Strojni{ki vestnik 45(1999)11, Journal of Mechanical Engineering 45(1999)11, ISSN ISSN UDK : UDC

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1 Strojni{ki estnik 45(1999)11, Journal of Mechanical Engineering 45(1999)11, ISSN ISSN UDK : UDC : Izirni znansteni Siuliranje ~lanek (1.01) prehodnih re`io deloanja - Siulation Original of the scientific Transient paper Operation (1.01) Siuliranje prehodnih re`io deloanja otorja z notranji zgoreanje Siulation of the Transient Operation of an Internal Cobustion Engine Ale{ Hribernik V prispeku sta predstaljena nelinearni odel enoaljnega dizelskega otorja za preraèun prehodnih delonih režio otorja in napoed spreenljiega oenta in rtilne frekence otorja. Model je razit iz odela za siuliranje terodinaiènega krožnega procesa otorja ustaljenih razerah, razširjen z odelo dinaike roèiènega ehaniza predstalja otor kot nelinearni dinaièni siste. Spreenljia rtilna frekenca otorja je rezultat rešeanja enaèbe dinaike zeze otor - ee, pri èeer je spreenljii oent otorja doloèen odisnosti od lege (kota) roèiène gredi. Model so preerili z rezultati erite enoaljnega dizelskega otorja. Prierjaa raèunskih in izerjenih rtilnih frekenc je pokazala zelo doo ujeanje ponaljajoèih se spreeb rtilne frekence in odzia otorja ed nagli pospešeanje Strojniški estnik. Vse praice pridržane. (Kljuène besede: otorji z notranji zgoreanje, odeli terodinaièni, dinaika otorje, siuliranje) A non-linear, transient, single-cylinder Diesel engine siulation has been deeloped to predict the instantaneous engine speed and torque. The basis of the odel is a therodynaic, steady state diesel engine cycle siulation. The transient extension of the original odel represents the Diesel engine as a non-linear, dynaic syste. The instantaneous crankshaft speed is deterined fro the solution of the engine-external load dynaic equation, where the engine torque is tracked on the crank-angle basis. Validation of the transient odel during rapid engine acceleration shows that both the cyclic fluctuations in the instantaneous engine speed line and the oerall engine response are in good agreeent with experiental easureents Journal of Mechanical Engineering. All rights resered. (Keywords: internal cobustion engines, therodynaic odels, engine-dynaic, siulation) 0 UVOD Motorji z notranji zgoreanje so osnoi nelinearni ehanski sistei. Zato je ogoèe prièakoati natanène rezultate siuliranj le, kadar so fizikalni odeli zasnoani kot pose nelinearni sistei. Siulirni odeli terodinaiènih krožnih proceso otorje z notranji zgoreanje se z izpopolnje-anje pojanega popisa proceso se bolj izpopolnjujejo in so zelo uspešni in dandanes že neizogibni za napoed karakteristik deloanja otorja ustaljenih razerah. Zato je pose narana pot razoja nelinearnega odela otorja z notranji zgoreanje razširite in dogradite odela terodinaiènega krožnega procesa otorja z upošteanje dinaike otorja. To je bilo tudi naše odilo pri razijanju nelinearnega odela otorja. Uporabili so preskušeni prograski paket za siuliranje terodinaiènih in tokonih proceso otorju z notranji zgoreanje [1] in ga dogradili z odelo dinaike otorja. 0 INTRODUCTION Since the internal cobustion engine is a highly non-linear echanical syste, truly predictie capabilities can only be attained if purely non-linear siulations are deeloped. Therodynaic engine siulations hae been refined with phenoenological process descriptions oer the years and hae been used ery successfully for the prediction of steady-state engine operation. Consequently, the natural approach to the deelopent of a non-linear engine siulation is by building on and extending such steady-state therodynaic odels to consider the engine dynaics. The deelopent of our nonlinear engine odel was undertaken by taking into account these factors. The foundation for the transient odel was the successfully tested therodynaic siulation of an internal cobustion engine [1] which was upgraded by the engine dynaics odel. stran 423

