letnik/volume 53 - {t./no. 5/07 - str./pp. 269 - 352 Ljubljana, maj/May 2007, zvezek/issue 505 STROJNIŠKI VESTNIK JOURNAL OF MECHANICAL ENGINEERING 19300 cena 3,34 EUR 9 770039 248001 ISSN 0039-2480 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5 Vsebina - Contents Vsebina - Contents Strojniški vestnik - Journal of Mechanical Engineering letnik - volume 53, (2007), številka - number 5 Ljubljana, maj - May 2007 ISSN 0039-2480 Izhaja mesečno - Published monthly Razprave Papers Širok, B., Rotar, M., Hočevar, M., Dular, M., Smrekar, Širok, B., Rotar, M., Hočevar, M., Dular, M., Smrekar, J., Bajcar, T.: Izboljšanje termodinamičnih J, Bajcar, T.: Improvement of the Thermodynamic lastnosti hladilnih stolpov na naravni vlek 270 Properties in a Natural-Draft Cooling Tower Mahkovic, R.: Položajno zaznavalo za premični robot 285 Mahkovic, R.: Position Sensor for a Mobile Robot Degiuli, N., Barbalič, N., Marijan, G.: Vzroki Degiuli, N., Barbalič, N., Marijan, G.: Causes of nezanesljivosti vzorčnih meritev pri Sampling Measurement Uncertainties when določevanju koncentracije delcev v plinastem Determining the Particle Concentration in a okolju 297 Gaseous Environment Grubišič, V. V.: Overitev trajnosti aluminijastih Grubišič, V. V.: Structural Durability Validation of sestavnih delov 310 Aluminium Components Veg, A.: Izpopolnjena metoda uravnoteženja modela Veg, A.: An Advanced Balancing Methodology for propelerja v vetrnem kanalu 319 the Propeller of a Wind-Tunnel Model Bulatovič, M., Šušič, J.: Vzdrževanje glede na stanje Bulatovič, M., Šušič, J.: Condition Maintenance - - uporaba endoskopske metode 329 Applying an Endoscopic Method Poročila Reports Evropska konferenca o tribologiji - ECOTRIB 2007 348 European Conference on Tribology - ECOTRIB 2007 Rehabilitacijski inženiring in tehnologija 348 Rehabilitation Engineering and Technology Osebne vesti Personal Events Doktorat in diplome 350 Doctor’s and Diploma Degrees Pisma uredništvu 350 Letters to the Editorial Board Navodila avtorjem 351 Instructions for Authors Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 UDK - UDC 536.7:66.045.5:621.311.22 Izvirni znanstveni članek - Original scientific paper (1.01) Izboljšanje termodinamičnih lastnosti hladilnih stolpov na naravni vlek Improvement of the Thermodynamic Properties in a Natural-Draft Cooling Tower Brane Širok - Maja Rotar - Marko Hočevar - Matevž Dular - Jure Smrekar - Tom Bajcar (Fakulteta za strojništvo, Ljubljana) Z uporabo metode CTP (Cooling Tower Profiler) v hladilnem stolpu na naravni vlek elektrarne Doel-3 (Belgija) smo določili hitrostna in temperaturna polja zraka nad izločevalniki kapljic. Meritve so pokazale, da so na obodu prečnega prereza stolpa področja z velikimi hitrostmi in nizkimi temperaturami zraka, kar ima za posledico manjšo učinkovitost v prenosu toplote in snovi. Postavljene pojavne povezave omogočajo rešitev problema s spremembo višine polnila in prerazporeditvijo masnega toka vode. Vpliv omenjenih parametrov smo preverili s simulacijo. Narejena je bila trirazsežna numerična simulacija enofaznega turbulentnega toka zraka. Lokalne izmerjene vrednosti hitrosti in temperature zraka so bile v model vključene prek izvirnih členov. Rezultati prikazujejo analizo vpliva lokalnih nepravilnosti na skupno značilko hladilnega stolpa. Predstavljeni so rezultati meritev, simulacija hitrostnega in temperaturnega polja po prerezu stolpa. Podani so ukrepi za odpravo nepravilnosti v delovanju stolpa, ki vključujejo povečanje višine polnil na obodu stolpa in ustrezno prerazporeditev celotnega masnega pretoka vode po prerezu stolpa. V numeričnem modelu smo ti dve spremenljivki opisali z lokalno spremembo izvirnih členov, kar vodi k ustreznejši porazdelitvi aerotermodinamičnih značilk in posledično k večji učinkovitosti hladilnega stolpa. Na primeru izbranega hladilnega stolpa Doel-3 je v prispevku predstavljena celovita diagnostična metoda lokalnih anomalij, ki temelji na eksperimentalnem in numeričnem modeliranju prenosnih pojavov v hladilnem stolpu. Opisana metoda omogoča povečevanje učinkovitosti delovanja hladilnih stolpov. Izračunana povprečna gostota toplotnega toka se je v tem dejanskem primeru povečala za 2,8 odstotka. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: hladilni stolpi, naravni vlek, termodinamične lastnosti, numerične analize) The velocity and temperature fields above droplet eliminators inside a natural-draft cooling tower of the Doel-3 powerplant (Belgium) were determined using the CTP (Cooling Tower Profiler) method. The measurements show regions of high velocities and low temperatures of air at the cooling tower circumference, leading to locally impaired heat and mass transfer. The established phenomenological relations enable the solution of this problem, which can be achieved by a variation of the fill height and the water mass-flow rate. The influence of these two parameters was analysed numerically. A 3D numerical simulation of a single-phase turbulent airflow was performed. Local values of the air velocity and air temperature were included in the numerical model through source terms. The numerical results present the analysis of local irregularities and their influence on the overall cooling-tower characteristics. Experimental and numerical results for the velocity and temperature fields in a cooling tower's transverse section are presented, followed by a procedure for reducing irregularities in the cooling tower's operation. This procedure includes the increase of the fill height and the rearrangement of the local cooling-water mass-flow rate in the cooling tower's transverse section. In the numerical model these two parameters were modelled by a local modification of the source terms. Modified source terms of the model lead to more uniform aero-thermodynamic properties in the tower and consequently to a higher cooling-tower efficiency. The paper presents a complete diagnostic method of local anomalies, based on the case of a representative Doel-3 cooling tower. The method is based on experimental and numerical modelling of the transport phenomena inside the cooling tower. It makes it possible to increase the efficiency of the cooling tower's operation. The calculated mean heat-flux density was increased by 2.8% in this particular case. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: cooling towers, natural draft, thermodynamic properties, numerical analysis) 270 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 OUVOD V termoenergetskih sistemih se v kondenzatorju prenaša toplota iz parnega krožnega postopka na hladilno sredstvo. Le-ta je običajno voda, ki se jo lahko črpa iz reke ali jezera oz. se jo zaradi okoljevarstvenih razlogov neprekinjeno uporablja v zaprtih sistemih -ohlajevanje vode in njena ponovna uporaba. V tem primeru toplo vodo, ki zapušča kondenzator, hladimo v hladilnem stolpu. Ker delovanje hladilnega stolpa vpliva na temperaturo vode na vstopu v kondenzator je njegov učinek bistvenega pomena za izkoristek celotnega sistema (delovanje kondenzatorja pri tem nižji temperaturi ima za posledico višji podtlak na parni strani, kar zagotavlja več pridobljenega dela iz turbine in večji izkoristek celotnega sistema). Hladilni stolp na naravni vlek deluje na podlagi prenosa toplote in snovi med vodo in zrakom, ki sta v neposrednem stiku. Voda se hladi tako v področju polnil kakor tudi v področju prhe. V protitočnem hladilnem stolpu je opazen protitok med vodo in zrakom. Zrak vstopa na vznožju stolpa in teče skozi polnila ter področje prhe. Voda, ki teče v nasprotni smeri, se z uporabo šob razprši in steče v obliki plasti skozi polnila. Bistvenega pomena za učinkovit prenos toplote in snovi v hladilnem stolpu je velika stična površina med zrakom in vodo ter velik količnik prenosa toplote in snovi. Prispevek prikazuje analizo delovanja hladilnega stolpa elektrarne Doel-3 z močjo 2040 MW. Možni problemi, ki se pojavljajo v hladilnih stolpih, so: omejen tlak prh, ki ga povzročajo odprti kanali, možnost prenapolnitve ob prehodnih pojavih - tveganje poškodbe polnil, poškodovanje polnil s peskom - zamašitev cevovodov in nalaganje nečistoč na polnilih, nerazprševanja hladilne vode zaradi odpadlih pršilnih glav, polomljene cevi in netesnosti razvodnih kanalov. Opravljene so bile standardne meritve celostnih parametrov hladilnega stolpa [1] in tudi dodatne meritve temperature in hitrosti zračnega toka z metodo CTP [2] nad izločevalniki kapljic. Raziskava lokalnega delovanja hladilnega stolpa je bila osredotočena na lokalni prenos toplote in snovi ter na lokalne količnike izgub v polnilih. Hitrost zraka nad izločevalniki kaplic je odvisna od geometrijske oblike hladilnega stolpa (na primer 0 INTRODUCTION In power-generation units (e.g., thermal and nuclear power plants) a circulating-water system supplies cooling water to a turbine condenser and thus acts as an instrument by which heat is extracted from the steam cycle to the environment. The turbine condenser is usually cooled with water from lakes or rivers, but often the use of cold, fresh water is limited for ecological reasons. Therefore, the continuous re-cooling and re-use of water in a closed system is necessary. In this case the warm water leaving the condenser is cooled in a cooling tower. The cooling tower’s operation influences the water temperature at the condenser inlet, so its performance is vital for the efficiency of the entire system, because a condenser operating at the lowest temperature possible results in a higher sub-pressure on the steam side, which in turn makes possible a higher turbine work output and overall cycle efficiency. The natural-draft cooling tower’s operation is based on a principle whereby energy is removed from hot water in direct contact with relatively cool and dry air. The water is cooled in both the fill and rain regions. In a counterflow cooling tower a gaseous phase (air) flows upwards and a liquid phase (water), in variously sized droplets, falls downwards. The airflow enters the cooling tower at the bottom and flows through the fill and the rain regions. The water is sprayed through nozzles and flows as a film down the sheets of the fill. The key factors required for intensive heat and mass transfer in the cooling tower are a large air-to-water interface area and high heat- and mass-transfer coefficients. In this study the operation of a Doel-3 (2040 MW) cooling tower was analysed. The problems that occur in the cooling tower are as follows: limited pressure of the sprayers caused by open channels, possible overflow during transients – risking fill damage and the fouling of fills by sand – clogging of the piping and deposit formation in fills, by-pass leaks due to lost end-caps, broken pipes, sprayers which have fallen off, and leaking baffles/distribution channels. Accordingly, in order to establish the operation of a particular cooling tower’s parts, standard integral measurements [1] as well as additional measurements of airflow temperature and velocity distribution above the droplet eliminators according to the CTP method [2] were performed. The investigation of the local operation of the cooling tower’s parts was focused on a determination of locally transferred heat between the water and the air and the local value of the fill-loss coefficient. The air velocities above the drift eliminators depend on the cooling tower’s geometry (e.g., the supporting walls, the water-distribution channels, etc.), on the local loss coefficient of the fill as well as on the difference between the air density inside and 271 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 sten, porazdelitvenih kanalov itn.), tlačnih izgub v polnilih ter od razlike gostot zraka v stolpu in okolici. Količnik izgub polnil je funkcija masnih tokov vode in zraka ter gostote in višine polnil. Lokalni količnik izgub je bil določen posredno iz padca statičnega tlaka in lokalne hitrosti nad izločevalniki kapljic. Temperatura zraka nad izločevalniki kapljic je odvisna od lokalnega prenosa toplote in snovi med vodo in zrakom. Lokalna vrednost prenesene toplote in snovi je bila izračunana iz masnega toka zraka in sprememb njegove temperature in vlažnosti. Glede na izmerjeni hitrostni in temperaturni polji zraka smo podali nekatere predloge za spremembe, ki bi se kazale v učinkovitejšem prenosu toplote in snovi med zrakom in vodo. Spremembe bi bilo mogoče doseči z zmanjšanjem tlačnih izgub v polnilih in z ustreznejšo porazdelitvijo vode po prerezu stolpa. Vpliv teh sprememb na lastnosti toka zraka je predmet tega prispevka. 1 PRENOS TOPLOTE IN SNOVI V HLADILNEM STOLPU Prenos toplote in snovi v določenem delu hladilnega stolpa je v veliki meri odvisen od lokalnih masnih tokov vode in zraka. Predstavljeni so osnovni modeli prenosa toplote in snovi v opazovanem sistemu, dobljene zakonitosti pa so vključene v enofazni trirazsežni model turbulentnega toka zraka skozi hladilni stolp na naravni vlek. Postopek hlajenja vode se odvija v območju pršil in polnil. Prenos toplote in snovi je v obeh primerih dosežen z neposrednim stikom med vodo in okolišnim zrakom. Mehanizem prenosa toplote in snovi je razlika delnim tlakov vodne pare v mejni plasti in obtekajočim zrakom ter v manj ši meri razlika temperatur med vodo in zrakom ([1] in [3]). Ker se večina toplote prenese v območju polnil ([4] in [5]), lahko območje pršil in polnil obravnavamo kot eno območje. Za ustaljene adiabatne pogoje zapišemo enačbo ohranitve energije v nadzorni prostornini dV [6\: mdadha = mwc Iz enačbe 1 vidimo, da je toplotni tok, ki ga prejme zrak, enak toplotnemu toku, ki ga odda voda. outside the cooling tower. For a particular fill the fill-loss coefficient is a function of the air and water mass-flow rates as well as of the density and the height of the fills. The airflow rate through the fill could be additionally obstructed because of broken or blocked fills and the mass-flow rate could be reduced because of sealed spray nozzles and broken or damaged splash-cups. The local loss coefficient was determined indirectly from the static pressure drop and the local velocity value above the droplet eliminators. The air temperatures above the droplet eliminators depend on the local transferred heat and mass between the water and the air. The local value of the transferred heat and mass was calculated from the air mass-flow rate and its temperature and humidity change. According to the obtained air velocity and temperature field some corrections are suggested to achieve a more efficient heat and mass transfer between the water and the air. This could be achieved by decreasing the air resistance in the fill system and by appropriately rearranging the water mass-flow rate in the cooling tower’s transverse section. The influence of these changes on the air-flow properties is reported in this paper. 1TRANSFER PHENOMENA IN A COOLING TOWER Transfer phenomena in particular segments of a cooling tower largely depend on the local water and air mass-flow rates. Basic models of heat and mass transfer in the observed system are presented later and the obtained relations are included in a single-phase 3D model of the turbulent airflow through the natural-draft cooling tower. The process of water cooling takes place in the cooling tower’s rain and fill region. In each of them the heat and mass transfer is accomplished by a direct contact between the water and the surrounding air. The heat and mass transfer is mostly driven by the difference between the partial pressures of the water vapour in the boundary layer and of the airflow, but the temperature difference between the water and the air also plays a role ([1] and [3]). Because the main heat exchange takes place in the fill region ([4] and [5]), the rain and fill regions are treated together as a fill system. For stationary adiabatic conditions the conser-vation-of-energy equation for the differential control volume, dV, can be written in the following form [6]: dTw + cpwTwd m&w (1). Eq. 1 states that the heat flux received by the air is equal to the heat flux delivered by the water. 272 Širok B. - Rotar M. - Hočevar M. - Dular M. - Smrekar J. - Bajcar T. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 Lokalno preneseni toplotni tok med vodo in zrakom The locally transferred heat flux between the water je odvisen od masnih tokov vode in zraka skozi and the air depends on the water and air mass flow določeno področje hladilnega stolpa ter od lokalnih through the particular segment of the cooling tower vrednosti količnikov prenosa toplote in snovi. and on the local values of the heat- and mass-trans- Krajevna masna tokova vode in zraka skozi hladilni fer coefficients. The water and airflow rates through stolp sta odvisna tudi od konstrukcijskih in okolišnih a cooling tower also depend on the structural and razmer. surrounding conditions. Različne predhodno navedene tehnične Various previously mentioned technical defects napake, ki se pojavijo po večletnem obratovanju that occur in a cooling tower after years of operation hladilnega stolpa, vodijo k neustrezni omočenosti lead to inappropriate fill-system moistening as well as to polnil ter k motenemu toku zraka skozi polnila. a disturbed airflow through the fill system. These anoma- Značilnost teh anomalij je ta, da se pojavljajo na lies can occur at various locations inside the cooling različnih mestih hladilnega stolpa in da jih je moč tower and can only be detected by the local measure- določiti le s krajevnimi meritvami temperaturnega in ments of velocity and temperature field of the cooling air hitrostnega polja hladilnega zraka v stolpu. Prenos across the cooling-tower area. The heat and mass trans- toplote in snovi ter tlačni padci v polnilih po prerezu fer as well as the pressure drop in the fills across the hladilnega stolpa so bili analizirani z numerično cooling tower’s transverse section were analysed nu- simulacijo. Izmerjene vrednosti padca tlaka v polnilih merically The measured values of the pressure drop in in lastnosti zraka nad izločevalniki kapljic so bile the fill region and the properties of the air above the uporabljene za izvirne člene v prenosnih in droplet eliminators were used as source terms in the energijskih enačbah numeričnega modela. transport and energy equations of the numerical model. Določitev prenosa toplote in snovi v The determination of heat and mass trans- določenem delu hladilnega stolpa temelji na port in a certain segment of the cooling tower is toplotnem toku, ki ga prejme zrak. Izračunamo ga po based on the heat flux received by the air. The latter enačbi [6]: is calculated using the following equation [6]: dQa=mdadha (2). Za rešitev enačbe (2) moramo poznati The solution of Eq. 2 requires the inlet and vstopno in izstopno temperaturo zraka, vlažnost zraka outlet air temperatures, the air humidity and the air in masni tok zraka. mass flow to be known. Vstopna temperatura zraka in njegova The inlet temperature and the air humidity were vlažnost sta bili izmerjeni v bližini stolpa - measured in the vicinity of the cooling tower, supposing predpostavili smo, da se vrednosti na vstopu v stolp that these parameters remain constant over the inlet area ne spreminjata. Na podlagi izkušenj prejšnjih of the cooling tower. It is also presumed that the relative meritev na različnih hladilnih stolpih [5] in priporočil humidity of the air that exits the fill system is 100%. This standarda DIN-1947 [5] smo privzeli tudi, da je presumption is based on experience and from experimen- relativna vlažnost zraka nad polnili 100 odstotna. tal results on various cooling towers [5], and is also in Temperatura zraka na izstopu iz polnil je bila accordance with the standard DIN-1947 [5]. The tempera- izmerjena. Masni tok vlažnega zraka na krajevni ture of the air exiting from the fill system was measured. ravni hladilnega stolpa je bil določen posredno z The local mass flow of the humid air through the respec- merjenjem hitrosti zraka. Entalpija vlažnega zraka je tive cooling-tower segment was determined indirectly by podana z vsoto entalpije suhega zraka in entalpije measuring the air velocity at the respective measurement vodne pare: points. The enthalpy of the humid air equals the sum of the dry-air enthalpy and the water-vapour enthalpy: ha=cpaTa+x(cpvTa+r) (3). Če uporabimo znane izraze mda = ma /(1 + x), Using the common relations mda = ma /(1 + x), ma = Vara in Va = S va, lahko gostoto toplotnega toka ma = Vara and Va = S va the heat-flux density from iz vode na zrak izrazimo z: water to air can be expressed as: Izboljšanje termodinamičnih lastnosti - Improvement of the Thermodynamic Properties 273 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 va ra (ha1 - ha2) 1 + x (4). Gostota vlažnega zraka je izračunana glede na izmerjeno temperaturo in predpostavko, da je relativna vlažnost zraka nad izločevalniki kapljic 100 odstotna. Izmerili smo lokalne vrednosti temperature zraka in njegove hitrosti, gostoto toplotnega toka v polnilih pa smo izračunali po enačbah (3) in (4). 