Module 2: Dynamics of Electric and Hybrid vehicles

Transcription

1 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Module : Dynamics of Electic and Hybid vehicles Lectue 3: Motion and amic equations fo vehicles Motion and amic equations fo vehicles Intoduction The fundamentals of vehicle design involve the basic pinciples of physics, specially the Newton's second law of motion. Accoding to Newton's second law the acceleation of an object is popotional to the net foce exeted on it. Hence, an object acceleates when the net foce acting on it is not zeo. In a vehicle seveal foces act on it and the net o esultant foce govens the motion accoding to the Newton's second law. The populsion unit of the vehicle delives the foce necessay to move the vehicle fowad. This foce of the populsion unit helps the vehicle to ovecome the esisting foces due to gavity, ai and tie esistance. The acceleation of the vehicle depends on: the powe deliveed by the populsion unit the oad conditions the aeoamics of the vehicle the composite mass of the vehicle In this lectue the mathematical famewok equied fo the analysis of vehicle mechanics based on Newton s second law of motion is pesented. The following topics ae coveed in this lectue: Geneal desciption of vehicle movement Vehicle esistance Dynamic equation Tie Gound Adhesion and maximum tactive effot Joint initiative of IITs and IISc Funded by MHRD Page 1 of 8

2 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Geneal desciption of vehicle movement The vehicle motion can be completely detemined by analysing the foces acting on it in the diection of motion. The foces acting on a vehicle, moving up a gade, ae shown in Figue 1. The tactive foce (F t ) in the contact aea between the ties of the diven wheels and the oad suface popels the vehicle fowad. The tactive foce (F t ) is poduced by the powe plant and tansfeed to the diving wheels via the tansmission and the final dive. When the vehicle moves, it encountes a esistive foce that ties to etad its motion. The esistive foces ae Rolling esistance Aeoamic dag Uphill esistance V F w h w Mgsin(a) F a T f h g T W f Mgcos(a) L a Mg L b a L W Figue 1: Foces acting on a vehicle going uphill [1] Using the Newton's second law of motion, the vehicle acceleation can be expessed as dv dt whee V vehicle speed t t esis tan ce F M F esistac F total tactive effot [ Nm] F total esistance [ Nm] M total mass of the vehicle [ kg] mass facto fo conveting the otational inetias of otating components into tanslational mass (1) Joint initiative of IITs and IISc Funded by MHRD Page of 8

3 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Rolling esistance The olling esistance of ties on had sufaces is due to hysteesis in the tie mateial. In Figue a tie at standstill is shown. On this tye a foce (P), is acting at its cente. The pessue in the contact aea between the tie and the gound is distibuted symmetically to the cente line and the esulting eaction foce (P z ) is aligned along P. P z P z Figue : Pessue distibution in contact aea [1] The defomation, z, vesus the load P, in the loading and unloading pocess is shown in Figue 3. Fom this figue it can be seen that, due to the hysteesis, the foce (P) fo the same defomation (z) of the tie mateial at loading is geate than at duing unloading. Hence, the hysteesis causes an asymmetic distibution of the gound eaction foces. Foce, P P 1 P Defomation, z Figue 3: Foce acting on a tye vs. defomation in loading and unloading [1] Joint initiative of IITs and IISc Funded by MHRD Page 3 of 8

4 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The scenaio of a olling tie is shown in Figue 4. When the tie olls, the leading half of the contact aea is loading and the tailing half is unloading. Thus, the pessue on the leading half is geate than the pessue on the tailing half (Figue 4a). This phenomenon esults in the gound eaction foce shifting fowad. The shift in the gound eaction foce ceates a moment that opposes olling of the wheels. On soft sufaces, the olling esistance is mainly caused by defomation of the gound suface, (Figue 4b). In this case the gound eaction foce almost completely shifts to the leading half. P z a Figue 4a: Foce acting on a tye vs. defomation in loading and unloading on a had suface [1] The moment poduced by fowad shift of the esultant gound eaction foce is called olling esistance moment (Figue 4a) and can expessed as T Pa Mga whee T olling esistance [ Nm] P Nomal load acting on the cente of the olling wheel [ N] M mass of the vehicle [ kg] g acceleation constant [ m / s ] a defomation of the tye [ m] P z () Joint initiative of IITs and IISc Funded by MHRD Page 4 of 8