2 A. Hribernik 1 TERMODINAMIÈNI MODEL MOTORJA Uporabili so ezdienzijski, terodinaièni odel za siuliranje dizelskega otorja ustaljenih razerah, ki je zasnoan na etodi polnjenje-praznjenje. Model so zadnjih desetih letih razijali in testirali na Fakulteti za strojništo Mariboru, ga obširno predstaili [1] in z njegoo uporabo izedli šteilne raziskae delonih karakteristik sesalnih in tlaèno polnjenih otorje [2], [3]. Osnone znaèilnosti odela so na kratko pozete nadaljeanju. Pretok plino otorju je odelu ponazorjen s pretoko snoi ed nadzornii prostorninai. Te predstaljajo polnilne in izpušne zbiralnike ter alje otorja. Pretok ase in energije ed nadzornii prostorninai doloèajo robni pogoji, ki so zapisani z izrazi pretoka skozi zaslonko. Predpostaljeno je, da je stanje plina nadzorni prostornini enotno, zato ga doloèata že diferencialni enaèbi o ohraniti ase in energije. Z robnii pogoji poežeo dojice diferencialnih enaèb posaeznih nadzornih prostornin siste naadnih nelinearnih diferencialnih enaèb prega reda. Rezultat rešeanja tega sistea diferencialnih enaèb èasu (kotu zartite roèiène gredi) pa so potek tlaka, teperature in sestae delone snoi posaezni nadzorni prostornini. 2 DINAMIKA ROÈIÈNEGA MEHANIZMA MOTORJA Slika 1 prikazuje poenostaljen dinaièni siste enoaljnega otorja. Lega roèice za dobao goria in z nji kolièina izganega goria ter stanje okolice sta osnona podatka za siuliranje otorskega krožnega procesa. Rezultat te je indicirani oent otorja, iz katerega sledi po odbitju oenta trenja otorju dejanski oent na otorski gredi. Razlika ed dejanski oento in oento zunanjega eena je rezultirajoèi oent, katerega posledica 1 THERMODYNAMICS MODEL OF THE ENGINE The therodynaic, zero-diensional, steady state Diesel engine siulation based on the Filling- Eptying ethod was used. The odel has been deeloped and tested at the Faculty of Mechanical Engineering in Maribor oer the last ten years. The parent siulation has been fully presented [1] and used to study operational characteristics of seeral naturally aspirated and turbocharged Diesel engines [2], [3]. The basic characteristics of the odel will be iefly presented. The flow of gases within the engine is presented by the flow of ass and energy between the control olues. These represent intake and exhaust anifolds and the cylinders of the engine. The flow of ass and energy into and out of the control olue are deterined by boundary conditions based on the analogy of conergent nozzle flow. It is assued, that the therodynaic state within the control olue is unifor. As a result, it ay be predicted by soling the ass and energy conseration equations. Differential equations of each control olue are connected into a syste of ordinary, non-linear differential equations of the first order by boundary conditions. The solution of this syste yields pressure, teperature and gas coposition ariation with tie (crank angle) within each control olue. 2 ENGINE DYNAMICS Figure 1 shows a scheatic representation of the single-cylinder engine dynaic syste. At a gien instant in tie, the operator coand, i.e. fuelling rate, and the abient conditions are key inputs to the Diesel engine cycle siulation. The indicated engine torque is the output required for the engine dynaics equation. The friction torque is subtracted fro the indicated torque to produce ake torque at the shaft. Subsequently, the resistance torque siuliranje krožnega procesa engine cycle siul. Sl. 1. Blokoni diagra enoaljnega otorja Fig. 1. Block diagra for the single-cylinder engine stran 424

