Strojarstvo 50 (6) 369-374 (008). vražić et. al., Mass Correlation Between Real Vehicle... 369 CODEN SSAO ZX470/360 ISSN 056-887 UDK 69.33.07:68.58.07 Mass Correlation Between Real Vehicle and Vehicle Laboratory Siulation Model Mario VRAŽIĆ), Helut WEISS) and Ivan GAŠPARAC) ) Fakultet elektrotehnike i računarstva, Sveučilište u Zagrebu (Faculty of Electrical Engineering and Coputing, University of Zagreb), Unska 3, HR - 0000 Zagreb Republic of Croatia ) University of Leoben, Institut for Electrical Engineeering, Franz-osef-Straße 8, Austria Original scientific paper he proble how easily to scale down real object of siulation to laboratory siulation odel, thus siplify equations to the extent of only one scaling factor that correlates between the real object and odel, is always present in laboratory siulations. his paper presents a siple way to scale down real to the odel level and also how to deterine the acceptable range of real that can be siulated by laboratory odel. he proble started when all field easureents on real ended, and laboratory siulation odel, saller than real, had to siulate that (drive achine had less rated power than a engine, and a load achine can create less load that of a real ). ario.vrazic@fer.hr Keywords Mass correlation Siulation oryue easureents Vehicle laboratory odel Ključne riječi Korelacija ase Laboratorijski odel vozila Mjerenje oenta Siulacija Received (priljeno): 007--5 Accepted (prihvaćeno): 008-0-3 Korelacije asa realnog vozila i laboratorijskog siulacijskog odela vozila Izvornoznanstveni članak Proble jednostavnog uanjivanja realnog odela kako bi se ogao siulirati na laboratorijsko siulacijsko odelu, pogotovo tako da se jednadžbe pojednostave do razine projene sao jednog faktora, uvijek je prisutan u laboratorijski siulacijaa. Ovdje se govori o jednostavno načinu da se paraetri realnog vozila sanje na razinu odela kao i o prihvatljivi granicaa takovog sanjivanja. Naie proble je nastupio kada su obavljena jerenja na realno vozilu i ono je trebalo biti siulirano na laboratorijsko siulacijsko odelu koji je anji od vozila (pogonski otor je anje snage, a opteretni stroj ože stvoriti anje opterećenje pogonsko otoru). Introduction Vehicle laboratory siulation odels are an essential part of ost researches on behaviour [] to [5]. Since laboratory odels are usually saller than real s, there is a proble of representation of real with a odel. he initial task was to create a laboratory odel (Fig.) for traction load siulation that includes drive (DC electrical achine), transission (gearbox), inertia (flywheel) and DC achine representing other losses (rolling resistance, air resistance )[6], [7]. he odel basic paraeters are following: the inertia 5 kg (flywheel plus load achine rotor) the drive achine power P 0 kw the load achine power P 40 kw rated odel rotation speed (rated flywheel and load achine rotation speed) nn500 r/in Figure Realized laboratory siulation odel with drive (), transission (), torque sensor (3), flywheel (4) and load achine (5) Slika. Ostvaren laboratorijski siulacijski odel s pogonski otoro (), prijenoso (), jerače oenta (3), zaašnjako (4) i opteretni stroje (5) After creating a laboratory odel, the following proble occurs: how to represent real (in our
370. vražić et. al., Mass Correlation Between Real Vehicle... Strojarstvo 50 (6) 369-374 (008) Sybols/Oznake inertia, kg oent inercije P power, W snaga n n rated rotation speed, r/in noinalna brzina vrtnje W air resistance load torque, N oent uzrokovan otporo zraka c air resistance factor, faktor otpora zraka A superficial front area, površina prednje strane vozila ρ air density, kg/ 3 gustoća zraka v velocity, k/h brzina vozila w wind speed towards, k/h brzina vjetra prea vozilu r drive wheel radius, radijus pogonskog kotača R rolling resistance load torqur, N oent otpora kotrljanja f 0 epirical factor, epirijski faktor ass, kg asa vozila g Earth gravity acceleration, /s ubrzanje Zeljine gravitacije a epirical factor, epirijski faktor Τ α road slope load torque, N oent uzrokovan nagibo puta α 0 road slope, nagib puta a inertia torque, N oent uzrokovan ubrzanje asa e equivalent ass factor, faktor ekvivalentne ase vozila e equivalent ass, kg ekvivalentna asa z nuber of wheels on the, broj kotača na vozilu tot total load torque, N ukupni opteretni oent i transission ratio, prijenosni ojer transisije k siulation factor, siulacijski faktor case 993 Fiat epra,9d) with a laboratory odel. A further proble is how to siulate other s (otorcycles, other cars, vans ) and what are the liitations of this laboratory odel. And, of course, it will be ideal to represent the difference between the real and siulation odel with one scaling factor.. Vehicle in otion torque equations In order to solve those probles, basic equations of in otion were set. he drive of the in otion feels four ajor loads: air resistance, rolling resistance, road slope resistance, inertia ass resistance [9]. caused by air resistance is: v w c W A ( ) ρ r [ N ] 36,, () For winds coing directly fro the rear side of the and when wind speed exceeds velocity, the equation is not valid any ore; this can also be caused by a different rear side air resistance factor. caused by rolling resistance is: f R g r 0 cosα f0ga v r cosα[ N]. caused by road slope is: α g sin α r N. [ ] (3) his equation is valid for α >0 for ascending road and α <0 for descending road as well. caused by inertia asses is: e r dn π a [ N] dt, (4) where: n [r/in] is drive wheel rotation speed and e [] is equivalent ass factor fro: drive wheel [ ] e z e kg r. (5) drive wehicle () he equivalent ass will, in further text, be presented as a product of the ass and equivalent ass factor e. hus, for exaple, the FIA epra, which will be the test object in this research, has 50 kg, while its equivalent ass is 576,8 kg and factor e is,037.
Strojarstvo 50 (6) 369-374 (008). vražić et. al., Mass Correlation Between Real Vehicle... 37 he total drive achine torque is: c A w r f g r g r tot ρ 0 cosα sinα 36, i i i If the torque is expressed generally (with the constant road slope α), it results in the following: dn tot k k n k3 n k4. (7) dt 3. Influence of ass change to siulation 3.. Siulation of different asses Load siulation of the traction syste requires an analysis of the ass change influence on the siulation process because of its total ass the drive units loading depend on (5). Soe of the accuulate kinetic energy in kinetic states and others irreversibly change energy into surface or air friction. he total ass consists of its base (factory) ass and asses of all the passengers and cargo. In order to siulate different asses, the equations (), (), (3) and (4) should be fulfilled. In all those equations, except (), the siulation process depends on paraeter, which represents total ass. Since this paraeter changes, i.e. it depends on passenger and cargo ass, the possibility of siulation with only one rotating ass should be found. 3.. Base, base ass Stated equations deterine the siulation process. In order to use this odel for different asses of the sae, i.e. that does not change its shape and size (so the equation () does not change), the concept of base is introduced. he base of soe siulation odel is the, for which, the siulation odel, without any corrective coefficients, can perfor siulation. he base has base ass, which corresponds to inertia odel : c A ρ wr 36, i [ ] odel rdrive wheel π n (6) 3 3 caρr π f0gar π cosα i n i e r i π dn dt. kg, (8) where: r drive wheel is siulated (base) drive wheel radius. With this equation, the base ass of all s in able, can be deterined. he odel will, without any correction, siulate base drive odes (real with base ass), i.e. it will siulate torques, powers and energies according to following equations: base air resistance torque c A w r c A wr n W base ρ ρ π 36, 36, 3 n π (9) ca ρ r [ N] base rolling resistance torque R base f0gr cosα 3 f0ga r π n cosα [ N] (0) base potential energy change torque α base g r sin α N () [ ] base acceleration torque e r dn a _ base π [ N] dt. 3.3. Siulation factor () he and its base ass ratio (i.e. ratio of corresponding inertia) is called siulation factor k k MODEL. (3) he siulation factor k represents a paraeter that will be used when inertia is different fro odel inertia odel. Later on, with the aid of siulation factor k, the possibility, that any (with ass different fro base ass ) can be siulated with the sae odel, will be shown. In the case of base siulation, i.e. real with base ass (k), siulation is perfor by equations (9) to (). 3.4. orque equations for with ass different fro base ass In the case of k, a correction of siulation process should be ade. A greater or saller value of k (copared to base one), indicates the ass change without shape and size change. It also eans that equation (9) does not change (air resistance torque), but paraeter in equations (0), () and () is changed with factor k. herefore, those equations should be corrected according to base ters.
