© Strojni{ki vestnik 49(2003)12,593-606 © Journal of Mechanical Engineering 49(2003)12,593-606 ISSN 0039-2480 ISSN 0039-2480 UDK 629.371.2:62-224.7 UDC 629.371.2:62-224.7 Strokovni ~lanek (1.04) Speciality paper (1.04) Oblikovanje dirkalnika Developing a Racing Car Stanislav Pehan - Breda Kegl - Primo` Pogorevc V prispevku sta prikazani dve možnosti izboljšanja lastnosti dirkalnika Formula S. Eden najskladnejših načinov za dvig moči motorja je spretno oblikovan dovod zraka v motor Zato je v prvem delu prispevka predstavljen postopek optimalnega oblikovanja sesalnega sistema. Postopek optimiranja temelji na uporabi metod matematičnega programiranja in pomeni učinkovit način za povečanje moči motorja v najbolj zanimivem področju obratovanja motorja. V drugem delu prispevka je pozornost posvečena novim zamislim izdelave celotnega dirkalnika. Za dosego vrhunskih rezultatov je treba narediti več, kakor le slediti konkurenci. Analiza postavitev glavnih agregatov je pokazala, da bi k večji okretnosti in stabilnosti dirkalnika pripomoglo to, da bi bil motor postavljen ob voznikovi strani. Optimiran sesalni sistem pomeni zanesljiv korak naprej v borbi za povečanje dejanske moči dirkalnika, kar je lahko uporabno takoj. Zasnova z bočno postavitvijo motorja pa predstavlja povsem novo pot razvoja dirkalnikov Formula S, kar bo morda prineslo dolgoročne prednosti. © 2003 Strojniški vestnik. Vse pravice pridržane. (Ključne besede: dirkalni avtomobili, Formula S, razvoj, optimiranje, sistemi sesalni) This article presents two approaches for improving a Formula S racing car. One of the best ways to increase the engine’s power is to skillfully design the air- supply system of the engine. This is the reason why the first part of the paper is about the intake-manifold optimization procedure. The procedure relies on mathematical programming and offers a way to significantly increase the engine power in the most important engine regimes. In the second part of the paper, attention is focused on new concepts of building the racing car. In order to be the best it is necessary to do more than symply follow the competion. An analysis of the positions of the main components has shown that a racing car would be more agile and stable if the engine was to be mounted beside the driver. Optimizing the intake manifold represents one significant step forward in the struggle to increase the effective power of the car, which brings an immediate advantage. The new position concept, however, which also eliminates the differential drive, represents a completely new development in the design of the Formula S car that might bring us long-term benefits. © 2003 Journal of Mechanical Engineering. All rights reserved. (Keywords: racing automobiles, Formula S, development, optimization, intake manifold) 0 UVOD Na mnogih univerzah po vsem svetu se vsako leto znova zberejo skupine študentov, ki načrtujejo, oblikujejo, snujejo, tržno obdelajo in izdelajo malo enosedežno dirkalno vozilo. Vse te skupine študentov se enkrat na leto zberejo v Veliki Britaniji na tekmovanju Formula Student. Na Fakulteti za strojništvo v Mariboru že od leta 1999 vsako leto znova izdelamo nov dirkalnik, ki nosi ime Formula S. Rezultati prejšnjih let kažejo, da naša skupina vedno zaseda odlične uvrstitve. Je med prvimi v Evropi in skoraj vedno med peščico tistih, ki jim uspe dokončati vztrajnostno dirko, ki je vrhunec tekmovanja, (sl. 1). Poglavitni namen tekmovanja Formula Student je vzbuditi pri študentih zanimanje za delo konstrukterjev in razvijati talente pri mladih ljudeh 0 INTRODUCTION Every year, groups of university students around the world, conceive, plan, economically evaluate and manufacture a small single-seat racing car. All these groups compete once a year at on event in Great Britain called the Formula Student Competition. The Faculty of Mechanical Engineering in Maribor has built a car every year since 1999 called Formula S. The results from past years show that our team was always among the best in Europe and that our car always finished the endurance race, which is the prestige event of the competition, Fig. 1, among the first few finishers. The basic intention of the Formula Student competition is to develop an