5 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles P P x z P z Figue 4a: Foce acting on a tye vs. defomation in loading and unloading on a soft suface [1] To keeps the wheel olling, a foce F, acting on the cente of the wheel is equied to balance this olling esistant moment. This foce is expessed as F whee P Nomal load acting on the cente of the olling wheel [ N] T Pa Pf T olling esistance [ Nm] f amic adius of the tye [ m] olling esistance coefficient The olling esistance moment can be equivalently eplaced by hoizontal foce acting on the wheel cente in the diection opposite to the movement of the wheel. This equivalent foce is called the olling esistance and its magnitude is given by F whee (4) P Nomal load acting on the cente of the olling wheel [ N] f Pf olling esistance coefficient When a vehicle is moving up a gadient, the nomal foce (P), in equation 4, is eplaced by the component that is pependicula to the oad suface. Hence, equation 4 is ewitten as F Pf cos( a) Mgf cos( a) whee (5) P Nomal load acting on the cente of the olling wheel [ N] f olling esistance coefficient a oad angle [ adians] (3) Joint initiative of IITs and IISc Funded by MHRD Page 5 of 8

6 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The olling esistance coefficient, f, is a function of: tie mateial tie stuctue tie tempeatue tie inflation pessue tead geomety oad oughness oad mateial pesence of absence of liquids on the oad The typical values of the olling esistance coefficient (f ) ae given in Table 1. Table 1: Refeence values fo the olling esistance coefficient (f ) Conditions Rolling esistance coefficient (f ) Ca tie on smooth tamac 0.01 oad Ca tie on concete oad Ca tie on a olled gavel 0.0 oad Ta macadam oad 0.05 Unpaved oad 0.05 Bad eath tacks 0.16 Loose sand Tuck tie on concete o asphalt oad Wheel on ion ail The values given in table 1 do not take into account the vaiation of f with speed. Based on expeimental esults, many empiical fomulas have been poposed fo calculating the olling esistance on a had suface. Fo example, the olling esistance coefficient of a passenge ca on a concete oad may be calculated as:.5 V f f0 fs 100 whee V vehicle speed [ km / h] (6) Joint initiative of IITs and IISc Funded by MHRD Page 6 of 8

7 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles In vehicle pefomance calculation, it is sufficient to conside the olling esistance coefficient as a linea function of speed. Fo most common ange of inflation pessue, the following equation can be used fo a passenge ca on a concete oad V f whee V vehicle speed [ km / h] The equation 7 can pedict the values of f with acceptable accuacy fo speed up to 18km/h. Aeoamic dag A vehicle taveling at a paticula speed in ai encountes a foce esisting its motion. This foce is known as aeoamic dag. The main causes of aeoamic dag ae: shape dag skin effect The shape dag is due to the shape of the vehicle. The fowad motion of the vehicle pushes the ai in font of it. Howeve, the ai cannot instantaneously move out of the way and its pessue is thus inceased. This esults in high ai pessue in the font of the vehicle. The ai behind the vehicle cannot instantaneously fill the space left by the fowad motion of the vehicle. This ceates a zone of low ai pessue. Hence, the motion of the vehicle ceates two zones of pessue. The high pessue zone in the font of the vehicle opposes its movement by pushing. On the othe hand, the low pessue zone developed at the ea of the vehicle opposes its motion by pulling it backwads. The ai close to the skin of the vehicle moves almost at the speed of the vehicle while the ai away fom the vehicle emains still. Between these two layes (the ai laye moving at the vehicle speed and the static laye) the molecules move at a wide ange of speeds. The diffeence in speed between two ai molecules poduces fiction. This fiction esults in the second component of aeoamic dag and it is known as skin effect. The aeoamic dag is expessed as 1 Fw Af CDV whee A f 3 density of ai [ kg / m ] vehicle fontal aea [ m ] V vehicle speed [ m / s] C D dag coefficient (8) (7) Joint initiative of IITs and IISc Funded by MHRD Page 7 of 8