37. vražić et. al., Mass Correlation Between Real Vehicle... Strojarstvo 50 (6) 369-374 (008) he equation (9) does not change, but, because of the clarity, it can be repeated: air resistance torque c A w r c A wr W k W base ρ ρ 36, 36, n π (4) 3 n π caρ r N [ ] Equations (0), () and () should be changed by ass deands: rolling resistance torque k f k gr cosα R k R base 0 3 f0kga r π n cosα (5) [ N ] potential energy change torque α k k α base k g r sin α N (6) [ ] acceleration torque e k r dn k _ π [ N] dt. (7) a_ k a base 3.5. Siulation odel torque equation When torques are recalculated to odel siulation level, all equations fro (4) to (7) should be divided by factor k, which gives siulation equation package that is applied to the odel: siulation air resistance torque k c A w r c A wr W el W ρ ρ od 36, k 36, k nπ c Aρr 3 n π (8) [ N] k siulation rolling resistance torque k f g r R odel R k R base 0 cosα 3 f0ga r π n cosα (9) N [ ] siulation potential energy change torque k g r k base sin. (0) α odel α α α able. Base ass for different s with odel 5 kg ablica. Bazna asa za različita vozila s odel 5 kg Vehicle / Vozilo Mass / Masa (kg) Drive wheel radius / Radijus pogonskog kotača r drive wheels () Inertia on drive wheels Moent inercije na pogonsko kotaču (kg ) Vehicle base ass Bazna asa vozila (kg) odel vozila vozila od ela Motorcycle (Gilera NEXUS500) Car (Fiat epra,9d) Van (Ford ransit Van 4 LWB) ruck (Mercedes Atego 0,5t ) Bus (Volvo BM ) ruck (Mercedes Actro 34K) 6 6,9 0,65 0,7380 333 6,94 0,9 00 0,955 0,00 94 4,08 50 9,0 5,7 55 0,36445 99,5 88,00 450 564,50,6 3680 0,39850 584,39 57 3,44 0500 667,4 66,88 600 0,53775 79,89 86 7,09 9000 5494,33 0,93 9700 640,56 05,43 0,575 9 00 87,4 347,83
Strojarstvo 50 (6) 369-374 (008). vražić et. al., Mass Correlation Between Real Vehicle... 373 siulation acceleration torque a _ odel e r π dn a _ k a _ base ]. [ N () k dt he equation () describes the torque siulated with the flywheel, while equations (8), (9) and (0) describe load torques siulated by load achine (No. 5 on Figure ). And finally, each siulation odel torque, ultiplied with siulation factor k, represents the whole corresponding torque, reduced to its drive axis, i.e. its drive wheels, in static operation as well as in dynaics. 4. Confiration by easureent on real Figure 3. orque sensor for torque easureent Slika 3. Mjerač oenta za vozilo Figures 4 to 7 shows good relation between siulation on laboratory odel and real. In order to prove stated, extended easureent on real (Fiat epra) was ade (Figure and 3) [8]. During those easureents torque and velocity and wind velocity were recorded. Figure 4. Coparison between and odel torque recorded for weight of 70 kg during acceleration to Figure. orque sensor ounted on real Slika 4. Usporedba izeđu sniljenog oenta vozila i odela za vozilo ase 70 kg tijeko ubrzavanja od irovanja do Slika. Mjerač oenta ontiran na realno vozilo he following tests were being ade: Slow acceleration 0- Fast acceleration 0- Road slope ascent with 0 k/h, 0 k/h and k/h Standstill (on the clutch) while ascending Standstill (on the clutch) while descending Road slope descent with 0 k/h, 0 k/h and k/h Continuous drive at 40 k/h, 50 k/h, 60 k/h, 70 k/h, 80 k/h, 90 k/h, 00 k/h and 0k/h Deceleration fro to standstill with gearbox in neutral position Figure 5. Coparison between and odel velocity recorded for weight of 70 kg during acceleration to Slika 5. Usporedba izeđu sniljene brzine vozila i odela za vozilo ase 70 kg tijeko ubrzavanja od irovanja do