2 KOLIČMK IZGUB V POLNILIH The density of humid air is calculated with respect to the measured temperature and the assumption that the relative humidity of the air above the droplet eliminators is equal to 100%. The measurements were performed to obtain local values of the heat-flux density in the fill system. The air temperatures and velocity were measured and the heat-flux density was calculated using Eqs. (3) and (4). 2 LOSS COEFFICIENT OF A FILL SYSTEM Količnik izgub v polnilih hladilnega stolpa je odvisen od padca tlaka v polnilih, ki ga lahko določimo s preizkusi. Količnik izgub je tudi odvisen od masnih tokov zraka in vode in je zato odvisen od vleka skozi hladilni stolp [7]. Padec statičnega tlaka v polnilih in količnik izgub sta povezana z [7]: The loss coefficient of the cooling tower’s fill system depends on the air-pressure drop across the fill, and this can be determined experimentally. The loss coefficient is also correlated with the air and water mass-flow rates and is therefore a function of the draft through the natural-draft cooling tower [7]. The static pressure drop through the fill system is coupled to the loss coefficient by the following relation [7]: Apfi =kfi pv (5). 3 POSTOPEK MERITEV 3 MEASURING PROCEDURE Hitrostna in temperaturna polja zračnega toka se v okviru metode CTP merijo z uporabo razvite daljinsko upravljane premične enote (si. 1), s katero je mogoče izmeriti hitrosti in temperature izstopnega In a CTP method, the velocity and temperature fields of the airflow are measured by a remotely controlled mobile unit (Fig. 1), developed to enable the air velocity and the temperature of the exit air mapping meas- HIIIHSVi : SI. 1. Premična enota s krilnim anemometrom in Pt-100 termometrom v hladilnem stolpu jedrske elektrarne Doel - Belgija Fig. 1. Mobile unit with a vane anemometer and a Pt-100 thermometer inside the Doel nuclear powerplant cooling tower (Belgium) 2 274 Širok B. - Rotar M. - Hočevar M. - Dular M. - Smrekar J. - Bajcar T. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 zračnega toka po celotni površini hladilnega stolpa urements over the entire cooling tower area at an arbi- v poljubni točki nad izločevalniki kapljic. trary measurement point above the droplet eliminators. Premična enota se giblje po površini The mobile unit (Fig. 2 (1)) moves gradually izločevalnikov kapljic (si. 2 (1)). Zaznavala so over the entire measuring plane - the droplet elimi- nameščena na premično enoto v skladu z zahtevami nator surface. A vane-anemometer, designed to op- standarda DIN 1947 [7]. Na premično enoto sta erate in 100% humidity, and Pt-100 thermometer sen- nameščena krilni anemometer, prirejen za delovanje sor are mounted on the mobile unit according to the v okolju nasičene vlažnosti ter Pt-100 temperaturno standard DIN 1947 [7]. The mobile unit measures zaznavalo. Premična enota izvaja meritve obeh both quantities simultaneously during its movement. parametrov med vožnjo. The external part of the equipment (Fig.2 (8)) com- Zunanji del (si. 2 (8)) sestavljajo: računalnik, ki prises a PC with the appropriate hardware for the commu- vsebuje strojno opremo za povezavo z računalnikom nications with the computer, mounted on the mobile unit premične enote (si. 2 (7)) in programska oprema za (Fig. 2 (7)), and the software for processing the acquired obdelavo dobljenih podatkov. Lega premične enote data The position of the mobile unit is determined by se določa z merjenjem radialne razdalje in kota od measuring the radial distance and the angle from a refer- referenčne točke v memi ravnini (si. 2 (2)). ence point in the measurement plane (Fig. 2 (2)). Hkrati z izvedbo zgoraj opisanih meritev se Simultaneously, measurements of the integral izvajajo meritve celostnih parametrov po standardu parameters are carried out according to the DIN 1947 DIN 1947 [7]. : vstopna in izstopna temperatura standard [14]: the inlet and outlet temperatures of the hladilne vode (si. 2 (4) in (5)), pretok hladilne vode, cooling water (Fig. 2 (4) and (5)), the cooling-water mass parametri okolice (si. 2 (6)) in izstopna moč flow, the parameters of the surroundings (Fig. 2 (6)) termoenergetskega sistema. and the output power of the thermo-energetic system. Z uporabo merjenih hitrostnih in The results of the velocity and temperature temperaturnih polj v memi ravnini hladilnega stolpa fields’ measurements in the measurement plane of SI. 2. Shema elementov meritev: (1) premična enota, (2) enota za merjenje položaja, (3) položaj merilnikov referenčnih meritev, (4) meritve temperature vstopne vode, (5) meritve temperature izstopne vode, (6) meritve parametrov okolice, (7) sistem za povezavo, (8) nadzorna meritev, obdelava podatkov in shranjevanje Fig. 2. Schematic view of the measurement elements: (1) mobile unit, (2) position-measurement unit, (3) position of the measurement equipment for reference measurements, (4) inlet-water temperature measurement, (5) outlet-water temperature measurement, (6) measurement of surroundings parameters, (7) communication system, (8) measurement control, data processing and saving Izboljšanje termodinamičnih lastnosti - Improvement of the Thermodynamic Properties 275 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 dobimo trirazsežne topološke porazdelitve hitrosti in temperature izstopajočega vlažnega zraka nad izločevalniki pri znanih celostnih parametrih elektrarne. Rezultati so osnova za določitev učinkovitosti prenosa toplote iz hladilne vode na okolišni zrak. Merilna negotovost merjenja temperature na premični enoti je znašala 1,5 odstotka, merilna negotovost anemometra pa 2 odstotka. Za merjenje lege premične enote pa je bila ključnega pomena merilna negotovost koračnega merilnika kota, ki je znašala 0,5° in je pri večjih oddaljenostih premične enote od izhodiščne točke značilno vplivala na določitev lege premične enote. Podrobnosti o merilni opremi, njeni kalibraciji in merilnem sistemu so opisane v [8]. Pretok hladilne vode je bil merjen z ultrazvočnim merilnikom. Vlažnost in temperaturo okolišnega zraka smo merili v bilžini hladilnega stolpa. Ker se obratovalni režim elektrarne med meritvami spreminja, smo hitrost in temperaturo zraka merili tudi v stalni točki. Te meritve so bila skupaj s celostnimi parametri, namenjene za popravo meritev na krajevni ravni. Sliki 3 in 4 prikazujeta rezultate meritev hitrosti in temperature vlažnega zraka. Iz diagramov lahko razberemo očitno nehomogenost hitrostnega in temperaturnega polja, kar kaže na to, da prenesena toplota po prerezu hladilnega stolpa ni nespremenljiva. Neenakomeren prenos toplote in snovi vodi k manjši učinkovitosti hladilnega stolpa in slabšemu izkoristku celotnega postrojenja [9]. Iz rezultatov meritev lahko sklepamo, da je ugodna rešitev težav prerazporeditev toplotnega toka v hladilnem stolpu. Povečana hitrost pretakanja hladilnega zraka na obodu stolpa (zunanje področje kolobarja s prekinjeno črto na sliki 3) in razmeroma nizka temperatura zračnega toka (zunanje področje kolobarja s prekinjeno črto na sliki 4) navaja na potrebo po povečani količini polnil odnosno na povišano plast polnil, ter hkrati povečanje dotoka vstopne hladilne vode v to področje. Nasprotno bi bilo treba dotok vstopne hladilne vode v osrednjem delu stolpa (notranje področje omejeno s sklenjeno neprekinjeno krivuljo s slik 3 in 4) sorazmerno zmanjšati ob hkratnemu zmanjšanju aerodinamičnega upora strujanja skozi osrednji del stolpa. Navedeni predlogi so v nadaljevanju prispevka ocenjeni z numeričnim modeliranjem, ki vključuje predstavljene the cooling tower provide essential data for obtaining 3D topological structures of the velocity and temperature distribution of the moist air above the droplet eliminators at known integral parameters of the powerplant. These results represent the basis for a determination of the heat-transfer efficiency between the cooling water and the surrounding air. The measurement uncertainty for the temperature measurements on the mobile unit was in the range of 1.5%, whereas the uncertainty of the anemometer amounted to 2%. The measurement uncertainty of the increment-angle measurement system was crucial for the measurement of the mobile unit’s position. Its value was 0.5o, and it significantly influenced the determination of the mobile unit’s position at greater distances from the origin point. The details of the equipment, its calibration and the measurement system operation are described in [8]. The cooling-water flow rate was measured with an ultra-sonic flowmeter. The air humidity and the air temperature were measured in the vicinity of the cooling tower. The power plant’s operating properties change during the measurements. For this reason the air velocity and the temperature at a stationary point were measured The stationary data, together with the integral parameters and the power plant’s operating data, serve as correction elements for the measurements on the local level. Figs. 3 and 4 show the results of the moist-air velocity and temperature measurements. From the diagrams in Figs. 3 and 4 the non-uniform velocity and temperature field is obvious, which suggests that the transferred heat over the area of the cooling tower is not uniform. The nonuniform field of the heat-flux density indicates that the cooling tower does not operate equally well over the entire area The non-uniformity of the heat and mass transfer leads to a lower efficiency of the cooling tower and thus to a lower efficiency of the entire powerplant [9]. It can be concluded from the measurement results that the problem of the mentioned non-uniformity could be solved by rearranging the heat flux inside the cooling tower. Higher cooling-air velocities at the cooling tower’s peripheral region (i.e., the region radially outwards of the dashed curve in Fig. 3) and the relatively low temperatures of the airflow (i.e., the region radially outwards of the dashed curve in Fig. 4) address the need to increase the fill height and to increase simultaneously the amount of the inlet mass flow of the cooling water in this specific region. The other solution is to decrease the amount of cooling water in the central region of the cooling tower (i.e., the region radially inwards of the solid closed curve in Figs. 3 and 4) as well as to simultaneously decrease the aerodinamic drag in this central region. These suggestions are assessed later on by 276 Širok B. - Rotar M. - Hočevar M. - Dular M. - Smrekar J. - Bajcar T. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 270-284 izmerjene vrednosti na slikah 3 in 4 kot dejanske robne pogoje v numerično shemo. V primeru drugih krajevnih anomalij, ki se kažejo kot naključne -krajevne nehomogenosti temperaturnega in hitrostnega polja na slikah 3 in 4, bi le-te morali odpraviti s krajevnim pregledom posameznih področij, npr. z uporabo pred kratkim razvite termovizijske metode za hitro odkrivanje anomalij [10], in ugotovitvijo dejanskih vzrokov, kakor so polomljeni razpršilniki kapljic, netesnosti razvodnih kanalov, zamašenih pretočnih kanalov polnil in izločevalnikov kapljic. JI* W*T* ^ •v M •# >> ^. M /^ N^^. W' -- .--------, NTV m-' s^ >*% // A • ^» * \ . 1/ / • V F/ 'i * * ' ^ - / » ^ \ \6 \ \ V y y' / ^^--"r -^v1 \ W)\ S"1 X' S x X Sl. 3. Geometrijska oblika premika za PMK Fig. 3. Geometrical illustration of the AMW-type movements Pri izpeljavi enačb si pomagamo s podobnimi trikotniki: The appropriate equations are derived from similar triangles: AS'Tfi * ABAG * AS'AE * ABT1E Izraza za ukrivljenost krožnic K in K1 izpeljemo, ker sta kota ZS'Tfi in ABAG prava, iz osnovnih trigonometričnih funkcij: K Since the angles ZS%G and ABAG are rectangles, the expressions for the curvatures K and K1 can be obtained using trigonometric functions: sin(j9) K a cos(/?) - c Jfcos(g) 1 + Jfcsin(/) Nadalje torej lahko izračunamo spremembo The expressions for the change of the orien- smeri A0 in spremembo premika Al, saj velja tation A0and the distance A/ can then be written: A0 A/ Al1 Al1K1 Al1Kcos(ß) 1 + Kcsin(ß) Al_A@_M1K1_ A/1cos(g) K K 1 +Kc sin(ß) (7) (8). 4 IZVEDBA SKUPNEGA MERILNEGA SISTEMA (NMK IN PMK) 4 REALIZATION OF THE ENTIRE MEASUREMENT SYSTEM (NMW AND AMW) Enačba (6) podaja razmerje med ukrivljenostjo Kb, začetnim kotom ß1, končnim kotom ß2 in razdaljo, ki jo prevozi merilno kolesce A/1. Vrednosti ß1, ß2 in Al1 so znane, izračunati pa je treba Kb, najbolje kar skupaj z odmaknjenostjo, ker se pač pojavljata skupaj. Enačbo (6) delimo s c in damo obe strani v eksponent. Upoštevamo še kosinus vsote kotov in vpeljemo novo spremenljivko F: cos(/?1 +arccos(— cKb)) - —cKb cc Eq. (6) determines the relationship among Kb, the starting angle L, the final angle Ä and the length of the straight line Al1, covered by the measurement wheel. The values ß1, ß2 and Al1 are known, whereas Kb should be calculated, conveniently together with the eccentricity, since they appear together. We divide Eq. (6) by c and put both sides in the exponent. After the cosine of the sum of the angles is taken into account, we introduce a new variable, F: cos(ß1) - sin(/?1) sin(arccos(— cKb)) c Položajno zaznavalo za premični robot - Position Sensor for a Mobile Robot 291 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 285-296 F cK cK sin(arccos(^)) 1-Rl,)2 Dobimo enačbo: The following equation is obtained: c__________F_____ iz katere izrazimo F: Sedaj lahko iz (10) izračunamo cK : cF from which F can be expressed: Lsin(/?2)-sin(/?1) L(-cos(j02)-1)--cos(A) + 1 cKb = + (Ta enačba ima dve rešitvi, +cKh in -cKh. Prav tako dobimo dve rešitvi tudi iz enačbe za p (1), skupaj imamo torej štiri kombinacije vrednosti p and cKy) 4.1 Postopek merjenja cKb follows from Eq. (10): F 1+(!F) 2 (9). (10). (11). (Since this equation has two solutions, +cKb and –cKb, and two more are obtained from the equation for r E q . (1), we are left with four combinations of r and cKb.) 4.1 Measurement procedure 1. Iz kodirnika smeri preberemo trenutno vrednost kota L, iz kodirnika premika pa premik A/1. 2. Če je trenutni kot zasuka merilnega kolesca ß2 enak zasuku iz prejšnje meritve ß1, je merilno kolesce poravnano v smeri vožnje, primer PMK, zato izračunamo A0 in A/ iz (7) in (8). Sicer nadaljujemo s točko 3. 3. Izračunamo vrednost cKh ((10) in (11)). 4. Določimo kot = arccosVdn. 5. Preverimo kateri par {(+p,+cKb),(+p,- cK), (–p,+ cKb),(–p,- cK)} ustreza (6). 6. Pravi par vstavimo v enačbo (5) in izračunamo spremembo kota A0. 7. Iz spremembe kota A0 določimo premik Al: . Če je sprememba kota A0 enaka nič, premični robot vozi naravnost, merilno kolesce pa se poravnava v smer vožnje: medtem ko se referenčna točka robota premakne za, recimo, l, se odmaknjenost merilnega kolesca zmanj ša z ß1 na ß2 Premik l je podan z enačbo: ,_ ftan(A/2) [tan(&/2) (natančna obravnava poravnavanja kolesca je podana v [3]). • Sicer iz spremembe A0 in ukrivljenosti Kb izračunamo premik referenčne točke robota A/ (glej trikotnika AS’ 71^ in AS’ 7^ na sliki 2): 1. Read current values: the value of angle ß2 from the steering encoder, and the length A/1 from the distance encoder. 2. If the current angle ß2 is equal to the angle ß1, from the previous measurement, the AMW case applies; A0 and A/ are calculated from Eq. (7) and Eq. (8). Otherwise we proceed with point 3. 3. Calculate^ (Eq. (10) and Eq. (11)). 4. Determine p= arccos(a/c cK). 5. Check which pair among {(+P,+cKb),(+p,- cKb), (–A+ cKb),(–p,- cKb)} correspond to Eq. (6). 6. Put the corresponding pair into Eq. (5) and calculate the change of orientation A0. 7. From A0 calculate Al: • If the change of the orientation A0 is zero, the mobile robot drives along a straight line, while the measurement wheel is still aligning with the direction of the drive: if the reference point moves by, for example, /, the nonalignment of the measurement wheel is decreased from ß1 to ß The move / is defined by the equation: (the complete explanation is given in [3]). Otherwise, calculate the movement of the robot’s reference point A/, using A0 and the curvature Kb (observe the triangles AS’T11B1 andAST1252 in Fig.2): c 292 Mahkovic R. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 285-296 Al = A0, 8. Iz spremembe kota A0 in premika Al izračunamo z uporabo dobro znanih razmerij spremembo položaja premičnega robota v kartezičnem koordinatnem sistemu. 5 DOLOČITEV PARAMETROV POLOŽAJNEGA SISTEMA Opisano položajno zaznavalo zahteva določitev vrednosti štirih parametrov: odmaknjenost c, ničelni kot ß0 (kot, ki ga kaže kodirnik smeri pri vožnji naravnost), obseg merilnega kolesca o1 oddaljenost položajnega zaznavala od referenčne točke robota a. Na začetku moramo te parametre seveda določiti ročno, toda tako dobljene vrednosti so le grobe ocene; natančnejše vrednosti določimo tako, da robot vozi po poteh, pri katerih se vpliv posameznih parametrov čim bolj osami. Pri vožnji naravnost, na primer, parameter a ne vpliva kaj dosti, vsak od preostalih treh pa vpliva drugače. Za določitev vrednosti parametrov smo zato izbrali prav vožnjo naravnost. Ob njej smo spremljali potek robotove lege in graf usmeritve robota 0. Grafi izmerjenih leg robota in njegove usmeritve so potrdili, da odmaknjenost c vpliva samo na začetku, ko merilno kolesce še ni poravnano, da ničelni kot ßn določa nagib spreminjanja kota 0 (ki bi pri vožnji naravnost sicer moral ostati stalen) ter da obseg kolesca o1 ne vpliva bistveno na spreminjanje 0, občutno pa vpliva na dolžino poti. Podrobnejše rezultate parametrične analize si lahko ogledamo v [3], kjer je tudi razloženo, zakaj mora biti vrstni red določanja parametrov naslednji: c, ß0 in o1 Parameter a določimo z vožnjo po krogih. Ker je položajno zaznavalo zasnovano na relativnem merjenju, se njegova napaka neprestano povečuje, zato je zelo pomembna ocena njegovih parametrov. V našem primeru so končne vrednosti parametrov bile: ß0 = 196,708°, c = 0,04014 m, o1 = 0,2985 m in a = 0,5678 m. Vse so bile seveda pridobljene programsko, na temelju testnih voženj robota. 