interest in design work and to foster the talents of the students [1]. To gfin^OtJJlMlSCSD 03-12 stran 593 |^BSSITIMIGC Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car Sl. 1. Dirkalnik Univerze v Mariboru Formula S v Veliki Britaniji leta 2002 Fig. 1. Formula S racing car from theUniversity of Maribor competing in Great Britain in 2002 [1]. Zgolj v nekaj mesecih opraviti ves razvoj dirkalnega vozila je veliko delo, ki ga zmorejo le izjemno sposobni in marljivi študenti pod dobrim strokovnim vodstvom. Na tekmovanju se ocenjujejo tako zamisli, inženirske rešitve, spretnosti oblikovanja, vozne lastnosti dirkalnika in tudi ekonomsko ozadje projekta. Zato je vsako od naštetih področij zase predstavlja velik izziv za celotno skupino. Prispevek obravnava dve področji dela skupine študentov mariborske Fakultete za strojništvo. Najprej je predstavljeno načrtovanje, snovanje in optimiranje sesalnega sistema. Potem pa so obravnavane možnosti izboljšave v osnovni zamisli celotnega dirkalnika. 1 OBLIKOVANJE SESALNEGA SISTEMA IN OPTIMIRANJE GLEDE NA NAJVEČJO MOČ Dirkalnik Formula S ima motor vgrajen za voznikovim hrbtom. Poleg same lege motorja pomeni varnostni lok, ki ščiti voznikovo glavo, podpore varnostnega loka in lupina avtomobila (sl. 2), osnovne geometrijske omejitve pri oblikovanju sesalnega sistema. Dirkalnik Formula S je opremljen z večtočkovnim sistemom za vbrizg goriva. Zahtevnik za oblikovanje sesalnega sistema je predstavljen v preglednici 1 [2]. 1.1 Oblikovanje sesalnega sistema Oblikovanje sesalnega sistema je v začetni fazi stvar iskanja konstrukcijskih rešitev v smislu, kam sploh postaviti določen element [3]. Običajno je del sesalnega sistema tudi zbiralnik. Mi ga nismo predvideli, ampak smo že v osnutku sledili zamisli, develop a racing car in just a few months is a hard task that can only be done by exceptionally skilled and active students under expert guidance. During the competition, the ideas, the engineering solutions, the design skill, the driving characteristics of the car and the economic aspects of the whole project are evaluated. All these fields represent a big challenge for the whole group of students. This paper deals with the two areas on which our students are working. In the first part the conceiving, the planning and the optimization of the intake system is presented. In the second part, the improvement to the conceiving phase of the whole vehicle is discussed. 1 CONCEIVING THE INTAKE MANIFOLD AND ITS OPTIMIZATION IN TERMS OF MAXIMUM POWER The engine of the Formula S racing car is positioned behind the driver’s back. The basic geometry constraints that influence the shape of the intake manifold are, in addition to the engine’s position, the main hoop that protects the driver’s head, its brackets and the car body, Fig. 2. The Formula S car is equipped with a multipoint fuel-injection system. The checklist relating to the manifold design is presented in Table 1 [2]. 1.1 Conceiving the intake manifold The first stage of the intake-manifold design is to look for the best positions for the parts [3]. The intake manifold usually also has an intake plenum. Instead of this, however, from the beginning it was decided to continually increase the cross-sectional 2 jgnnatäüllMliBilrSO | | ^SSfiflMlGC | stran 594 Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car Sl. 2. Motor Honda 600 cm3 stoji povprek v zadku dirkalnika Fig. 2. The Honda 600 ccm engine is positioned crosswise in the rear of the car Preglednica 1. Zahtevnik za sesalni sistem Formula S 2003 Table 1. Checklist relating to the intake manifold Formula S 2003 Št. No. Zahteve v zvezi z obliko sesalnega sistema Requirements concerning the manifold design 1 Zajemalnik zraka nad glavo voznika Air capture is positioned above the driver's head desired 2 3 4 5 6 7 The intake-manifold system™placed i^ri^'*pace frame obvezno required V TZ^^^z^z^;^zs^r'20mm obvezno required Omejilnik mora biti vgrajen med loputo in sesalno odprtino motorja The restrictor is positioned after the throttle and before the engine intake obvezno required Vsak valj motorja mora dobiti enako kolfino zraka obvezno required Moe~er is ove 40 kW desired Sesalni vod naj daje im manji upor zraku, ki se po njem pretaka