8 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The aeoamic dag coefficients and the fontal aea fo diffeent vehicle types ae given in Table. Table : Refeence values fo dag coefficient (C D) and the fontal aea (A f in m ) fo some vehicle types Vehicle C D A f Motocycle with ide Open convetible Limousine Coach Tuck without taile 0.8 Tuck with taile Aticulated vehicle Gading esistance When a vehicle goes up o down a slope, its weight poduces a component of foce that is always diected downwads, Figue 5. This foce component opposes the fowad motion, i.e. the gade climbing. When the vehicle goes down the gade, this foce component aids the vehicle motion. The gading esistance can be expessed as Fg Mg sin( a) whee M mass of vehicle [ kg] g acceleation constant [ m / s ] a oad angle [ adians] In ode to simplify the calculation, the oad angle a, is usually eplaced by the gade value, when the oad angle is small. The gade value is defined as (Figue 5) H i tan( a) sin( a) (10) L (9) Joint initiative of IITs and IISc Funded by MHRD Page 8 of 8

9 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles In some liteatue, the tie olling esistance and the gading esistance taken togethe and is called oad esistance. The oad esistance is expessed as F F F Mg f cos( a) sin( a) d f g acceleation constant[ m / s ] whee (11) M mass of vehicle [ kg] g f olling esistance coefficient Mgsin(a) h g H Mgcos(a) a Mg a L Figue 5: Vehicle going up a gade [1] Acceleation esistance In addition to the diving esistance occuing in steady state motion, inetial foces also occu duing acceleation and baking. The total mass of the vehicle and the inetial mass of those otating pats of the dive acceleated o baked ae the factos influencing the esistance to acceleation: Fa M whee ot M mass of vehicle [ kg] ot intetia of otational components [ ] V speed of the vehicle [ km / h] J dv dt J kg m amic adius of the tye [ m] The otational component is a function of the gea atio. The moment of inetia of the otating dive elements of engine, clutch, geabox, dive shaft, etc., including all the oad wheels ae educed to the diving axle. The acceleation esistance can be expessed as dv Fa M dt (1) whee otational inetia constant M mass of the vehicle [ kg] V speed of the vehicle [ m / s] (13) Joint initiative of IITs and IISc Funded by MHRD Page 9 of 8

10 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Total diving esistance The taction foce (F t ) equied at the dive wheels is made up of the diving esistance foces and is defined as F F F F F (14) esis tan ce w g a Substituting the values of all the foces in equation 14, gives 1 dv (15) Fesis tan ce Mgf cos( a) Af CDV Mg sin( a) M dt The equation 15 may be used to calculate the powe equied (P eq ): P F V (16) eq esis tan ce Dynamic equation In the longitudinal diection, the majo extenal foces acting on a two axle vehicle (Figue 1) include: the olling esistance of the font and ea ties (F f and F ), which ae epesented by olling esistance moment, T f and T the aeoamic dag (F w ) gade climbing esistance (F g ) acceleation esistance (F a ) The amic equation of vehicle motion along the longitudinal diection is given by dv M Ftf Ft Ff F Fw Fg Fa dt (17) The fist tem on the ight side is the total tactive effot and the second tem is the total tactive esistance. To detemine the maximum tactive effot, that the tie gound contact can suppot, the nomal loads on the font and ea axles have to be detemined. By summing the moments of all the foces about point R (cente of the tie-gound aea), the nomal load on the font axle W f can be detemined as W f dv MgLb cos( a) Tf T Fwh w Mghg sin( a) Mhg dt (18) L Similaly, the nomal load acting on the ea axle can be expessed as dv MgLa cos( a) Tf T Fwh w Mghg sin( a) Mhg dt W (19) L Joint initiative of IITs and IISc Funded by MHRD Page 10 of 8