374. vražić et. al., Mass Correlation Between Real Vehicle... Strojarstvo 50 (6) 369-374 (008) Figure 6. Coparison between and odel power recorded for weight of 70 kg during acceleration to Slika 6. Usporedba izeđu sniljene snage vozila i odela za vozilo ase 70 kg tijeko ubrzavanja od irovanja do Figure 7. Coparison between and odel energy recorded for weight of 70 kg during acceleration to Slika 7. Usporedba izeđu sniljene energije vozila i odela za vozilo ase 70 kg tijeko ubrzavanja od irovanja do 5. Conclusion his laboratory odel can siulate real in otion traction syste loads according to equations fro chapter 3. he siulation factor k describes real and odel equations. he odel easureent syste accuracy can be assessed to %. If one wants to siulate traction syste loads of a big (trucks or bus fro able I), then the value of siulation factor k is very big (fro 60 up to 350). With the assessed accuracy of odel easureent syste and largeness of siulation factor k, one could see that the error, due to odel easureent syste accuracy, would be big for considerable siulation factor k. herefore, one should liit the application of laboratory siulation odel to the siulation of traction syste load to s with saller siulation factor k, i.e. for k<. Expectations considering siulation deands were copletely fulfilled. Naely, after the siulation of Fiat epra traction syste loads was conducted, siilar tests were carried out on the sae (Fiat epra). A coparison of real and siulated loads showed an excellent atch. he research of odel possibilities enables the extension of its application by introduction of the following paraeters and ideas: base, base ass and siulation factor. References [] Lin, B.: Conceptual design and odeling of a fuel cell scooter for urban Asia, Master of Science work, Princetown Univerity, USA, 999. [] Antoniou, I.A.; Koyathy,.; Bench,.; Eadi, A: Modeling and Siulation of Various Hybrid-Electric Configurations of the High-Mobility Multipurpose Wheeled Vehicle (HMMWV), IEEE RANSACIONS ON VEHICULAR ECHNOLOGY, VOL. 56, NO., pp. 459-465, MARCH 007. [3] Bogosyan, S.; Gokasan, M.; Goering, D..: A Novel Model Validation and Estiation Approach for Hybrid Serial Electric Vehicles, IEEE RANSACIONS ON VEHICULAR ECHNOLOGY, VOL. 56, NO. 4, pp. 485-497, ULY 007. [4] Syed, F.U.; Kuang, M.L.; Czubay,.; Ying, H.: Derivation and Experiental Validation of a Power-Split Hybrid Electric Vehicle Model IEEE RANSACIONS ON VEHICULAR ECHNOLOGY, VOL. 55, NO. 6, pp 73-747, NOVEMBER 006. [5] Filippa, M.; Mi, Ch.; Shen,.; Stevenson R.C.: Modeling of a Hybrid Electric Vehicle Powertrain est Cell Using Bond Graphs IEEE RANSACIONS ON VEHICULAR ECHNOLOGY, VOL. 54, NO. 3, pp. 837-845, MAY 005. [6] Vrazic, M.; Gasparac, I.; Ilic, I.: Structure of physical odel for research of traction paraeters of electrical, ICI03, Maribor, Slovenia, Deceber 0-, 003. [7] Vrazic, M.; Ilic, I.; Weiss, H.: Laboratory odel for siulation of s traction syste load, APEIE-004, Novosibirsk, Russia, Vol. 6, pp. 07-, Septeber -4, 004. [8] Vrazic, M.; Ilic, I.; Gasparac, I: Vehicle Drive Wheel orque Measureent for the Purpose of the Vehicle raction Syste Siulation Model Evaluation, ISIE 005, Dubrovnik, Croatia, pp. 6-65, une 0-3, 005. [9] Balzer, W.: Autootive handbook,. english edition, Stuttgart, Robert Bosch GBH, 978.