desired naj se prerez sesalnih kanalov od omejilnika do vstopa v motor zvezno povečuje. Osnutek sesalnega voda, ki izpolnjuje prve štiri zahteve iz zahtevnika, je predstavljen na sliki 3. Da bi lahko izpolnili še preostale tri zahteve iz zahtevnika, je treba najprej analizirati, kaj se sploh dogaja z zračnim tokom, ki teče skozi predpostavljeni sesalni sistem. Ta korak pomeni osnovo za optimalno oblikovanje sesalnega sistema. Analizo tokovnih karakteristik ustaljenega zračnega toka skozi sesalni vod smo naredili z uporabo paketa računske dinamike tekočin AVL FIRE [4], ki temelji na metodi končnih prostornin. V izračunu sta bili upoštevani enačba zzveznosti: area of the intake manifold, from the restrictor to the engine input. The adopted concept that fulfilled the first four requirements from the check list is presented in Figure 3. In order to fulfill the other three requirements it is necessary to analyze what actually happens to the air flow that streams through the manifold. This step forms the basis for the optimization of the manifold. The analysis of a stationary air flow that runs through the intake manifold was made by the dynamic fluid computation package AVL FIRE [4], which is based on the finite-volumes method. The mathematical model is based on the continuity equation: — +—(r-u = 0 dt dx j) (1) in gibalna enačba: and the motion equation: gfin^OtJJlMlSCSD 03-12 stran 595 |^BSSITIMIGC Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car omejilnik restrictor \ loputa throttle plenum sesalni vod intake manifold okvir dirkalnika car frame Jjf7 dovod goriva fuel supply" vstopni kanali intake runners \ motor engine Sl. 3. Osnutek sesalnega sistema, ki izpolnjuje prve štiri zahteve iz zahtevnika Fig. 3. The concept of the intake manifold that fulfills the first four requirements from the check list 5t ( ui) dx (r-uru +r-uru tij)+ p r-g (2), kjer so: uj - komponenta hitrosti v smeri kartezične koordinate x, p - tlak, r - gostota, tij - pa tenzor napetosti. j Prenosni enačbi k-e izbranega turbulentnega modela sta: (u-V)k where uj is the component of the velocity in the xj Cartesian coordinate direction, p is the pressure, r is the density and tij is the stress tensor. The two transport equations of the chosen k-e turbulent model are: -V n+ skrj -Gk - 11n -C e 1 (Gk k (u-V)e-V kjer so: nt - turbulentna viskoznost , Gk - nastajanje turbulentne kinetične energije, Gb - nastajanje turbulence zaradi gravitacije, YM - vpliv stisljivosti tekočine na turbulenco in C1, C2, C, sk, se - izkustvene stalnice modela. Oblika in izmere sesalnega sistema so bile na začetku predpostavljene po inženirskih izkušnjah. Robni pogoji so podani z nespremenljivim padcem tlaka, ki je značilen za sesalni sistem. Izvedena je bila numerična analiza predpostavljenega začetnega sesalnega sistema. Izračunali smo polja hitrosti, tlaka in turbulentne kinetične energije vzdolž sesalnega sistema. Kot vzorčni rezultat sta na sliki 4 prikazani hitrostni polji na površini kanalov, ki vodita zrak v prvi oziroma v drugi valj. Slika 5 kaže, kako se spreminja prerez sesalnega sistema. Razvidno je, da se zrak bolj ali manj enakomerno razporedi v posamezne vstopne kanale. Sesalni vod je glede na podatke v preglednici 2 v osnutku odlično oblikovan, saj je razlika v količini zraka, ki prihaja v valje manj ko 1%. Porazdelitev zraka po valjih je torej enakomerna. Vbrizgalne ventile za gorivo C3Gb)-C2 2 (3) (4), where nt is the turbulent viscosity, Gk is the production of turbulent kinetic energy, Gb is the turbulence production due to the gravitation, YM is the influence of the fluid compressibility on the turbulence and C1, C2, Cm, sk, se are the empirical constants of the model. At the beginning the shape and the dimensions of the intake manifolds were estimated on the basis of engineering experience. The boundary conditions are defined by the constant drop of the air flow pressure, which is characteristic for the intake manifold. The initial intake manifold was numerically analyzed and the velocity fields, the pressure distribution and the turbulent kinetic energy distribution along the intake-manifold channels were calculated. Figure 4 presents the velocity fields of the two channels that lead