojnih razdaljah (sl. 6) constraints (11.) and (11.6) are applied to our formulation. Finally, constraint (11.7) is imposed in order to ensure that the sum of the AMC is constant, and the constraint (11.8) is to prevent ahe contact ratio of less than 1.1 appearing. Expressions in (11) are well known from the literature dealing with gear design [7]. 2.2 Solution approach The global optimisation method is used in the present work. An Adaptive Grid Refinement (AGR) algorithm within Mathematica [11] is applied. The AGR algorithm is, in essence, a generalised-descent method. These methods are [12] classified as heuristic deterministic methods. They are based on the evolution of the cost function and its change only along certain paths, each considered as a design history as a function of time from starting point to minimum point at the current iteration. The algorithm works as follows. The interval to be searched for a solution is covered by a grid of n initial equi-distant grid points (Fig. 6). Sl. 6. Omreženo področje - simbolično Fig. 6. Symbolic grid domain V vsaki točki izračunamo vrednost namenske funkcije. Točke, v katerih je vrednost namenske funkcije relativno manjša, prenesemo v naslednjo iteracijo, preostale točke pa zavržemo in izločimo iz nadaljnjega postopka. Ob vsaki obdržani točki algoritem ustvari novi točki, ki sta od začetne točke oddaljeni za tretjino začetne razdalje med točkami. Ponovno izračunamo vrednosti namenske funkcije v novih točkah. Iterativni postopek zgoščevanja mreže, določanja vrednosti namenske funkcije in izbire možnih rešitev se ponavlja, dokler niso izpolnjeni podani konvergenčni kriteriji. Vrednost namenske funkcije v točkah se z iteracijami zmanjšuje, in sicer v različnih smereh za več delov definicijskega območja. Enak postopek v splošnem poteka za poljubno število projektnih spremenljivk, vendar se s tem eksponentno poveča tudi število mrežnih vozlišč, kar je povezano z znatnim povečanjem numerične zahtevnosti. Algoritem je nadvse robusten, ne zahteva zveznosti in At each point, the objective function is evaluated. The best points with the lowest objective function values are kept, while the rest are excluded from the subsequent procedure. For each kept point, the new points are evaluated on each side at one-third distance between the first set of points. The objective function value is evaluated once again for the new points. This process of grid refinement continues until a termination criterion is met. When the above procedure is applied, the population of the working set is reduced over the iterations while the solution set can spread over multiple possible regions and directions. The same procedure can be used for any of the design variables, although the number of grid points and computation effort increases exponentially with the number of design variables. The algorithm acts in a very stable way and gfin^OtJJIMISCSD 01-7 stran 293 |^BSSITIMIGC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature odvedljivosti namenske funkcije ter dobro obvladuje tudi definicijsko območje, podano z zahtevnejšimi omejitvenimi pogoji. 3 REZULTATI IN NJIHOVA POTRDITEV requires no calculation of the derivatives. It can also handle discontinuities and calculations in the vicinity of a complex constraint boundary. 3 OPTIMISATION RESULTS AND VERIFICATION 3.1 Rezultati Predlagan postopek optimalnega projektiranja smo uporabili na primeru valjaste zobniške dvojice, definirane s parametri, prikazanimi na sliki 2. Pri tem smo predpisali naslednje spodnje in zgornje meje projektnih spremenljivk: x= [-0,4, x = [1,2, ki pomenijo običajne mejne vrednosti stopnje profilnega premika [5]. S predlaganim algoritmom smo izračunali naslednje optimalne vrednosti koeficientov profilnega premika: *x = [0,307; Optimalna rešitev izpolnjuje tudi omejitve, podane z izrazi (11). Kljub temu je treba poudariti, da mora izračunane vrednosti pred uporabo oceniti še izkušen snovalec zobniških gonil. 3.2 Overitev V postopku overitve oblike zob, dobljene z optimizacijskim algoritmom, so bile uporabljene analitične in numerične metode. Za porazdelitev PP po enačbi (15), kakor jo predlaga DIN3992 [4], je bil v vsaki od značilnih točk vzdolž ubirnice (A, B, C, D, E) izračunan polmer ukrivljenosti: 3.1 Optimisation results To verify the suggested approach, a spur gear pair was analysed, defined by the parameters given in Figure 2. The upper and lower bounds of the design-variable vector are: -0,4] 1, 2]T (13), respectively, and represent common gear-design limits [5]. Using the presented algorithm, the following results were obtained: 0,046]T (14). Where the constraints of equations (11) were considered as well. Nevertheless, it should be pointed out, that the experienced gear designer should always review the computational results, prior to the final decision. 3.2 Verification Analytical and computational methods were used to verify the geometry obtained by the optimisation algorithm. The radii of curvature at every characteristic contact point along the path of contact (A, B, C, D, E) was calculated for the distribution of the AMC suggested by the standard procedure (DIN3992 [4]): x0 = [0, 23; 0,12]T (15). Zgornje vrednosti so bile izračunane tudi za porazdelitev PP, kakor jo predlaga optimizacijski algoritem(13). Za obe porazdelitvi PP je bil izračunan Hertzov tlak. Rezultate kaže slika 7. Da bi potrdili učinkovitost predlaganega algoritma, je bilo v vseh točkah izračunano še relativno drsenje. Primerjavo vrednosti prikazuje slika 8. Kakor je razvidno s slik 7 in 8, so tako vrednosti Hertzovega tlaka, kakor tudi relativnega drsenja manjše in bolj enakomerno porazdeljene v primeru optimirane porazdelitve PP. Na podlagi prikazanega je moč sklepati, da bo obraba zobnih bokov zobnikov, oblikovanih na način, kakor je predlagano z optimizacijskim algoritmom, manjša in bolj enakomerna. Da dokažemo pravilnost postopka, smo enak algoritem uporabili še za optimiranje porazdelitve koeficientov PP zobniške dvojice z naslednjimi podatki: P=25kW, n1=700min1, i=3, z1 =21, m =4mm, a=170mm. Rezultati so podani na sliki 8a. and the calculated optimum distribution (13) of the AMC. The Hertz pressure was calculated at every characteristic contact point (continuous line) and compared to the values obtained for a non-optimum distribution (dashed line). The results are presented in Figure 7. To establish the efficiency of the suggested algorithm, relative sliding at each of the typical contact points was calculated as well, as shown in Figure 8. As can be seen from Figures 7 and 8, respectively, the normal pressure and relative sliding values for the optimised AMC distribution are lower and more equally distributed. Consequently, it can be assumed that the expected abrasion wear of the gear-teeth flanks, shaped in accordance with the optimisation algorithm, will be reduced and equally distributed. To prove the regularity of the approach, the same algorithm was used for another gear pair with the following data: P=25kW, n1=700rpm, i=3, z1=21, mn=4mm, a=170mm. The results are presented in figure 8a. VH^tTPsDDIK stran 294 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature Neoptimiran profilni premik Non-optimised AMC Optimiran profilni premik Optimised AMC Sl. 7. Porazdelitev Hertzovega tlaka vzdolž ubirnice v MPa Fig. 7. Hertz pressure distribution along the path of contact in MPa Neoptimiran profilni premik Non-optimised AMC Optimiran profilni premik Optimised AMC Sl. 8. Porazdelitev specifičnega drsenja vzdolž ubirnice Fig. 8. Specific sliding distribution along the path of contact 3.2.1 Uporaba MKE v postopku snovanja zobnikov Porazdelitev normalnih napetosti v analizirani zobniški dvojici je bila, z namenom prikaza uporabnosti numeričnih metod, izračunana z metodo končnih elementov. Uporabljen je bil lasten program za analizo kontaktnih problemov, 3.2.1 Application of the FEM in general gear design To demonstrate the applicability of computational tools in the gear- design process, the normal stress distribution of the analysed gear pair was calculated using the finite-element method (FEM). An in-house contact code, based on the FEM | IgfinHŽšlbJlIMlIgiCšD I stran 295 glTMDDC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature Neoptimiran profilni premik Non-optimised AMC Optimiran profilni premik Optimised AMC Neoptimiran profilni premik Non-optimised AMC Optimiran profilni premik Optimised AMC Sl. 8a. Porazdelitev specifičnega drsenja in Hertz-ovega tlaka vzdolž ubirnice Fig. 8a. Specific sliding and Hertz pressure distribution along the path of contact \L- Sl. 9. Kontaktne napetosti po MKE za optimirano obliko zob - točka B Fig. 9. FEM contact stresses distribution for optimum tooth profile - B point VH^tTPsDDIK stran 296 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature ki sloni na metodi končnih elementov [13]. V programu je za predpisovanje kontaktnih robnih pogojev uporabljena metoda Lagrangeovih množiteljev Ker MKE ne daje ‘gladkega’ opisa analizirane geometrijske oblike, je bil uveden dodaten opis kontaktnih robov s pomočjo Overhauserjevih parametričnih zlepkov, ki omogoča preprosto in natančnejše zaznavanje kontakta in izračunavanje velikosti prodiranja. Program omogoča še nekatere koristne funkcije, to je Prosti algoritem Lagrangea-Eulerja (Arbitary Lagrange-Euler Algoritem - ALE) [14] za razdelitev kotalnega kontakta na enostavnejše odseke. Za zmanjšanje števila prostostnih stopenj so v algoritmu na voljo posplošeni robni pogoji [15], ki omogočajo, da s povezovalnimi izrazi povežemo poljubno število prostostnih stopenj. Za optimirano in neoptimirano obliko zob so bile izračunane normalne napetosti. Na spodnji sliki je prikazan primer porazdelitve normalnih napetosti, za optimirano porazdelitev PP (14), izračunanih s pomočjo kontaktnega algoritma po MKE. Predlagan algoritem MKE je uporaben za modeliranje kontaktnih pogojev med ubiranjem zob. Algoritem omogoča modeliranje dejanske geometrijske oblike zobnih profilov, trenja, toplotnih obremenitev, različnih elastičnih lastnosti materiala [13] itn. Prednost uporabe MKE pred običajnimi postopki je v tem, da poleg ekstremnih vrednosti ponujajo tudi celotno porazdelitev napetosti v telesu. Slednje je nujno za napovedovanje jamičenja in drugih oblik poškodb zobnikov. Pomanjkljivost uporabe MKE v postopku snovanja zobnikov je, da moramo, če želimo natančno modelirati geometrijsko obliko zob, uporabiti v okolici kontakta zelo gosto mrežo. Posledica so bistveno povečani računski časi. 4 SKLEP V prispevku je predlagana uporaba različnih vrst inženirskih znanj, združenih v uporabna konstrukterska orodja. Standardnemu postopku konstruiranja zobniških gonil so dodane nove funkcije, ki izboljšajo učinkovitost. Predstavljen je algoritem za optimiranje porazdelitve koeficientov premikov profila. Optimalna rešitev je poiskana glede na relativno drsenje in dovoljene normalne napetosti ter ob upoštevanju splošnih robnih pogojev za konstruiranje zobnikov. Uporabljena je globalna optimizacijska metoda, in sicer algoritem prilagodnega izboljševanja mreže. Vzdolž ubirnice so za optimirano obliko zob preverjene vrednosti relativnega drsenja in normalnih napetosti. Rezultati so primerjani z vrednostmi, izračunanimi za was used for the gear design [13]. The Lagrange multiplier method was used for the imposition of the contact boundary conditions. A redundant geometry definition was used to avoid a non-smooth geometry description provided by the FE shape function. Overhauser splines were used for the gear design providing simplified and more accurate contact detection and penetration-size calculation. Some other useful features were used within the computer program as well, and an Arbitrary Lagrangian Eulerian (ALE) algorithm for a decomposition of the rolling contact was applied [14]. To reduce the number of degrees of freedom, a system of generalised constraints, as suggested [15] was introduced, enabling arbitrary degrees of freedom to be linked by specified expressions to maintain desired relations. Optimised and non-optimised profiles of the gear teeth were modelled and the normal stresses calculated. Some results of the FEM contact algorithm for the optimum AMC distribution (14) are presented in the following figure. The proposed FE algorithm is capable of modelling the contact conditions during the gear-teeth mating. It also allows for consideration of the real tooth profile; the friction and temperature loading; and the different elastic properties of the mating materials [13], etc. There are many reasons for proposing the application of computational methods in combination with conventional ones. Contact interaction between any two or more mechanical components can significantly affect their operating conditions. Due to their importance it is imperative to gain a proper insight into the process of contact interactions. FE analyses provide the complete stress-strain distribution of the mating gear teeth, which is necessary for predicting the possibility of pitting and other forms of gear failure. From the users’ point of view it should be stressed that a comprehensive knowledge of general gear design is necessary to be able to use the computational tools properly. 