8. The change of the robot’s position in the Cartesian coordinate system is calculated from A0 and Al using the well-known relations. 5 DETERMINATION OF THE PARAMETERS OF THE SENSOR The position sensor requires the determination of four parameters: the eccentricity c, the zero angle ß0 (the angle, the steering encoder reports when the robot is moving straight ahead), the circumference of the measurement wheel o1, and the distance from the position sensor to the reference point of the robot a. At the beginning these parameters have to be determined manually, yet these are only coarse approximations of the real values; the finer values are obtained by letting the robot move along the kind of paths on which the impact of the individual parameter is isolated as much as possible. If the robot moves along the straight line, for example, parameter a does not have much influence, while each of the remaining affect the movement in their own way. That is why we chose exactly this type of movement to determine the parameters values. The robot’s position and the graph of its orientation were observed carefully along the path. The graphs of these positions and orientations proved that the eccentricity c has an impact at the beginning only, when the measurement wheel is still not aligned, that zero angle L determines the inclination of the 0 graph, which should stay constant, when moving straight ahead- constant, and that circumference of the wheel o1 does not have an observable impact on the graph 0, but it does have a substantial influence on the length of the paths. Detailed results of the parametric analysis can be found in [3], where the explanation as to why the order of the parameter determination should be c, ß0 and o1, is given. The parameter a is determined by the circular paths. Since the presented sensor is based on relative measurements, its error grows without bounds, so a correct estimation of the parametric values is crucial. The final values in our case were: ß0 = 196.708°, c = 0.04014 m, o1 = 0.2985 m and a = 0.5678 m. All of them were, of course, obtained from the dedicated software that analyzed the paths of the robot Položajno zaznavalo za premični robot - Position Sensor for a Mobile Robot 293 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 285-296 6 REZULTATI 6 RESULTS Položajno zaznavalo smo preizkusili na The position sensor was tested on our own lastnem premičnem robotu (si. 4). Premični robot je mobile robot, Fig.4. The robot was equipped with bil opremljen z dvema merilnima sistemoma. Ob two measuring systems. To the left and to the right pogonskih kolesih zadaj je imel pritrjen par pomožnih of the driving wheels there was a pair of additional merilnih kolesc, ki zagotavljajo tudi za več ko red measurement wheels, which guarantee an order more velikosti [4] natančnejšo lego, kot jo dobimo na accurate position than the one calculated from the podlagi kodirnikov, pritrjenih na samih pogonskih readings of the encoders mounted directly on the kolesih, spredaj pa v prispevku predstavljeni driving wheel shaft; in the front, the presented posi- pozicijski merilnik (si. 4a). Podlaga so bila gladka tla tion sensor can be observed, Fig.4a. The floor was iz linoleja (si. 4b). smooth, made of linoleum, Fig.4b. Položajno zaznavalo smo preizkušali na dveh The position sensor was tested on two types vrstah poti: na prvi (si. 5a), smo robota programirali, of paths: on the first (Fig.5a), the robot was pro-da je vozil “osmico”, torej štiri leve in štiri desne grammed to make 8 turns, i.e., four left and four right zavoje; na drugi (si. 5b), smo preverili vožnjo turns; on the second (Fig. 5b), the robot moves along naravnost, po dolgem in ozkem hodniku. a long and narrow corridor. a) b) SI. 4. V preizkusih uporabljeni premični robot: a) zadaj, ob pogonskih kolesih, klasični par dodatnih merilnih kolesc; spredaj, v prispevku predstavljeno zaznavalo; b) vožnja v laboratoriju Fig. 4. The mobile robot from the experiments: a) at the back, on each side of the driving wheels, a pair of classical measurement wheels, at the front, the proposed sensor, b) the drive in the laboratory a) b) Sl. 5. Dve vrsti poti: a) osmica, b) dolg in ozek hodnik Fig. 5. Two types of paths: a) a figure-of-eight path, b) a long and narrow corridor 294 Mahkovic R. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 285-296 6.1 Prva vrsta poti: osmica 6.1 The first type: figure-of-eight path V tem primeru naj bi se robot, potem ko je na približno trimetrskem kvadratu opravil osem zavojev za 90°, vrnil v izhodiščno točko. Namen tega testa je bil preverjanje položajnega merilnika ob zavijanju. Dolžina poti je bila približno 20 m, robotovo napako po desetih preizkusih pa vidimo na sliki 6a. Napaka je nekoliko večja v vzdolžni smeri (Y), kot v prečni smeri (X), vendar še vedno precej majhna (<0,4%), tudi za skupino robotov s pomožnimi merilnimi kolesi [2]. The robot was supposed to come back to the starting point, after accomplishing eight 90° turns on a square of 3m x 3m. The purpose of the test was to examine the behaviour of the sensor when a lot of turning is involved. The length of the path was approximately 20m; the positional error after ten trials can be seen in Fig.6. The error is somewhat bigger in the longitudinal (Y) than in the lateral (X) direction, but it is still reasonably small (<0.4%), even for the group of robots with additional measurement wheels [2]. 6.2 Druga vrsta poti: hodnik 6.2 The second type: corridor Glavni problem dolgih in ozkih poti, kakršen je hodnik pred laboratorijem (si. 5b), je natančnost ničelnega kota ß0 kodirnika smeri, ki na usmeritev robota vpliva najbolj. Nenatančen povzroči vrtenje izračunanih poti, zato se pri tako dolgih poteh robot kaj lahko znajde v bližnjih stenah. Naše ocene za ß0 so se tako z že omenjenih 196,708° znižale na 196,617°, dokler se robotu pri 196,608° končno ni uspelo vrniti skozi vrata laboratorija na izhodiščni položaj; po prevoženih približno 120 m. Relativna napaka je tudi v tem primeru ostala <0,4% (si. 6hK_____________________________ Ay[cm] Ax[cm] a) The main problem with long and narrow working places, like the corridor in front of the lab, Fig. 5b, is the accuracy of the zero angle ß0 of the steering encoder, which has the strongest impact among all the parameters. An inaccurate ß0 results in the rotation of the paths, and the robot can quickly find itself hitting the walls. Our starting estimations for the ß0 values were reduced from the value already mentioned 196.708°, to 196.617°, until the robot finally at 196.608° managed to re-enter through the lab door to the approximate starting position; after a 120-m-long journey The relative error also remained <0.4% in this case (Fig. 6b). Št. preizkusa Exp. no. Dx [m] Dy [m] 1 -0,101 -0,309 2 0,079 0,430 3 0,024 0,261 4 0,068 0,372 b) SI. 6. Napaka po opravljenih testnih poteh: a) napaka robotove lege po prevoženih osmicah; b) napaka robotove lege po vožnjah v hodniku Fig. 6. Position error after the tests: a) position error after the figure-of-eight turns ; b) position error after the journey in the corridor 7 SKLEPI 7 CONCLUSIONS Predstavili smo rezultate položajenja premičnega robota z izvirnim odometričnim položajnim zaznavalom, zasnovanim na samo enem dodatnem The results of the experiments with a new odometrical position sensor, designed with one additional measuring wheel only, are presented. The Položajno zaznavalo za premični robot - Position Sensor for a Mobile Robot 295 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 285-296 merilnem kolescu. Položajno zaznavalo sestavljata absolutni kodirnik za merjenje usmerjenosti merilnega kolesca in relativni kodirnik za merjenje prevožene poti. Preizkusi so pokazali, da je predlagano zaznavalo v natančnosti povsem primerljivo običajni rešitvi z dvema dodatnima merilnima kolescema ob pogonskih kolesih. Njegova prednost pa je v tem, da ga lahko namestimo na poljubnem mestu na robotu, zato je uporabnik z njegovo namestitvijo bistveno manj omejen. Pravzaprav bi lahko robota opremili celo z več takimi zaznavali in njihove rezultate povprečili. Težavo pri uporabi pa pomeni razmeroma zamudno določanje vrednosti štirih parametrov: ß0, c, o1 in a. Na prvi pogled se zdi, da bi bila lahko težava, ali pa vsaj omejitev, morebitna neporavnanost med usmerjenostjo robota in izmaknjeno nameščenim merilnim kolescem zaznavala ob vklopu robota: izkaže se, da matematični opis v primeru NMK povsem zadovoljivo podaja položaj tudi v tem primeru. Kako je merilno kolesce zasukano, torej ni treba skrbeti niti pred prvo vožnjo. sensor consists of an absolute encoder, which measures the orientation of the measuring wheel, and of a relative optical encoder, which measures the length of the path. Experiments proved the proposed sensor to be completely comparable to the classical solution with two measurement wheels mounted on each side of the driving wheels. However, it has the advantage that it can be mounted at an arbitrary place around the robot, so the user is far less restricted in terms of its use. In fact, one could equip the robot with even more position sensors and average their results. The main problems associated with its use relate to the determination of its four parameters, b0, c, o1 and a. At first sight it appears that the problem might be a possible misalignment of the orientation of the robot and the eccentrically mounted measuring wheel; however, it turned out that the discussion given in the case of NMW also holds good in this example. The actual orientation of the measuring wheel is not a problem, even before the first run. 8 LITERATURA 8 LITERATURE [1] J.Borenstein, H.R.Everett, L.Feng (1996) Navigating mobile robots-systems and techniques, A K Peters, Wellesley, Massachusetts. [2] J.Borenstein, L.Feng (1994) UMBmark - a method for measuring, comparing and correcting dead-reckoning errors in mobile robots, Technical Report UM-MEAM-94-22, University of Michigan. [3] M.Blatnik (1996) Navigacija mobilnega robota z enim merilnim kolesom, Diplomsko delo, Fakulteta za računalništvo in informatiko, Ljubljana. [4] Z.Fan, J.Borenstein, D.Wehe, Y.Koren (1995) Experimental evaluation of an encoder trailer for dead-reckoning in tracked mobile robots. Proc. of the 10th IEEE Int.Syposium on Intelligent Control. [5] J.Borenstein (1994) Internal correction of dead-reckoning errors with smart encoder trailer, Proc. of International Conf. on Intelligent Robots and Systems (IROS’94), Munich, Germany, September 12-16, 1994, str. 127-134. [6] RMahkovic, TSlivnik (2000) Constructing the generalized local Voronoi diagram from laser range scanner data, IEEE Transactions on Systems, Man, and Cybernetics, let.30, št.6, str.710 - 719, 2000. [7] N.S.V.Rao, S.Kareti, S.S. Iyengar (1993) Robot navigation in unknown terrains: Introductory survey of non-heuristic algorithms. Tecnical report, ornl/tm-12410, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 37831. Avtorjev naslov: doc. dr. Rajko Mahkovic Univerza v Ljubljani Fakulteta za računalništvo in informatiko Tržaška 25 1000 Ljubljana rajko.mahkovic@fri.uni-lj.si Author’s Address: Doc. Dr. Rajko Mahkovic University of Ljubljana Faculty of Computer and Information Science Tržaška 25 1000 Ljubljana, Slovenia rajko.mahkovic@fri.uni-lj.si Prejeto: Received: 15.3.2006 Sprejeto: Accepted: 25.4.2007 Odprto za diskusijo: 1 leto Open for discussion: 1 year 296 Mahkovic R. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 UDK - UDC 628.83:531.755 Izvirni znanstveni članek - Original scientific paper (1.01) Vzroki nezanesljivosti vzorčnih meritev pri določevanju koncentracije delcev v plinastem okolju Causes of Sampling Measurement Uncertainties when Determining the Particle Concentration in a Gaseous Environment Nastia Degiuli1 - Nikola Barbalič2 - Goran Marijan2 ('University of Zagreb, Croatia; 2Hrvatska elektroprivreda Zagreb, Croatia) Merjenje koncentracij delcev je pomembno za veliko področij uporabe. Tako je predvsem od šestdesetih let prejšnjega stoletja, ko je bilo dokazan njihov škodljiv vpliv na zdravje ljudi. Pri merjenju koncentracij delcev pride do precej večjih napak, kakor pri merjenju emisij in/ali imisij drugih onesnaževal na področju ohranjanja kakovosti zraka. Pregledovanje posebnosti delcev v skupini onesnaževal zraka ter priprava splošnih standardnih oznak za emisijske in/ali imisijske količine za primer delcev zahtevata uporabo ene od dveh nasprotujočih si in skrajnih poenostavitev: sistem plin-delci obravnavamo v razmerah kontinuiranega okolja ali kot niz diskretnih trajektorij delcev v plinu. Zaradi omejitev razpoložljivih merilnih postopkov je rezultat v obeh primerih prikaz srednje vrednosti jakosti masnega toka, kot zmnožek srednje hitrosti in srednje vrednosti koncentracij, ki že v naprej vsebuje merilno napako. V tem prispevku smo se osredotočili na vzorčne lastnosti med določevanjem koncentracije delcev, ki so glavni vir merilne nezanesljivosti, ter na omejitve njihove izločitve v praksi. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: koncentracija delcev, merilne negotovosti, vzorčenje, pogreški) Measuring particle concentrations is very important in many applications; this has been particularly so since the 1960s, when their harmful influence on human health was proved. Measuring particle concentrations has a much greater measurement error than when measuring the emissions and/or immissions of other pollutants in the field of air-quality protection. Viewing the peculiarities of particles within the group of air pollutants, the elaboration of general standard specifications for emissions and/or immission quantities in the case of particles requires an approach to one of the two contradictory and extreme simplifications: the gas-particle system is either viewed in terms of a continuous environment or as a set of discrete particle trajectories in a gas. Due to the limitations of the available measurement procedures the result in both cases is the presentation of the mean value of the mass flow density as a product of velocity and concentration mean values, implying in advance a measurement error. In this paper attention has been focused on the sampling characteristics during the determination of the particle concentration, which are the main sources of measurement uncertainty, and on the limitations of their elimination in practice. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: particles concentration, measurement uncertainties, sampling, measurement errors) 0 INTRODUCTION An investigation of the state and/or the motion of a discrete, dispersed particle system in a fluid environment is of great importance for scientific and professional developments in many areas of human activities: the power industry, processing techniques, agriculture, meteorology, protection of the environment, health services, etc. For example, fluid flows and their dispersed particles (solid particles, droplets, bubbles) are the working body in various types of equipment with technical applications. In 297 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 such cases, the behaviour of the dispersed phase directly determines the equipment’s operational characteristics, and for this reason particle trajectories represent an important step in the investigation of their function and are a basis for the development of their designs. Moreover, the problem of air pollution caused by flowing particles has been given increasing importance since it has been proved that their concentration in the air is one of the components that determines the level of their harmful influence on health. Other important components of health risks are the proportions in particular fractions according to particle size, chemical composition, mixtures, corrosiveness, radioactivity, fusibility, roughness, etc. Because of this, measurement procedures for the determination of the properties of different flowing particles are more demanding and are subject to a greater measurement uncertainty than the measurement procedures for the determination of the properties of other air pollutants. For every investigation of particles it is necessary to ensure a representative material sample. Exceptions are particular optical procedures that are preceded by a calibration with a material particle sample. Sampling is almost always a major source of measurement uncertainty when determining the particle state and/ or the properties in a particle–fluid discrete, dispersed system. For such a system the sampling is realized by the suction of a limited volume (sample) of the particle–fluid dispersed system through a corresponding suction opening. The basic requirement is the sample’s representative quality, i.e., its (sufficiently approximate) identity with the authentic dispersed system, with regard to the quantity that is established (concentration, particle size distribution, chemical composition, etc.). The question of representative quality should be dealt with during every sampling procedure. Changes in the characteristics of the particle–fluid dispersed system sample, especially its concentration and particle size spectrum, can occur at the spot where the sample was taken, i.e., before being taken into the measurement device, as well as on the path through the suction pipe and through other components of the device, and finally, during further handling actions to the place where the desired analysis is performed. In this way, smaller or greater differences between the measured and the real quantities that are measured occur, resulting in corresponding measurement errors that belong to the group of systematic errors. Attention will be di- rected to the part of the errors that occur during the sampling of the particle-fluid dispersed system to the point where the sample is taken into the suction opening of the measurement equipment. As opposed to gas mixtures, for which the representative sample is relatively simply achieved, the representative sample of particle-fluid, and especially particle-gas, dispersed system is always questionable and requires additional verification. 