the air flow to the first and the second cylinders. Figure 5 shows the cross-section changes of the intake manifold. It is obvious that the air is more or less equally distributed among the individual intake channels. The data in Table 2 suggest that the intake manifolds have an excellent design, because the difference in the quantity of air that goes into the individual cylinders is less than 1%. The air 2 jgnnatäüllMliBilrSO | | ^SifirlMffiC | stran 596 Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car I 4?! I Mil !?ll Sl. 4. Hitrostni polji na površini kanalov, ki vodita zrak v prvi in drugi valj Fig. 4. The velocity fields on the surfaces of the channels that lead the air flow to the first and second cylinders Sl. 5. Hitrostno polje v značilnih prerezih sesalnega sistema Fig. 5. The velocity fields in the characteristic cross sections of the intake manifold Preglednica 2. Primerjava tokovnih značilnic med cevmi sesalnega sistema Table 2. Comparison of the airflow characteristics between the pipes pretok snovi, m& v kg/s mass flow, m& [kg/s] hitrost, v v m/s velocity, v [m/s] cevi v valju 1 in 4 pipes 1 and 4 cevi v valju 2 in 3 pipes 2 and 3 0,0648 0,0653 85,380 85,043 razlika difference 0,77 % 0,39 % vgradimo tako, da curek goriva brizga v območje največjih hitrosti zraka ([4] in [5]). Zato je izbrana lega šob na zadnjem kolenu cevi sesalnega sistema, in sicer pod kotom 5° glede na središčno os vstopnih kanalov na motorju (sl. 6). distribution among the cylinders is almost perfect. The injection valve has to be mounted so that the spray of fuel is directed into the field of the maximum air velocities ([4] and [5]). That is the reason why the fuel valve is positioned on the last pipe knee and inclined at an angle of 5° with respect to the central line of the intake channels, Figure 6. gfin^OtJJIMISCSD 03-12 stran 597 |^BSSITIMIGC Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car 120 W H Šfi 40 Sl. 6. Vbrizgalni ventil vbrizga gorivo v območje največjih hitrosti Fig. 6. Injection valve sprays the fuel into the field of maximum velocities 1.2 Izračun značilnic motorja Za opis termodinamičnega postopka pri nespremenljivi vrtilni frekvenci v motorju je bil uporabljen program AVL Boost [6]. Tok snovi je obravnavan enorazsežno. Pretočne izgube na določenih mestih v motorju se upoštevajo z uporabo pretočnih koeficientov. Model delovanja motorja temelji na prvem zakonu termodinamike: 1.2 Calculation of the engine’s characteristics In order to describe the thermodynamics process at a constant engine speed, the AVL Boost [6] package was used. The material flow is described by a one-dimensional model. Flow losses at the particular locations are considered by taking into account the discharge coefficients. The model of the engine’s activity is based on the first law of thermodynamics: da dV dQf -pc------+ — da da dQw da dm da (5), kjer člen na levi strani opisuje spremembo notranje energije znotraj valja, členi na desni pa delo bata, dovedeno toploto goriva, izgubo toplote na stenah in entalpijski tok. Predpostavljeno je, da je mešanica goriva in zraka povsem homogena, kar pomeni, da je razmerje med zrakom in gorivom med postopkom zgorevanja vedno enako, pa tudi, da sta tlak in temperatura med zgorelim in nezgorelim delom zmesi vedno enaka: where the term on the left-hand side of the equation describes the change of the internal energy inside in the cylinder, while the terms on the right-hand side of the equation represent the piston work, the heat release energy from the fuel, the heat losses through the cylinder liners and the enthalpy flow. It is supposed that the air and the fuel mixture is perfectly homogenous, which, as a result, means that the relation between the air and the fuel during the burning process is always constant. Consequently, the pressure and the temperature in the burned as well as in the unburned mixture are the same: dTc da = ( 1 \dQf du mBpc duB 8T + Tc ' dp 1 Hu uF + lLSTuAir - (1 + lLST)\uB + pc uBT O 1 dQw\ da Vc dp dm BB da h BB -uc - pc c mBduB mc dp (6), kjer so: Tc in pC - temperatura in tlak znotraj valja, mC, mB in mBB - masa zmesi v valju, masa zgorelega dela zmesi in masa zmesi, ki uide med batom in steno valja, a - kot