4 CONCLUSIONS In this work, an attempt to bring together different areas of engineering knowledge to create a useful design tool is presented. Some novel features within a general gear-design procedure are applied in the work to improve the efficiency of the standard gear-design procedures. An optimisation algorithm for the addendum modification coefficient distribution is presented. An optimum distribution is found with respect to the specific sliding and permissible Hertz pressure, taking general gear-design constraints into account. The global optimisation method is used for the above purpose. An adaptive grid refinement algorithm is applied. The gear-tooth profile resulting from the optimisation procedure is tested in terms of the specific sliding and the normal pressure distribution along the transverse path of the contact. Results are compared for the optimised and non-optimised AMC distribution. A FEM contact algorithm | lgfinHi(š)bJ][M]lfi[j;?n 01-7_____ stran 297 I^BSSIfTMlGC S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature neoptimirano obliko. Ugotovljeno je, da so is used to compare the analytical and computational gear- vrednosti normalnih napetosti in relativnega design procedures. It was established that the relative sliding drsenja za optimirano obliko zoba manjše in bolj and Hertz pressure of the mating tooth flanks of pinion and enakomerno porazdeljene. Na podlagi prikazanih gear resulting from the calculated optimum AMC distribution rezultatov lahko sklepamo, da je podani algoritem are reduced and more equally distributed From the presented primeren za uporabo pri konstruiranju zobniških results it can be concluded that the proposed approach is gonil. Uporabljen je tudi kontaktni algoritem po applicable to the general-purpose gear-design procedure, MKE, kot primerjava z analitičnimi postopki but it will be tested on an extensive selection of cases prior to snovanja zobnikov. it being proposed for general use. 5 OZNAKE 5 SYMBOLS stične točke P1,P2,P1’,P2’ points of contact značilne točke vzdolž ubirnice A, B, C, D, E characteristic points along the line of contact del zobnega boka f1, f2 teeth flank section obodna hitrost vT1, vT2 circumferent velocity kotna hitrost w1, w2 angular velocity število zob z1, z2 gear teeth number normalni modul m normal modulus medosna razdalja a centre distance koeficient premika profila x1, x2 addendum modification coefficient širina zobnika b tooth face width debelina vrha zoba sa tooth tip thickness medsebojno drsenje V1, V2 specific sliding trenutna točka stika Y actual point of contact robne točke uporabnega področja ubiranja N1, N2 boundary points of the utilisable domain premer temenskega kroga da1, da2 tip diameter premer korenskega kroga db1, db2 base diameter premer kinematičnega kroga dw1, dw2 pitch diameter dejanski polmer ukrivljenosti r1y, r2y actual radii of curvature vrtišče zobnikov O1, O2 gear centre of rotation ubirni kot na delilnem krogu at transverse pressure angle ubirni kot na kinematičnem krogu a wt working transverse pressure angle ubirni kot na temenskem krogu aa1, aa2 pressure angle at tip diameter nagibni kot bočnic b helix angle modul elastičnosti E, E1, E2 modulus of elasticity normalna napetost sH normal stress največja izračunana normalna napetost s Hmax maximum calculated normal stress dovoljena normalna napetost s Hlim permissible normal stress upogibna napetost sF bending stress dovoljena upogibna napetost s Flim permissible bending stress normalna sila Fb normal force Poissonovo število n Poisson’s ratio širina stičnega področja bH width of the contact area nelinearen problem programiranja P non-linear programming problem ciljna funkcija f0 objective function omejitvena funkcija fi constraint function projektna spremenljivka x design variable definicijsko območje Rk domain space dovoljeno območje S feasible domain spodnja in zgornja meja projektne x(, x) variable lower and upper band spremenljivke optimalni vektor projektnih spremenljivk *x optimal solution vector ______01 7 SnnBjtgleJUpillOlflugO | ^BSfirTMlliC | stran 298 S. Ulaga - J. Fla{ker - B. Zafo{nik - I. Ciglari~: Optimizacijski postopek - Optimisation Feature [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] 6 REFERENCES 6 REFERENCES Zhong, Z. H. (1993) Finite element procedures for contact-impact problems, Oxford University Press. DIN 3990 (1996) Tragfahigkeitberechnung von Stirnradern, Deutsch Norme, Beuth Verlag. ISO 1122/1 (1983) Glossary of gear terms DIN 3992, Ausgabe:1964-03 (1996) Profilverschiebung bei Stirnradern mit AuBenverzahnung, Deutsch Norme, Beuth Verlag. Niemann, G., H. Winter (1985) Maschinenelemente - Band II, Springer-Verlag. Obersmit, E. (1982) Ozubljenja i zupčanici, SNL, Zagreb, 593 p. Johnson, K. L. (1985) Contact mechanics, Cambridge University Press. Beitz, W., K.H. Kiittner (1983) Dubbel - Taschenbuch fiir den Machinenbau, Springer-Verlag. Arora, J.S., O A. Elwakeil, A.I. Chahande and C.C. Hsieh (1995) Global optimization methods for engineering applications: a review, 1995. Structural optimization Vol. 9, No. 3/4, 137-159, Springer -Verlag Editor: G. Rozvany. Decker, K. H. (1985) Maschinenelemente - Gestaltung und Berechnung, Carl Hanser Verlag, Miinchen, 576 p. Global nonlinear optimization using Mathematica (user manual). Loehle Enterprises, 1258 Windemere Ave. Naperville, IL 60564. Arora, J.S., OA. Elwakeil, A.I. Chahande and C.C. Hsieh (1995) Global optimization methods for engineering applications: a review, 1995. Structural optimization Vol. 9, No. 3/4, 137-159, Springer -Verlag Editor: G. Rozvany. Ulaga, S. (1998) Extended algorithm for contact problems using finite element method, PhD thesis, University of Maribor - Slovenia, (In Slovene, abstract in English), 127 p. Nackenhorst, U. (1993) On the finite element analysis of steady state rolling contact, Proceedings of the 1st International Conference on Computational Methods in Contact Mechanics, CMP, Southampton, 53-60. Hellen, T.K., A.B. Haines (1972) Generalised constraints for finite elements and their application to curve-bladed pump impellers, CEGB Report, RD/B/N2252. Glodež S., Z. Ren (1998) Modelling of crack growth under cyclic contact loading. Theor appl. fract. mech., 30, Vol. 2, 159-173. Glodež, S., Z. Ren, G. Fajdiga (2001) Computational modelling of the surface fatigue crack growth on gear teeth flanks. Commun. numer methods eng., vol. 17, no. 8, 529-541. Kramberger, J. (2001) Širjenje razpok v zobnikih s tankim vencem: Doktorska teza/PhD thesis, University of Maribor - Slovenia. Šraml, M. (2001) Modeliranje kontaktnega utrujanja strojnih delov: Doktorska teza/PhD thesis, University of Maribor - Slovenia. Naslova avtorjev: dr. Samo Ulaga profdr. Jože Flašker mag. Boštjan Zafošnik Fakulteta za strojništvo Univerza v Mariboru Smetanova 17 2000 Maribor dr. Iztok Ciglarič Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana Authors’ Addresses: Dr. Samo Ulaga ProfDr. Jože Flašker Mag. Boštjan Zafošnik Faculty of Mechanical Eng. University of Maribor Smetanova 17 2000 Maribor, Slovenia Dr. Iztok Ciglarič Faculty of Mechanical Eng. University of Ljubljana Aškerčeva 6 1000 Ljubljana, Slovenia Prejeto: Received: 3.9.2001 Sprejeto: Accepted: 12.10.2001 © Strojni{ki vestnik 47(2001)7,300-312 © Journal of Mechanical Engineering 47(2001)7,300-312 ISSN 0039-2480 ISSN 0039-2480 UDK 621.57:536.7:004.94 UDC 621.57:536.7:004.94 Predhodna objava (1.03) Preliminary paper (1.03) Model in simuliranje delovanja odprtega hladilnega postopka brez uporabe CFC Design and Simulation of a CFC-Free Open Air-Conditioning System Uro{ Stritih - Mitja Mo`e - Peter Novak V prispevku sta opisana model in delovanje hladilnega postopka, ki za hladilno sredstvo uporablja zrak. V uvodu so opisana običajna hladiva, ki jih primerjamo z alternativnim hladivom - zrakom. Opisana je sestava sistema in termodinamični model. Model je namenjen za študij delovanja CFC-prostega zračnega klimatizacijskega sistema, pri katerem so ob referenčnih podatkih izbrani parametri spremenljivke, preostali pa konstante. Karakteristične krivulje so definirane s hladilnim številom COP, temperaturo ohlajenega zraka, kompresijskim tlakom in drugimi parametri. Karakteristike sistema so dobljene s dejanskimi obratovalnimi razmerami. Razmerja med specifičnimi parametri in veličinami so predstavljena z diagrami. Obrazložene so izgube sistema zaradi neizentropne kompresije v centrifugalnem kompresorju, ekspanzije v turbinskem ekspanderju in nepovračljivosti postopka prenosa toplote v prenosniku toplote. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: sistemi hladilni, naprave klimatske, CFC, modeli termodinamični, simuliranje) In this paper a model is presented and its operation of a cooling process that uses air as the cooling medium. In the introduction, conventional refrigerants are compared with an alternative refrigerant - air. The system construction and the thermodynamic model are presented. The model is used to study the performance of a CFC-free air-conditioning system, in which some parameters of the individual components are variable while the others are constant for the referenced data. The characteristic performance curves of a simple air-conditioning system are defined as the coefficient of performance (COP), the temperature of the cooled outlet air, the compression pressure and other parameters. Using actual data from an air-conditioning system we obtained performance curves of the system. Relations between specific parameters and quantities are presented in diagrams. Losses in the system, resulting from non-isentropic compression in the centrifugal compressor and expansion in the turbine expander and the irreversible losses of the heat transfer in the heat exchanger are explained. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: cooling systems, air conditioning systems, CFC free, thermodynamic models, simulation) 0 UVOD Teoretično bi lahko uporabili katerikoli plin kot hladivo, praktično pa uvrščamo med hladiva samo tiste pline, ki izpolnjujejo določene pogoje: fizikalne, kemične in fiziološke. Ker je hladivo v samem hladilnem krožnem postopku izpostavljeno širokemu območju tlakov in temperatur, so možnosti fizikalnih in kemičnih sprememb zelo velike. Izbira hladiva za posebno uporabo je pogosto odvisna od lastnosti, ki niso neposredno vezane na zmožnost prenašanja toplote. Na primer vnetljivost, strupenost, gostota, viskoznost, dostopnost in druge podobne karakteristike so pogosto odločujoči dejavniki. 0 INTRODUCTION Theoretically, any gas can be used as a refrigerant, in practice, however, only certain gases that meet various physical, chemical and physiological requirements are used. Every refrigerant is exposed to a wide range of pressures and temperatures in a cooling/refrigerating cycle, so the possibility of physical and chemical changes must be great. The choice of refrigerant for a particular application often depends on properties not directly related to its ability to remove heat, for example, flammability, toxicity, density, viscosity, availability and other similar characteristics are often the most important factors. VBgfFMK stran 300 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation 0.1 Obstoječa hladiva: Halogeno-ogljikova hladiva Halogeno-ogljikova hladiva so sintetična, na osnovi ogljika, ter vsebujejo ogljik in halogene atome, kakor so fluor, klor in brom. Lahko vsebujejo tudi vodik. Primeri vključujejo klorfluorogljike (CFCs), fluorogljikovodike (HFCs), halone itn. Halogenirana hladiva se uporabljajo v številnih uporabah: hlajenje in klimatizacija. Halogeni zadevajo domač in mednaroden vidik, ker povzročajo tanjšanje ozonske plasti (ODP), prispevajo pa tudi h globalnemu učinku tople grede (GWP). Slednji je dandanes bolj znan kot sprememba podnebja, ki je povezana s kožnim rakom in zmanjšanjem odpornosti človeškega imunskega sistema. Tanjšanje ozonske plasti lahko vpliva na življenje rastlin do točke, od katere vodi pot do pretrganja celotne prehranjevalne verige. Te kemijske sestavine so znane pod kratico ODS. Najbolj pogosta hladiva so [1]: - izpeljanke metana: R11, R12, R13, R14, R22, R23, R50 - izpeljanke etana: R113, R114, R115, R152a - azeotropne zmesi: R500 (R12+R152a), R512 (R22+R115), R503 (R23+R13) 0.2 Alternativno hladivo: Zrak Zrak [2] je naravno, okolju popolnoma neškodljivo hladivo. Poleg tega je tudi najcenejše. Okoljska vprašanja o tanjšanju ozonske plasti, učinku tople grede in vedno bolj nujno potrebna zakonodaja so obnovili zanimanje za alternativne tehnologije hlajenja. Zračni hladilni sistemi imajo določene specifične prednosti, ki so značilne za vse potencialne uporabe: - Delovno sredstvo (zrak) je naravno, okolju neškodljivo, popolnoma nenevarno in nestrupeno. - Sistemska oprema zračnega kroga je zelo zanesljiva, s tem pa so manjši stroški vzdrževanja in obraba sistema. - Učinkovitost sistema zračnega kroga se ne zmanjšuje tako kakor pri parno-kompresijskih enotah, če obratujejo zunaj predpisanega območja. - Sistem zračnega kroga lahko daje toploto pri uporabni temperaturi, če deluje kot hladilni sistem. Uporaba zraka kot hladiva temelji na načelu plinske izentropne ekspanzije pri določeni temperaturi, končna izstopna temperatura plina pri nekem novem tlaku pa je zato nižja. Ohlajeni plin, v tem primeru zrak, lahko potem uporabimo kot hladivo, in sicer neposredno v odprtem sistemu ali posredno skozi prenosnik toplote v zaprtem sistemu. Izkoristek takih sistemov je omejen z velikostjo izkoristka kompresije in ekspanzije, prav tako z učinkovitostjo prenosa toplote v prenosniku toplote. Prvotno so se uporabljali počasi tekoči kompresorji in turbine. Majhen izkoristek in zanesljivost takih strojev so bili 0.1 Existing refrigerants: Halocarbons Halocarbons are synthetic, carbon-based compounds that contain carbon and halogen atoms such as fluorine, chlorine and bromine. They may also contain hydrogen. Examples of halocarbons include chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), halons, etc. Halocarbons are found in a number of applications including refrigeration and air-conditioning systems. Halocarbons are of both national and international concern, because they cause stratospheric ozone depletion (Ozone Depletion Potential - ODP) and also contribute to global warming (Global Warming Potential - GWP). Today, global warming is better known as climate change, which in turn has been linked to cataracts, skin cancer and human immune-system suppression. Decreased ozone levels can affect plant life to the point where it leads to a disruption of the entire food chain. Such chemicals are known as ozone-depleting substances (ODS). The most common refrigerants are [1]: - Methane Series R11, R12, R13, R14, R22, R23, R50 - Ethane Series R-113, R-114, R-115, R152a - Azeotropic Blends: R500 (R12+R152a), R512 (R22+R115), R503 (R23+R13) 0.2 An alternative refrigerant: Air Air [2] is by its nature the safest and cheapest refrigerant. Environmental concerns about ozone depletion, global warming and increasingly stringent legislation have renewed interest in alternative refrigeration technologies. Air-cycle systems have specific advantages that apply to all potential applications: - The working fluid (air) is free, environmentally benign, totally safe and non-toxic. - Air-cycle equipment is extremely reliable, thereby reducing maintenance costs and system down-time. - The performance of an air-cycle unit does not deteriorate as much as the performance of a vapour-compression unit when operating away from its design point. - When an air-cycle unit is operating in a refrigeration cycle it can also produce heat at a useful temperature. The use of air as a refrigerant is based on the principle that when a gas expands isentropically from a given temperature its final temperature at the new pressure is much lower. The resulting cold gas, in this case air, can then be used as a refrigerant, either directly in an open system, or indirectly by means of a heat exchanger in a closed system. The efficiency of such systems is limited to a great extent by the efficiencies of compression and expansion, as well as those of the heat exchangers employed. The first systems used slow compressors and turbines, however, the low efficiency and reliability of these | lgfinHi(Š)bJ][M]lfi[j;?n 01-7_____ stran 301 I^BSSIfTMlGC U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation glavni dejavniki za zamenjavo teh sistemov s parno-kompresijskimi. Klub temu je prišlo do razvoja rotirajočih kompresorjev in turbin ter s tem tudi do višjih izkoristkov in večje zanesljivosti zračnih krogov. Napredek turbinske tehnologije skupaj z razvojem zračnih ležajev in keramičnih komponent ponujajo nadaljnje izboljšave. Skupaj z novimi zgoščenimi prenosniki toplote z boljšimi karakteristikami prenosa toplote postajajo taki sistemi vedno bolj konkurenčni že znanim parno-kompresijskim sistemom in vsekakor tudi sistemom na tekoči dušik. V nadaljevanju je prikazan potek računalniškega simuliranja zračnega hladilnega sistema brez uporabe CFC, ki lahko simulira dejanski hladilni sistem. Za simuliranje smo vzeli zračni hladilni postopek z odprto zanko, torej odprt sistem s hladivom na zrak. 1 OBLIKOVANJE SISTEMA Hladilni sistem je sestavljen iz centrifugalnega kompresorja, prenosnika toplote zrak/ voda in ekspanzijske turbine. vstop hladilne vode inlet cool water machines were the main reasons why they were replaced with vapour-compression machines. Despite their lack of popularity there were developments in rotary compressors and turbines that resulted in high efficiencies and higher reliabilities. The development of turbine technologies with air bearings and ceramic components offered further improvements. Together with new compact heat exchangers and their higher heat-transfer characteristics these systems have become more and more competitive with vapour-compression systems. In this paper we present a computer-simulation program of CFC-free air-conditioning system that can simulate the performance of actual systems. For our simulation we chose an open-cycle air-conditioning system with air as the refrigerant. 