3 Siuliranje prehodnih re`io deloanja - Siulation of the Transient Operation Sl. 2. Model dinaike sistea otor-zunanje ee Fig. 2. Equialent syste for engine-external load dynaics je zeèanje ali zanjšanje rtilne frekence otorja. Zaradi ponaljajoèega se deloanja otorja je rtilna frekenca otorja neustaljena, tudi kadar je srednje šteilo rtljaje otorja konstantno, kar je posledica hitrih spreeb tlaka alju in z njii sil, ki delujejo na roèièni ehanize. Kakor prikazuje slika 2, lahko siste otor - zunanje ee ponazorio s sisteo deh disko, poezanih z elastièno gredjo. Pri te je polarni ztrajnostni oent prega diska ekialent polarnega ztrajnostnega oenta rotirajoèih delo otorja. Podobno je ztrajnostni polarni oent drugega diska ekialent ztrajnostnega polarnega oenta zunanjega eena, ki je lahko ozilo, deloni stroj ali zaora preskušališèu otorje. V prieru elastiène gredi popišeta dinaiko sistea s slike 2 naslednji enaèbi: is subtracted fro the ake torque and the net alue calculated. If the net alue is positie the engine will accelerate and ice ersa. The instantaneous rotational speed of the crankshaft is unsteady during any engine cycle, een if the ean engine speed is constant, due to rapid changes in cylinder pressure and the consequent changes in forces acting on the crank during the cycle. As shown in Fig. 2, the engine/load syste can be odelled as two disks connected by a weightless shaft, one disk haing the equialent polar oent of inertia of the engine oing parts, and the other haing the equialent polar oent of inertia of the load (ehicle or dynaoeter in the test cell). The following two equations describe the dynaic syste in the case of an elastic shaft: tr ( q - ) M I w& + M + k q = ( q q ) I w& + M = k - (1) (2). Z doolj eliko natanènostjo lahko predpostaio, da je gred toga in da lahko zasuk (q - q ) ed diskoa zaneario. Iz tega torej izhaja, da sta kotni hitrosti otorja in zunanjega eena enaki: In ker zato elja: lahko siste enaèb zapišeo kot: Enaèbo (3) so urstili siste diferencialnih enaèb prega reda, s kateri so popisali terodinaièni odel otorja in razširjeni siste enaèb nuerièno integrirali po etodi Runge-Kutta 4+. Ker se integracija izaja po kotu zartite roèiène gredi in ne po èasu, je treba siste diferencialnih enaèb kljuèiti še enaèbo za spreebo èasa po kotu: w = w q = q M - w& = I The power transission shaft can usually be considered sufficiently rigid, and consequently the twist (q - q ) between the two disks can be neglected. Hence, the rotational elocity of engine is equal to one of the external load: Thus there is no phase shift: and the syste dynaic equation becoes: M tr - M (3). + I Equation (3) was incorporated into a syste of differential equations of the first order that for the engine therodynaic cycle siulation. This extended syste was nuerically integrated by the Runge-Kutta 4+ ethod. The engine cycle siulation uses the angular position of the crank shaft in degrees crank-angle and not explicitly the tie. Hence, the following equation: dt ð = dq 180w (4), stran 425

4 A. Hribernik saj zaradi spreenljie kotne hitrosti roèiène gredi èasoni korak ni eè sorazeren integracijskeu koraku, podani s koto roèiène gredi. 2.1 Doloèite trenutnega indiciranega oenta in polarnega ztrajnostnega oenta otorja was added to the syste of differential equations in order to deterine the crank-angle tie interdependence, since the tie step is no longer proportional to the crank-angle integration step when the rotational engine speed is not constant. 