zasuka ročične gredi, u, uB, uF in uAir - specifična notranja energija, notranja energija zgorelega dela zmesi, notranja energija goriva in zraka. Hu - je spodnja kalorična vrednost, Q - energija goriva, l - razmernik zraka, Lst - stehiometrično razmerje, Q - izguba toplote na steni in hBB - entalpija zmesi, ki uide med batom in steno valja. where Tc and pC are the temperature and the pressure inside the cylinder, mC, mB and mBB are the mass of the mixture in the cylinder, the burned mass of the mixture, and the escaped mass of the mixture that leaks away through the gap between the piston and the liner, a is the angle of the crankshaft rotation, u, uB, uF and uAir are the specific inner energy, the inner energy of the burned mixture, the inner energy of the fuel and the inner energy of the air. Hu is the lowest caloric value, Qf is the fuel energy, l is the air ratio, Lst is stehiometric ratio, Qw the heat loss on the liner and hBB is the enthalpy of the mixture that escapes through the gap between the piston and the liner. 2 SnnataieJlIFiJDŽIrSD | | ^@©^ifW]D[lC | stran 598 Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car enačba: V izračunu je upoštevana tudi plinska The gas equation is also involved in the calculation procedure: pc= ¦m-R-T (7), kjer je R0 splošna plinska stalnica. V našem primeru simuliranja delovanja motorja so bile izbrane naslednje funkcije. Za določitev sproščene toplote je bila uporabljena funkcija “Vibe”: where R0 is the general gas constant. In our engine simulation the following formulas were chosen. To describe the heat release the so-called ‘Vibe’ function was used: dx a = da Da • (m +1) • ym dx = dQ Q y Da (8) (9) (10), kjer so: Q - toplotna vrednost dovedenega goriva, a - koeficient “Vibe” (popolno zgorevanje: 6,9), m -koeficient oblike, a, a0 in Da - kot zasuka ročične gredi, začetek in trajanje zgorevanja. Prenos toplote je bil znotraj valja računan s funkcijo “Woschni 1978”: where Q is the heat value of the intake fuel, a is the ‘Vibe’ (perfect burning: 6.9) coefficient, m is the coefficient of the shape, a, a0 and Dac are the angle of the crankshaft rotation, the angle of the combustion start and the angle of the combustion duration. The heat exchange inside the cylinder was calculated using the formula “Woschni 1978”: ¦pc C-c + C V -T p c,rVj ¦(pc-pc,o ) (11), kjer so: a - koeficient prenosa toplote na stenah valja, D - premer bata, c - srednja hitrost bata, Vd -delovna prostornina enega valja, p 0 - čista kompresija, pc1 in Tc1 - tlak in temperatura znotraj valja v trenutku zaprtja sesalnega ventila, C - pa numerične stalnice. Sproščanje toplote v kanalih je bilo opisano z uporabo funkcij “Zapf za sesalno in za izpušno stran: where aw is the coefficient of heat transfer through the liner walls, D is the piston diameter, cm is the mean piston velocity, Vd is the working displacement of one piston, pc,0 is the pure compression, pc,1 and Tc,1 are the pressure and the temperature inside the cylinder at the moment of the intake valve closing, while Ci is a numerical constant. The heat release in the channels was described by using the “Zapf” formulae for the intake side and the exhaust side respectively: ap=[C7+C8-Tu-C9-Tu2}Tu0,33- ap=[C4+C5-Tu-C6-Tu2}Tu0,44- kjer so: a - koeficient prenosa toplote skozi sesalne oziroma izpušne kanale, m - masni pretok, T -temperatura na vstopu v kanal, di in h - premer sedeža ventila in njegov dvig. Za potrditev omenjenega enorazsežnega modela motorja smo izračunane rezultate primerjali z izkustveno dobljenimi rezultati (sl. 7). Kakor je razvidno, so razlike med preskusom in numeričnimi izračuni zelo majhne. Zaradi tega lahko predpostavimo, da je opisan numerični model motorja dovolj zanesljiv in ga lahko vključimo v postopek optimiranja sesalnega sistema. 1.3 Optimiranje sesalnega sistema Obliko sesalnega sistema pustimo takšno, kakršna je bila predpostavljena v začetnem osnutku ¦d- 1-0,765- 1-0,797- (12) (13), where ap is the coefficient of heat transfer through the intake/exhaust channels, m& is the mass flow, Tu is the temperature on the channel input side, dvi and hv are the valve seat diameter and the valve lift, respectively. In order to verify the one-dimensional model above, the calculated results were compared to the experimental data, Figure 7. As can be seen, the differences between the experiment and the numerical calculations are rather small. Therefore, one can assume that the described numerical engine model is good enough to be employed for the intake-manifold optimization. 