1 DESIGN OF THE SYSTEM The cooling system is composed of a centrifugal compressor, on air/water heat exchanger and an expansion turbine. izstop segrete vode outlet heated water IS izstop ohlajenega zraka outlet cooled air prenosnik toplote zrak/voda air/water heat exchangeer P ET____________________ ekspanzijska turbina yS expansion turbine 4p 1 P CO centrifugalni kompresor centrifugal compressor vstop zraka inlet air Sl. 1. Shema preprostega (odprta zanka) zračnega hladilnega sistema Fig. 1. Shematic diagram of a simple (open-loop) air-conditioning system Na sliki 2 sta prikazana diagrama T-s in kratek opis za odprti zračni proces [3]. Obrnjen Jouleov proces je sestavljen iz treh korakov (sl. 2a). Prvi korak je kompresija delovnega medija, drugi korak je izmenjava toplote med delovnim (zrak) in hladilnim (voda) sredstvom in tretji korak ekspanzija delovnega medija. Izvedba obrnjenega Jouleovega procesa je lahko mogoča z različnimi kompresorji, prenosniki toplote in ekspanzijskimi turbinami. Delo, pridobljeno pri ekspanziji, se uporabi za kompresijo (sl. 1). Če sta delo kompresije in ekspanzije enakega reda velikosti, bo že majhno povečanje dela kompresije ali majhen padec dela ekspanzije poguben za ves proces. Zaradi tega je eden od odločilnih problemov doseganje In Fig. 2 T-s diagrams and a short description of the open-air process are presented [3]. The reversed Joule cycle is composed of three steps (Fig. 2a). First, a working medium is compressed, then heat is exchanged between the working medium (air) and the cooling medium (water), finally, the medium is expanded. The reversed Joule process can be realised with many different compressors, heat exchangers and expanders. The work gained by the expansion is used for the compression (Fig. 1). As they are both of the same order of magnitude, a small increase in the compressor work or a small decrease in the expander work will be detrimental to the process. One of the crucial problems is, therefore, to achieve sufficiently high efficiencies in VH^tTPsDDIK stran 302 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation Ta izentropna ekspanzija isentropic expansion visok tlak high pressure T visok tlak high pressure 2 tropna kompresija isentropic compression adiabatna ekspanzija adiabatic expansion nizek tlak low pressure s1 = s2 Sl. 2a. Izentropna kompresija in ekspanzija (idealna kapljevina brez trenja) Fig. 2. Isentropic compression and expansion (ideal fluid with no friction) primerno visokih izkoristkov kompresorja in ekspanderja. To še posebno drži pri majhnih napravah, pri katerih imajo tradicionalni turbo-stroji majhne izkoristke. Tehtnost izkoristkov je prikazana v diagramu T-s (sl. 2b). T je absolutna temperatura in s je entropija. Če se entropija med kompresijo in ekspanzijo močno zvečuje, je to ekvivalentno majhnemu izkoristku procesa. Hladilna moč se zelo zmanjša. Izentropen proces ni nikoli 100-odstotno izvedljiv. Če bi bilo to mogoče, bi pomenilo, da v procesu ni spremembe entropije (proces kompresije in ekspanzije). Dejansko je proces kompresije, prenosa toplote in ekspanzije vedno adiabaten. Torej je delo kompresorja in ekspanderja omejeno z izentropnim izkoristkom. Proces prenosa toplote poteka pri nespremenljivem tlaku. Toda to je le idealna predpostavka, kajti dejansko pride do najmanjšega znižanja tlaka. Glavna kriterija pri izbiri komponent zračnega hladilnega sistema sta določitev primerne velikosti enote prostora, ki ga moramo ohladiti, in razmerje energijske učinkovitosti (EER) - hladilno število (COP) sistema. EER (ali COP) je izračunan z deljenjem hladilne moči (BTU/h - British Thermal Unit ali W-moč v vatih) in vložene električne energije (W-moč v vatih). Višji ko je rezultat, večji je izkoristek hladilne naprave. 2 TERMODINAMIČNI MODEL ZRAČNEGA HLADILNEGA SISTEMA Termodinamični model, ki simulira delovanje preprostega zračnega hladilnega sistema je bil razvit za določevanje učinkovitosti sistema. Model se tudi hladilna obremenitev cooling load 2p adiabatna kompresija adiabatic compression T3 T1 nizek tlak low pressure s3 s4 4p s1 s2 1 2p s Sl. 2b. Adiabatna kompresija in ekspanzija (realna kapljevina s trenjem) Fig. 2b. Adiabatic compression and expansion (real fluid with friction) the compressor and expander. This is especially true for small machines, where traditional turbo-machines have a low efficiency. The importance of the efficiencies is best shown in a T-s diagram (Fig. 2b). T is the absolute temperature and s is the entropy. If the entropy increases significantly during the compression or expansion, this is equivalent to low efficiency. The refrigeration power decreases immensely. The isentropic process cannot be 100% practicable. If it were, this would mean that there is no change of entropy during the process of compression and expansion. In fact the process of compression, heat exchange and expansion is always adiabatic (real fluid). So the compressor‘s and expander‘s mechanical work (power) is limited by the isentropic efficiency. The process of heat exchange in a heat exchanger flows at constant pressure. But that is just an ideal supposition, because in reality there is always some pressure drop. The main criteria when choosing the components of an air-conditioning system are to determine the correct size of the unit for the area to be cooled and to look for a unit with a high energy-efficiency ratio (EER) or coefficient of performance (COP). An EER (or COP) is computed by dividing the cooling output (BTU/h or W) by the electrical input (W). The higher the result, the more efficient is the appliance. 2 THERMODYNAMIC MODEL OF THE SYSTEM A thermodynamic model that simulates the working of a simple air-conditioning system has been developed for determining the performance of a sys- U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation uporablja za napovedovanje optimalnih vrednosti potrebnih parametrov. Vsaka komponenta sistema mora biti pravilno izbrana in povezana z drugo komponento. Med seboj povezane komponente pomenijo sistem. V našem primeru imamo opravka s hladilnim sistemom. Delovno sredstvo je zrak zato sta v sistemu zračni masni in toplotni tok. Model simuliranja prikazuje, kaj se dogaja z določenimi parametri znotraj hladilnega sistema in kako ti vplivajo med seboj. V ta namen uporabljamo računalniŠki program, ki je napisan v programskem jeziku FORTRAN. To je preprost model, kjer sodeluje veliko spremenljivih parametrov, ki jih poda uporabnik simulirnega progama. Nespremenljivi parametri, kakršna sta atmosferski tlak (p1) in plinska konstanta zraka (R) ter drugi, so vstavljeni v program. Prilagodljivost je ena od glavnih karakteristik simuliranja. 2.1 Vrednosti parametrov Nespremenljivi parametri (vstavil jih je programer modela simuliranja in so fiksni): - plinska konstanta zraka: R = 287 J/kgK - specifična toplota zraka: c = 1005 J/kgK, - atmosferski/začetni tlak: p1 p = p4 = pp = 0,101325 MPa (opomba: tlak pred kompresijo in po ekspanziji je enak atmosferskemu tlaku), - razmerje specifičnih toplot za zrak: c = 1,4, - specifična toplota vode: c = 4200 J/kgK, - entropija in entalpija je enaka ničpri (zrak): p0 =1 atm in T0 = 78,8 K; Spremenljivi parametri (poda jih uporabnik modela simuliranja): - vstopna temperatura zraka: T = 303 K, - prostorninski tok zraka: V1 = 0,1 m3/s, - tlak kompresije: p2 = pp = p3 = 0,2 MPa, - (opomba: tlačni padec v prenosniku toplote je zanemarjen), - izkoristek kompresije: h = 0,85, - masni tok hladilne vode: m = 0,083 kg/s, - vstopna temperatura hladilne vode: T = 288 K, - toplotna prehodnost prenosnika toplote: k = 1342 W/m2K - površina prenosnika toplote: A = 0,08 m2, - stopnja izmenjave temperature v prenosniku toplote: f = 0,554 [6], - izkoristek ekspanzije: h = 0,85, Ti parametri so vrednosti simuliranja referenčnega hladilnega procesa. 2.2 Zaporedje izračuna parametrov A) Prvi korak: Proces kompresije od točke 1 do točke 2p Izračun specifične entropije in specifične entalpije za točko 1: tem. The model is also used for predicting the optimum formation of included parameters. Each component of a system has to be defined and connected properly. Furthermore, these connected components comprise a composition, which is called the system. In our case we are dealing with an air-conditioning system. The working medium is air, therefore, an air flow takes place through the system. The simulation shows the relations between different parameters and how they impact on the performance of this system. The system was simulated with a computer program written in the FORTRAN language. Constant parameters like atmospheric pressure (p1), the gas constant for air (R) and the others are fixed in the program. Flexibility is one of the main characteristics of this program. 2.1 Values of the parameters Constant parameters in the model: - gas constant for air: R = 287 J/kgK, - specific heat for air: cp air = 1005 J/kgK, - atmospheric/initial pressure: p1 = p4 = p4p = 0,101325 MPa (note: pressure before compression and after expansion – atmospheric pressure), - ratio of specific heat capacity for air: c = 1.4, - specific heat for water: cp w = 4200 J/kgK, - entropy and enthalpy zero for liquid boiling (air) at: p0 =1 b and T0 = 78.8 K. Variable parameters (inserted by the user of the simulation model): - temperature of intake air: T1 = 303 K, - volume flow of air: V1 = 0.1 m3/s, - compression pressure: p2 = p2p = p3 = 0,2 MPa; - (note: pressure drop in heat exchanger is omitted), - compression efficiency: hCO = 0.85, - mass flow of cooling water: mw = 0.083 kg/s, - temperature of cool inlet water: TIN = 288 K, - thermal conductance of heat exchanger: k = 1342 W/m2K, - surface of heat exchanger: A = 0.08 m2, - degree of reciprocity of temperature in heat exchanger: f = 0.554 [6], - expansion efficiency: hET = 0.85. These parameters are simulation values of the referenced air-conditioning process. 2.2 Computation sequence of parameters and quantities A) First step: Process of compression from point 1 to point 2p Calculation of specific enthalpy and specific entropy for point 1: VH^tTPsDDIK stran 304 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation h=c T 1 p zrak 1 ln-T -R V o ln p0 Masni tok zraka: Temperatura zraka po izentropni kompresiji: Mass flow rate of air: p1-V1 R-T1 Temperature of air after isentropical compression: (1), (2). (3). s+R-ln2-s p2 -s T =e (4). Specifična entalpija in specifična entropija za točko 2: Specific enthalpy and specific entropy for point 2: h=c T 2 p zrak 2 (5), (6). Specifična entalpija, temperatura in entropija po Specific enthalpy, temperature and entropy after poly- politropni kompresiji (točka 2p): tropic compression (point 2p): h2 -h1 2p Eksponent politrope: c zrak T \ V 0 ln p 2p p0 (7), (8), (9). Polytropic exponent: log lo n CO p p (10). log p 2p log Volumski tok zraka po kompresiji: Moč kompresije in izguba energije (trenje): 2p J Volume flow rate of air after compression: n V=V- p 2p (11). Compression power and losses of heat energy (friction): Pco=mzrak-(h1-h2p) Q izgube odstotno: QI C= Z nCO PCO Z-1 nCO percentage: IZGUBE.100 CO (12), (13), (14) B) Drugi korak: Postopek prenosa toplote iz točke 2p na točko 3 (postopek izračuna za prenos toplote v protismernem prenosniku toplote [4]) B) Second step: Process of heat exchange from point 2p to point 3 (calculation procedure for heat exchange is developed by [4]) Kapaciteta zraka in vode: Capacitance rate for air and water: zrak zrak p zrak W voda voda p (15), (16). gfin^OtJJIMISCSD 01-7 stran 305 |^BSSITIMIGC 1 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation Razmerje kapacitet: W Wv Ratio of capacitance: 0-J (21). Temperatura zraka iz prenosnika toplote (točka 3): Temperature of cooled air from heat exchanger (point 3): T3 =T2p - D t 1 Prostorninski tok zraka po prenosu toplote: Volume flow of air after heat exchange: V3 =V2 T T V/2p J (22). (23). Temperaturna razlika med vstopno in izstopno vodo: Temperature difference between inlet and outlet water: Dt2 =t D t 1 (24). Temperatura izstopne segrete vode: Temperature of outlet heated water: TOUT =TIN + D t 2 (25). Izmenjava toplote med zrakom in vodo: Heat exchange between air and water: Q =m c Dt OUT zrak p zrak 1 (26). C) Tretji korak: Postopek ekspanzije od točke 3 do točke 4p C) Third step: Process of expansion from point 3 to point 4p Specifična entalpija in specifična entropija točke 3: Specific enthalpy and specific entropy for point 3: '3 = c p zrak T 3 V T0 (27), (28). Temperatura zraka po izentropni ekspanziji: Temperature of air after isentropical expansion: lnT0 +0 T =e c p zrak (29), Specifična entalpija in specifična entropija točke 4: Specific enthalpy and specific entropy for point 4: h=c T 4 p zrak 4 (30), (31). Specifična entalpija, temperatura in entropija Specific enthalpy, temperature and entropy po politropni ekspanziji (točka 4p): after polytropic expansion (point 4p): grin^(afcflM]SCLD ^BSfiTTMlliC | stran 306 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation h4 p = h3 -hET (h3 -h4 ) T4p = h 4p c p zrak (32), (33), 4p p zrak Eksponent politrope: T4 T log 4p - R log (34). 