1 DEFINITIONS OF EMISSION AND IMMISSION QUANTITIES According to HRN ISO - Vocabulary [1], emission and emission quantities are expressed as follows: D.1. Emission: Discharge of substances into the atmosphere. The point or the area from which the discharge takes place is called the source. The term is used to describe the discharge and the rate of discharge. The term can also be applied to noise, heat, etc. D.2. Emission rate (emission velocity): The mass (or any other physical quality) of pollutant emitted into the air per unit of time. D.3. Emission rate density (emission flux): Emission flux divided by the area of a corresponding emission source. Immission and immission quantities have the same meaning as emission and emission quantities, but with the opposite sign. Simply, the receptor substitutes the source, and all the rates/transitions are in the direction from the air to a particular receptor instead of in the direction from a source into the air. Thus, the HRN ISO Vocabulary [1] confirms: “immission.....is the opposite of emission”. A mathematical determination of the terms immission and emission is given in ISO/TR 4227 [2] in terms of immission and emission flow, but unfortunately, with some omissions and errors [3]. Taking into consideration the discussion in paper [3], the immission/ emission flow terms, in relation to ISO/TR 4227 [2], could be correctly defined in the following manner: D.4. Immission rate 1(f) to a particular receptor is defined by the enveloping surface integral: l(t)=\r-(v-n)-dF, (1). Fl D.5. Emission rate E(f) of a source is defined by the enveloping surface integral: E(t)=\r-(v-n)-dFE (2), Fe 298 Degiuli N. - Barbalič N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 where (in two preceding equations): Fj\FE - is the smallest enveloping surface around the receptorl | source, p - is the density (a property divided by volume) at the enveloping surface Fj\FE, v - is the velocity vector of the property at the enveloping surface Fj\FE, n - is the normal vector of the enveloping surface element dFj\dFE pointing outwards so that the following is valid: J(v-«)dF/>0, j"(v-«)dFL>0 (3), p-v - is the immissioni|emission flux/rate density on the enveloping surface Fj\FE. The definition of Equation (1)||(2) for the immissioni | emission rate cannot be strictly applied to solid or liquid particles because of their discrete distribution. Here, the quantity p - property (for particles it is usually the mass m) divided by volume, might be considered in the following two ways: (i) The elementary volume AKin the vicinity of each observed point P(r) in space is sufficiently large at a given moment of time and it still contains a large number of particles, which makes it representative for describing the spatial distribution of particles. Thus: P = = CmV,t) AV (4), represents the particle mass concentration field that, from the said condition, is continuous at all points on the surface Fj\FE so the immissioni|emission rate according to Equation (1)||(2) is equal to: l(t)\\E(t) = rhp(t)= } cm(f,t)-vp(f,t)-n(f)dF {^KM}^c».(fK(0^ (5), where for average values cm (t) and vp (t) over the surface Fj\FE the following applies: (') = J c ( r,t ) dF w=t I [%(?,t )-m]dF (6), where F = F}\FE. (ii) The elementary volume AKin the vicinity of each observed point P(r) at a given moment in time is sufficiently small (to the continuity limit of the dispersed medium - fluid phase). Then: Am \pp for P(r)eV p = lim----- = 1 a^0aF [pf for P(r)e Vf (7), where it has been taken into account that the observed volume K consists of the particle volume, V, and the fluid volume, Vf , i.e., V = Vp+VfoF = Fp+Ff,{V = k-F) (8). For the particle volume concentration 7v and porosity s , the following is valid: — V F F V c =VJL = jL = 1-J = 1-LL = 1-ë (9), VF F V i.e., F = c -F, F 0-^ (10). From the definition of Equation (1)||(2), the immissioni|emission rate is as follows: l(t)\\E(t) = mp(t)= j p(r,t)-vp(r,t)-n(r)dF = -f/ll-fi = lpp-vp(r,t)-n(r)dF = ppYJ[vp(r,tyn(r)l-(AFp\ = F i =pP-(^}F*pP^yW>F=^JJY^Ät)-F where, L^pV,V 'H'/],- - is the projection of i-th particle velocity in the direction n, (AF ). - is the projection surface of the ;-th particle normal to n, taking into account that, = 0 for P(r)iFp (12). In Equations (5) and (11), in which the particle immissionilemission rate is reduced to the mean values over the surface F}\FE, attention should be drawn to the inequality sign, which emphasises that the immissioni | emission particle flow is not equal to the product of the product of concentration and velocity mean values over the surface F}\FE. This product is the basis of the measurement procedures for determining the immision|| emission particle flow. Thus, the initial measurement uncertainty is built-in in advance into the measurement procedures for the determination of the immision||emission particle rate. The value of the measurement uncertainty for a particular measurement procedure is proportional to the quantity ratio on the left- and right-hand sides of the inequality in Equations (5) and (11). Generally, the particle mass concentration is determined by Equation (4). However, according to the regulations [4], a definition for the mass concentration of the pollutants is: D.6. The mass concentration of pollutants in exhaust gases is the pollutant mass per volume unit of dis- Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 299 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 charged gas at a temperature of 273.15 K and a pressure of 101.325 kPa. It is obvious that this defines the mass of the discharged pollutant in the discharged gas. Thus, it is the mass flow concentration cM(t)= (t) (t) V&n(t) (t) (13), where the indices denote z for the pollutant and n for the standard gas parameters (e.g., 273.15 K, 101.325 kPa). The denominator in Equation (13) is determined from the followinrg equation: 1 T p(r,t)rr V&n(t) Pn (t) Pn T (rr,t) ¦vf(f,t)-n(f)dF T __n Pn T{t) (t) (14). F From Equations (5), (13) and (14), the mass flow concentration for the particulate matter (index: z = p) is: (t) Pn _Cn,(t)-Vp(t)_ T n T(t) f ) (15). Furthermore, the volume flow concentration, cV, for particulate matter is: (t) m Pn (t) 1 P, (t) (16). Vntrpm&ft &() () A concentration measurement is essential for any measurement method for determining the immission and emission quantities. In an immission measurement, that is usually the final objective: the concentration field of some area, space and the like, on the basis of which the immission rate, the rate density, and the immission dose are evaluated in relation to particular receptors. The concentration for emission monitoring and evaluating has the meaning of a subsidiary quantity in order to determine/monitor the source emission flow, i.e., its significance in terms of the environmental contamination. 2 SAMPLING OF PARTICLES IN THE DETERMINATION OF THEIR CONCENTRATIONS IN A GASEOUS ENVIRONMENT There are two essentially different cases of sampling of particles that can be found in applications [5]: (i) the sampling of flowing particle-gas systems, (ii) the sampling of stationary particle-gas systems. A direct quotation from the English original [5] describes the division as: (i) sampling of flowing aerosols, (ii) sampling of stationary aerosols. The correct interpretation of the term aerosol can be considered as questionable. This headword in the Croatian version of the three-language dictionary [1] is cited with following meaning: D.7. Aerosol: a two-phase system in which the continuous phase is gaseous and the dispersed phase is liquid and/or solid; dispersed system particles have a negligible deposition velocity in the gravitational field. In this definition, the limit of neglecting the deposition velocity is not determined and with no reason aerosols are attributed to a relatively narrow subclass of particle-fluid dispersed systems. Since during every sampling of the particle-gas system care must be taken about the influence of gravitational forces (i.e., how to avoid their influence on the measurement error), it is more correct to accept the following definition [6]: D.8. Aerosol: a two-phase system in which solid and/or liquid particles are dispersed in a gas. Yet, for that, as well as for any other particle system dispersed in a fluid, it should be kept in mind that its existence depends on the mutual ratio of the gravitational and carrying forces. According to such a rule, aerosols would be a subclass of a particle-fluid dispersed system, for which, approximately, the size of the dispersed solid/liquid particles is in the range (aerodynamic diameter) of 2 nm to 100 mm [6]. Essentially, such a particle size range covers aerodispersed systems, which are a subject of interest for environmental protection (air-quality protection). In accordance with the introduced classification, the sampling of the flowing gas-particle system includes aerosols that flow through pipe ducts and the like, as well as atmospheric aerosols in the presence of wind, while the sampling of the stationary gas-particle system includes aerosols in quiet conditions, including both the outside air and the air of working or indoor living spaces. In the sampling of flowing aerosols, measurement errors are mainly a consequence of particle inertia forces that condition the deviation of the particle trajectory from the streamline (Fig. 1) [7]. If the sample opening is not placed isoaxially (Fig. 1.a)), or if the sample suction velocity is higher (Fig. 1.b)) or lower (Fig. 1.c)) than the fluid velocity in the undisturbed flow, the sample particle concentration will be smaller (Fig. 1.a) and b)) or greater (Fig. 1.c)) than the real particle concentration. cM: 300 Degiuli N. - Barbalič N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 a) I 1 T T b) I I 1 I c) i t t T Fig. 1. Errors in the flowing aerosol sampling: a) non-isoaxial, b) non-isokinetic, c) sub-isokinetic Therefore, sampling should be isoaxial, isokinetic and the wall of the suction pipe (probe) should be sufficiently thin. The sampling of stationary aerosols has no analogy with the sampling of flowing aerosols because the flow field in the neighbourhood of the sampler opening in the case of the flowing fluid environment (Fig. 1) is completely different from the flow field created around the sampler opening in the case of the stationary fluid environment (Fig. 2). In addition, this type of sampling has been less frequently investigated than the sampling of flowing aerosols. Regardless of the difference in the fluid flow field created in the two mentioned opposite cases in the neighbourhood of the sampler input opening, the increase in the measurement error of aerosol sampling, compared to other (gaseous) pollutants, is a consequence of the particle trajectory in the fluid environment. 3 PARTICLE TRAJECTORY PROPERTIES The measure of the particle size is its equivalent diameter [1]: D.9. The equivalent diameter is the diameter of a round particle that has the same geometrical, optical, electrical or aerodynamic behaviour as the tested particle. The hydrodynamic/aerodynamic particle behaviour is of major importance for the sampling of aerosols. As such, the measure of the particle size is its diameter, the Stokes diameter or the aerodynamic diameter. If us denotes the stationary deposition velocity of some observed particle in an infinitely spread fluid environment at rest under the action of gravitational force, the equivalent diameter of that particle in relation to the deposition velocity comes to: r f xs=x = --Cw(Re)- 4 (Pp-Pf)- (17), Fig. 2. Flow field during suction from a stationary fluid environment Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 301 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 where Cw(Re) is the resistance coefficient of a sphere of diameter x and Re us-x-ps /J (18) is the Reynolds number. For Re < 0.25 (the range in which the Stokes law is valid), according to [8] the following is valid: 24 C = —, Re < 0.25 Re (19), and the diameter determined by Equation (17), according to (19), is the Stokes equivalent particle diameter : 18 • jU ¦ us \g{pp-Pf) (20). Regarding the range in which the Stokes law is valid (Equation (19)), Equation (20), in usual fluid conditions, can be applied up to xst < 50 mm for air, and up to xst < 80 mm for water. When aerosols are concerned, one can also use the aerodynamic equivalent diameter xae for which the particle deposition velocity is reduced to the Stokes sphere deposition velocity at rp – rf = 1 g/cm3, i.e., ¦JPp-Pf (21). Also, in the application of Equations (17), (20) and (21) for aerosols, because p/p « 10-3,/? is neglected in most cases. A starting model for the aerosol sampling analysis in order to determine the corresponding immission and emission quantities is based on the following assumptions: - particles are considered individually, without taking into account their mutual influence, - the particle motion equation is set on the basis of the equilibrium of inertia, resistance, gravitational and pressure forces, i.e., d = Cw(Äe).^.^.|v-S|.(v-S) + f1-^i.f + ^.d dt ' 2.„ ' { P,J PP dt (22), where now, Re Jv-u\-pf-x p (23), where x is the equivalent diameter in relation to the deposition velocity, and m = pp n-x n-x (24). In the application for aerosols, it is justified in the second and the third terms on the right-hand side of Equation (22) to take the value n1 = pf / pp« 0, thus obtaining the motion equation, du 3 Pf u .. 1 / ,~ ^ _ - = --f-\v-u\-x C^Re)iV-u) + g (25), and to accept the fact that the investigation of aerosols in the range of smaller particles (Re < 0.25), for which Equation (22) has a much simpler form, is particularly important, i.e., according to (19), (22), (23) and (24): d « 18-// dt p -x rr r (v -u)+ g (26). However, for very small particles (for example xst < 1 |am), the assumption of a fluid environment continuity gradually retreats as their magnitudes approach the magnitude of the free trajectory of fluid molecules, A (for air in standard conditions A « 65 nm). Then the particle resistance coefficient, C , depends on the Knudsen number Kn (27), so, the following is valid (for: 0.1 < Kn < 1000; Re < 0.25): C Re x 2.514 + 0,800-exp -0.55 24 Re Cu- (28), where Cu denotes the Cunningham correction factor. When applying Equations (27) and (28) one should know how the equivalent particle diameter, x, has been determined because, due to the importance of the resistance coefficient, Cw, for the deposition velocity, the following is valid: I Cu (29). The possibility of reducing Equation (22) to its forms (25) and (26), and the possible necessity of using corrections (28) and (29), is validated by means of the values of the similitude numbers: Pr \v-u\-pf-x A n = —^ , n2= Re Pp M In order to reach a complete understanding of the terms in Equation (26) it is necessary to recognize the remaining important similitude numbers. By applying the integral analogy procedure [9], from A x 302 Degiuli N. - Barbalič N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 Equation (26) it follows that: T ¦— azv ozu ozz ¦ g where 2 P„ ¦ X u 18-// "g (31), (32) is the so-called particle relaxation time. Taking into account that for the characteristic length ratio the . relation L = v t is valid, the following similitude numbers are derived: T-g Us T-V g-L St = St-Fr~ where St T ¦ V _ Pp ¦ X -V L ~ 18-ju-L is the Stokes number, and Fr k-L (33), (34), (35), (36) (37) is the Froude number. In a general case, Equations (25) or (26) cannot be analytically solved. To solve them it would be necessary to know the fluid velocity field v = v (r ), and then the solution could be obtained numerically (for example, the Runge-Kutta method). However, possible analytical solutions, for the simplest cases, give very important data concerning the behaviour of aerosol particles in sampling procedures. a) Uniform particle motion. If the fluid velocity v is constant, particle motion can be divided into two periods. The first one (usually very short), in which a particle is decelerated or accelerated, and the second one, in which a particle is moving at constant speed, i.e., when dü/dt - 0. According to (25), for the second period the motion equation reads, -¦^¦\v-a\---Cw(Re)-(v-a) + g = 0 (38). Obviously, in this case, the relative fluid velocity (here, it is a gas) and the particle velocity have the direction of the vector g, so Equation (38) can be written in scalar form, from which the vector rrr r (v-u)Pg is obtained. For a fluid at rrest v =0 , the particle deposition velocity (us=u) will be obtained. b) Vertical motion. If all the vectors in Equation (25) r or (26) have the direction of the vector g , it is possible to find a complete solution for Equation (26) (which includes the period of acceleration/deceleration and the period of uniform motion), while in a general case (Re > 0.25) the solution of Equation (25) should be limited to the period of the particle uniform motion (i.e., the case described in a)). c) Accelerated particle motion. If the first term on the right-hand side of Equation (25) is distinctly predominant in relation to the other term, that other term (gravitational acceleration) can be neglected. This is valid for very small particles. If the particle motion in the field with constant velocity ( vr = const.) is concerned, the particle motion equation becomes, d(vr -ur) ----------' =---^-\v-u\---C (Re)-(v-u)(39), dt 4 pp x from which it follows that a change in the relative fluid and particle velocities can happen only in the direction of that relative velocity, i.e., only the intensity of the relative velocity can change, not its direction. The case for the range Re < 0.25 (i.e., the range for very small particles) is of particular importance. Then, the differential Equation (39) assumes the form d(v dt 18// Pp-x2 (vr -ur) -¦(v-m) z (40), and the equation for the intensity of the relative velocity (vr -ur) follows, dv-Ü dt the solution of which is, \v-u\ = \v-u\0-exp (41), (42), where |v-«|0 is the initial intensity of the relative velocity. Obviously, - for t =r |v-«| = (1/e)-|v-«|0 is valid (43), - for t -+ oo | v - « | = 0 is valid (44), i.e., the particle assumes the fluid velocity. In a fluid at rest ( v = 0 ), according to (42), ds dt u =u0- exp , (u i.e., 1-exp - ur) (45), (46), t t Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 303 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 from where, for t -* , the so-called stopping particle path (the penetration of the particle into the fluid at the starting velocity w0) is obtained: «„="0•*" (47). Thus, during the sampling of aerosols the ratio s/D is very important because, 2 St = ^ = U0'Pp'X (48), D 18-//-Ö where D is the diameter of the suction probe opening. However, as a rule, the upper limit of the applicability of equations derived from the condition Re > 0.25 (which is, for the air, approximately equivalent to the condition xst < 50 |om) is not taken into account in applications. For the range Re > 0.25, the relaxation time r= t * should be defined directly from Equation (25), so then, *4 pp-x and the stopping trajectory, sm=u0-T*=u0-T-ç(Re0) (50), where ç (Re0) is the correction function depending on the Reynolds number, Re=U0'X'Pf (51), the values of which are given in Table 1. Table 1. Correction function values Re0 10-1 100 101 102 103 ç(Re0) 1.00 0.97 0.72 0.38 0.17 According to the correction function values, it follows that for Re > 0.25 the calculation of the stopping path from Equation (47) would give overestimated values. 4 SAMPLING WHEN DETERMINING THE EMISSION AND IMMISSION QUANTITIES 4.1 Emission measurements Since it is either almost impossible or very difficult to correctly measure the pollutant emission at corresponding points of the minimum enveloping surface around the source (definition D.5), in the case of point sources, the emission measurements are best conducted on the discharge lines (e.g., smoke ducts, stacks, various exhaust pipes and the like). Generally, such measurements are particularly important in fossil-fuel fired power generation facilities, district heating and the chemical industry. If there are no reverse air flows or particle depositions or similar phenomena, i.e., generally, if there is no source and sink in the discharge conduit, then the below applies for steady-state conditions (Fig. 3): m&p = const(FE), m&g = const(FE) (52), i.e., as from Equations (11) and (14): cM = const(FE), cV = const(FE) (53), it would generally be irrelevant where (in which cross-section of the discharge duct) the emissions are measured. Even a possible reverse flow of air in the discharge line and/or gas discharge downstream of the measurement point and/or the deposition of particles upstream of the measurement point, and the like, do not affect emission quantities, which are, according to the regulations, reduced to dry gases, their standard condition and specified oxygen percentages. The selection of an appropriate measurement cross-section is actually determined by the limitations imposed by the measurement procedures and equipment. Specified rules (or guidelines) pertaining to the specified monitoring of emission usually regulate the selection of an appropriate measurement cross-section. Particularly important is the distance from the upstream and/or downstream sources of the fluid flow disturbance (expressed through a hydraulic diameter multiple) ([10] to [12]) and, for particles, the properties related to their inertial characteristics: possible deposition (the advantage of vertical in relation to horizontal ducts); a possibly more pronounced non-uniform particle concentration across the section of discharge ducts, for example, after flow disturbances; the dependence of inertial effects on the particle granulometric composition and the particle density [12]. In applications, when monitoring pollutant emissions into the air, the selected conditions are usually those that enable a rational use of the available measurement techniques and also enable simplifications, while having an acceptable effect on 304 Degiuli N. - Barbalié N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 ms ,ms, Vs,Vs,p Pp,fAx) Pf,T,