11 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles In case of passenge cas, the height of the cente of application of aeoamic esistance (h w ) is assumed to be nea the height of cente of gavity of the vehicle (h g ). The equation18 and 19 can be simplified as L h g b dv Wf Mg cos( a) Fw Fg Mgf cos( a) M L L hg dt and L h g a dv W Mg cos( a) Fw Fg Mgf cos( a) M L L hg dt Using equation 5, 17, 0 and 1 can be ewitten as L h a g W Mg cos( a) Ft F 1 L L h g (0) (1) () L h a g W Mg cos( a) Ft F 1 L L h g (3) The fist tem on the ight hand side of equation and equation 3 is the static load on the font and the ea axles when the vehicle is at est on level gound. The second tem is the amic component of the nomal load. The maximum tactive effot (F tmax ) that the tie-gound contact can suppot is descibed by the poduct of the nomal load and the coefficient of oad adhesion (m). In Table 3, the values of coefficient of adhesion ae given fo diffeent speeds of the vehicle and diffeent oad conditions. Fo the font wheel dive vehicle, F tmax is given by L h b g Ft max W f Mg cos( a) Ft max F 1 L L h F t max Mg cos( a) Lb f hg / L 1 h / L g g (5) (4) Joint initiative of IITs and IISc Funded by MHRD Page 11 of 8

12 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Fo the ea wheel dive vehicle, F tmax is given by L h b g Ft max W Mg cos( a) Ft max F 1 L L h F t max Mg cos( a) La f hg / L 1 h / L g g (6) (7) Table 3: Coefficient of oad adhesion Road speed Coefficient of oad Coefficient of oad [km/h] adhesion fo dy adhesion fo wet oads oads Adhesion, Dynamic wheel adius and slip When the tactive effot of a vehicle exceeds the maximum tactive effot limit imposed by the adhesive capability between the tye and gound, the diven wheels will spin on the gound. The adhesive capability between the tye and the gound is the main limitation of the vehicle pefomance especially when the vehicle is diven on wet, icy, snow coveed o soft soil oads. The maximum tactive effot on the diven wheels, tansfeed fom the powe plant though the tansmission should not exceed the maximum values given by equation 5 and equation 7. Othewise, the diven wheels will spin on the gound, leading to vehicle instability. The slip between the tyes and the suface can be descibed as: dive slip S whee T R angula speed of the tye [ ad / s] R R V (8) Joint initiative of IITs and IISc Funded by MHRD Page 1 of 8

13 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The amic wheel adius ( ) is calculated fom the distance tavelled pe evolution of the wheel, olling without slip. The amic wheel adius is calculated fom a distance tavelled at 60km/h. The inceasing tye slip at highe speeds oughly offsets the incease in. The values of fo diffeent tye sizes ae given in table 4. Rolling Cicumfeence Tye Size [m] Passenge cas Table 4: Dynamic wheel adius of common tye sizes R Rolling Tye Cicumfeence [m] Size [m] R [m] Passenge cas 05/ R R / R R /60 R 155 R /70 R Light commecial vehicles 155/70 R R /70 R R /70 R R /75 R 175 R /75 R 185 R /70 R Tucks and buses 185/65 R 1 R /60 R 315/80 R /60 R /80 R Joint initiative of IITs and IISc Funded by MHRD Page 13 of 8

14 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles /70 R 15 15/75 R /65 R15 75/70 R /65 R15 305/70 R Refeences: [1] M. Ehsani, Moden Electic, Hybid Electic and Fuel Cell Vehicles: Fundamentals, Theoy and Design, CRC Pess, 005 Suggested Reading: [1] I. Husain, Electic and Hybid Electic Vehicles, CRC Pess, 003 [] C. C. Chan and K. T. Chau, Moden Electic Vehicle Technology, Oxfod Science Publication, 001 [3] G. Lechne and H. Naunheime, Automotive Tansmissions: Fundamentals, Selection, Design and Application, Spinge, 1999 Joint initiative of IITs and IISc Funded by MHRD Page 14 of 8