0 Polytropic exponent: log p 4p n ET T (35). Moč ekspanzije: Potrebna moč kompresije: Hladilno število: log p 4p T log T V Expansion power: Pet =mzrak (h3 - h 4 p ) Required compression power: W =PCO - P E T Coefficient of performance: Q COP = IN W (36). (37). (38). Slika 3 prikazuje diagram poteka delovanja simulirnega preprostega zračnega hladilnega sistema, ki je sestavljen iz treh korakov: A. Prvi korak je kompresija, v katerem so vhodni podatki temperatura in prostorninski tok vstopnega zraka, tlak kompresije in izkoristek kompresije. Izhodni podatki so masni tok zraka, specifična entalpija in specifična entropija, temperatura zraka v točki 1, 2 in 2p, kompresijski eksponent politrope, prostorninski tok zraka po kompresiji, moč kompresije in izgube energije med kompresijo (trenje). B. Drugi korak je prenos toplote, v katerem so vhodni podatki masni tok vode, vstopna temperatura hladilne vode, toplotna prehodnost prenosnika toplote, površina prenosnika toplote in stopnja izmenjave temperature v prenosniku toplote. Izhodni podatki so kapaciteta zraka in vode, razmerje kapacitet, karakteristično število kapacitete, temperaturna razlika med vstopnim zrakom in vstopno vodo, temperaturna razlika med vstopnim in izstopnim zrakom, temperatura zraka iz prenosnika toplote, prostorninski tok zraka po prenosu toplote, temperaturna razlika med vstopno in izstopno vodo, temperatura izstopne segrete vode in izmenjava toplote med zrakom in vodo. C. Tretji korak je ekspanzija, v katerem se prične postopek z izračunom specifične entalpije in Figure 3. shows the flow chart of the performance simulation program of a simple air-conditioning system that consists of three steps: A. The first step is compression, where the input data are the temperature and volume flow of the inlet air, the compression pressure and the compression efficiency. The output data are the mass flow of the air, the specific enthalpy and specific entropy, the air temperature for points 1, 2 and 2p, the polytropic exponent of compression, the volume flow after compression, the compression power and the heat losses during compression. B. The second step is heat exchange, where the input data are the mass flow of water, the temperature of the inlet cooling water, the heat conductance of the heat exchanger, the surface of the heat exchanger and the degree of reciprocity of the temperature in the heat exchanger. The output data are the capacitance rate for the air and water, the ratio of the capacitance, the characteristic number of capacity, the temperature difference between the inlet air and the inlet cooling water, the temperature difference between the inlet and outlet air, the temperature of the cooled air from the heat exchanger, the volume flow of air after heat exchange, the temperature difference between the inlet and outlet water, the temperature of the outlet heated water and the heat exchange between the air and water. C. The third step is expansion, where the operation starts with a calculation of the specific enthalpy gfin^OtJJIMISCSD 01-7 stran 307 |^BSSITIMIGC U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation specifične entropije točke 3. Vhodni podatek je izkoristek ekspanzije, izhodni podatki pa so temperatura, specifična entalpija in specifična entropija točke 4 in 4p, ekspanzijski eksponent adiabate, moč ekspanzije, potrebna moč kompresije in hladilno število. Ta korak je na blokovni shemi označen z zelenim okvirom (sl. 3). and the specific entropy for point 3. The input data is the efficiency of expansion, the output data are the temperature, the specific enthalpy and the specific entropy for points 4 and 4p, the adiabatic exponent of expansion, the expansion power, the required compression power and the coefficient of performance. Start Nespremenljivi parametri: R, Cp air, p1, c Constant parameters: Vhodna parametra: Operating conditions: T1, V1 Vhodna parametra: Operating conditions: (p2, hCO) Izračun: h1 (En./Eq. 1) in/and s (En./Eq. 2) Calculation of: mzrak/mair (En./Eq. 3) Izračun: T2 (En./Eq. 4) Calculation of: h2 (En./Eq. 5) in/and s2=s1 (En./Eq. 6) h2 (En./Eq. 7), T2 (En./Eq. 8) in/and s2 (En./Eq. 9) nCO (En./Eq. 10) V2 (En./Eq. 11) PCO (En./Eq. 12), QLOSE (En./Eq. 13) in/and X (En./Eq. 14) Predpostavka: Supposition condition: p2 =p3 =const Vhodni parameter: m Operating condition: voda Izračun: Wzrak/Wair (En./Eq. 15) in/and Wvoda/Wwater (En./ Eq. 16) Calculation of: t (En./Eq. 17) Izračun Calculation of: KSK/CNC (En./Eq. 18) Vhodni parametri: TIN, k, A Operating conditions: Vhodni parameter: f Operating condition: Izračun: J (En./Eq. 19) Calculation of: Dt1 (En./Eq. 20) T3 (En./Eq. 21) V3 (En./Eq. 22) Dt2 (En./Eq. 23) Tout (En./Eq. 24) Qout (En./Eq. 25) Predpostavka: Supposition condition: p4=p1=const Vhodni parameter: Operating condition: hET Calculation of: h3 (En./Eq. 26) in/and s3 (En./Eq. 26) Izračun: T4 (En./Eq. 28) Calculation of: h4 (En./Eq. 29) in/and s4=s3 (En./Eq. 30) h4p (En./Eq. 31), T4p (En./Eq. 32) in/and s4p (En./Eq. 33) hET (En./Eq. 34) COP (En./Eq. 37) Konec/End -" Sl. 3. Blokovna shema simuliranja termodinamičnega modela Fig. 3. Flow chart for the thermodynamic model 3 REZULTATI SIMULIRANJA 3 SIMULATION RESULTS Spodnji diagrami prikazujejo, kako določeni In the diagrams below we show how certain parametri sistema vplivajo med seboj. Podobno so parameters of the system impact on each other. Similar rezultate predstavili tudi drugi avtorji ([5] in [6]): results were presented by other authors ([5] and [6]): VH^tTPsDDIK stran 308 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation 1) Diagram Izstopna temperatura zraka / Tlak kompresije 1) Diagram Temperature of outlet Air / Compression Pressure 300 295 290 285 280 275 270 265 260 Tlak kompresije [Pa] Pressure after compression[Pa] Bolj ko zrak komprimiramo, nižjo izstopno temperaturo zraka dobimo. Karakteristika ni linearna. Obstaja točka, kjer je tlak kompresije zelo nizek in izstopna temperatura zraka ostane enaka kakor temperatura zraka pred komprimiranjem. Če hočemo torej zrak ohladiti, ga moramo komprimirati na določen nadtlak. 2) Diagram Izstopna temperatura zraka / Površina prenosnika toplote 300 295 290 285 280 275 270 265 260 255 250 245 The more the air is compressed, the lower the temperature of the outlet air. The characteristic is non-linear. There is a point where the compression pressure is very low and the temperature of the outlet air is the same as the temperature of the inlet air. So, if the air must be cooled some compression work has to be done. 2) Diagram Temperature of outlet Air / Surface of Heat Exchanger Temperatura izstopnega zraka je podobno odvisna od površine prenosnika toplote, kakor je tlak kompresije odvisen od temperature izstopnega zraka. Tudi tu obstaja točka, kjer je površina prenosnika toplote premajhna, da bi se zrak ohladil. Karakteristika je približno linearna. The temperature of the outlet air is similarly dependent on the surface of the heat exchanger as the compression pressure affects the temperature of the outlet air. There is a point where the surface of the heat exchanger is too small to cool the air. The characteristic is approximately linear. gfin^OtJJlMISCSD 01-7 stran 309 |^BSSITIMIGC U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation 3) Diagram COP / Površina prenosnika toplote 3) Diagram COP / Surface of Heat Exchanger Iz diagrama ugotovimo, da se COP s From the diagram we can see that the COP povečano površino prenosnika toplote povečuje. increases with the surface of the heat exchanger. 4) Diagram COP / Toplotna prehodnost prenosnika toplote 4) Diagram COP / Thermal Conductance 1. 960 1. 940 1. 920 1. 900 1. 880 1. 860 1. 840 1. 820 1. 800 1. 780 1. 760 1. 740 1200 1250 1300 1350 Toplotna prehodnost [W/m2K] Thermal conductance [W/m2K] 1400 1450 Vidimo lahko, da je COP linearno sorazmeren s toplotno prehodnostjo prenosnika toplote. 5) Diagram COP / Tlak kompresije We can see that the COP is directly proportional to the thermal conductance of the heat exchanger. 5) Diagram COP / Compression Pressure VBgfFMK stran 310 U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation Zgornji diagram prikazuje, kako je hladilno število odvisno od tlaka kompresije. Manj ko dovedemo kompresijskega dela v sistem, večje je hladilno število. Hkrati pa to pomeni, da pri nižjih tlakih zrak tudi manj ohladimo. Teoretično obstaja točka, kjer je optimalno razmerje mod COP in temperaturo izstopnega zraka. 4 SKLEP Razvili smo preprost simulirni program delovanja odprtega zračnega hladilnega procesa brez uporabe CFC, v kar je usmerjen razvoj klimatizacijske tehnike z namenom ohranjanja okolja. Računalniški program, napisan v programskem jeziku FORTRAN, temelji na termodinamičnih enačbah. Ta specifičen hladilni sistem je sestavljen iz treh osnovnih stopenj: kompresijska enota, prenosnik toplote in ekspanzijska enota. Veliki izkoristki centrifugalnih kompresorskih in ekspanzijskih turbin ter učinkovit prenos toplote med obema tekočinama so bistveni za izkoristek celotnega sistema. Kompresorska in ekspanzijska turbina morata biti narejeni tako, da so torne izgube (toplotne izgube) na stene in izgube zaradi spremembe hitrosti zmanjšane. V prenosniku toplote lahko opazimo dva glavna vira izgube eksergije: temperaturni in tlačni padec. Posledica prvega vira izgub je nižja temperatura hladilnega sredstva (vode), delovnega sredstva (zraka) ali kot višje razmerje T 3/T1, kar zmanjša hladilno število COP (sl. 2). Tlačni padec je vzrok za nižje pridobljeno delo ekspanzije, čeprav nismo upoštevali tlačnega padca v prenosniku toplote. Iz rezultatov simuliranja lahko ugotovimo, da ne moremo poiskati celovite točke optimalnega delovanja. Le to lahko določimo za vsak primer posebej. Pravilnost in natančnost tega simulirnega programa bomo potrdili z izvedbo preskusa odprtega zračnega hladilnega cikla, katerega demonstracijsko progo postavljajo na Inštitutu za okoljske znanosti in energijske raziskave - TNO, Nizozemska [7]. Izmerjene vrednosti določenih parametrov sistema bodo pokazale odstopanja med preskusom, torej realnim postopkom, in računalniškim simuliranjem delovanja hladilnega zračnega kroga. The diagram shows how the cooling number depends on the compression pressure. The less compression work is lead to the system, the lower is the cooling number. At the same time this means that air is less effectively cooled. Theoretically, there exists a point that is the best comprimise between the COP and the temperature of the outlet air. 4 CONCLUSION A performance simulation program for a CFC-free air-conditioning system has been developed. Such air-conditioning systems are popular because of their low environmental impact. A computer program was written in the FORTRAN language and based on thermodynamic equations. The cooling system consisted of three basic units: compression unit, heat-exchanger unit and expansion unit. High efficiencies of the centrifugal compressors and expanders and an effective heat exchange between fluids are essential for the efficiency of the system. Both compressor and expander must be built so that fric-tional losses (power-heat losses) to the walls and the velocity-change losses are reduced. Two main losses of exergy can be identified in a heat exchanger: the temperature drop and the pressure drop. The first loss will result in a lower temperature of the cooling heat-transfer fluid (water) or a higher than necessary T3/T1 that will reduce the COP (Fig. 2). A pressure drop will result in a lower regained power in the expander, though we did not observe that a pressure drop in the heat exchanger occurred. From the results of the simulation we found that a global optimum cannot be determined. It can only be found for each individual case. The correctness and accuracy of this simulation program will be confirmed by performing an experiment on an open-cycle air-conditioning system that has been made at the Institute of Environmental Sciences, Energy Research and Process Innovation TNO, Netherlands [7]. The measured values of certain parameters of the system will show any differences between the simulation performance and an actual CFC-free air-conditioning system. specifična entalpija stanja i entalpijska razlika plinska konstanta zraka specifična toplota posameznega fluida tlak razmerje specifičnih toplot zraka temperatura stanja i volumski tok stanja i masni tok za posamezen fluid 5 SIMBOLI 5 SYMBOLS hi J/kg specific enthalpy at state point i Dh J/kg enthalpy difference R J/kgK gas constant for air cp i J/kgK specific heat for an individual fluid pi Pa pressure c - ratio of the specific heat capacity for air Ti K temperature at state point i Vi m3/s volume flow rate at state i mi kg/s mass flow rate for individual fluid gfin^OtJJlMISCSD 01-7 stran 311 |^BSSITIMIGC U. Stritih - M. Mo`e - P. Novak: Model in simuliranje - Design and Simulation toplotna prehodnost površina stopnja izmenjave temperature v prenosniku toplote izkoristek stanja i specifična entropija stanja i eksponent politrope stanja i kompresijska moč moč ekspanzije izgube toplotne energije v kompresorju odstotne izgube toplotne energije v kompresorju toplotna vrednost pretoka za posamezen fluid razmerje toplotnih vrednosti karakteristično število kapacitete prenosnika toplote temperaturna razlika med vstopnim zrakom in izstopno hladilno vodo temperaturna razlika odvedena toplota s prenosnikom toplote hladilna obremenitev hladilno število k W/m2K Am2 f hi si J/kgK i PCO W PEX W QW LOSE X Wi W/K t CNC JK Dt K QW OUT QIN W WW COP thermal conductance surface degree of reciprocity of temperature in heat exchanger efficiency at state point i specific entropy at state point i polytropic exponent at state point i compression power expansion power losses of heat energy in compressor percentage losses of heat energy in compressor capacitance rate for individual fluid ratio of capacitance characteristic number of capacity for heat ex changer (NTU) temperature difference between inlet air and inlet cooling water temperature difference heat transferred by heat exchanger refrigerating power, also QR cooling load coefficient of performance 6 LITERATURA 6 REFERENCES [1] Thermophysical properties of refrigerants (1993) ASHRAE - American Society of Heating, Refrigerating and Air-Conditioning Engineers, SI edition. [2] Cavalini, A., F. Steimle (1998) Natural working fluids in historic perspective: IIR Conference Natural Working Fluids ‘98, Oslo, Norway. [3] Nowacki, J.