. ), the following applies: (VP -Cm)-FE ~(V/ 'C,,,)-FE*Vf -C,n -Fl E (64). 4.2 Immission measurements The sampling of aerosols is a particularly complex procedure if it is carried out in outdoor conditions, because the intensity, line and direction of F E vs Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 305 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 the wind and, also, the concentration and size of the flowing particles are very changeable quantities [13]. For example, an increase in the wind velocity causes, in most cases, an increase in the size of the dispersed particles, so, in this way, the Stokes number value (Equation (48)) is significantly increased. It is almost impossible to ensure the conditions of isokinetic suction of an aerosol sample for all possible values of wind velocity; therefore, the measurement error increases with the increase in Stokes number. Theoretical approaches to the problem of aerosol sampling are reduced to the range of laminar fluid flow, although, in the real atmosphere, the flow of the air is more or less turbulent. The necessity of simulating the flows of monodispersed particles with a constant concentration accounts for the limitations and relatively large errors of the experimental approach. In applications, for routine emission measurements, suction is usually carried out through an opening with a section mounted in the horizontal plane, in the top-to-bottom direction. In order to make the direct deposition of (especially big) particles in the suction opening impossible, and to prevent the penetration of atmospheric precipitation, the suction opening is covered with plates of different shapes, placed at a small distance from the opening. In this way, a relatively efficacious suction of particles of approximately 100 mm is realized, and there is only a slight probability of the suction of significantly larger particles. The aerosol sampled in this way can be conducted through impaction degrees if it is necessary to determine the particle size distribution or the concentration of particle PM10 or PM2 5 in the aerosol (the concentration of the fine particle fraction with the limiting particle size of 10 |om or 2.5 |om). In theoretical procedures, because of the difficulties in solving particle trajectory equations (Section 4), the cases where either inertia or gravitational forces can be neglected are usually considered separately. Evidently while sampling, no inertial particles with a probe/pipe placed in the vertical line, at the suction velocity v, the particle concen-tration ( 1 ± us /vs ) times changed (“+”: top-to-bottom; “–”: bottom-to-top) is obtained in the sample. The theoretical solution of the case of aerosol suction through a point sink placed in a vertical plane (wall) ([5] and [7]) is of particular importance. The starting point of the consideration is a two-dimensional case (Fig. 4): the aerosol is sucked in through an infinitely narrow clearance of infinite length (point 0) from the half-space (right half-plane in Fig. 4) limited by the wall plane. The differential equation of the motion of small particles ( Re < 0.25 ), according to (26) and (32), is, du dt -¦(v-u) + g, t (65). Neglecting the inertia forces, the following is valid: 0,5 1,5 Y-us V Fig. 4. Sampling of aerosols through an infinitely narrow clearance 0 306 Degiuli N. - Barbalič N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 U =V + T¦ i.e., dxi dt v +u -S (66), (67), where L are coordinates of particle position vector, ^={XJ\ (68). If V is the volume flow of the air that is sucked per unit length of clearance, the components of the air velocity vector are (Fig. 4): [ V-X V-Y R-n R-n (r2=X2 + Y2) (69). System (67) reduces to the following differential equation, dY_ji_jw^ x2+y2 dX~ X V X i.e., V 1 dX with the solution, O = ^.[X0-X], 0 = arctg X (70), (71), (72), where X0 is the particle initial position for Y = - oo. In terms of the obtained trajectories, the particle trajectory for which X0 ¦ us /V = 1 separates the particles that will be sucked from those that will miss the clearance. Consequently, all the particles, which for Y = - oo started from the length L = V/(1-us), pass through the unit of clearance length. Then, for Y = - oo, particles move only at the velocity « , so if c is their concentration, the mass flow through the surface L . 1 amounts to m = c-us-1-L = c-us-1-V/(1-us) = c-V . The concentration of particles sucked through the clearance is exactly m/ V, i.e., it is equal to the initial concentration. Obviously, it is clear (Fig. 4) that in-ertial particles depart from these trajectories and that they either run into the wall under the clearance or keep on moving in the positive direction of the Y axis. Consequently, the final result is a decrease in the sample concentration. The magnitude of the deviation is exactly proportional to the stopping path ,„=«•* Because of this, the suction velocity CO s should usually be several times higher than the deposition velocity, but then the question of the representative quality of the deposition velocity still needs to be dealt with because aerosol particles are regu- larly polydispersed in the range of several orders of magnitude. Regarding a possible exceptional influence of the wind on sampling errors, it is important to mention the conclusions of the experimental results of Maya and Druetta [5]: if the suction velocity, v, is constant, and the inlet velocity, v, of the g particle-fluid dispersed system changes from 0 to v, the ratio of the sample particle concentration to the inlet aerosol A will change in a way that for v = 0, A = 1, so with the increase in v, A decreases, passes through a minimum and again, for v = v, assumes the value of A = 1. It should be pointed out that the departure of the value A from unity significantly decreases with the decrease of the particle size and is practically negligible for a particle size of approximately 1|om. 5 CONCLUSION In the group of measurement procedures intended for the determination of immission and emission quantities of substances considered as air pollutants, the measurement procedures for the determination of quantity, the condition and properties of the particle-fluid dispersed systems have particular significance because these procedures are subject to a significantly greater measurement uncertainty than the same measurement procedures intended for the determination of the immission and emission quantities of other air pollutants. Because of the discrete particle distribution in space, the definition of particle concentration in a gaseous environment demands a two-pronged approach: either by taking into account the discrete characteristics of particles, or by accepting the assumption of their continuous distribution - according to the conditions of the continuous environment. Using both the above mentioned approaches, the definition equations for the immission and emission flow are reduced to analogue expressions that are the basis for the corresponding measurement procedures. In these expressions it is necessary to accept approaches in relation to the averaging of the measurement quantities per surface of particle transition (emission/emission surface). In this way, the measurement uncertainty is built-in in advance. The greatest cause of measurement uncertainty is the non-representative quality of the particle sample, as a consequence of the inertial properties of the particles, i.e., the impossibility of real- Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 307 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 izing the condition of the isoaxial and/or isokinetic sample suction, and the difference between the particle and the gas velocity vectors inside the sucked control volume of the particle-gas system. Regarding the fluid flow field that is formed in the neighbourhood of the suction opening, the difference between the sampling of the stationary and the flowing particle-gas system is of crucial importance because in the former and the latter cases the particle trajectories have a qualitatively different shape and hence a different demonstration of inertial action. The immission monitoring of air pollution with particles is particularly subject to sampling errors. In this case, the measurement uncertainty decreases with the particle size decrease, so the regulatory evaluation of the air quality with respect to pollution with particles by using the fraction PM10 (the concentration of the fine particle fraction with a limiting particle size of 10 |im), as recently introduced in the European Union, is more convenient from the point of view of measurement uncertainty in relation to the former evaluations carried out by means of the concentration of the total amount of flowing particles. 6 NOMENCLATURE a average of variable a d Kronecker symbol: dij = I a& time derivation of variable a e porosity l0 {i*j c concentration e is an element of const(a) constant concerning the choice of a m dynamic viscosity E(t) emission rate r density I(t) immission rate t particle relaxation time F surface inv(a) invariance concerning a Indices k constant E emission L length I immission m mass f fluid/gas p pressure g gas r r position vector GR gravimetry t time m, M mass T temperature n standard parameters u particle velocity N number v velocity p particle V volume s sample; deposition x equivalent particle diameter v, V volume 7 LITERATURE [1] [2] [3] [4] [5] [6] [7] [8] [9] HRN ISO 4225: 1997, Air quality - General views - Dictionary (ISO 4225: 1994), Threelingual edition, Zagreb, 1997 - in Croatian. ISO/TR 4227, Planning of ambient air quality monitoring (1989) ISO, Geneve. Barbahč N., Marijan G., Bilie Ž. (2001) Conditions and phenomena which a priori limit the confidence of continuous measurement of particulate emission in the air, 12th IUAPPA world clean air and environment congress. Proceedings: ref TS1-72c, Seoul. Regulation of limiting values for pollutant emission from stationary sources, Narodne novine No. 140, pp. 4406 - 4425, 1997; Narodne novine, No. 105, pp. 4008 - 4096, 2002. Fuchs N.A. (1975) Sampling of aerosols, Atmospheric Environment 9, pp. 697-707, 1975. Šega K. (2004) Flowing particles, Gospodarstvo i okoliš 12, No. 66, pp. 11-16, 2004. Fuchs N.A. (1955) Mehanika aerozoli, Izd. AN SSSR, Moskva. Löffler F (1988) Staubabscheiden, Georg Thieme Verlag, Stuttgart - New York. Smolik J. (1977) Odlučovani tuhych Častic, Fakulta strojni, ČVUT, Praha. 308 Degiuli N. - Barbalič N. - Marijan G. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 297-309 [10] BS 893: Measurement of the concentration of particulate matter in ducts carrying gases, 1978; BS 3405: Measurement of particulate emission including grit and dust (simplified method), 1983; HRN ISO 9096: 1997, Stationary source emissions - Determination of concentration and mass flow rate of particulate material in gas-carrying ducts - Manual gravimetric method (ISO 9096: 1992), State Office for Standardization and Metrology, Zagreb, 1997. [11] Bilie Ž., BarbahčN. (1985) Gravimetric procedure for concentration and mass flow measurements of solid particles in flowing gases in flow ducts, Recommendation SDČVJ 301, SDČVJ, Sarajevo - in Croatian. [12] Hawksley P. G. W., Badzioch S., Blackett J. H. (1961) Measurements of solids in the flue gases, The British Coal Utilization Research Association, Leatherhead. [13] Belyaev S.P., Levin L.M. (1974) Techniques for collection of representative aerosol samples, Aerosol Science 5, pp. 325-328, 1974. Author’ Addresses: Doc. Dr. Nastia Degiuli University of Zagreb Faculty of Mechanical Engineering and Naval Architecture Ivana Lučiča 5 10000 Zagreb, Croatia nastia.degiuli@fsb.hr Prof. Dr. Nikola Barbaric Goran Marijan Hrvatska elektroprivreda Sektor za termoelektrane Ulica grada Vukovara 37 10000 Zagreb, Croatia goran.marijan@hep.hr Prejeto: Sprejeto: Odprto za diskusijo: 1 leto 6.6.2006 25.4.2007 Received: Accepted: Open for discussion: 1 year Vzroki nezanesljivosti vzorčnih meritev - Causes of Sampling-Measurement Uncertainties 309 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 UDK - UDC 620.17:669.715 Pregledni znanstveni članek - Review scientific paper (1.02) Overitev trajnosti aluminijastih sestavnih delov Structural Durability Validation of Aluminium Components Vatroslav V. Grubišič (Reinheim, Germany) Zaradi povečane uporabe aluminijevih zlitin za sestavne dele vozil je treba povzeti najsodobnejša spoznanja o presoji trajnosti sestave v delovnih pogojih. V prispevku smo predstavili postopke za preizkusno in numerično vrednotenje delovne trdnosti vlitka, kovanih in varjenih sestavnih delov iz aluminijevih zlitin. Predstavili smo tudi rezultate raziskav vpliva korozije, prav tako pa tudi metode pospešenega odobravanja preizkusov. Ti so nato potrjeni in priporočeni za uporabo v praksi. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: delovni pogoji, trdnost materialov, trajnost, vplivi korozije, utrujenost materialov) The increasing trend to use aluminium alloys for vehicle components makes it necessary to summarize the state of the art related to the approval of their structural durability under operational conditions. In this paper the procedures for the experimental and the numerical service-strength evaluations of cast, forged and welded aluminium-alloy components are presented. We also present the results of investigations of the influence of corrosion as well as the methods for accelerated test approval; these are then validated and a practical approach recommended. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: service evaluation, strength of materials, structural durability, corrosion-fatigue-influence) 0 INTRODUCTION The demands of the automotive industry for lightweight design and weight saving can only be fulfilled by going to the limits of the materials’ properties, the manufacturing process, the behaviour of the structural part and the behaviour of the system. An increase in the reliability is required, but at the same time there is a desire to reduce test costs, coupled with efforts to improve the methods of numerical design. Structural durability validation covers, on the one hand, special event loading and loading during misuse, and, on the other hand, service fatigue loading, characterized by the criteria of the structural yield point, the fracture behaviour and the fatigue strength ([1] and [2]), Fig. 1. Whereas an experimental proof of the strength safeguards the product safety, the numerical service strength evaluation serves as a pre-design procedure. An intensive cooperation between the Fraunhofer Institute for Structural Durability and System Reliability (LBF), Darmstadt, and the Technical Faculty Ljubljana, was started about 40 years ago by Jože Hlebanja and Ernst Gassner, and was continuously supported by co-workers and younger scientists. One of them, who contributed not only to this cooperation but also to the development of structural durability validation, was Matija Fajdiga. This cooperative research, especially the investigations related to the structural durability of aluminium components, which were supported by the EU ([3], [4] and [6]), are of great value. This paper is a review of the results of all the available investigations about the structural durability of aluminium components, the study of which was initiated and supported by experts from AUDI AG, BMW AG, Daimler Chrysler AG, Porsche AG and Volkswagen AG, and carried out by authors of Ref. [1]. In it the procedures for the experimental and the 310 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 Structural durability of safety components Loading from special and misuse events 1 Service loading(inclusive environment) Investigation of the structural yield point Investigation of the fracture behaviour under impact loading Investigation of fatiguestrength Gassner-curve (variable amplitudes) F,.' Local deformation eloc Global deformation s N WL Cycles N Fig. 1. Partition of the structural durability numerical service-strength evaluation of cast, forged and welded aluminium-alloy components are presented. Furthermore, the results of the investigations of the influences of corrosion as well as the methods for accelerated test approval are presented, validated, and a practical approach is recommended. 1 THE EVALUATION OF SERVICE STRENGTH 1.1 Fracture strength The relevant design criterion for a special event, for example, pressing a wheel against the curbstone edge when parking or when hitting a pothole with front wheel at braking, is usually the component’s yield point. However, depending on the material and the component, a misuse criterion may become more relevant. The component’s yield point is defined as the local equivalent strain or the corresponding equivalent stress, causing a plastic deformation of an allowable size, Fig. 2. A prerequisite is that neither an unacceptable global deformation of the component remains nor the required fatigue strength of the component decreases. Experimental investigations to determine the component’s yield point are carried out with vehicle-and component-relevant quasi-static loading, simulating the relevant special event. A recording of the load-local strain behaviour is recommended, making it possible to evaluate the material’s fatigue behaviour and make a comparison with calculation results. Fig. 3 shows the investigations on cast wheels (material G-AlSi7Mg T6), which were preloaded on the inner-rim side before the experimental structural durability validation was carried out. During preloading a special, seldom-occurring event is simulated, when the user drives over a “speed bump” or curbstone. Under such a loading a plastic, simply non-detectable, deformation can occur on the wheel, which could decrease the structural durability because of premature fatigue cracks on the rim, as shown in Fig.3. Within the pre-design process the component yield point may be estimated by elastic/plastic finite-element analysis based on the monotonic stress-strain curve for the local stress state. If any indications exist that plastic deformations may cause damage, fatigue testing with a load spectrum derived from the component’s service-load history is recommended. The relevant design criterion for misuse events, for example, high-speed curbstone impact, is the fracture behaviour during impact loading, with which fractures without deformation, e.g., brittle fractures, must be excluded. 