2.1 Instantaneous indicated engine torque and polar oent of inertia of the engine Roèièni ehanize prikazuje slika 3. Trenutna lega bata in razerje sil doloèata kot zartite roèiène gredi in geoetrijske oblike roèiènega ehaniza: dolžina ojnice L in roèica gredi R. Poenostaljeno delujeta na bat de osnoni sili. To sta tlaèna sila: F = - ki je posledica razlike tlako alju in karterju otorja ter ztrajnostna sila: Sl. 3. Diagra sil na roèiène ehanizu Fig. 3. Forces on the slider-crank echanis F tl ztr ( p p ) = - s, A scheatic of the piston (slider) crank echanis is shown in Fig. 3. The instantaneous piston position and the relationship between the acting forces are deterined by the crank shaft angular position and the geoetrical paraeters of the slider-crank echanis: connecting rod length L and crank radius R. There are two forces acting on the piston, i.e. the pressure force: ðd 2 b k (5), 4 which is the result of the pressure difference in the cylinder and in the crank case, and the inertial force: ( b + ojn' ) ab (6) Pri te je ojn asa dela ojnice, katerega gibanje lahko približno oznaèio s translatorni gibanje bata (obièajno 1/3 ojn [4]), a b pa je linearni pospešek bata, ki ga natanèno doloèa izraz: where ojn is the reciprocating part of the connecting rod ass (usually 1/3 ojn [4]), and a b is the linear acceleration of the reciprocating parts. The acceleration can be calculated using the following exact expression: a b = Rw 2 é l êcosq + ê ë 2 4 ( cos 2q + l sin q) ù é l cosq ( ) ( ) ú ú ù ú+ Rw& sinq ê ú ê l sin q ë 1-l sin q 1 û û (7), stran 426

5 Siuliranje prehodnih re`io deloanja - Siulation of the Transient Operation pri èeer je l definiran z razerje: Rezultirajoèa sila, ki deluje na bat, je torej: where l is defined by the ratio: R l = L The resultant force on the piston is therefore: Fb = Ftl + Fztr (8). (9). Njena koponenta seri osi ojnice je: C = F b Ta deluje na ležaj ojnice in roèiène gredi, pri èeer je njena koponenta tangentni seri: C sin ( q + b) = b Moent, ki se z roèiènega ehaniza prenaša na otorsko gred, je torej: T The coponent force in the direction of the connecting rod axis is: 1 (10) cos b and the coponent of the force on the crank journal in the tangential direction is: sin( q + b) = F (11). cos b The torque on the shaft can be calculated therefore by: M = RT (12). Pri nižjih rtilnih frekencah otorja, ki so znaèilne za eèino dizelskih otorje, lahko z doolj eliko natanènostjo predpostaio, da je polarni ztrajnostni oent otorja konstanten. Sestaljajo ga prispeki ztrajnika in rotirajoèih delo roèiènega ehaniza, to je otorske gredi z roèico in dela ojnice, katerega gibanje lahko oznaèio za rotacijo (obièajno 2/3 ojn [4]). Pri elikih rtilnih frekencah, ki so znaèilne predse za bencinske otorje in anjše hitro tekoèe dizelske otorje pa je pli spreinjajoèega polarnega ztrajnostnega oenta že tako elik, da ga je dinaiène odelu otorja treba upošteati [5]. 2.2 Naor trenja in zunanjega eena Notranje trenje otorju obièajno doloèao na podlagi erite delonih karakteristik gnanega otorja. Znaèilni izraz za doloèite izgub srednjega indiciranega tlaka dizelskega otorja je oblike [6]: Under low and ediu engine speeds, characteristic for ost Diesel engines, it can be assued that the polar oent of inertia of the engine is constant. It consists of the oent of inertia of the flywheel and of the rotating parts of the slidercrank echanis, i.e. the engine crankshaft and the rotating part of the connecting rod (usually 2/3 ojn [4]). Howeer, under high engine speeds, characteristic for gasoline engines and high speed Diesel engines, the influence of the fluctuating part of the polar oent of inertia becoes ery high, and it has to be considered in the engine dynaics odel [5]. 