-E. (1999) COMHEX - a concept for a Joule cycle, Theoretical analysis and study, Department of Energy Technology, The Royal Institute of Technology, Stockholm, Sweden. [4] Reknagel, Sprenger, Schramek (94/95) Taschenbuch fuer Heizung + Klima Technik. [5] Jameel-ur-Rehman Khan, Syed M. Zubair (1999) Design and performance evaluation of reciprocating refrigeration systems, International Journal of Refrigeration 22, 235- 243. [6] Lee, G.H., L. Y. Yoo (2000) Performance analysis and simulation of automobile air conditioning system, International Journal of Refrigeration 23, 243-254. [7] Van Gerven, R.J.M., M.J.E. Verschoor (1999) CFC Free heat pump systems for heating and cooling of existing and new buildings, IIR/IIF Conference, 19-24 September, Sydney, Australia. Naslov avtorjev: dr. UrošStritih Mitja Može prof.dr. Peter Novak Univerza v Ljubljani Fakulteta za strojništvo Aškerčeva 6 1000 Ljubljana Authors’ Address: Dr. UrošStritih Mitja Može Prof.dr. Peter Novak University of Ljubljana Faculty of Mechanical Eng. Aškerčeva 6 1000 Ljubljana, Slovenia Prejeto: Received: 26.6.2001 Sprejeto: Accepted: 12.10.2001 VBgfFMK stran 312 © Strojni{ki vestnik 47(2001)7,313-324 © Journal of Mechanical Engineering 47(2001)7,313-324 ISSN 0039-2480 ISSN 0039-2480 UDK 65.015:373.62 UDC 65.015:373.62 Predhodna objava (1.03) Preliminary paper (1.03) Analiza delovnega postopka pri prakti~nem pouku s poudarkom na projektni nalogi An Analysis of the Working Process in Practical Classes with the Accent on the Project Task Samo Fo{nari~ Prenovljene vsebine predmeta Tehnika in tehnologija zahtevajo na izvedbeni ravni temeljitejso proučevanje praktičnih elementov pouka. Glede na dejstva, da lahko učitelj za izvedbo zadanih ciljev uporabi številne strategije, oziroma zvrsti dela pri praktičnem pouku, mu za optimalno praktično delo z učenci ostaja sorazmerno malo taksnih, ki bi bile posebej primerne. Še posebej je to pomembno takrat, kadar elimo delo v razredu opravljati čim bolj racionalno. Prispevek tako nakazuje raziskovalno analizo uporabe projektne naloge kot ene izmed primernejših zvrsti pri praktičnem pouku, upoštevajoč časovne, fiziološke, pedagoške ter psihološke vidike praktičnega dela. Vse skupaj pa lahko poimenujemo tudi “ergonomska analiza delovnega postopka” projektne naloge. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: postopki delovni, naloge projektne, metode trenutnih opažanj, analize zornega kota) The renewed contents of the subject Technique and Technology require more research and a study of the application of the practical elements of classes. In terms of the number of strategies and the different methods that a teacher is able to use to realize the goals of teaching, the number of options for practical studies available to the student is less than ideal. This is especially important where we wish to do the work in the class more rationally. This paper shows that a research analysis of a working project is one of the most appropriate approaches at the physiological, pedagogical, and psychological levels of the practical part of work. We can call the ”Ergonomic analysis of the working process” of the project task. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: working processes, project tasks, multi-moment methods, viewing angle) 0 UVOD Poučevanje predmeta Tehnika in tehnologija terja od učitelja upoštevanje številnih zahtev, ki vzgojno-izobraževalno delo pri tem predmetu delajo uspešnejše. Med takšne zahteve sodijo vsekakor želje po uvajanju čim bolj raznolikih zvrsti dela v neposredno prakso. Zvrsti vzgojno-izobraževalnega dela pri tem predstavljajo določene usmeritve, ki vodijo učni postopek in temeljijo na pridobivanju znanj, izkušenj in delovnih navad. Tako vzgojno-izobraževalno področje tehnike in tehnologije lahko uporablja naslednje zvrsti dela: - delovno nalogo, - konstrukcijsko nalogo, - razstavljanje, analizo in sestavljanje tehničnih predmetov, - preskus tehnoloških lastnosti, - metodo štirih stopenj in - projektno nalogo [3]. 0 INTRODUCTION In order to teach the subject of Technique and Technology the teacher is asked to fulfil the requirements that make the educational work more successful. One of the requirements is the move to introduce a greater variety of work, which has specific orientations guiding the learning process and is based on gaining knowledge, experience and working habits. The educational field of “Technique and Technology” can use the following types of work: - working lesson, - design lesson, - decomposition, analysis and composition of the technical objects, - experience of technological qualities, - the method of four degrees, - project task [3]. stran 313 S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process Uporaba posameznih zvrsti je odvisna od vsebine dela, zadanih ciljev, usklajenosti ustreznih programov dela, povezave z drugimi predmeti itn. 1 DOLOČITEV PROUČEVANEGA PODROČJA Naše proučevanje je vzelo pod drobnogled projektno nalogo, za katero menimo, da ima nekako največje možnosti za problemsko zasnovo učnega postopka Gre seveda za takšno zvrst vzgojno-izobraževalnega dela, ki je v praktičnem pomenu idealna pot za izvajanje učnega procesa pri predmetu tehnika in tehnologija. Dejstvo je, da je projektna naloga načrtna dejavnost, ki pomeni sintezo učenčevih notranjihželja in potreb. Hkrati pa večino svojih prvin črpa iz elementov projektnega učnega dela, ki se nekako zrcalijo predvsem v: - skupnem izvajanju nalog iz vsakodnevne življenjske prilike s postavljanjem praktičnega cilja; - sodelovanju; - uporabi znanj iz različnih strokovnih področij; - udeležbi prav vseh učencev pri izvajalnih delih, ki pa so med seboj različna; - prevladovanju izkustvenega učenja, v katerem se prepletajo med seboj različni deleži učenčeve dejavnosti (npr. kognitivni, afektivni, motorični, socialni itn.) [2]. Tako je lahko organizacijsko-izvedbena shema projektne naloge pri predmetu Tehnika in tehnologija naslednja: The use of a specific type depends on the content of work, goals, reconciliation with work programmes, correlation with other subjects, etc. 1 DEFINITION OF THE RESEARCH PROBLEM Our research took a closer look at the project task that we believe has the best possibilities for the learning process plan. In the practical sense it is the ideal way of accomplishing the learning process in the particular subject of Technique and Technology. The project task is a planned activity, representing a synthesis of the students’ inner needs and wishes. Most of the elementary matters come from the project learning process, which is: - to carry out the tasks together with the fulfilment of a practical goal, - cooperation, - using the knowledge of different professions, - cooperation of all students in different kinds of work, - the primary emphasis on experimental learning, including different segments of student activities (social, affective, cognitive, etc.) [2]. The scheme of the project task for the subject Technique and Technology can be illustrated in this way: analiza in ovrednotenje izdelka - projekta analysis and estimating of product - project work izvedba dela na tekočem traku work realization on the assembly line rr obisk delovne organizacije excursion to the working organization ^ priprava serijske proizvodnje preparing the serial production Sl. 1. Organizacijsko - izvedbena shema vzgojno-izobraževalnega dela pri pouku tehnike in tehnologije Fig. 1. Organizational and practical scheme of educational work for the subject Technique and Technology \ws^mmi stran 314 S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process Učne enote, ki sestavljajo projektno nalogo, so nastavljene tako, da se lahko projektna naloga izvaja s sodelovanjem učencev enega razreda ali pa več vzporednih oddelkov različnih razredov. Pri tem so dejavnosti v projektni nalogi takšne, da razvijamo izdelek od njegove zamisli do potrditve problema. Vse to pa pomeni dober didaktični model za pridobivanje znanja, spretnosti, delovnih navad ter ustvarjalnih zmožnosti učencev na področjih, ki jih obsega pouk tehnike in tehnologije. V bistvu je to nekakšna zrcalna slika proizvodnega dela, oziroma uporaba v malem glede na industrijske razsežnosti. Glede na dejstva, da je proizvodni uporabniški sistem skupek več dejavnikov; začenši od delovne naloge, izvajalca dela (učencev), delovne priprave, vstopnih elementov, izstopnih elementov, proizvajalnega postopka in motenj, smo se v naši Learning units are composed so as to enable project work to be conducted with the cooperation of students of one or more classes. The activities in the project work include the development of the object from the idea to the verification of the problem. All of this introduces a good didactic model for improving the knowledge, the working habits, the skills and the creative abilities of students in the field of Technique and Technology. It is a mirror image of production work, an application in miniature in accordance with industrial extensions. Because the production–application system is a mixture of several elements, starting with working lessons, the performers (students), working equipment, incoming and outgoing elements, production process and disturbances, we decided to PROJEKTNA NALOGA PROJECT TASK J3L metoda trenutnih opažanj multimoment me thod (MT O) tt spremembe v pomenu časovne in materialne racionalizacije modification in the sense of time and material rationality razvoj zamisli developement of idea I izdelava prototipa making a prototype 1 konstruiranje designing | priprava serijske proizvodnje preparation of serial production ekskurzija excursion delo work sklep conclusion O ocenjevalna metoda za analizo telesnih položajev ovaco working postures analysis system (OWAS) spremembe v ergonomsko-ekološkem pomenu modification in the ergonomics-ecological sense ---------> UČITELJEVA ANALIZA PRAKTIČNEGA DEL A TEACHERS ANALYSIS OF PRACTICAL WORK -------r i i H-------- PREDLOG ZA IZBOLJŠAVO PROJEKTNE NALOGE ALI NOVA PROJEKTNA NALOGA SUGGESTION FOR IMPROVEMENT OF PROJECT TASK OR NEW PROJECT TASK Sl. 2. Struktura projektne naloge pri praktičnem pouku in povezanost z metodo trenutnih opažanj ter ocenjevalno metodo za analizo telesnih položajev Fig. 2. Structure of project task in the practical lesson in connection with the Multimoment Method and method Ovaco Working Postures Analysing System ^vmskmsmm 01-7 stran 315 |^BSSIrTMlGC S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process raziskavi odločili obdelati nekatere dejavnike, ki so obremenilni dejavniki določenih dejavnosti pri praktičnem delu v šoli. Tako smo z vključitvijo projektne naloge v raziskovalni postopek podrobno analizirali delovne dejavnosti učencev, tako iz vidika racionalizacije dela kakor z vidika njihove obremenitve (sl. 2). 2 RAZISKOVANJE AKTIVNOSTI PO METODI TRENUTNIH OPAŽANJ V prvem delu raziskave je imela glavno vlogo posebna analitično-statistična metoda, imenovana “metoda trenutnih opažanj” (MTO). To je metoda ugotavljanja vnaprej izbranih stanj določene osebe ali predmeta s posnetki ob naključnih trenutkih. Pri tem je sistematika snemanja takšna, da oseba, ki snemanja izvaja v njegovem toku, ki lahko traja tudi daljše časovno obdobje, vsakdan ob naključno izbranih časih obide vsa pripadajoča delovna mesta, ter na svojem snemalnem listu napravi zapis, ki označuje vrsto dogodka. Na ta način lahko dobimo za vsako dejavnost v delovnem postopku objektivno sliko o določeni dejavnosti v fazi dela [5]. Področja uporabe te metode so zelo velika, zato jo lahko vpeljemo tudi v področje proučevanja delovnih razmer pri praktičnem pouku. Ker pa se samo delo in postopek pri delu nekoliko razlikujeta od stanja v industriji, je treba poprej temeljito proučiti uporabnost in vsebinsko naravnanost tega pouka. Šele na podlagi takšne razgradnje je mogoče kasnejše praktično delo snovno razdeliti in ga opredeliti na različne faze dela, ki spremljajo raznovrstne dejavnosti. Proučevanje dejavnosti v nadaljnji fazi daje veliko odgovorov na vprašanje, ali delamo uspešno ali neuspešno? Zelo pomembno vlogo ima na tem mestu čas, ki je potreben da se delovna dejavnost izvede. Tega navadno pri šolskem, - praktičnem delu navedemo v tehnološkem listu in pomeni čas, ki je okvirno določen za vsako delovno operacijo na podlagi demonstracijske izdelave izdelka, ki ga je opravil učitelj tehnike. Do pravih, dejanskih časov izdelave izvajanja posamezne delovne operacije bi lahko prišli šele na podlagi izvajanja dela učencev in pazljive analize vsakega njihovega giba. Ker pa je v našem primeru šlo samo za veliko uporabo serijske proizvodnje, tako ni bilo treba, natančno in temeljito proučiti ter analizirati prav vseh pomembnih dejavnikov porabe časa. Morali smo samo najti tisto časovno optimalno pot, ki bo ustrezala raznolikim interesom, zmožnostim in znanjem učencev. Pri tem je bila izjemno pomembna pravilna snovna razdelitev dela, z vsemi delovnimi fazami. Na podlagi snovne razdelitve, so bile izvedene meritve, ki so pokazale zastopanost posameznih dejavnosti v procesu izvedbe vzgojno-izobraževalnega dela pri izbrani projektni nalogi. _____01 7 SnnBjtgleJUpillOlflugO | ^BSfirTMlliC | stran 316 research some elements which are the principle disturbances in practical activities during practical work in the school. By including the project work into the research process, we analysed in detail the working activities of students in terms of work rationality and labour burden (Figure 2). 