1.3 The intake-manifold optimization The basic form of the intake manifold was taken from the initial concept because it was clearly evident | IgfinHŽslbJlIMlIgiCšD I stran 599 glTMDDC Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car • ¦ , t —" f"! i ^^"^^* moč 35 , ^—¦*¦ T power [kW] *"""""*"T—— A preskus 1/exp. 1 ¦ preskus 2/exp. 2 • preskus 3/exp. 3 ___izr/calc. ¦ 1 --------------1--------------- ¦ ¦ i ¦ 20 l ¦ 7000 8000 9000 10000 11000 vrtilna frekvenca motorja [min1] engine speed [rpm] 12000 Sl. 7. Izmerjena in izračunana (izr) dejanska moč motorja Fig. 7. Measured and calculated (calc.) effective engine power saj je dokazano, da je polnjenje valjev enakomerno. Spreminjamo le izbrane izmere. Zamisel je bila taka, da določimo njihove optimalne vrednosti, tako da čimbolj povečamo moč motorja v najbolj pomembnih delovnih področjih obratovanja motorja. 1.3.1 Problem optimalnega projektiranja that this shape ensures equal loading of the mixture for each cylinder. Some of the manifold dimensions, however, can still be changed. The idea now is to determine the optimum values for these dimensions so that the engine power will be increased as much as possible in the most important operating regimes of the engine. 1.3.1 The problem of optimum design Problem optimalnega projektiranja lahko The problem of optimum design can be zapišemo v naslednji obliki: written in the following form: ob upoštevanju pogojev in enačbe stanja min g0(b,u) subject to the constraints: gi(b,u)<0,i = 1,...,j and the response equation: u=f(b,t,u) (14) (15) (16), kjer je b e Rn vektor projektnih spremenljivk. Vektor ueRm označuje odzivne spremenljivke, ki opisujejo odziv sistema, ueRm so njihovi časovni odvodi, t je časovna spremenljivka. Enačba stanja (2.16) označuje odvisnost u od t in b. Skalarne funkcije g0 in g označujejo namensko in omejitvene funkcije. Namenska funkcija je odvisna od kakovosti oblikovanja b, medtem ko omejitvene funkcije odsevajo mehanske, tehnološke in druge omejitve. Simbol n označuje število projektnih spremenljivk, m število odzivnih spremenljivk in j število omejitev. V našem primeru so funkcije g0 in gi odvedljive po b in projektne spremenljivke so zvezne, zato je problem optimalnega projektiranja where b e Rn is the vector of the design variables. The vector u e Rm denotes the response variables that describe the response of the system, u e Rm are their time derivates and t is the time variable. The response equation (2.16) establishes the dependence of u on t and b. The scalar functions g0 and g denote the objective and constraint functions respectively. The objective function depends on the quality of the design, meanwhile the constraint functions reflect the mechanical, technological and other constraints. The symbol n denotes the number of design variables, m denotes the number of response variables and j denotes the number of constraints. In our case the functions g0 and g are differentiable with respect to b and the design variables are continuous. Therefore, the problem 2 jgnnatäüllMliBilrSO | | ^SSfiflMffiC | stran 600 Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car mogoče reševati z uporabo približne metode kot ene izmed gradientnih metod matematičnega programiranja. 1.3.2 Postopek optimalnega projektiranja Za reševanje problema optimalnega projektiranja je bil uporabljen program iGO, ki je bil razvit na temelju približne metode ([7] in [8]). Pravzaprav iGO zaganja zunanje programe - tako imenovane simulatorje - za določitev vrednosti namenske in omejitvenih funkcij. Potem kliče svoj lastni optimizator za izboljšanje vrednosti projektih spremenljivk. Celoten iteracijski postopek reševanja problema optimalnega projektiranja je prikazan na sliki 8. b0 iGO optimizacijski program iGO optimization program of optimum design can be solved by using an approximation method, which is one of the gradient methods of mathematical programming 