1.2 Fatigue strength The fatigue strength of aluminium alloys decreases continuously for a large number of stress cycles. Based on experience, the knee point of the Woehler curve is assumed to be between 1-106 and 2-106 cycles. However, it may diverge from this, de- ll N GL Overitve trajnosti - Structural Durability Validations 311 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 a. S tres s-strain cu rv e (M at er ial beh av iou r , K t = 1.0) b . L o ad -strain cu rv e (Compon en t beh aviou r , K t > 1.0) R p0 .2 e©q,M i Ua uctural yield point % - component‘s yield point 0.2% e ee eq,M Fy eq,0 .2 Local equivalent strain eeq Fig. 2. Structural yield point and plastic deformation 10,5 Design Weight [kg] Plastic Deformation AD [mm] Durability Test Life [km] A 10.9 -0.85 cracks at 4 973 =0.5 B 11 -0.55 cracks at 10 141 »1.0 C 11.35 -0.35 without cracks 14 920 >1.5 fatigue crack Fig. 3. Influence of the rim design on plastic deformation and durability pending on the component, the material and the loading mode. As separately manufactured specimens do not inherit the shape, the surface condition and the residual stresses of the component, a direct transmission of the specimen’s test results to the components is not possible. Fig. 4 shows the empirically derived shape of the Woehler curve recommended for the pre-design-ing of the components from wrought or cast aluminium alloys according to the local stress concept when the specific component data are missing. The available, published quantitative material data are summarized in [1]. In Fig. 5 a generalized Woehler-curve for welded aluminium joints is presented. Compared to the aluminium base material the fatigue strength of the welded joint is less by a factor of between 1.3 and 3.0, assuming an equal stress distribution along the highly stressed section. The tensile strength, Rm, and the yield strength, Rp,0.2, of the base material have only a minor influence on the fatigue strength. Residual tensile stresses caused by the change of microstructure as well as the solidification may degrade the fatigue strength. Such a degradation prevails in the range of large numbers of cycles (N>1 • 106). When the magnitude of the residual stresses is known they may be assessed like mean stresses. Otherwise, it is recommended to cover the effect of residual stresses by choosing the allowable stresses resulting from the fatigue loading with R=0. In the case of a fatigue-life estimation under variable-amplitude loading the recommended slopes of the Woehler curve are k=5 in the cycle region of N<1107 and k’ = 2k-2 in the region of N >1107, as shown in Figs. 4 and 5. For the design of welded joints the automotive industry normally applies the structural stress concept ([5] and [6]). The structural stress incorporates the influence of the weld geometry and the loading mode, but should not be mistaken for the maximum notch stress or the hot-spot stress [5], Fig. 6. 0.2 % e 312 Grubišič V. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 "\^5 g ' = 0 30 ¦ f ¦ R (accordng to the German Association mof Mechanica Engineering FKM) f =f (surface, constraint, environment ...) n _____k1 = j | F c" ~ > - ~ k=2k-2 = 8 "\" -LBF-recommendation for j f ati gu e l i f e esti mai on ' ' 10' !0 tO" 10" 10' Cycles to failure Nf (log) Fig. 4. Schematical presentation of the Woehler-curve for components of wrought and cast aluminium alloys | "., = f (joint geometry, loading mode) FAT-category (according to IIW or Eurocode) ^~~--^_^ LBF-recommendation for I9' b tl Z3 ¦w ^ * ^ - a fatigue life estimation *) IIW or FKM: k = 3 Eurocode 9: k = 3.2 to 6 course accordi Eurocode 9 ig to i )' 1(f 1f 2 5 t 1 :.' t )! Cycles to failure Nf (log) Fig. 5. Schematical presentation of Woehler-curves for aluminium welded joints The local geometry substantially influences the en- the analytical proof must take into account the influ- durable structural stresses of welded joints [6], Fig. 7. If no specific data are available a structural stress of CT *(R=-1, N=1106, P =90%) = ±40 MPa may be a s used for the pre-design. 2 THE INFLUENCE OF CORROSION If components are exposed to a corrosive en- ence of the corrosion [7]. For instance, for a cast steering rod and a welded rear-axle carrier the Woehler and Gassner curves resulting from constant and variable amplitude loading in air and in a corrosive medium (5% NaCl) are displayed in Figs. 8 and 9. The applied stress variation and the spectra are presented in Figs. 10 and 11. Concerning the effect of corrosion on the fa-vironment during service the experimental as well as tigue strength special attention should be paid to Overitve trajnosti - Structural Durability Validations 313 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 s : structural stress s : max imu m n ot ch s t r es s hs : hot-spot-stress s 100 MPa 90 80 70 60 50 : f ( w eld geom et ry, loadingmode) structura stress dstribution (stran gauge or FE) linear extrapolation strain gauge d Notch str es s distri buti on (FE) Str ess-concentrati on factor: s s hs weld-toe radius weld angle 9 weld-toe' t = 1-5 mm: Gauge length lo = 1.5 mm, d = 1 mm t > 5 mm : lo = 3.0 mm, d = 2 mm Fig. 6. Definition of stresses in a weld A Base material 40 30 20 10 0 Material: AlMg 4,5Mn (filler metal AlMg5) Loading: Bending, R = -1 = 2 · 10 , P= 90% B Butt weld MIG C Butt weld, ground 'wj MIG D L ap joint MIG E L ap joint MIG F L ap j oi nt TIG ) ~: l i HI .6 - 7. Ç=3 ) ^ y t 8 - 9 ( HI 1 1 I T^^100-120° H ti ^m 1 ¦^^-1 30-140° H XT G Lap joint, milled J ^"^^ MIG "^ij J AB CDE F G *) in 2mm distance of the notch transition of the weld; length of the strain gage: l0= 3mm Fig. 7. Influence of geometry on supportable stresses of aluminium welded joints the following: • To reveal the damaging influence of corrosion fatigue load levels we should allow at least 5-106 cycles. • During corrosion the slopes of the Woehler curves do not change. A constant slope of k = 4 is recommended. • Available results show a significant drop in the fatigue strength due to the corrosion being less during random loading. If the surface is not treated (coated, shot-penned) the fatigue strength after 5-106 load cycles reduces to 50% under constant-amplitude loading and to 20-25% under variable-amplitude loading. This applies to the intensified corrosive conditions imposed in the laboratory on aluminium alloys belonging to the 5000 and 6000 groups of the international alloy register. • Regarding components made of standard alloys, service experience has confirmed the following approach: the damaging influence of corrosion for a real component can be covered by proof testing in air with a 15% increase in the fatigue loads, provided the component’s yield point is not exceeded. Otherwise, a design life increased by a factor of 2 must be proven [1]. • Although cast skin and shot-penning diminish the strength drop due to corrosion this effect should be neglected in the numerical design process. In the case of corrosion protection (surface coats) the design process may be conducted as if no s s 150° 8 J. 5 314 Grubišič V. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 Component: Materia: Surface Loadng: Frequency: Environment: Cast rearaxle steering rod A 361 T6 (GD-AlSi10Mg T6) vacum investment casting as cast axial, R, R = -0.44 10 to 16 s1 RT Test in air A Constant amplitudes A Variable amplitudes, L = 2.3 103 Tests under corrosion (5% NaCl) 4 Constant amplitudes Variab le amplitudes, L = 2.3103 4.0 2.0 III.115 "Ö 1.0 5 0.6 ¦§ N 70 0.4 0.1 2 4 6 8 4 6 2 4 5 6 8 7 2 4 10 8 104 105 106 Fig. 8. Fatigue strength of cast aluminium rear axle steering rods in air and under corrosion Component: Welded rea"axle car rier Material: AA 5454 (AlMg3Mn) Weldng: MIG Loadng: axial, R, R = -1 Frenqu en cy 10 to 20 s1 Environment: RT Tests in air a Constant amplitudes ^ Variable amplitudes, Ls = 5 . 104, Gauss, I = 0.99 Tests under corrosion Corrosion cycle spraying 5 min, dry 20 min L Constant amplitudes Q Variable amplitudes, L = 5 104 , Gauss, I = 0.99 2.0 I b 0.6 0.2 0.1 Gassner-curves Woehler-curves TF = 1 : 1.30 Ps = 50% I0 6 S Cycles to failure Nf (10% stiffness loss) Fig. 9. Fatigue strength of welded rear axle carriers in air and under corrosion corrosive environment were active. • So far, generally valid knowledge about the influence of distinct corrosion cycles on fatigue behaviour and knowledge about an appropriate selection of service-like environmental conditions are still missing. Thus, for future testing concepts, first of all a unification of simulated environmental conditions is to be recommended, for example, a 5-min period of salt spraying with 5% NaCl solution followed by a drying period of 20 to 25 min. Investigations on preconditioning with subsequent fatigue loading in air do not have a real influence on the fatigue strength. Therefore, corrosive preconditioning should not be recommended to assess fatigue corrosion. 3 STRUCTURAL DURABILITY VALIDATION 3.1 Experimental validation The experimental validation of structural durability must be based, on the one hand, on representative operational stress spectra including the loading sequence, and on the other, be carried out in a time- and cost-saving way [8]. Therefore, it is necessary to accelerate the durability testing for which the different possibilities exist: • The increase of the maximum and of all other spectrum loads with a simultaneous decrease of the spectrum size. This modification is suitable only when the structural yield point of the component 0.2 -J- 1.0 0.8 0.4 Overitve trajnosti - Structural Durability Validations 315 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 a. Stress-time history b. Cu mu lat ive amplit u de dis t r ibu t i on Fig. 10. Test spectrum of cast aluminium rear axle steering rods a Stress-time histor +1 b. Cumulative amplitude distibution +1 R= -1 I = 0.99 Spectrum size: Ls = 5 · 104 Fig. 11. Test spectrum of welded aluminium rear axle carriers is not exceeded by this measure. • Omission (cutting off the low loads); “real-time load-sequence testing” applies omission very often. Omitting the small loads with their large number of occurrences may change the component’s behaviour, depending on the omission level, the material, the loading mode, the manufacturing and the environment, occasionally leading to a wrong evaluation. • A change of spectrum shape, keeping the maximum spectrum load, but with an increased load on the lower levels. Here, the omitted small spectrum loads and the corresponding decreased total frequency are compensated by the increased loads, maintaining the damage content of the design spectrum. The modified load spectra should obey the following rules: • The load spectrum must contain a sufficient number of cycles, 2-106 up to 5-106, to cover the eventually occurring effects of fretting and environmental corrosion as well as the degradation of the fatigue strength in the region of a large numbers of cycles. • The equivalence of the damage caused by the test and the design spectrum, which should be verified by calculation with a modified Palmgren-Miner rule using Woehler curves for wrought or cast aluminium-alloy components, Fig. 4, or for welded joints of aluminium alloys, Fig. 5. • The sequence length of the test spectrum must be fixed in such a way that a sufficient mix of loads with the appropriate repetition is achieved, as applied during testing, Figs.10 and 11. 3.2 A theoretical estimation of the fatigue life To estimate the fatigue life two different concepts, namely the concept of local strain or stress for cast and forged components, and the concept of structural stress for welded joints, are used. Correspondingly, the local stress concept utilizes a local stress Woehler curve, as shown in Fig. 4, and the structural stress concept a structural stress Woehler curve, as shown in Fig. 5. A comparison of the experimentally generated strength data with the data derived from a German design guideline (FKM) [9] or from the Uniform Material Law shows large differences caused by the influences of component manufacturing. It is therefore advisable to use data obtained with specimens removed from components or with components. The local stress concept covers the mean-stress effects with the material-related mean-stress sensitivity parameter M = [a (R=-1) / a (R=0)]-1. It 0 0 -1 -1 316 Grubišic V. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 Damage sum of the spectrum: X r =Dsp8c. i-1 N i -D Cumulative frequency1 distri buti on (spectrum) Woehler curve N i = 1: steel , aluminium i = 2: cas t an d s in t ered mat er i als L s Cycles N, N Fig. 12. Modification of the Woehler-curve and calculation of fatigue life (schematically) has values between 0.2 and 0.3 for wrought aluminium alloys (Mwrought=0.25) and between 0.4 and 0.5 for cast aluminium (Mcast=0.45), depending on the tensile strength. For welded joints, mean-stress sensitivity parameters between 0.2 and 0.7 are determined, depending on the residual stress state; Mweld=0.45 is recommended. Furthermore, it is recommended to use Palmgren-Miners-Rule modified by Haibach ([1], [2] and [8]) within the local and structural stress concept to estimate the fatigue life, Fig. 11. The damage accumulation is based on the Woehler curves, Figs. 4 and 5, recommended above. If components are prone to corrosion effects, damage accumulation is recommended by the elementary Palmgren-Miner-Rule using a Woehler curve with a constant slope of kcorr=kair–1. Various investigations revealed damage sums between 0.05 and 2.0, depending on the stress-time history, the stress distribution and the failure criterion (the cracking or fracture of a test specimen). A real damage sum of Dreal = 0.5 is recommended for use with the fatigue-life estimation [10]. In the case of a large mean-stress variation, smaller damage values should be used. Assuming proportional loading and a constant direction for the principal stresses, multi-axial fatigue loading of wrought aluminium-alloy components can be assessed by equivalent stresses based on the distortion energy (Mises) or the shear-stress criterion (Tresca); in the case of cast alloys the normal (principal) stress criterion (Galilei) should be used. In the case of changing the principal stress directions the use of the distortion energy or the shear-stress criterion is not appropriate. They may lead to significantly overestimated fatigue lives of components with ductile material (e>10%) behaviour; thus a ductility-depend- ent modification is needed. For less ductile cast alloys (e<2%) the normal stress criterion delivers correct equivalent stresses [11]. In welded joints a multi-axial stress state with the constant direction of the principal stresses due to proportional loading can also be represented by equivalent stresses based on the conventional fracture criteria of Mises, Tresca or Galilei. In the case of non-proportional loading and a varying direction of the principal stresses, the fatigue-life estimation applying these criteria results in an unrealistic increase in the life compared to the case of proportional loading. The local equivalent stress, based on a modified Mises criterion, is calculated for the combination of normal and shear stresses in different interference planes of a surface element; the maximum value of the combination determines the critical plane and the equivalent stress [11]. The pre-designing of components, subjected to multi-axial loading with variable amplitudes, still contains large uncertainties requiring experimental verification. 4 CONCLUSIONS The state-of-the-art knowledge and the already-existing experience make the reliable design of aluminium components feasible. However, in future experimental investigations of components’ structural durability the local stresses or strains, with their dependencies on manufacture, geometry, and loading, should be determined, because the resulting data are more appropriate than the data derived from specimen testing or taken from guidelines. Such data may form a basis for verifying calculations and for the transfer of data to other components and for different loading modes. L N s ca c. D spec. D Overitve trajnosti - Structural Durability Validations 317 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 310-318 To profit by eventually extending the avail- special events on the fatigue life under subse- able lightweight design potentials, supplementary quent random loading. investigations to extend the database are desirable. • The influence of temperature combined with the pres-This mainly concerns: ence of a corrosive environment and random loading. • A determination of the maximum allowable plastic • The improvement of the accuracy of fatigue-life deformation with regard to the structural yield assessment methods for welded aluminium com-point of various components and the effects of ponents, also when they are multi-axially loaded. 5 REFERENCES [I] Sonsino C. M., Berg A., Grubisic V. (2004) Stand der Technik zum Betriebsfestigkeitsnachweis von Aluminium-Sicherheitsbauteilen (State of the art for the structural durability proof of aluminium alloy safety components). Fraunhofer-Institute for Structural Durability and System Reliability (LBF), Darmstadt, LBF-Report No. TB 225. [2] Grubisic V. (1998) Bedingungen und Forderungen für einen zuverlässigen Betriebsfestigkeitsnachweis (Conditions and requirements for a reliable structural durability proof). DVM-Report No. 125 (1998), pp. 9-22. [3] Fajdiga M., GrubisicV. et al. (1998) Improvement of strength properties of Aluminium alloy components by manufacturing process. -Partners summary report in Grubisic,V and Wessling,U.- Final report of Copernicus project No. CIPA-CT 94-0219. Fraunhofer-Institute for Structural Durability and System Reliability (LBF),Darmstadt. [4] Pukl B. (2000) Obratovalna trdnost mehanskih zvez delov iz jekla in aluminijevih zlitin (Fatigue life of mechanical connections made up from steel and aluminium alloys.). Ph.D.