2 RESEARCHING THE WORKING ACTIVITY WITH THE “MULTI-MOMENT METHOD” In the first part of the research work the principle role was played by the analytical statistical method called the “Multi-moment method” or the method of momentary observation. This method uses a camera at particular moments to capture the states of a person, or subject, chosen beforehand. The system of recording can last for longer periods at fixed times every day, incorporating visits to all working places and the taking of notes about events. For every activity in the working action we can get a very objective picture about the presence of specific activities in the state of work [5]. We can use this method in many areas, which is why we can also introduce it to the fields of researching the working conditions of practical lessons. It is necessary to assess the application and contents of these classes beforehand because the work itself and access to it are slightly different than in industrial conditions. On the basis of this deconstruction it is possible to break down the content of the practical work and define it with different phases of work, which are accompanied by a variety of activities. The study of activities gives many answers to the question, whether we are working successfully or not. A very important aspect is the time required for the work activity to be accomplished. In the practical work at school we document the time needed for every activity, based on the demonstrational production of some object, in the form of a specialized technical paper. To determine the time needed for students to accomplish specific working operations, we can carefully observe and analyse their movements. As our research incorporated only an application of serial production, it was necessary to analyse and assess every detail of time usage. For all factors of time usage we merely needed to determine an optimum time method in accordance with the interests, abilities and knowledge of the students. Especially important was the right material distribution of work at all stages. Base measurements were taken that showed the activities in the process of educational work during the chosen project work. S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process Preglednica 1. Razdelitev delovnih aktivnosti po posameznih učnih temah pri projektni nalogi Table 1. Distribution of working activities on different subjects during project work UČNA TEMA TEACHING THEME DEJAVNOSTI ACTIVITY razvoj zamisli development of idea risanje, pospravljanje drawing, cleaning izdelava prototipa making a prototype zarisovanje,žaganje, vrtanje, brušenje, sestavljanje, površinska zaščita, pospravljanje delineate, sawing, boring, grinding, assembling, surface protection, cleaning konstruiranje designing risanje, pospravljanje drawing, cleaning priprava serijske proizvodnje preparing the serial production rezanje, risanje cutting, drawing obisk excursion opazovanje observation delovne operacije po korakih work operations by steps zarisovanje, žaganje, vrtanje, brušenje, struženje, sestavljanje, ponovno brušenje delineate, sawing, boring, grinding, turning, assembling, repeatedly grinding konec dela z ovrednotenjem conclusion and evaluation nadzor, preskus,vrednotenje control, testing and evaluation Preglednica 2. Posamezne delovne dejavnosti pri postopku izvedbe projektne naloge Table 2. Presence of specific working activities in the realization process in project work DELOVNA DEJAVNOST Zastopanost dejavnosti v postopku izvedbe projektne naloge WORK ACTIVITY Representing of activity in the process of project task realization NEPOSREDNO DELO: DIRECT WORK: % risanje / drawing 22,1 izbiranje gradiv / selecting materials 0,7 zarisovanje / delineate 4,5 žaganje / sawing 5,6 vrtanje / boring 6,5 brušenje / grinding 5,8 sestavljanje / assembling 8,6 površinska zaščita / surface protection 5,2 rezanje / cutting 2,7 opazovanje / observation 12,2 struženje / turning 8,4 nadzor / control 2,1 pospravljanje / cleaning 3,1 preizkus / testing 1,7 NEPOSREDNO DELO SKUPAJ: DIRECT WORK – TOGETHER: 89,3 DRUGO NAČRTOVANO DELO: OTHER PLANNED WORK: razgovori / talking 2,1 fiziološke potrebe / physiological needs 2,1 ostale dejavnosti / other activity 1,7 počitek / rest 0,6 DRUGO NAČRTOVANO DELO SKUPAJ: OTHER PLANNED WORK - TOGETHER: 6,5 DRUGO NENAČRTOVANO DELO: OTHER UNPLANNED WORK: 3,1 nedisciplina / undiscipline: 1,1 SKUPAJ: TOTAL: 100,0 | lgfinHi(š)bJ][M]lfi[j;?n 01-7_____ stran 317 I^BSSIfTMlGC S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process Kakor vidimo, so iz prejšnjih preglednic dobro vidne posamezne delovne operacije in dejavnosti, ki jih učenci izvajajo med delovnim postopkom. Tako lahko dobimo dokaj zanesljivo predstavo o zastopanosti neposrednega dela med projektno nalogo ter zastopanosti načrtovanih in nenačrtovanih elementov dela, ki jih pri pouku lahko označimo kot dobre ali slabe izgube1. Bolj nazorno lahko takšne ugotovitve predstavimo z naslednjo preglednico in grafičnim prikazom: In the synoptic tables we can see the presence of individual activities in the working process. We can get a reliable image of the activities as well as of planned and unplanned elements of work, which can be characterized as “good or bad losses1”. We can see this more clearly in the next index and graphics: Preglednica 3. Razmerja med posameznimi oblikami dela med projektno nalogo Table 3. Relation between separate forms of work in the project task DELOVNA DEJAVNOST V % HOURS AT THE TEACHING UNITS: razvoj zamisli izdelava konstruiranje priprava obisk delo sklep WORKING prototipa proizvodnje ACTIVITY IN % development making the design preparing excursion work conclu- of idea prototype the production sion 1 2 3 4 5 6 7 8 9 10 11 12 NEPOSREDNO DELO DIRECT WORK 86,6 86,6 96,7 100 80,0 93,3 90,3 86,7 86,7 92,4 95,6 60,0 NA CRTO VANO IN DRUGO NENA CRTOVANO DELO PLANNED AND 13,4 13,4 3,3 0 20,0 6,7 9,7 13,3 13,3 7,6 4,4 40,0 OTHER UNPLANNED WORK RAZMERJE MED DELOVNO DEJAVNOSTJO IN NEDELOM RELATION BETWEEN WORKING ACTIVITY AND INACTIVITY 100 90 80 70 60 50 40 30 20 10 0 NEDEL O - " IZ GUB E" INACTIVITY - “WASTE” DELOVNA DEJAVNOST WORKING ACTIVITY 1 2 3 4 5 6 7 8 910 Delovne ure / Working hours 11 12 Sl. 3. Grafični prikaz razmerja med posameznimi oblikami dela med projektno nalogo Fig. 3. Graphical views of the relation between separate forms of work in the project task 1 “Dobre ali slabe izgube” so, gledano s pedagoško-didaktičnega vidika, težje predstavljive, saj na tem področju lahko govorimo predvsem o slabem ali dobrem učnem delu, vendar gledano analitično, predstavljajo neizogibne dejavnike vsakega postopka ter so sestavni element vsakega pouka. 1 “Good or bad losses”; from the pedagogical-didactical points are not easy to envision, because we are concerned for the most part about good or bad learning processes, but analytically they introduce unavoidable facts pertinent to every process and are therefore part of every lesson. VBgfFMK stran 318 S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process 3 ANALIZA DELOVNIH POLOŽAJEV PO METODI “OWAS” Do sedaj smo se več zanimali za racionalno plat izvedbe operativnih funkcij učenca pri praktičnem pouku. Sedaj pa poglejmo, kaj lahko še v pomenu ergonomskega proučevanja naredimo iz zornega kota ocene obremenjenosti učencev pri istem delu. Gledano iz proučevalno analitičnega zornega kota je lahko v te namene zelo primerna opazovalna metoda OWAS, ki se celotne zadeve loteva na fiziološki osnovi in predstavlja enega izmed elementov Ocenjevalne analize delovnega mesta [7]. Pri tej metodi oseba, ki opravlja meritve opazuje učenca ter opažene položaje zapisuje v določene formularje v naključnih časovnih obdobjih. Pri tem lahko tako spremlja enega ali več učencev, pri čemer se zapiski označijo s črticami ali pikicami. Sušnik [9] navaja naslednjo sistematiko opazovanja pri omenjeni analizi: Ob vsakem pogledu, podobno kakor s fotografsko kamero zapišemo po eno črtico v skupini 1, 2, 3 in 5.1 do 5.4. V skupinah 3, 5.5 in 6 pa več, kadar so roke v neki delovni funkciji, glava zasukana za kot, večji od 45 ° ali kadar se premagujejo sile večje od 10 N. Zato morajo biti seštevki v skupinah 1, 2, 4 in 5.1 do 5.4 enaki. Če nekako na hitro pogledamo rezultate takšnega “snemanja”, lahko kljub premajhnemu številu posnetkov in nepopolni analizi pridemo do nekaterih sklepov: - večina opazovanih položajev je v območjih, kjer ukrepi niso potrebni; - pri opazovanju hrbtenice v ledvenem delu, so vidne določene obremenitve v segmentih 1.2 in 1.4, kar pomeni, da bi v prvem primeru bili ukrepi potrebni v nekem krajšem časovnem obdobju, v drugem pa takoj. Ukrepi bi bili prav tako takoj potrebni pri pretiranem sklanjanju glave naprej - nekako nad kot 30° (segment 5.2) Tako lahko po izvedeni analizi povzamemo, da so preobremenitve hrbtenice in glave v delovnem procesu izvajanja projektne naloge tisti dejavniki, ki lahko vidno vplivajo na končni rezultat dela in tako tudi negativno na zdravstveno stanje učencev. Načrtovanje delovnega postopka pri praktičnem pouku zahteva vsekakor takšna delovna mesta učencev, pri katerih bo njihovo delo lahko potekalo učinkovito ter z dobrimi delovnimi rezultati ob normalnem utrujanju. Vse to pa lahko dosežemo takrat, kadar je delovno mesto učenca zasnovano tako: - da učenec dela v telesni drži, ki je najmanj naporna; - da dela na delovnem mestu, ki je po obliki in merah prilagojeno učenčevem telesu in gibljivosti njegovega telesa; - da je delovno mesto opremljeno z delovnimi sredstvi, ki so tako po fiziološki in psihološki ravni prilagojeni telesu učenca. 3 ANALYSIS OF WORKING POSITION WITH THE “OWAS” METHOD So far we have seen the rational part of realizational-operational functions of the student in practical lessons. Now we can look at what can be achieved by increasing a student’s labour burden during the same work. For the research-analytical point of view we can use the OWAS (Ovaco Working Postures Analysing System) observation method, which treats the subject on a physiological basis and represents one of the elements of our analytical estimation of the working place [7]. The measurement involves observing the student and writing down the postures on a specific form in chosen coincident time periods. One can observe one or more students, making notes with dots or lines. Sušnik [9] gives the system of observation of the analysis mentioned above: At every look -similar to a camera - we create for example a group of 1, 2, 3 and 5.1 to 5.4. In the groups 3, 5.5 and 6 there are more lines, when the arms are engaged in one working function, the head is turned for more than 45° or when there is bigger force than 10 N. The sum must therefore be the same in the groups 1, 2, 4 and 5.1 till 5.4. If we take a quick look at the results of this “recording” we can come to some conclusions in spite of the insufficient number of examples and imperfect analysis, showing: - most observed postures are in the areas where it is not necessary to make special arrangements; - observing the spine in the kidney area, we can see specific burdens in the segments 1.2 and 1.4. In the first instance we should take appropriate steps within a short time period, in the second case action should be taken immediately. Measures should also be taken at once in the case of bowing the head forward more than 30° (Segment 5.2). After the analysis we can conclude that the overburdening of spine and head are those factors in the working process which visibly influence the final work result as well as having negative health effects on students. The planning of the work process in practical classes calls for working conditions which allow for effective and productive work with an acceptable level of fatigue. We can achieve this when the workplace is designed with these factors in mind: - the student should be able to work in the least fatiguing physical posture; - the student works in a workplace that is physically proportioned to the student’s body and body movements; - the workplace must be equipped with tools and equipment that are, at a physiological and psychological level, suited to the student. | lgfinHi(š)bJ][M]lfi[j;?n 01-7_____ stran 319 I^BSSIfTMlGC S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process Preglednica 4. Kratka opazovalna analiza drže telesa pri izvedbi projektne naloge po prilagojeni metodi OWAS na primeru treh učencev. Predstavitev deleža posamezne drže telesa v delovnem krogu projektne naloge (Karakteristike posameznih delov so podane pod sliko 4!) Table 4. Short observation analysis of the postures during project work using the modified OWAS method. Representation of the proportional occurrence of specific postures in the working cycle of project work (See Figure 4!) SEG. OWAS v / in % 10 50 60 70 80 100 HRBET / SPINE 1.1 i / | ___ V + + + - + + + + + + + 1.2 40 + - - * 90 + * * * 1.3 7 1.4 ^A. 20 + + + - + + + + + + + 30 + + - - + + - - + + + - * * * * * * * * * ZGORNJA UDA / UPPER LIMBS 2.1 Q A 2.2 2.3 V V t \ 2.4 t t ROKI / ARMS 3.1 3.2 3.3 + + * + + + X X X X X X X X X + + + + SEG. OWAS v / in % 10 100 SPODNJA UDA / LOWER LIMBS 4.1 20 + + + - + + X X + + + + + + + + 4.2 / 4.3 4.4 4.5 4.6 ft 30 + + + - + + X X 40 + + - * - + X X 90 - - * * * - X 50 + + - * - + X X 60 + + - * - + X X 70 + + - * - + X X 80 + + - * * + X X * * - X 4.7 (A 4.8 X X SEG. OWAS v / in % 10 50 60 100 GLAVA / HEAD 5.1 a + + + + + + 5.2 > 30° 20 + + + - + + 5.3 > 30° \ 40 + - - * - 70 + * * * - + 80 + * * * * - 90 + * * * * 5.4 >30° *\ 30 + - - - + + 5.5 J, > 45° SILA / FORCE 6.1 10 N DO / TO 99 N * - + * - + legenda / legend: + ukrepi niso potrebni preventive measures are not necessary - ukrepi so potrebni v doglednem času preventive measures are necessary in the foreseeable future ukrepi so potrebni takoj preventive measures are necessary immediately X za razjasnitev so potrebne * I * I - I podrobnejše raziskave for clarification more detailed research is needed VBgfFMK stran 320 S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process ZASTOPANOST D EJ AVN OS TI REPRESENTING OF AC TIVITY (%) 100 90 80 70 60 50 40 30 20 10 0 t ffl o fin JID Segment 1.1. 1.2. 1.3. 1.4. 2.1. 2.2. 2.3. 2.4. 3.1. 3.3. 4.1. 4.2. 5.1. 5.2. POLOŽAJI TELESA BODY POSITIONS Opisi karakteristik (položajev telesa) po metodi OWAS: Description of body position with the OWAS method: OWAS Telesni del in opis karakteristike Segment and description of body positions HRBET / SPINE 1.1. Pokončna drža hrbta, pri katerem je pripogib manjši od 15° Upright posture of spine (flexion < 15°) 1.2. Sklonjena drža hrbta, pri kateri je pripogib večji od 15° Bowed posture of spine (flexion > 15°) 1.3. Pokončna drža hrbta s torzijo ali stranskim pripogibom hrbta, ki je večji od 30° Upright posture of spine with torsion or lateral flexion > 30° 1.4. Sklonjena drža hrbta, pri kateri je pripogib večji od 15° in kombiniran s torzijo ali stranskim pripogibom hrbta, ki je večji od 30° Bowed posture of spine (flexion > 15°), combination with torsion or lateral flexion > 30° ZGORNJA UDA UPPER LIMBS 2.1. Obe nadlakti ob trupu Upper arms at body 2.2. Ena ali obe nadlakti dejavno odročeni in pod nivojem ramen (komolca nista oprta) One or both upper arms activity abduction 2.3. Ena nadlaket nad nivojem ramena One upper arm is above the level of shoulder 2.4. Obe nadlakti nad nivojem ramen Both upper arms are above the level of shoulder ROKI / ARMS 3.1. Drobni ali grobi prijem ene ali obeh rok Fine and rough hold one or both arms 3.3. Druge dejavnosti ene ali obeh rok Other activity of one or both arms SPODNJA UDA LOWER LIMBS 4.1. Sedenje (fiziološko ali nefiziološko) Siting (physiological or unphysiological) 4.2. Stanje Standing GLAVA / HEAD 5.1. Pokončni nevtralni položaj glave Upright - neutral position of head 5.2. Glava je sklonjena naprej nad 30° Head is ventral bowed above 30° Sl. 4. Grafična predstavitev deleža posameznega položaja v delovnem krogu projektne naloge, izražena v odstotkih z opisom karakteristik telesnih obremenitev po metodi OWAS Fig. 4. Graphical representation of proportional occurrence of specific postures in the working cycle of project work using the OWAS method. S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process 4 NEKATERE DRUGE UGOTOVITVE Glede na to, da je za dobro počutje in dvig produktivnosti pomembna dobra razsvetljava, je treba določeno pozornost nameniti tudi načrtovanju pravilne osvetlitve šolske delavnice. Znano je, da je učinkovitost učenčevega vida odvisna od ploskovne osvetljenosti vidnega polja in kontrasta med osvetljenostjo vidne naloge ter okolice. Tako lahko, upoštevajoč standarde ter normative, pravilno izberemo zahtevane osvetljenosti notranjih prostorov. Ker je večina delovnih prostorov v delavnicah osvetljenih s fluorescentnimi svetili in ker je zahtevana stopnja osvetljenosti splošne razsvetljave označena kot »srednja«, mora biti povprečna vrednost osvetlitve večja od 150 luksov. Če pa bi hoteli določena delovna mesta dodatno osvetliti, kar pa v našem primeru ni bilo potrebno, bi potrebovali dodatno razsvetljavo v razponu med 50 in 300 luksi. Na podlagi dejstva, da so bili v naši študiji učenci med samim učnim procesom videti dokaj utrujeni, smo sklepali da so lahko vzroki za takšno reakcijo tudi v svetlobi. Slednja je bila za delavnico, kjer smo izvajali projektno delo, v določenih delih prešibka, drugod pa premočna Tako je bilo pri samem delu tudi opaziti moteče bleščanje, ki je najverjetneje posledica slabo načrtovane delavnice, saj so luči, ki osvetljujejo prostor, prenizko. Posledično se to kaže v prevelikih kontastih v zornem kotu učencev. Pravilno oblikovano delovno mesto učenca bi torej moralo upoštevati številne dejavnike, ki bi zadovoljili zahteve po pravilni osvetlitvi pri delu. Tudi toplotno okolje v našem primeru ni bilo takšen faktor, ki bi ga kar prezrli. Za učilnice praktičnega pouka v osnovnihšolah je nekako značilno, da se nahajajo v kletnih prostorih, ki pa so v bližini kurilnic in podobnih izvorov dodatne toplote, kar je bilo tudi v našem primeru. Skupna značilnost postavitve učilnic na takšno lokacijo je ta, da so pozimi zelo suhe in pretirano segrete, medtem ko so poleti nadpovprečno vlažne in hladne. Pri tem prihaja do problemov zaradi neprestanega menjavanja učencev (hladno in toplo), tako da pravega časa za aklimatizacijo dejansko nimajo. Tudi telesna drža je pomemben dejavnik na delovnem mestu. Delo, ki ga učenci opravljajo, je namreč tudi za njih lahko bolj ali manj obremenjujoče. Tako je za vsakega učenca najmanj obremenjujoča sedeča drža, medtem ko bi tajna stojeČa drža lahko povzročala povečano prekrvitev spodnjih okončin in tako kopičenje krvi v spodnjih udih. V takšnih primerih in na takšnih delovnih mestih je primerno načrtovati sedeže, ki omogočajo občasno menjavo med stoječo in sedečo držo telesa. Povzamemo lahko nekako takole, da so prav obremenitve hrbtenice tiste, ki bi pri praktičnem šolskem delu morale biti deležne podrobnejših proučevanj. 