1.3.2 The optimum design procedure To solve the optimum design problem, the program iGO was employed. This is a stand-alone program containing the approximation method described in ([7] and [8]). Essentially, iGO runs external programs – called simulators – in order to get the values of the objective and constraint functions. After that it calls its own built-in optimizer to improve the values of the design variables. This procedure is then repeated iteratively as shown in Figure 8. b* bi VHODNI VMESNIK Spremeni Boost vhodno datoteko z veljavnimi vrednostmi za projektne spremenljivke INPUT WRAPPER Modifies the Boost input file with current values of design variables AVL Boost program (enačba stanja) AVL Boost program (response equation) IZHODNI VMESNIK Vzame zahtevane podatke iz Boost izhodne datoteke OUTPUT WRAPPER Gets the required data from the Boost output file Sl. 8. Postopek reševanja problema optimalnega projektiranja Fig. 8. The procedure for solving the optimum design problem 1.3.3 Optimalno projektiranje sesalnega voda Kot projektni spremenljivki v problemu optimalnega projektiranja se pojavljata premer d in dolžina L primarnih cevi sesalnega sistema: 1.3.3 Optimum design of the intake manifold The design variables in the problem of optimizing the intake-manifold design are the diameter d and the length L of the manifold intake pipes: b =[d,L]T (17). Začetne vrednosti projektnih spremenljivk so bile določene z geometrijskimi merami predpostavljenega sesalnega sistema b1(0) = 37mm,b2(0) = 340mm. Zaradi možnosti takojšnje vgradnje sesalnega sistema v sedanji dirkalnik, je bilo treba glede na spreminjanje geometrijske oblike primarnih cevi, spreminjati tudi geometrijsko obliko difuzorja, tako da je skupna dolžina sesalnega sistema ostala nespremenjena. Ker smo želeli povečati moč motorja, je bila namenska funkcija definirana kot vsota moči pri posameznih vrtilnih frekvencah, pomnožena z ustreznimi utežnimi faktorji. Karakteristične vrtilne frekvence so bile določene glede na pogoje vožnje. Tako lahko namensko funkcijo zapišemo kot: The initial values of the variables are taken from the basic intake-manifold form as follows b1(0) = 37mm,b2(0) = 340mm . In order to ensure proper fitting of the intake manifold into the racing car, it is necessary to change the geometry of the manifold in such a way that the total length of the intake manifold does not change. Since we want to increase the power of the engine, the objective function was defined as the sum of the individual engine powers at the corresponding rotation speeds and multiplied by appropriate weighting factors. The characteristic rotation speeds were selected according to the driving regime. As a result, the objective function can be written as follows: stran 601 Pehan S., Kegl B,, Pogorevc P.:Oblikovanje dirkalnika - Developing a Racing Car N (18), kjer oznake V, z = 1, ..., N označujejo utežne faktorje za N posameznih delovnih režimov, medtem ko P 1, P 2 ..., P N označujejo dejansko moč na posameznem delovnem režimu. Z minimiziranjem vsote v enačbi (2.18) se pričakuje povečanje moči motorja. Zahtevani pogoji, ki morajo biti izpolnjeni pri optimiranju sesalnega sistema, se nanašajo na celotno dolžino cevi L (najmanjša dolžina cevi L ), specifično porabo goriva g (največja dovoljena poraba^ = 350 g/kWh ), hrup z (največji dovoljeni hrup L e, = 110 dBA) in na projektne spremenljivke 20 mm < b1 < 60 mm in 300 mm < b < 400 mm. Te omejitve lahko zapišemo kot: where the symbols yz, z = 1, ..., N denote the weighting factors for N individual operating regimes, meanwhile the symbols Pe,1, Pe,2 ..., Pe,N denote the effective powers for individual operating regimes. By minimizing the sum defined in (2.18) it is possible to increase the engine’s power. The constraints that should be taken into account during the optimization are related to the total pipe length L (the minimum pipe length is Lmin), the specific fuel consumption ge,z, (the maximum allowed fuel consumption is ge,max = 350 g/kWh ), the noise z (the maximum allowed noise is xmax = 110 dBA) and to the design variables 20 mm < b1 < 60 mm as well as 300 mm < b2 < 400 mm. These constraints can be written as: g -g <0, z = 1,...,N l-^<0, z = 1,...,N biL