-Thesis on Technical Faculty of University of Ljubljana. [5] Radaj D., Sonsino C. M. (1998) Fatigue assessment of welded joints by local approaches. Abington Publishing, Cambridge. [6] Fischer G., Grubisic V (1999) Data for the design of welded aluminium sheet suspension components. SAE Paper 1999-01-0662, Detroit/USA. [7] Morgenstern C, Streicher M., Oppermann H. (2004) Leichtbau mit Aluminiumschweißverbindungen des Fahrzeugbaus unter korrosiven Umgebungsbedingungen und variablen Belastungsamplituden (Lightweight design of vehicle structures with welded aluminium joints under corrosive environment and variable amplitude loading). DVM- Report No. 131 (2004), pp. 75-88. [8] Grubisic V. (1994) Determination of load spectra for design and testing. International Journal of Vehicle Design 15 (1994) No. 1/2, pp. 8-26. [9] FKM-Richtlinie (German design recommendation): Rechnerischer Festigkeitsnachweis für Bauteile aus Aluminiumwerkstoffen (Numerical strength proof of aluminium alloy components). FKM-Forschungsheft No. 241 (1999), VDMA-Verlag, Frankfurt am Main [10] Grubisic V., Lowak H. (1986) Fatigue life prediction and test. Results of aluminium alloy components. „Fatigue Prevention and Design“, Ed. by J.T. Barnby, EMAS, Warley, pp. 171-187. [II] Küppers M., Sonsino C. M. (2003) Critical plane approach for the assessment of the fatigue behaviour, of welded aluminium under multiaxial loading. Fatigue & Fract. of Eng Mat. & Structures 26 (2003) No.6, pp.507-514. [12] Eurocode No. 9: Design of Aluminium Structures, Part 2: Structures susceptible to fatigue. European Committee for Standardization (CEN), Brussels, Ref. No. ENV 1999-2: 1998 E. Author’ Address: Prof. Dr. Vatroslav V. Grubisic Independent Consultant Zum Stetteritz 1 Reinheim, Germany vgrubisic@hotmail.com Sprejeto: 4.2007 Odprto za diskusijo: 1 leto Accepted: 25. Open for discussion: 1 year Prejeto: 10.7.2006 Received: 318 Grubišič V. V. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 UDK - UDC 629.7.035:533.6.07 Strokovni članek - Speciality paper (1.04) Izpopolnjena metoda uravnoteženja modela propelerja v vetrnem kanalu An Advanced Balancing Methodology for the Propeller of a Wind-Tunnel Model Aleksandar Veg (Faculty of Mechanical Engineering Belgrade, Serbia) Prispevek obravnava učinkovit postopek uravnoteženja, ki je bil razvit zato, da z njim popravimo asimetričnost nastavljivega kota kraka propelerja v razponu od -5 do +35 . Ker s standardnim postopkom uravnoteženja (ISO 1940-1) ni bilo moč doseči zahtevane kakovosti, smo razvili novo tehniko uravnoteženja. Študija propelerjeve neuravnoteženosti je razkrila številne pomembne podrobnosti, ki jih moramo posamično proučiti za potrebe zapletene naloge uravnoteženja. V znanih dokumentih ISO so te podrobnosti omenjene, ne pa tudi natančno opisane. Novi osnutek uravnoteženja pa določa naslednje: sprejemljive tolerance (glede oblike, izsrednosti in hrapavosti), zaporedje poteka uravnoteženja in prednostne naloge, spodnjo mejo neuravnoteženega preostanka, potrebno opremo in postopke, korekcijo neuravnoteženosti in preverjanje rezultatov. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: veterni kanali, uravnoteženje propelerjev, stopnje kakovosti, dinamično obnašanje) The focus of this paper is a versatile balancing procedure, developed to compensate for the asymmetries of a propeller blade's settable angle, in the range -5 to +35 . The standard balancing procedure (ISO 1940-1) was found to be inconsistent with the required quality grade, so a new balancing technique was created. A case study of propeller unbalance revealed a set of important details that must be uniquely assessed for such a complex balancing task. For the existing ISO notes, most of these details are descriptive rather than comprehensive. The new balancing concept defines the following: acceptable tolerances (shape, run-out and roughness), balancing order and priorities, a lower margin of residual unbalance, balancing accessories and regimes, unbalance correction and the verification of the results. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: wind-tunnels, airplane propellers, balancing control, quality control, dynamic behaviour) 0 UVOD 0 INTRODUCTION V postopku razvijanja novega turbopropelerskega letala običajno proučujemo delovanje modela z motorjem v vetrnem kanalu. Hitrost propelerja tovrstnega modela običajno preseže 10.000 min '. Pri tolikšni hitrosti pa na dinamično obnašanje modela vplivajo različni dejavniki, na primer resonanca motorja, frekvenca vrtenja krakov, neuravnoteženost propelerja, naravna stanja upognjenosti in torzičnosti propelerja, plapolanje in drugo. Med temi dejavniki ima poseben pomen kakovost propelerjeve uravnoteženosti, ki pomeni glavni vir sil vzbujanja. Z iskanjem nove metode uravnoteženja smo pričeli, ko so testne meritve pokazale, kako lahko The development of a new turbo-prop aircraft usually involves wind-tunnel research with a powered model. The propeller speed with such a model typically exceeds 10,000 rpm. At such a speed, the dynamic behavior of the model is influenced by various factors, for example, power-group resonance, blade-pass frequency, propeller unbalance, flexural and torsional blade natural modes, flutter and so on. From among all these factors, the quality of the propeller balance is of particular importance, as the main generator of excitation forces. The research process for a new balancing methodology began when the first test measurement 319 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 skoraj popolno uravnotežen propeler ob novi nastavitvi kota krakov dramatično pade iz tolerance. Kljub natančno uporabljenemu postopku uravnoteženja ISO (1940-1) nismo mogli izboljšati nastalega stanja, to pa zaradi vplivov geometrijske oblike priležnih elementov in porazdeljenosti mase, ki sta preprečili nastanek potrebne kakovosti. (Več podatkov o tem problemu je v razdelku 1). Ker je bilo treba ustvariti dobro uravnotežen propeler, ki bi ustrezal različnim kotnim nastavitvam, sta se kot mogoči rešitvi pokazali dve možnosti: ¦ posamično uravnoteženje za vsako kotno nastavitev posebej (zapletena in dolgotrajna, vendar včasih edina mogoča rešitev); ¦ neka nova metoda uravnoteženja, ki bi zagotavljala sprejemljivo stopnjo kakovosti za vse kotne nastavitve. Prva možnost je preprosta ponavljajoča se uporaba standardnega postopka; druga možnost bi bila bolj dobrodošla, a je težko izvedljiva. Motivacija za premostitev tehničnih in znanstvenih izzivov je bila dovolj velika in prvi korak v raziskavi je bila poglobljena študija spremenljive strukture propelerjeve zgradbe ter študija dejavnikov, ki vplivajo na kakovost uravnoteženosti. 1 DEJAVNIKI, KI ZMANJŠUJEJO KAKOVOST URAVNOTEŽENOSTI Shema propelerjeve zgradbe (si. 1) je večplastna; sestoji iz zadnje (01) in prednje (02) puše, ki vpenjata štiri vgrajene krake propelerja (03). Štirje vijaki z valjasto glavo (04) trdno povezujejo prednjo in zadnjo pušo. V zadnjo pušo je izvrtana osrednja odprtina z dvema simetričnima utoroma, ki se prilegata glavni gredi motorja. Ti štirje deli (01 do 04) sestavljajo jedro sestave propelerjeve zgradbe. Preostali deli - matica (05), blokirni obroč (06), vrtavka (07) in pritrdilni vijaki (08) - so drugotnega pomena, četudi njihova uravnoteženost močno vpliva na celotno zgradbo propelerja. Kraki propelerja so oblikovani v zmanjšanem merilu izvirnih krakov. Izdelani so iz titana 6A1-4V; poprave mase ali oblike niso dovoljene. Vsak krak je z vrhnjim delom vstavljen med zadnjo (01) in prednjo (02) pušo. Vpadni kot določimo z natančnim zavojem ob osi kraka; vsi štirje kraki so nameščeni pod enakim kotom. Kakor je omenjeno že v uvodu, so vzroki za asimetričnost propelerjevih nastavljivih delov, ki povzroča neuravnoteženost, naslednji: showed how an almost perfectly balanced propeller dramatically dropped out of tolerance when a new blade-angle setting was applied. However, a strictly applied ISO-proposed balancing procedure (1940-1) provided a poor result, because of the influences of the adjacent parts’ geometry and mass distribution, which prevented the required quality grade being achieved. (For more details, see Section 1). Since it was necessary to obtain a well-balanced propeller for the whole range of angle settings, two options arose as possible solutions: ¦ Individual balancing for each angle setting (although complicated and time consuming, sometimes the only possible solution), ¦ Some new balancing methodology that will guarantee an acceptable quality grade across the whole range of angle settings. The former alternative is a simple, repeated application of a standard procedure, and the latter one, although much preferable, is difficult to realize. The motivation to overcome the technical and scientific challenge was strong enough, and the first step was to make an in-depth study of the propeller assembly’s reconfigurable structure and the factors that affect the balance quality. 1 FACTORS THAT REDUCE THE BALANCE QUALITY The design of a propeller assembly (Fig. 1) is a complex one, consisting of a rear (01) and a front (02) hub that clamp together four embedded blades (03). Four cylinder-head bolts (04) fix the rear and the front hub tightly together. A central hole is bored in the rear hub, with two symmetrical keyways to fit the engine’s main shaft. These four items (01-04) form the core structure of the propeller assembly. The remaining assembly parts: the nut (05), the locking plate (06), the spinner (07) and the fixing bolts (08) are of secondary importance, although their balance seriously affects the complete assembly. The propeller blades are shaped as a scaled-down version of the original blades. They are made of titanium 6Al-4V, and no mass or shape correction to the body is permitted. Each blade is head-nested between the rear (01) and the front (02) hub and the attack angle is adjusted by a precise twist about body axis, the same amount for all blades. As mentioned in the introduction, the asymmetry of the propeller’s adjustable parts, resulting in the unbalance, originates from: 320 Veg A. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Sl.1. Sestava propelerja Fig. 1. Propeller assembly ¦ geometrična asimetričnost pritrditvenih točk (teža vsakega kraka znaša približno 1/6 celotne teže propelerja). Odstopanje lege težišča posameznega kraka je preveliko, kadar je večje od šestkratne tolerance propelerja; ¦ ohlapen stik med priležnimi deli (Netočne tolerance reže bodo povzročile enak učinek, kakor je opisan v prejšnji točki); ¦ razlika v teži (Vsak krak je enkraten element z določeno porazdelitvijo mase, zaradi katere ima krak tudi svojo lastno maso in statični moment; vsakršna razlika v tovrstnih značilnostih posamičnih krakov povzroči določeno začetno neuravnoteženost); ¦ nenatančna nastavitev kota (Razlike v nastavitvi začetnih kotov krakov prav tako povzročijo znatno neuravnoteženost). Glede na te ugotovitve, bi morala nova metoda uravnoteženja določiti naslednje: ¦ preglednico sprejemljivih toleranc (glede oblike, izsrednosti in hrapavosti); ¦ zaporedje poteka uravnoteženja in prednostne naloge za vse posamezne dele; ¦ spodnjo mejo neuravnoteženega preostanka (bolj strogo kakor v priporočilih ISO), ¦ potrebno opremo in postopke; ¦ navodila za popravo neuravnoteženosti; ¦ natančnost nastavitve kota kraka; ¦ preverjanje rezultatov. Tako bi nastal izpopolnjen postopek, ki bi omogočal zadovoljivo uravnoteženje. ¦ geometrical asymmetry of the clamping points (the weight of each blade is approximately 1/6 of the assembly weight). When the variation of the blade’s centre-of-gravity position becomes greater than six times the assembly’s tolerance it becomes excessive. ¦ a loose contact between adjacent parts. (Inaccurate tolerances of the gap will cause the same effect as the previous point); ¦ weight difference. (Each blade is a unique part with a particular mass distribution resulting in its own mass quantity and static moment; any difference in these attributes for opposed blades imposes a certain initial unbalance); ¦ an inaccurate angle setting. (The dispersion of the blades’ preset angle is also a source of significant unbalance). According to these explanations, the main task for the new balancing methodology would be to propose: ¦ a table of acceptable tolerances (shape, run-out and roughness), ¦ a balancing order and priorities for all items, ¦ a lower margin for residual unbalance (more rigorous than the ISO recommendations), ¦ balancing accessories and regimes, ¦ instructions for unbalance correction, ¦ an accuracy for the blade-angle setting, ¦ a verification of the results, so that an advanced procedure would provide satisfactory balancing results. Izpopolnjena metoda uravnoteženja - An Advanced Balancing Methodology 321 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 2 PODLAGA ZA RAZVOJ IZPOPOLNJENE METODE URAVNOTEŽENJA 2 THE BASIS OF THE ADVANCED BALANCING METHODOLOGY Preden lahko uporabimo izpopolnjeno metodo uravnoteženja propelerja, moramo sprva opraviti pomembno uvodno nalogo. Glede na njihove mase in statične momente, moramo krake postaviti v ustrezne dvojice; s tem znatno zmanjšamo potrebo po popravi mas v nadaljnjem postopku. Gre za rutinski postopek, ki ga izvedemo vzajemno s primerjanjem in kombiniranjem različnih tež. Delovanje konstrukcije propelerja obsega Širok razpon vrtenja, od 2.000 min ' do 10.000 min ', in tako največja hitrost (10.000 min ') določa stopnjo neuravnoteženega preostanka. Ker je osrednja odprtina konstrukcije izvrtana v zadnjo pušo, moramo ta del obravnavati kot glavni element. Velikost radialne reže D med osrednjo odprtino in glavno gredjo, mora biti takšna, da ustvarja manj kot polovično vrednost dovoljenega specifičnega neuravnoteženega preostanka (1). Zadnja puša iz aluminijske zlitine se mora precej tesno prilegati jeklenemu vretenu, ki ustvarja uravnoteženost (si. 2). An important introductory activity precedes the advanced process of balancing the propeller. The blades must be matched in appropriate pairs, in terms of their mass and static moment, which then significantly reduces the need for any mass correction in subsequent steps. It is a routine operation that is conducted interactively by using weigh-compare matching. The propeller assembly operates over a wide spinning range, from 2,000 rpm to 10,000 rpm. Consequently, the maximum speed (10,000 rpm) dictates the amount of residual unbalance. Since the assembly’s central hole is machined in the rear hub, this part should be considered as a core element. The radial gap, D, between the central hole and the main shaft, must be less than half the value of that allowed for specific residual unbalance (1). There is quite a tight tolerance in the fit of the aluminum-alloy rear hub on the steel-made balancing-tool mandrel (Fig. 2). A — 2 1 ^ 10.000 RPM * 3 Mm (1). Poleg strogo določenih zahtev glede oblike vretena in njegovega imenskega premera (si. 3), moramo uvesti še nekaj dodatnih kriterijev: • hrapavost površine mora biti pod mejo 0,2 |im (kar omogoča gladko drsenje), • celotna izsrednost mora biti pod mejo 3 |im (kar se ujema z normativi ISO [1]), • specifični neuravnoteženi preostanek mora biti pod mejo 3|im. Glede na meritvene in poprave postopke lahko kasneje sestavne dele in posamezne sklope celotnega propelerja razdelimo v tri stopenjske skupine: Sl. 2. Vreteno Fig. 2. Mandrel Besides the strictly defined requirement for the mandrel shape and the nominal diameter (Fig. 3), a few additional criteria must be introduced: • a surface roughness below 0.2 |im (which guarantees smooth sliding), • an overall run out below 3 |im (which complies with ISO norms [1]), • a specific residual unbalance below 3 |im. Later on, the items and subassemblies of the propeller assembly can be classified into three order groups, according to the measuring and correcting procedure: N5, Y/110.0031 AB Sl. 3. Tolerance vretena Fig. 3. Mandrel tolerances 322 Veg A. 0.003 A B Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Preglednica 1. Vrstni red uravnoteženja Tabel 1. Balancing order SESTAVNI DEL ITEM MERITEV NEURAVNOTEŽENOSTI UNBALANCE MEASUREMENT POPRAVA NEURAVNOTEŽENOSTI UNBALANCE CORRECTION STOPNJA ORDER ZADNJA PUŠA REAR HUB NEPOSREDNA DIRECT NEPOSREDNA DIRECT I PREDNJA PUŠA FRONT HUB POSREDNA INDIRECT NEPOSREDNA DIRECT II VRTAVKA SPINNER POSREDNA INDIRECT NEPOSREDNA DIRECT II KRAKI BLADES POSREDNA INDIRECT POSREDNA INDIRECT III NEPOSREDNA meritev - meritev neuravnoteženosti določenega sestavnega dela z ustreznim orodjem POSREDNA meritev - meritev neuravnoteženosti z uporabo kakega drugega dela ali sklopa propelerja NEPOSREDNA poprava - poprava ugotovljene neuravnoteženosti na določenem neuravnoteženem delu propelerja POSREDNA poprava - neuravnoteženost določenega dela je popravljena na drugem delu propelerja Osrednje novosti izpopolnjene metode uravnoteženja so: • uravnoteženje posameznilidelov propelerja (namesto enkratnega uravnoteženja celotnega propelerja), • strogo določene geometrijske tolerance (popolna usklajenost s potrebami kakovosti uravnoteženja), • seznam prednostnih nalog (vsak del je uravnotežen v skladu z izhodišči predhodne določitve uravnoteženosti), • vnaprej določene ravnine za popravo mase (dosežena kakovost se ne sme zmanjšati ob ponovni namestitvi krakov propelerja) • dosledna zasnova neuravnoteženega preostanka (določen tako natančno, da omogoča neobčutljivost za spremembe kotov propelerjevih krakov) Glede na prednostne naloge uravnoteženja lahko oblikujemo vrstni red postopkov uravnoteženja, ki je predstavljen v preglednici 2, pri čemer smo predlagani neuravnoteženi preostanek izračunali z enačbama (2) in (3). PREDLAGANI SPECIFIČNI NEURAVNOTEŽENI PREOSTANEK DIRECT measurement - a single-part unbalance measurement using the appropriate balancing tool INDIRECT measurement - an unbalance measurement, using some other part or subassembly as a tool DIRECT correction - a correction of the detected unbalance on that particular part INDIRECT correction - an unbalance of one part is corrected on some other part The core innovations of the advanced balancing methodology are: • a decomposed propeller balancing (instead of an overall balancing), • strictly defined geometrical tolerances (total compliance with the required balance quality), • a queue of balancing priorities (each part is balanced as originally allocated on the pre-bal-anced platform), • predefined plains of mass correction (the achieved quality should not be spoiled by the blades’ resettlement) • a firm frame of residual unbalance (as sharp as needed in order to be insensitive to different blade angles) Regarding the balancing priorities, the balancing-procedure schedule can be formed as presented in Table 2, where the proposed residual unbalance is calculated from the following formulas (2) and (3). PROPOSED SPECIFIC RESIDUAL UNBALANCE L — L10.000 RPM — 6 kg PREDLAGANI NEURAVNOTEŽENI PREOSTANEK PROPOSED RESIDUAL UNBALANCE U = »zL = m[kg]6 kg (2) (3). Izpopolnjena metoda uravnoteženja - An Advanced Balancing Methodology 323 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Preglednica 2. Postopek uravnoteženja Tabel 2. Balancing procedure STOPNJA ORDER m SESTAVNI DEL ITEM PRIPOMOČEK TOOL SLIKA DRAWING VRETENO MANDREL PREDLAGANI NEURAVNOTEŽENI PREOSTANEK PROPOSED RESIDUAL UNBALANCE (G 6,3 - ISO 1940) g 0,78 ZADNJA PUŠA REAR HUB PREDNJA PUŠA FRONT HUB VRETENO MANDREL VRETENO + ZADNJA PUŠA MANDREL + REAR HUB VRTAVKA SPINNER VRETENO + ZADNJA PUŠA + PREDNJA PUŠA MANDREL + REAR HUB + FRONT HUB KRAKI BLADES VRETENO + ZADNJA PUŠA + PREDNJA PUŠA MANDREL + REAR HUB + FRONT HUB 1,32 0,90 0,30 3 REZULTATI IZPOPOLNJENE METODE URAVNOTEŽENJA C A 4k C _ DOLOČEN NA PODLAGI PREJŠNJIH REZULTATOV TO BE DEFINED ACCORDING TO PRELIMINARY RESULTS 3 THE RESULTS OF THE ADVANCED BALANCING METHODOLOGY Postopek uravnoteženja, določen v preglednici 2, smo izvedli do vključno celotne Il.stopnje. Tu pa se začne najbolj negotova faza nove metode; negotovost je povezana z uravnoteženjem nastavljivih krakov. Začetno meritev izvedemo za najbolj običajno kotno nastavitev [15°] (si. 4). Ugotovljeno neuravnoteženost potem popravimo na najbolj zunanjih ravninah ZADNJE in PREDNJE PUŠE (si. 5). Neuravnoteženi preostanek približamo predlaganemu preostanku (pregi. 