5 PRAKTIČNI SKLEPI Na podlagi poskusnega snemanja dajejo dobljeni rezultati določeno sliko o posameznih dejavnostih pri praktičnem pouku na modelu projektne naloge. S temi podatki že lahko najdemo nekatera področja in stanja, ki bremenijo učence in tako vplivajo na uspešnost opravljenega dela. Čeprav pomeni _____01 7 SnnBjtgleJUpillOlflugO | ^BSfirTMlliC | stran 322 4 SOME OTHER FINDINGS For well–being, and in order to increase productivity, it is important to have good lighting; therefore, we should pay attention to the correct planning of light installation in working places and schools. It is well known that the efficiency of a student’s sight depends on the light base of the sight field and the contrast between the lighting of the sight field and the surrounding. Accordingly, we should respect the standards and correctly choose the lighting system of inner spaces. Most work locations have florescent lights and because the required level of lighting is described as “medium” there should be the medium value of lighting, more than 150 lux. In the case of additional lighting (not needed in our case) it should be between 50 and 300 lux. Because the students were looking tired during the learning process, we concluded the reason could be the light, which was in some places too weak and in others too strong. During the work we saw disturbing glare as the result of a poorly planned working place in which the lights were set too low. This contributes to too great a contrast between light views. The appropriate place for students to work requires the consideration of many factors, for example a satisfactory heating system is important. For classes in primary school it may be an idea to be in cellar areas, which are close to the central heating and other warming resources. However, it is characteristic of the classrooms in such a location that they are too hot and dry in the winter and, for the most part, too cold and damp in summer. The problem is a constant change from wet to dry, and from cold to warm, and the students not having time to acclimatize. Body condition is also an important factor in the working place. The work done by students can vary in terms of fatigue. The sitting position is the least fatiguing, while a constant standing posture could cause increased blood circulation in the lower limbs, causing blood to collect in the lower extremities. In this case it makes sense to vary the posture between standing and sitting. In short, we concluded that the research of practical work should pay detailed attention to the burdening of the spine. 5 PRACTICAL CONCLUSIONS The results of our recording give us a picture of some activities in the model of the project work. With this information we can find some situations and conditions which fatigue the pupils and influence the success of the work. Despite the very positive inclusion of the active components of S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process projektna naloga najvišjo stopnjo vključevanja vseh dejavnih komponent učenčeve osebnosti v učno-vzgojni postopek, pa iz podatkov le vidimo pomanjkljivosti, ki so tukaj sicer časovno-organizacijskega značaja, dajejo pa kljub temu dobro sliko uspešno ali pa neuspešno zastavljenega dela (pri tem je izvzet vsebinski sklop, ki pa je še pomembnejši!). V bistvu je omenjeno proučevanje naravnano bolj na obremenjujoče psihološko-fiziološke dejavnike, kakor pa na vsebinske. Pri omenjeni analizi je še posebej pomembno to, da opazimo izstopanje določenih dejavnosti, npr.: risanje, opazovanje, struženje in sestavljanje. Pri tem sta delovni aktivnosti tehnično risanje in struženje tudi tisti, pri katerih so obremenitve določenih telesnih segmentov večje kakor drugje (glej metodo OWAS). Razmerje dela in delovnih »izgub« v različnih urah skozi ves delovni postopek pri projektni nalogi je zelo neenakomerno. Ta neenakomernost je posledica načrtovanih izgub, ki se v največji meri kažejo ob koncu dela, ko je »nedela« največ in se izražajo v različnih razgovorih med učenci in drugih šolskih dejavnostih. Pri drugih učnih urah je to razmerje v povprečju usklajeno. Zanimivo je tudi to, da je na splošno bolj moteč dejavnik delovnega postopka opravljanje določenih fizioloških in higienskih potreb kakor pa nedisciplina. To je najverjetneje zato, ker so učenci bili za delo zelo motivirani skozi ves postopek projektne naloge ter v določenih fazah dela tudi tekmovalno navdahnjeni. Domnevam, da bi morale biti delovne dejavnosti enakomerneje zastopane pri projektni nalogi, saj gre v tem primeru bolj za spoznavne postopke. Še posebej naj bi bila dejavnost opazovanja zmanjšana, saj je bilo vidno, da pri tej dejavnosti zbranost hitro upada in učence zavede v področje nedela, kar pa ima hitro za posledico nedisciplino. Za “izgube” v pomenu fizioloških in higienskih potreb bi bilo dobro poudariti, da so v šoli za to odmori. Če bi upoštevali vse te dejavnike, bi bilo razmerje med delom in “izgubami” takšno, da slednje ne bi vplivale na končni rezultat dela. Tudi iz zornega kota dimenzioniranja bi morali narediti določene popravke. Tako bi lahko določena delovna sredstva in pripomočke bolj približali učencem. Npr. delovno površino, kjer je pritrjen delovni stroj, bi lahko znižali, delovnemu mestu bi lahko dodali določene pomožne mize, ki bi rabile za racionalnejše jemanje in odlaganje materialov, delovno orodje bi pomaknili bliže robu mize, ogrodje delovnega orodja bi stalno pritrdili v delovno podlago, ipd. Proučevanje takšnega ergonomsko-dimenzijskega dela projektne naloge pri praktičnem pouku pomeni samo drugačen vpogled v vzgojno-izobraževalni postopek. Upoštevanje uporabnosti takšnega dela je pri nas v šolstvu zelo redko, oziroma ga sploh še ni. pupils’ personalities into the educational process, we can find shortcomings in the project in the areas of time and organization. However, the data gives us a good picture of successful or unsuccessful approaches to the planned work (excluding the content which are even more important!) The research was more oriented on psychological and physiological aspects than on the contents. During the analysis it was especially important to notice the particularities of some activities such as: drawing, observing, composing, rasping. The activities of technical drawing and rasping create a higher burdening of particular body parts than other activities (see OWAS method). The relation of work and work losses in different time periods throughout the work process is disproportional. The irregularity is the consequence of anticipated losses which are primarily visible toward the end of the work period. The peak of productive inefficiency is evidenced by private conversation among pupils and the transfer of attention to extraneous activities. During forms of instruction other than work classes, this relation between effective and ineffective use of time is more harmonized. It is interesting that the most disturbing element in the working process is the fulfilment of certain physiological and hygienic needs rather than a lack of discipline. The lack of disciplinary problems may be due to the enthusiasm shown by the pupils for the work project, an enthusiasm which showed itself in a friendly competitive atmosphere. It is suggested that applied activities take a primary place in the classes. The phase of the learning process, which focuses on observation by the pupil, should be limited in time, as it is during this phase that the pupils lose concentration. While engaged in work activity, there are fewer disciplinary problems and a reduced loss of focus. For the losses due to physiological and hygienic needs it would be good to point out that that is why there are breaks in school. Considering all the facts, the relation between work and loss would not influence on the end product. Dimensioning should be improved as well, in order that working equipment be more suitable for the students. An example: the working surface, where the machines are fixed could be moved lower, there could be some additional tables for placement and storage of materials, the working tools could be closer to the edge of the table, the frame of a machine could be fixed to a working surface, etc. The researching of the ergonomics– dimensional segment of the project work in practical classes provides a different view of the educational process. Consideration of the applicability of this kind of work is very rare, or absent, in the Slovenian school system. | lgfinHi(š)bJ][M]lfi[j;?n 01-7_____ stran 323 I^BSSIfTMlGC S. Fo{nari~: Analiza delovnega postopka - An Analysis of the Working Process [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] 6 LITERATURA 6 REFERENCES Fošnarič, S. (1996) Problemsko izvajanje pouka tehnične vzgoje v osnovni šoli. Pedagoška obzorja, štev. 5-6. Novo mesto, 250 - 256. Novak, H. (1990) Definiranje in opis projektnega učnega dela. Sodobna pedagogika 5 - 6. DZS Ljubljana, 303. Papotnik, A. (1988) Od ideje do proizvodnje. Tehniška založba Slovenije, Ljubljana. Papotnik A. (1991) Tehniška ustvarjalnost v srednji šoli. DZS, Ljubljana. Polajnar, A. (1999) Študij dela. Fakulteta za strojništvo, Maribor, 163-166. Sanders, M.S. and Mc Cormik (1990) Human factors in engineering and design. McGraw - Hill International Edition, New York. Stoffert, G. (1985) Analyse und Einstufung von Korperhaltungen bei der Arbeit nach der Owas - Methode. Z Arb. Wiss. 39, 31 - 38. Sušnik, J. (1983) Ocenjevalna analiza delovnega mesta. Gospodarski vestnik, Ljubljana. Sušnik, J. (1987) Položaj in gibanje telesa pri delu. Univerzitetni zavod za zdravstveno in socialno varstvo, Ljubljana, 147-153. Weiner, J.S. (1982), The measurement of human workload. Ergonomics 25, 953 - 965. Avtorjev naslov: doc.dr. Samo Fošnarič Pedagoška fakulteta Univerza v Mariboru Koroška cesta 160 2000 Maribor Prejeto: 16.3.2001 Received: Author’s Address: Doc.Dr. Samo Fošnarič Faculty of Education University of Maribor Koroška cesta 160 2000 Maribor, Slovenia Sprejeto: 12.10.2001 Accepted: VBgfFMK stran 324 © Strojni{ki vestnik 47(2001)7,325-335 © Journal of Mechanical Engineering 47(2001)7,325-335 ISSN 0039-2480 ISSN 0039-2480 UDK 699.86:006.06:536.21 UDC 699.86:006.06:536.21 Strokovni ~lanek (1.04) Speciality paper (1.04) Toplotne izgube v tla pri stavbah glede na standard SIST EN ISO 13370 -poenostavljena metoda izra~una Heat Losses to the Ground According to the SIST EN ISO 13370 Standard - a Simplified Calculation Method Bo{tjan ^erne - Sa{o Medved Toplotne izgube v tla imajo, se posebej pri velikih stavbah, velik vpliv na rabo energije za ogrevanje. V uporabi so različne metode za določitev teh izgub, vključno z metodo, ki jo predpisuje standard SIST EN ISO 13370. Ta metoda je razmeroma zahtevna. Zato smo oblikovali poenostavljeno metodo z utežnimi faktorji, ki jo predstavljamo v prispevku. Utežni faktorji so določeni za nepodkletene in podkletene stavbe z različnimi toplotnimi prehodnostmi konstrukcij, ki so v stiku s tlemi. Zmanjšano je bilo tudi število vplivnih parametrov, ki so uporabljeni v SIST EN ISO 13370. Uporaba poenostavljene metode je posebej primerna pri postopku načrtovanja toplotne zaščite stavb in določevanja specifičnih toplotnih izgub le-teh. © 2001 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: zaščita toplotna, zaščita zgradb, prenos toplote, metode izračunavanja) Heat losses from buildings through contact with the ground, especially in the case of large buildings, have a strong influence on energy demand. Various methods for calculating these heat losses are available, including one method that is defined by the SIST EN ISO 13370 standard. Due of the complexity of this method we have developed a method that is presented in this paper. Using our method we have calculated weighting factors for buildings with and without basements with a variety of thermal transmittances of structures in the contact between the building and the ground. Also the number of influential parameters used in SIST EN ISO 13370 is reduced. Our simplified method is particularly appropriate for use in the process of designing the thermal insulation of buildings and determining the specific heat losses from buildings. © 2001 Journal of Mechanical Engineering. All rights reserved. (Keywords: thermal insulation, building insulation, heat transfer, calculation methods) 0 UVOD Izkušnje kažejo, da toplotno zaščito in njeno pravilno vgradnjo načrtujejo arhitekti v začetni fazi snovanja stavbe. Zato je odločitev arhitektov povezana z dolgoročnimi posledicami. Metode za določitev toplotnih lastnosti gradbenih konstrukcij, ki potrebujejo veliko vhodnih podatkov, so zahtevne in lahko vodijo k nepravilnostim. Kot zahtevno lahko ocenimo tudi metodo za izračun toplotnih tokov v tla, ki jo določa SIST EN ISO 13370. V tem prispevku je opisan razvoj poenostavljene metode, s katero določimo toplotni tok skozi gradbeno konstrukcijo, ki je v stiku s tlemi. Toplotni tok lahko normaliziramo glede na ogrevano prostornino ali površino ovoja stavbe in se tako prilagodimo različnim predpisom o toplotni zaščiti stavb. Ker je razvita metoda namenjena načrtovanju toplotne izolacije, smo uporabili izraze, ki določajo največji mesečni toplotni tok. 0 INTRODUCTION Experience shows us that heat insulation and its appropriate installation is the responsibility of the architect in the early stages of a building’s design. The decisions made by architect are, therefore, bound to long-term consequences. Methods for determining the thermal and technical properties of building structures, with their large amount of input data, are complicated, which leads to calculation inconsistencies. SIST EN ISO 13370 is one such method for determining heat losses through floors and walls. In this paper we develop a simple method for calculating heat losses to the ground, which can later be normalised to the volume or the surface of the building according to the different regulations of building’s thermal insulation. As the simplified method is designed to be used for rating a building’s thermal insulation, the expression for maximum monthly heat flow rate will be used. gfin^OtJJIMISCSD 01-7 stran 325 |^BSSITIMIGC B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground 1 DOLOČITEV TOPLOTNIH IZGUB V TLA -OPIS METOD Raba energije za ogrevanje v sodobnih stavbah se zmanjšuje zaradi vse večjega spoznanja o omejenih zalogah fosilnih goriv, spoznanj o njihovih negativnih vplivih na okolje in tudi vse strožjih predpisov o toplotni zaščiti stavb. Toplotna zaščita stavb je lahko predpisana z dovoljenimi toplotnimi prehodnostmi gradbenih konstrukcij, specifičnimi toplotnimi izgubami poslopja ([2], [15] in [16]), ali letno rabo energije za ogrevanje ([3] do [5]). Zaradi manjših toplotnih prehodnosti zunanjih zidov, strehe in še posebej oken se je povečal relativni delež toplotnih izgub v tla. To je še posebej pomembno pri poslopjih z veliko tlorisno površino, kakršno imajo trgovski centri in industrijski objekti. Toplotni tok v tla lahko določimo na različne načine: analitično z reševanjem diferencialnih enačb neustaljenega prevoda toplote ([6] in [7]); s primernimi numeričnimi metodami in programskimi paketi ([8] in [9]); semiempiričnimi enačbami v obliki linijskih toplotnih prehodnosti ([10], [11] in [13]) ali z utežnimi faktorji ([2], [12] in [14]). 