2.2 Friction torque and external load torque Engine friction is usually estiated fro experients by using otoring tests. A typical correlation for the frictional losses of the ean indicated pressure of a Diesel engine has the following for [6]: 48n p = tr C1 0, 4A b (13), pri èeer je C 1 koeficient, ki ga dobio na podlagi erite. Srednji oent trenja pa izhaja iz izraza: where C 1 is a coefficient that can be deterined by experient. The friction torque can be calculated fro: M tr = ptrvh ðn (14). Moent zunanjega eena kakor tudi njego polarni ztrajnostni oent pa sta odisna od tipa gnanega stroja. Tako ju za prier otornih The torque of an external load and its oent of inertia depend on the engine application. If the odel is to be used to siulate engine transients stran 427

6 A. Hribernik ozil doloèio z ustrezni dinaièni odelo, ki popiše prenos oenta od otorske gredi, prek sklopke, enjalnika in diferenciala na pogonska kolesa ozila. Pri te je oent oeenite doloèen z upori ožnje, polarni ztrajnostni oent pa s prispeki rotirajoèih delo, ki sodelujejo pri prenosu oenta od otorja in prek pogonskih koles na cestišèe. Precej preprostejši pa je prier otorja na preskušališèu, kjer oent eena uranaa zaora, katere polarni ztrajnostni oent je tudi ztrajnostni oent zunanjega eena. 3 REZULTATI SIMULACIJ IN PRIMERJAVE Z MERITVAMI Model so uporabili za siuliranje razer ed pospešeanje enoaljnega, zraèno hlajenega, 4-taktnega dizelskega otorja z direktni izgo goria. Osnoni podatki o otorju so zani preglednici 1. Na sliki 4 je prikazan spreenljii oent oanaanega enoaljnega otorja, izraèunan po enaèbi (12) in pri ustaljenih oatoalnih razerah, tj. n sr = konst. Kljub ustaljeni deloni razera so spreebe naora toku otorskega ciklusa zelo elike. V zaèetni fazi (zgoreanje 0 do RG) in konèni fazi (kopresija 540 do RG) preladuje within the ehicle, an additional odel of ehicle dynaics that represents the transission of torque fro the engine shaft, oer a clutch, gear box, and differential onto the driing wheels is necessary. The load torque is then deterined by the driing resistance, while the oent of inertia consists of contributions fro all of the rotating parts that help to transit the torque fro the engine to the road. Howeer, if the odel is intended to siulate an engine on a transient test bed, the load is applied and controlled by the dynaoeter and the polar oent of inertia of the load is siply equal to the dynaoeter inertia. 3 RESULTS OF SIMULATION AND EXPERIMENTAL VALIDATION A odel has been used for the siulation of transient operation of an air-cooled, directinjection, 4-stroke, single-cylinder Diesel engine. Basic engine data are specified in Table 1. The instantaneous engine torque of a single cylinder engine, calculated using Eq. (12) under steady-state operation, i.e. n sr = const., is shown in Fig. 4. Despite steady-state engine operation huge fluctuations of engine torque are obsered. In the 1 st period (cobustion 0 to CA) and in the 4 th one (copression 540 to CA) doinates the pressure force, while the inertial force doinates Preglednica 1. Podatki o otorju Deutz MAG F1L 210 D Table 1. Deutz MAG F1L 210 D engine specification preer alja bore gib stroke dolžina ojnice connecting rod length kopresijsko razerje copression ratio najeèja dobaa goria axiu fuel per cycle 0,095 0,095 0, M N M N zgoreanje cobustion izpuh exhaust sesanje intake kopresija copression q θ RG RG Sl. 4. Spreeba naora otorja odisnosti od kota roèiène gredi pri ustaljene režiu n sr =960 in -1 Fig. 4. Fluctuations of the engine torque with crank angle under steady state operation n sr =960 rp stran 428