3, osenčena vrsta). Vpadni kot nato povečamo do skrajnih vrednosti, The balancing procedure, specified in Table 2, is realized up to the last issue of order II. At this stage the most uncertain phase of the new method definition starts; this is connected with the balancing of the re-settable blades. An initial measurement is conducted for the most common angle setting [15°] (Fig. 4). The detected unbalance is then compensated in the outer-most planes of the REAR and FRONT HUB (Fig. 5). The residual unbalance is tuned close to the proposed one (Table 3, shaded row). Afterwards, the attack angle is changed to the extreme values [-5°] o i ii ii 324 Veg A. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Preglednica 3. Spreminjanje neuravnoteženega preostanka glede na vpadni kot (začetni rezultati) Tabel 3. Fluctuation of residual unbalance vs. attack angle (initial results) Vpadni kot Attack angle Vrsta dejavnosti Sort of activity Predlagani rezultat Proposed Dobljeni rezultat Attained Ocena Evaluation Stopnja kakovosti Qual. grade Neuravnoteženi preostanek Resid. Unbal. Stopnja kakovosti Qual. grade Neuravnoteženi preostanek Resid. Unbal. o opis description preostanek residual g dovoljeno permitted g - + 15 uravnoteženje balancing G 6,3 6,0 G 4,3 4,5 sprejemljivo acceptable - 5 preveritev inspection G 6,3 6,0 G 8,6 9,0 nesprejemljivo unacceptable + 35 preveritev inspection G 6,3 6,0 G 7,7 7,2 nesprejemljivo unacceptable [-5°] in [+35°], zdaj preverjanje neuravnoteženosti pokaže znatno povečanje neuravnoteženega preostanka, kar pa ni sprejemljivo (pregi. 3). Standardna stopnja kakovosti G 6,3 (ISO 1940-1), ki jo pri zgradbi propelerja upoštevamo v prvi fazi (začetni rezultati, pregi. 3), ne ponuja primernega and [+35°] and the unbalance check-up showed a significantly deteriorated residual unbalance, which is considered to be unacceptable (Table 3). The standard quality grade, G6.3 (ISO 1940-1), applied to the propeller assembly in the first stage (initial results, Table 3), could not provide adequate Sl. 4. Prilagoditev vpadnega kota Fig. 4. Attack-angle readjustment SI. 5. Popravne uteži za uravnoteženje krakov propelerja Fig. 5 Correction weights for the blades’ unbalance Izpopolnjena metoda uravnoteženja - An Advanced Balancing Methodology 325 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 uravnoteženja za celoten razpon mogočih vpadnih balance quality over the whole range of attack angles kotov (-5° do +35°). Zato določimo bolj zahtevno (-5° to +35°). For this reason a more rigorous qual- stopnjo kakovosti: približno G 1,5. Zdaj ponovno ity grade is established: approximately G1.5. The uravnotežimo zgradbo propelerja (si. 6) v skladu z propeller assembly is now rebalanced (Fig. 6) ac- novim kriterijem, nato pa preverimo nastalo stanje za cording to the newest criterion, and then verified for celoten razpon vpadnih kotov (pregi. 4). the whole range of attack angles (Table 4). Zdaj so rezultati uravnoteženja, ki smo jih Now the balancing results achieved by the dosegli z upoštevanjem spremenjene stopnje implementation of the new residual quality grade G1.5 kakovosti neuravnoteženega preostanka G 1,5, v are within the proposed tolerances. okvirih predlaganih toleranc. 4 PREIZKUS DELOVANJA 4 OPERATIONAL VERIFICATION Preveritev dinamičnega delovanja modela The inspection of the model’s dynamic smo izvedli v vetrnem kanalu (si. 7), z vrtečimi se behavior was conducted in a wind tunnel (Fig. 7) Preglednica 4. Zmanjšano spreminjanje neuravnoteženega preostanka glede na vpadni kot (končni rezultati) Tabel 4. Refined fluctuation of residual unbalance vs. blade angle (final results) Vpadni kot Attack angle Vrsta dejavnosti Sort of activity Predlagani rezultat Proposed Dobljeni rezultat Attained Ocena Evaluation Stopnja kakovosti Qual. grade Neuravnoteženi preostanek Resid. Unbal. Stopnja kakovosti Qual. grade Neuravnoteženi preostanek Resid. Unbal. o opis description preostanek residual g dovoljeno permitted g - + 15 uravnoteženje balancing G 1,5 1,6 G 1,2 1,3 sprejemljivo acceptable - 5 preveritev inspection G 6,3 6,6 G 5,0 5,2 sprejemljivo acceptable + 35 preveritev inspection G 6,3 6,6 G 4,4 4,6 sprejemljivo acceptable SI. 6. Propelerska zgradba na stroju za uravnoteženje Fig. 6. Propeller assembly on the balancing machine 326 Veg A. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Sl. 7. Model propelerja v vetrnem kanalu Fig. 7. Propeller model in the wind tunnel -1 Preglednica 5. Celoten razpon vibriranja (10.000 min ) Tabel 5. Vibrations in the whole range (10,000 rpm) Merilno mesto Measuring point Moč vibriranja Vibration severity (Vrms mm/s) Ocena Evaluation leva gondola motorja left engine gondola 2,0 sprejemljivo acceptable desna gondola motorja right engine gondola 1,8 sprejemljivo acceptable trup fuselage 1,5 dobro good propelerji, za celoten razpon hitrosti in vpadnih kotov. Vibriranje telesa modela je, ne glede na način delovanja in število vključenih energijskih enot, ostalo znotraj predlaganih mej ISO 10816-1, kar je bil tudi glavni cilj vseh dejavnosti uravnoteženja (pregi. 5). with spinning propellers for the whole range of speeds and attack angles. The vibrations of the model body, regardless of the regime and the number of engaged power units, were kept within the ISO 10816-1 proposed limits, which was the main goal of all the balancing activities (Table 5). 5 SKLEPI 5 CONCLUSIONS Na temelju rezultatov pridobljenih s standardno in izpopolnjeno metodo uravnoteženja, lahko sklenemo naslednje: ¦ Zaradi nezadovoljivega osnovnega postopka uravnoteženja in ne dovolj natančne določitve neuravnoteženega preostanka, z uporabo standardnega postopka uravnoteženja ne moremo dobiti sprejemljivih toleranc. ¦ Sprejemljive tolerance smo dobili z izpopolnjeno metodo, ki obsega resnično preverjanje vseh pomembnih toleranc, usklajevanje krakov propelerja, postopno izvedbo osnovnega uravnoteženja glede na prednostne naloge, natančno popravo mase in natančno določitev spodnje meje neuravnoteženega preostanka. Based on the results obtained by standard and advanced balancing procedures one can conclude the following: ¦ Acceptable tolerances could not be obtained with the standard balancing procedure, because of the inconsistent elementary balancing and the insufficiently sharp residual margin. ¦ Acceptable tolerances were obtained with the advanced balancing procedure, consisting of a true inspection of all the relevant tolerances, blade matching, step-by-step elementary balancing with priorities, a precise mass correction and a sharp definition of the residual unbalance lower margin Izpopolnjena metoda uravnoteženja - An Advanced Balancing Methodology 327 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 319-328 Izpopolnjen postopek uravnoteženja resnično pripomore k razumevanju pomembnih dejavnikov in lahko prepreči, da bi le-ti vplivali na kakovost uravnoteženosti nastavljivih sestavov. The advanced balancing procedure has real power in the stratification of all the influential factors, and can prevent them affecting the balance quality of reconfigurable structures 6 POJASNILO IN ZAHVALA 6 ACKNOWLEDGMENT Opisano metodo uravnoteženja smo razvili in uporabili v postopku proučevanja indonezijskega turbo-propelerskega transportnega letala za srednje proge, z uporabo modela vetrnega kanala, ki smo ga izvedli na Letalskem institutu, VTI Žarkovo, ob pomoči Instituta za strojno dinamiko pri Fakulteti za strojništvo v Beogradu. Opremo za uravnoteženje in druge pripomočke je priskrbela gospodarska družba Rotech Beograd, proizvajalec strojev za uravnoteženje in vibrodiagnostičnih naprav. Navedeni partnerji so močno pripomogli k uspehu projekta, zato se jim avtor iskreno zahvaljuje. The balancing methodology described in the paper was developed and applied as part of the research on an Indonesian middle-range turbo-prop transport aircraft with a powered wind-tunnel model, which was realized at the VTI Aeronautical Institute Ž arkovo with the assistance of the Machine Dynamics Institute, Faculty of Mechanical Engineering, Belgrade. The balancing equipment and other accessories were provided by the RoTech Company, Belgrade, a producer of balancing machines and vibrodiagnostic instruments. All of the above contributed a great deal to the success of the project and are deserving of the sincere gratitude of the author. 7 VIRI 7 REFERENCES [1] ISO 1940-1 (1986) Mechanical vibration – Balance quality requirements of rigid rotors – Part 1; Determination of permissible residual unbalance. [2] ISO 10816-1 (1995) Mechanical vibration – Evaluation of machine vibration by measurement on non-rotating part. [3] Veg A. (1993) Nonlinearity of an isotropic measuring frame, Ph.D. Thesis, University of Belgrade. [4] Victor W. (1995) Machinery vibration – Balancing, Mc Graw Hill. Avtorjev naslov: prof. dr. Aleksandar Veg Fakulteta za strojništvo Institut za strojno dinamiko Kraljice Marije 16 11 000 Beograd, Srbija aveg@mas.bg.ac.yu Author’s Address: Prof. Dr. Aleksandar Veg Faculty of Mechanical Eng. Machine Dynamics Institute Kraljice Marije 16 11 000 Belgrade, Serbia aveg@mas.bg.ac.yu Prejeto: Received: 15.3.2006 Sprejeto: Accepted: 25.4.2007 Odprto za diskusijo: 1 leto Open for discussion: 1 year 328 Veg A. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 329-347 UDK - UDC 658.58:620.179/.19-7 Strokovni članek - Speciality paper (1.04) Vzdrževanje glede na stanje - uporaba endoskopske metode Condition Maintenance - Applying an Endoscopic Method Miodrag Bulatovič - Jovan Šušič (University of Montenegro, Podgorica) Vzdrževanje glede na stanja, ki temelji na merjenju in nadzoru parametrov stanja predmetov z uporabo tehničnega razpoznavanja, je osnova vseh sodobnih zasnov vzdrževanja, predvsem dejavnega vzdrževanja. V prispevku sta na splošno prikazana vloga in pomen tehničnega razpoznavanja ter vrste metod in tehnik razpoznavanja. Posebej sta poudarjena pomen in uporaba endoskopa pri razpoznavanju notranjih površin delov motorjev, na primeru ladijskih motorjev. Podani so delni rezultati obsežnega raziskovalnega projekta. Prikazane so uporabljene metode razpoznavanja, značilke inštrumentov in kratek opis njihove uporabe. Posebej so prikazani rezultati merjenj, ki so ponazorjeni s fotografijami opaženih pojavov. Podani sta preglednična in besedna analiza rezultatov. Namen prispevka je opozoriti na veliko potrebo in učinkovitost uporabe prikazanih metod razpoznavanja v postopkih vzdrževanja, ne samo velikih (ladijskih) motorjev temveč tudi drugih strojev, pri katerih razpoznavanje notranjosti predstavlja osnovni podatek za načrtovanje ustreznih dejavnosti vzdrževanja. © 2007 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: vzdrževanje, tehnična diagnostika, endoskopija, parametri stanja) Maintenance according to a condition based on measuring and controlling the parameters of the object's condition using technical diagnostics represents the basis of all modern concepts of maintenance, and primarily of proactive maintenance. This paper shows the role and significance of technical diagnostics as well as of the various types of diagnostic methods and techniques. The importance and the application of endoscopes, in particular, have been shown in the domain of the diagnostics of the internal surfaces of engine elements in ships' engines. This paper presents research that was performed in the context of a larger research project. It shows applied methods of diagnostics and instrument characteristics and gives a brief description of their use. Furthermore, the results of measurements, illustrated with photographs of the observed phenomena, are shown, followed by an analysis of these results. The aim of this paper is to emphasise the effectiveness of using the described methods of diagnostics in the maintenance processes not only of large ship engines, but also of other engines for which the diagnostics of internal surfaces offers essential information for planning the appropriate maintenance activities. © 2007 Journal of Mechanical Engineering. All rights reserved. (Keywords: condition-based maintenance, technical diagnostics, endoscopes, condition parameters) 0 UVOD 0 INTRODUCTION Stanje določenega predmeta, stroja opišemo z določeno množico parametrov (pretok tekočine, debelina stene, hrup, temperatura in druge značilnosti), ki naj bi zadovoljili načrtovano funkcijo cilja v določenih razmerah in v določenem časovnem obdobju [1]. Spremembe parametrov vodijo k spremembi funkcije predmeta, najpogosteje se ta poslabša. Kakovostna analiza razpoznavnega signala temelji na sedanjem znanju o določenih značilnostih The condition of an object or a machine is described by a specific group of parameters, for example, the thickness of a wall, the noise, the temperature, and other characteristics [1]. All of these parameters should achieve the designed function of a goal under particular conditions in a fixed amount of time. However, changing the parameters leads to a change in the object’s function, which then usually weakens the object’s function. The qualitative analysis of a diagnostic signal is based on already generated knowledge about 329 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 329-347 in pojavih različnih primerov in stanj. Vzdrževanje glede na stanje temelji na razpoznavanju stanja z uporabo ([2] in [3]): • časovne slike stanja oz. analize dejavnikov učinkovitosti sistema v odvisnosti od časa, • nadzora parametrov stanja z uporabo tehničnega razpoznavanja. Vzdrževanje glede na stanje z nadzorom parametrov pomeni množico pravil za določanje režima diagnostike sestavnih delov sistema v dejanskem postopku uporabe kakor tudi za odločanje o nujnosti zamenjave ali nujnih dejavnosti vzdrževanja na podlagi informacij o dejanskem tehničnem stanju sistema ter njegovih sestavnih delov. Merjenje parametrov stanja se izvaja z razstavljanjem ali brez njega, oziroma z zaustavitvijo sistema ali brez nje, z uporabo opreme in sredstev za tehnično diagnostiko. Diagnostika stanja naj bi bila zveznega značaja, brez zaustavitve ali razstavljanja sistema. Napetosti in deformacije, ki se pojavljajo v mehanskih delih sistema, običajno povzročajo neposredne spremembe kinematike, obstojnosti, vibracij, hrupa, temperature in drugih odločilnih pojavov. Poleg tega posredno povzročajo spremembe mazalnih značilnosti, npr. pojav obrabnih delcev kot znamenje povečanega trenja. Da bi parameter izhodnega postopka lahko postal parameter razpoznavanja, mora zadovoljiti pogoje homogenosti, široko področje uporabe in dostopnost merjenja. Za zahteven sistem se ne da teoretično podati vseh možnih stanj, zato preizkušamo in ugotavljamo verjetnost pojavljanja posameznih stanj, s čimer se omogoča izbira parametrov razpoznavanja v odvisnosti od stanja celotnega sistema ali dela sistema. Parametri stanja so definirani z ustreznimi signali. Razvrstitev razpoznavnih signalov sloni na: predmetu razpoznavanja, stanju signala, vlogi razpoznavnih signalov in fizikalnih lastnostih. Postopki in pojavi, ki povzročajo odpovedi, so naključne narave, kar ima za posledico: en simptom - eno razpoznavanje, dva simptoma ali več - eno razpoznavanje, en simptom - dve razpoznavanji ali več. Merjenje parametrov stanja je mogoče z razstavljanjem ali brez njega oz. z zaustavitvijo celotnega sistema ali brez nje, z uporabo posebnih inštrumentov in opreme za tehnično diagnostiko ([4] do [7]). the specific characteristics and phenomena of various cases and conditions. The condition maintenance is based on the diagnostics of this condition, using the following elements ([2] and [3]): • Time pictures, either of a condition or analyses of the effectiveness of a system as a function of time, • Control of condition parameters, using technical diagnostic methods. Maintenance according to a condition, by controlling the parameters, represents a group of rules for determining a diagnostic regime in a real exploitation process. In addition, it serves the purpose of making decisions about the necessity for a replacement or maintenance activity, based on information about the real technical condition of the system and its parts. It is important that the measuring of condition parameters happens with or without disassembling the system, which means with or without detaining the system by using the equipment and the facilities for technical diagnostics. Therefore, a tendency exists for the condition diagnostics to always be continuous, without halting or disassembling the system. Tensions and deformities appearing in the mechanical segments of the system usually cause a direct change in cinematic forms, resistance, vibrations, noise, temperature and in other crucial phenomena. Furthermore, they indirectly cause changes in lubricant characteristics, such as the appearance of particles as a sign of friction. In order for the parameter of an output process to become a diagnostic parameter, it must fulfil the conditions of homogeneousness, broad use and measurement attainability. It is not possible to number all the conditions of a complex system; it is therefore useful to examine, investigate and determine the probability of some of them appearing. This makes the selection of diagnostic parameters possible in the function of the whole or a part of the system condition. The condition parameters are defined by appropriate signals. The categorisation of diagnostic signals is conducted according to the following: the subject of the diagnosis, the signal status, the role of diagnostic signals and the physical characteristics. The processes and occurrences that cause failures have a stochastic character. This means, therefore: one symptom - one diagnosis, two or more symptoms - one diagnosis, one symptom - two or more diagnoses. The measuring of condition parameters could be done with or without stopping the whole system, using special instruments and equipment for technical diagnostics ([4] to [7]). 330 Bulatovič M. - Šušič J. Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 329-347 Osrednja naloga razpoznavanja je odkriti številne povezave med strukturnimi elementi U1, U2, .... Un in The main task of a given diagnosis is to discover many relations between the entities Uv U2, .... Un ustreznimi razpoznavnimi parametri Sv S2, .... Sn, z and the diagnostic parameters Sv S2, .... Sn, using a uporabo diagnostične matrike [3]: diagnostics matrix [3] : U 1 U 2 U 3 U 4 U 5 S 1 0 0 1 0 0 S 2 1 1 0 1 1 S 3 0 0 0 0 0 S 4 0 1 1 0 1 S 5 0 1 0 0 0 izvajanje potrebnih dejavnosti vzdrževanja undertake needed maintenance activity Sl.1. Algoritem za razpoznavanje parametrov stanja Fig.1. Algorithm of diagnostic parameters’ condition Vzdrževanje glede na stanje - Condition Maintenance 331 Strojniški vestnik - Journal of Mechanical Engineering 53(2007)5, 329-347 Ul II s< n U2 12 Un In STANJE / CONDITION si w, Ä s2 11} h =