1 DETERMINATION OF THE HEAT FLUX TO THE GROUND – A DESCRIPTION OF COMMON METHODS The energy used for heating in new buildings is being reduced as a result of better understanding of the limited quantities of fosil fuels, their negative influence on the environment and also because of the tighter regulations that apply to the heated building’s. The thermal insulation thickness can be determined by the permitted thermal trasmittance, the specific building heat losses ([2], [15] and [16]) or the annual heat use ([3] to [5]). As a consequences of the lower thermal transmit-tances of external walls, roofs and especially windows, the relative amount of heat lost to the ground has increased. This point is particularly important for large-area buildings, such as modern shopping centres and industrial premises. Heat flux to the ground can be determined using various methods: analiticaly by solving differential equations of non-stationary heat conduction ([6] and [7]); with appropriate numerical methods and program codes ([8] and [9]); semi-empirical equations in the form of linear thermal transmittance ([10], [11] and [13]); or weighting factors ([2], [12] and [14]). Sl. 1. Časovno ustaljene temperature tal pod ogrevano nepodkleteno stavbo, določene numerično z metodo nadzornih površin; zgoraj stavba s tlorisno površino 100x50 m, specifični toplotni tok skozi pod je 2,1 W/m2; spodaj stavba s tlorisno površino 10x10 m, specifični toplotni tok skozi pod je 7,3 W/m2 [9] Fig. 1. Steady state temperatures below the buildings on the ground - above for building with foor area 100 x 50 m, below for the building with floor area 10 x 10 m, specific heat flux to the ground is 2.1 W/m2 in case of the larger and 7.3 W/m2 in case of the smaller building [9] V standardu SIST EN ISO 13370 je toplotni tok v tla določen s semiempiričnimi enačbami, ki vsebujejo različne parametre, kot so velikost in oblika poda, toplotne prehodnosti gradbenih konstrukcij, toplotne prevodnosti tal, povprečne mesečne temperature znotraj in zunaj stavbe itn., torej razmeroma veliko število različnih vhodnih podatkov. Z uporabo metode utežnih faktorjev lahko število vplivnih parametrov zmanjšamo. Toplotni tok v tla je tako določen z enačbo: In SIST EN ISO 13370 the heat flux is determined with semi-empirical equations that are dependent on many different factors, such as the size and shape of the building’s floor, the thermal transmittances of the building’s structures, the ground’s thermal conductivity, the average monthly temperatures inside and outside building, etc., a relatively large number of different input data. With the introduction of weight factors, the amount of input data required is reduced. The heat flux to the ground is then determined by: FG=FG-UG-AG-(di-0ep) (1). Utežni faktorji (F), ki so v uporabi, so ali The weight factors (FG) in use recently are nespremenljivi (npr. 0,5 [2]) oziroma nespremenljivi v either constant (for instance 0.5 [2]) or expresed as con- VH^tTPsDI wm$!&\ grin^(afcflM]SCLD stran 326 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground določenem območju parametrov [12]. Glede na standard SIST EN ISO 13370 utežne faktorje lahko določimo iz enačbe za največji mesečni toplotni tok: stants for different variable ranges [12]. According to EN ISO 13370 the weight factor can be determined from the expression for the maximum monthly heat flux: F max (ei-ee) ) FG-UG-AG ¦(3-m/3- Sl. 3. Analizirane oblike podov stavb Fig. 3. Analysed shapes of building floors Ta karakteristična izmera je uporabljena tudi v [1] in [12]. Obseg P je opredeljen v [1]. Slika 3 prikazuje analizirane oblike podov stavb z enotnim mrežnim korakom m. Utežni faktorji (F*), določeni glede na SIST EN ISO 13370 z upoštevanjem izraza (2) za različne pode stavb, so prikazani na sliki 4. Izračuni so bili narejeni za m med 2 in 50 oziroma površino poda od 10 do 10000 m2. Vrednosti utežnih faktorjev F* so neodvisne od oblike in velikosti stavbe pri enaki karakteristični izmeri, zato pri oblikovanju poenostavljene metode ta parametra v celoti nadomestimo s karakteristično izmero stavbe B’. This characteristic dimension is also used in [1] and [12]. The perimeter P is defined in [1]. Figure 3 shows the analysed shapes of building floors with a unified raster m. Weight factor (FG*) determined according to EN ISO 13370 by using equation (2) for differently shaped building floors are shown in Figure 4. In the calculations the raster m from 2 to 50 and floor areas from 10 to 10000 m2 were taken into account. We can see that the characteristic dimension B’ is appropriate to value the building’s shape influence since the values of FG* are independent of the building shape with the same characteristic dimension B’. 1,4 1,2-1 0,6- 0,4- 0,2-0 x oblika "H" / shape "H" oblika "L" / shape "L" ¦ pravokotnik / rectangle ¦kvadrat / square 0 10 20 30 40 50 B' Sl. 4. Utežni faktorji F* so določeni za k = 1,5 W/mK, U = 0,4 W/m2K, za nepodkleteno stavbo, zgrajeno v klimatskem območju z SD = 2985 Kdan in 6 = -18°C, črtkani črti pomenita mejo ±20% Fig. 4. Values F* are determined for k =1.5 W/mK, UF = 0.4 W/m2K, building without basement built in city (area) with DD = 2985 Kday and 6 = -18oC, dotted lines represent border ±20% Največji toplotni tok v tla je v SIST EN ISO 13370 določen s povprečno letno zunanjo temperaturo in letno periodično spremembo povprečnih mesečnih temperatur. V naši metodi smo želeli te temperature nadomestili z zunanjo projektno temperaturo. Podatki o zunanjih projektnih temperaturah so namreč na voljo za veliko število krajev. Za analizo primernosti take zamenjave je bilo izbranih pet tipičnih krajev v različnih klimatskih območjih. Njihovi osnovni The maximum heat flux through a building floor according to SIST EN ISO 13370 is defined with the average annual external temperature and the annual variation in the average monthly temperatures. In the simplified method the average annual temperatures and the variation in temperatures are replaced by an external project temperature. External project temperature data are available for a larger number of cities. Also, the determination of the specific heat losses of the building is easier. For the analysis, five VH^tTPsDI wm&\ grin^sfcflMiscsD stran 328 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground Preglednica 1. Meteorološki podatki izbranih krajev (območij) Table1. Meteorological data of selected cities (areas) klimatsko področje climatic area mediteransko mediteranean celinsko continental alpsko alpine SD/DD (Kdan/Kday) 1874 q e,p (oC) -6 13,8 9,0 qe (oC) 2700 -12 10,8 9,5 2985 -18 9,7 10,5 3208 -21 9,2 11,0 3505 -24 8,2 11,0 ) qe (oC) meteorološki podatki so prikazani v preglednici 1. Za vsak izbran kraj smo izračunali utežne faktorje FG* za široko območje karakteristične izmere B’. Rezultati s prikazom funkcijske odvisnosti so prikazani na sliki 5. Razvidno je, da so vrednosti FG * za dani primer znotraj območja -8% do +12%. Pri vseh preostalih analiziranih primerih pa je pričakovana nenatančnost med metodo po SIST EN ISO 13370 in razvito poenostavljeno metodo znotraj območja, ki ga predpisuje standard [13] za metode, ki temeljijo na “izračunu z uporabo kataloga”. Iz tega izhaja, da je povprečne letne zunanje temperature in letne periodične spremembe povprečnih mesečnih temperatur mogoče nadomestiti z zunanjo projektno temperaturo določenega kraja. 1,4 typical cities in different climatic areas were chosen. Their basic meteorological data are shown in Table 1. The values of weight factors (FG*) for each selected city and a wide range of characteristic dimension’s B’ were calculated. The results, together with a function curve, are shown in Figure 5. It is evident that all FG* values are within –8% and +12% limits. It was also observed that for all analysed combinations of the influencing parameters, the differences between the Fmax calculated using EN ISO 13370 and our simplified method are smaller than expected uncertainly for manual calculations and “catalogue” methods according to reference [13]. Therefore, the average annual temperature and the variation in the average monthly temperatures can be replaced by project temperatures that are characteristic of a wide range of climatic conditions. 1,2 1 0,8 0,6 0,4 0,2 9e,p x - 6 ¦ - 12 o - 18 ¦ - 21 * - 24 0 10 20 30 40 50 B' Sl. 5. Utežni faktorji F* so določeni za k =1,5 W/mK, U=0,4 W/m2K, za nepodkleteno stavbo, 6=20 °C, črtkani črti pomenita mejo ±20 odstotkov Fig. 5. Values F* are determined for k =1.5 W/mK, U=0.4 W/m2K, building without basement, 6 = 20oC, dotted lines represent border ±20% Vrednosti (F*) pa so odvisne tudi od drugih toplotnih in konstrukcijskih parametrov. Pri razvoju poenostavljene metode smo upoštevali, da so tla bodisi glinena (k=1,5 W/mK), peščena (k=2 W/mK) ali skalnata (k=3,5 W/mK). Predpostavili smo, da so stavbe enakomerno ogrevane na 6=20 °C in da je debelina zunanjega zidu na stiku s i podom 0,35 m. Te vrednosti so bile izbrane kot najbolj The values of the weight factors (FG*) also depend on other thermal and design parameters. When designing the simplified method we took into consideration that the ground can be clay (kG = 1.5 W/m2K), sand (kG = 2.0 W/m2K) or homogeneous rock (kG = 3.5 W/m2K). The buildings are assumed to be uniformly heated to a constant temperature qi=20oC and have constructions in contact with the ground | IgfinHŽšlbJlIMlIgiCšD I stran 329 glTMDDC 0 B. ^erne - S. Medved: Toplotne izgube v tla - Heat Losses to the Ground pogoste, v praksi pričakovana odstopanja pa ne vplivajo bistveno na rezultat analize. Toplotne prehodnosti gradbenih konstrukcij v stiku s tlemi, ki smo jih analizirali, so bile 0,3; 0,4; 0,5 in 0,6 W/ m2K. Te vrednosti so bile izbrane glede na predpis o toplotni zaščiti stavb in trdnostne lastnosti gradbene konstrukcije. Glede na lastnosti konstrukcije in globino podkletitve so stavbe razdeljene na tri kategorije, kakor je prikazano na sliki 6: - nepodkletene stavbe, - podkletene stavbe z različnima toplotnima prehodnostima poda in vkopanega zidu, - podkletene stavbe z enakima toplotnima prehodnostima poda in vkopanega zidu. that are 0.35 m wide. These values were chosen as the most representative, but in any case their influence on the results is negligible. The analysed thermal trans-mittances of the building structures were 0.3, 0.4, 0.5 and 0.6 W/m2K. When choosing these values, civil engineering technologies and common building thermal protection regulations were taken into consideration. According to the building’s structural properties and the depth of the basement, buildings are divided into three categories, as shown in Figure 6: - buildings without basement - buildings with basement with different thermal trans-mittances of the basement floor and basement walls; - buildings with basement with the same thermal trans-mittances of the basement floor and basement walls; Sl. 6. Shematski prikaz analiziranih stavb. Na levi nepodkletena stavba, na sredini podkletena stavba z različnima toplotnima prehodnostima poda in vkopanega zidu, na desni podkletena stavba z enakima toplotnima prehodnostima poda in vkopanega zidu Fig. 6. Schematic survey of the buildings analysed in this work; on the left is building without a basement; in the middle is a building with a basement with different thermal transmittances of the basement floor and basement wall; and on the right, a building with a basement with equal thermal transmittances of the basement floor and the basement wall 3 OBLIKOVANJE ENAČBE UTEŽNIH FAKTORJEV (FG*) Enačbe utežnih faktorjev smo določili s statistično analizo 18720 analiziranih primerov. Enačbe za toplotni tok skozi tla (0 ) in utežne faktorje (F*) za različne tipe stavb so prikazane v nadaljevanju: - za nepodkletene stavbe je največji toplotni tok v tla določen z izrazom : kjer FG,F* določimo z izrazom: Utežni faktorji v odvisnosti od karakteristične izmere stavbe B’ za izbrano nepodkleteno stavbo so prikazani na sliki 7. Vrednosti konstant aF za analizirano polje spremenljivk so podane v preglednici 2. - za podkletene stavbe z različnima toplotnima prehodnostima poda in vkopanega zidu je največji 3 DESIGNING OF WEIGHT FACTOR (FG*) EQUATIONS Weight factor equations were determined with a statistical analysis of 18720 analysed combinations. The equations for the heat flux to the ground (Fmax) and the weight factors (FG*) for different types of buildings are shown below: - for buildings without a basement the maximum heat flux to the ground is determined by: (4), max =F* G,F ¦UF ¦AF(3-X-.-^-..-^.-.-^.-.-^l_-.- --.-7- : -.--.-^r ¦¦-¦¦-¦¦-¦¦-¦¦- : -I 0 10 20 30 40 50 B' Sl. 8. Vrednosti utežnih faktorjev FG, * in FG, * za podkleteno stavbo z = 3 m, k =1,5 W/mK, 0 =20 °C, 2