7 Siuliranje prehodnih re`io deloanja - Siulation of the Transient Operation /in 1000 n 1/in n zgoreanje cobustion izpuh exhaust sesanje intake kopresija copression RG θ qrg Sl. 5. Spreeba rtilne frekence otorja odisnosti od kota roèiène gredi pri ustaljene režiu n sr =960 in -1 Fig. 5. Fluctuations of the engine speed with crank angle under steady state operation n sr =960 rp /in 2500 n n 1/in št. otorskih cikluso - Engine Cycle No. Sl. 6. Prierjaa izerjenega ( ) in izraèunanega ( ) šteila rtljaje otorja odisnosti od šteila krožnih proceso otorja ed pospešeanje (M =0 N, 40 3 /proces) Fig. 6. Coparison of predicted ( ) and easured ( ) instantaneous engine speeed during acceleration (M =0 N, 40 3 /cycle) pli tlaène sile, edte ko je toku izenjae delone snoi (180 do RG) preladujoè pli ztrajnostnih sil, prispeek tlaènih sil pa je zaradi ajhnih razlik tlaka prostoru nad bato in pod nji neznaten. Posledica tako elikih spreeb oenta je nihanje rtilne frekence otorja (slika 5). To je še posebej izrazito pri enoaljne otorju. V oanaane prieru dosegajo razlike rtilni frekenci otorja do 150 in -1, oziroa prek 15% srednje rednosti. Na sliki 6 je prikazana prierjaa izraèunanih in izerjenih rednosti rtilnih frekenc otorja prehodne oatoalne režiu. Razeenjen otor pri najeèji dobai goria pospešuje od prostega teka do ejne rtilne frekence, pri katere krilnik ustai dobao goria in prepreèi nadaljnje pospešeanje. Pri te preide otor skozi celoten spekter rtljaje. Znaèilno zanj je, da se aplitude ariacij rtilne frekence zanjšujejo z eèanje hitrosti otorja. Ugotoio lahko, da je ujeanje izerjenih in izraèunanih rednosti se do 2000 in 1 zelo doo, nato pa zaène during the gas exchange process (180 to CA) when the pressure force is insignificant, because of the sall difference of pressures aboe and below the piston. As a consequence of the huge fluctuations in engine torque, the ariations in the instantaneous engine speed are also ery pronounced (Fig. 5). This is especially characteristic for a single cylinder engine. In the presented exaple these ariations exceed 150 rp, i.e. ore than 15% of the noinal (ean) engine speed. A coparison of easured and predicted alues of the instantaneous engine speed during an engine transient is presented in Fig. 6. The engine accelerates fro idle under full load, defined as a 100% fuelling rate, and goes through the whole speed range until it reaches its axiu speed. Fro that point on, the controller cuts off the fuel in order to preent the engine fro oer speeding. The aplitudes of cyclic speed fluctuations tend to decrease as the ean engine speed increases. The agreeent between calculated and easured alues below 2000 rp is ery good. After that point the stran 429

8 A. Hribernik izraèunana hitrost se bolj zaostajati, tako da je raèunsko potreben celotni otorski krožni proces eè, da otor doseže najeèje rtilne frekence pri 2500 in 1. Vzroko za to je lahko eè. Med osnonii pa so gotoo poanjkanje podatko o spreebi teperature azalnega olja in njene pliu na trenje otorja, kakor tudi natanènejši podatki o dobai goria, ki je odisna od rtilne frekence otorja. 4 SKLEP Ustaljeni, fenoenološki, ezdienzijski odel je bil uporabljen kot podlaga za razoj odela za popis prehodnih delonih režio enoaljnega dizelskega otorja. Razširite odela z zasledoanje spreenljiega oenta otorja po kotu roèiène gredi in z rešeanje enaèb dinaike otorja je oogoèila popis neustaljenih razer in prehodnih pojao. Natanènost odela so preerili na podlagi prierjae raèunskih rezultato z eritai. Napoedi fluktuacije rtilne frekence ed krožni proceso se zelo doo ujeajo z izerjenii rednosti. Tudi pospešeanje razeenjenega otorja pri najeèji dobai goria je prailno napoedano. Pri anjših hitrostih otorja so ariacije šteila rtljaje znotraj procesa tudi do 200 in 1, edte ko se zaradi poeèanja ztrajnostnih sil roèiènega ehaniza pli plinskih sil ed zgoreanje nekoliko oili in so zato ariacije rtilne frekence precej anjše, deloanje otorja pa precej bolj stabilno. odel underpredicts the engine speed and it takes the odel one extra cycle to reach the axiu engine speed at 2500 rp. The inor discrepancies at ery high speed can be attributed to insufficient odel inputs that are difficult to easure during a transient, such as the change of oil teperature and friction, and the effect of engine speed on the cyclic aount of fuel injected. 4 CONCLUSION A steady-state, phenoenological zerodiensional odel has been used as the basis for the deelopent of a transient, single-cylinder, Diesel engine odel. Its extension has inoled an instantaneous engine torque and engine dynaics odel. Subsequently, the transient siulation has been alidated against experiental results fro a singlecylinder engine. Siulation predictions of the cyclic fluctuations in the instantaneous crankshaft speed characteristic are in good agreeent with the experient. The oerall engine response during free acceleration with the axiu aount of fuel injected also agrees well with the easured data. The aplitude of the fluctuation in the rotational speed of the crankshaft can be as high as 200 rp, at low speed. Howeer, increased inertia forces on the reciprocating coponents at higher speeds causes a reduction of the peak instantaneous pressure force during cobustion. Hence, instantaneous fluctuations in the crankshaft angular elocity are significantly reduced at higher speeds, where the engine operation is uch ore unifor. 5 LITERATURA 5 REFERENCE [1] Hribernik, A.: Prierjaa ez- in eno-dienzionalnih etod za siulacijo proceso tlaèno polnjene dieselske otorju, Strojniški estnik, 41, Šte. 7-8, 1995, str , ISSN [2] Doboišek, Ž., Èernej, A., Hribernik, A.: Napoedni ezdienzijski enoconski odel za siuliranje zgoreanja dieselske otorju, Strojniški estnik, 39, Šte. 5-8, 1993, str , ISSN [3] Hribernik, A.: Prierjaa izedb 4-aljnega tlaèno polnjenega otorja z dojni in enojni natoko turbine, Strojniški estnik, 43, Šte. 9-10, 1997, str , ISSN [4] Tuccillo, R., Arnone, L., Bozza, F., Nocera, R., Senatore, A.: Experiental correlations for heat release and echanical losses in turbocharged Diesel engines, SAE TRANSACTIONS, Journal of Engines, Vol. 102, 1993, SAE Paper , p.p , ISSN X [5] Shiao, Y., Pan, C., Moskwa, J.J.: Adanced dynaic spark ignition engine odelling for diagnostic and control, Int. J. of Vehicle Design, Vol. 15, No. 6, 1994, p.p [6] Heywood, J.B.: Internal cobustion engine foundaentals, McGraw-Hill, 1988 stran 430

9 Siuliranje prehodnih re`io deloanja - Siulation of the Transient Operation Uporabljeni siboli Noenclature poršina pospešek koponenta sile seri osi ojnice preer sila polarni ztrajnostni oent togost gredi dolžina ojnice oent asa rtilna frekenca otorja tlak koponenta sile seri tangente na roèico èas gibna prostornina kot nihanja ojnice okoli osi bata razerje ed roèico in dolžino ojnice kot zartite roèiène gredi kotna hitrost Indeksi: bat ee dejansko otor sesalni zbiralnik srednji tlaèni trenje alj ztrajnost A a C D F I k L M n p T t V h b l q w b ef s,k sr tl tr ztr area acceleration coponent force in the direction of the connecting rod axis diaeter force polar oent of inertia shaft rigidity connection rod length torque ass engine speed pressure coponent of the force on the crank journal in the tangential direction tie swept olue angle of swing of the connecting rod fro the cylinder axis ratio of crank radius and connecting rod length angular position of crankshaft in degrees crank-angle angular elocity Subscripts: piston load effectie engine intake anifold ean pressure friction cylinder inertia Naslo atorja: doc.dr. Aleš Hribernik Fakulteta za strojništo Unierze Mariboru Setanoa Maribor Author s Adress: Doc. Dr. Aleš Hribernik Faculty of Mechanical Engineering Uniersity of Maribor Setanoa Maribor, Sloenia Prejeto: Sprejeto: Receied: Accepted: stran 431