15 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Lectue 4: Vehicle Powe Plant and Tansmission Chaacteistics Vehicle Powe Plant and Tansmission Chaacteistics Intoduction The topics coveed in this chapte ae as follows: The dive tain configuation Vaious types of vehicle powe plants The need of geabox in a vehicle The mathematical model of vehicle pefomance Dive tain Configuation An automotive dive tain is shown in Figue 1. It consists of: a powe plant a clutch in a manual tansmission o a toque convete in automatic tansmission a gea box final dive diffeential shaft diven wheels The toque and otating speed fom the output shaft of the powe plant ae tansmitted to the diven wheels though the clutch o toque convete, geabox, final dive, diffeential and dive shaft. The clutch is used in manual tansmission to couple o decouple the geabox to the powe plant. The toque convete in an automatic tansmission is hydoamic device, functioning as the clutch in manual tansmission with a continuously vaiable gea atio. The geabox supplies a few gea atios fom its input shaft to its output shaft fo the powe plant toque-speed pofile to match the equiements of the load. The final dive is usually a pai of geas that supply a futhe speed eduction and distibute the toque to each wheel though the diffeential. Joint initiative of IITs and IISc Funded by MHRD Page 15 of 8

16 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Clutch Diven wheel Vehicle Powe Plant R Diffeential Dive Shaft Tansmission Diven wheel Figue 1: An automobile powe tain Vehicle powe plant Thee ae two limiting factos to the maximum tactive effot of the vehicle: Maximum tactive effot that the tie-gound contact can suppot Tactive effot that the maximum toque of the powe plant can poduce with the given diveline gea atios. The smalle of these factos will detemine the pefomance potential of the vehicle. Usually it is the second facto that limits the vehicles pefomance. The classification of vaious types of powe plants used in a vehicle is shown in Figue. Pime Move Intenal Combustion Engine (ICE) Hybid Dives Electic Motos Single Ignition Continuous Combustion AC Motos DC Motos Spak ignition engine Gas tubine Diesel engine Figue : Classification of vehicle powe plat Joint initiative of IITs and IISc Funded by MHRD Page 16 of 8

17 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles In selecting a suitable powe plant, the following factos ae consideed: Opeating pefomance Economy Envionment fiendliness Fo vehicula applications, the ideal pefomance chaacteistic of a powe plant is constant powe output ove the full speed ange. Consequently, the toque vaies hypebolically with espect to speed as shown in Figue 3. This ideal pefomance chaacteistic of the powe plant will ensue that the maximum powe is available at any vehicle speed, thus esulting in optimal vehicle pefomance. In pactice howeve, the toque is constained to be constant a low speeds. This is done so as not to be ove the maxima limited by the adhesion between the tye-gound contact aeas. The intenal combustion (IC) engines ae the most commonly used powe plants fo the land vehicles. In hybid and electic vehicle technology, the electic moto is used. Toque Powe Speed Figue 3: Ideal pefomance chaacteistics fo a vehicle powe plant Intenal combustion engine The intenal combustion engines used in the vehicles ae based on two pinciples: spak ignition (petol engines) pinciple Diesel pinciple. The key featues of the ICs based spak ignition pinciple ae: high powe/weight atio good pefomance low combustion noise. Joint initiative of IITs and IISc Funded by MHRD Page 17 of 8

18 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The disadvantages of ae the ICs based spak ignition pinciple ae: quality of fuel equied highe fuel consumption. The advantages of the diesel engines ae: low fuel consumption low maintenance equiement due to absence of ignition system low fuel quality equied The disadvantages of the diesel engine ae high level of paticulate emission geate weight and highe pice highe levels of noise The two typical chaacteistic cuves used to descibe the engine chaacteistic ae: toque vs. engine speed cuve at full load (100% acceleation pedal position) powe vs. engine speed cuve at full load (100% acceleation pedal position) These two chaacteistic cuves ae shown in Figue 4. In Figue 4 the following nomenclatue is used: P max PT ( ) Engine powe at maximum toque T max P Maximum engine powe = Nominal powe max Maximum engine toque T ( P ) T Engine at maximum powe = Nominal Toque max n( P ) n Engine speed at maximum powe = Nominal speed max max n n n nt ( ) Engine speed at maximum toque Vaious indices ae used to facilitate compaison between diffeent types of engine. The two most impotant indices ae: toque incease (toque elasticity) defined as T T whee T max n max max T engine toque at max imum powe, also known as nomin al toque n imum engine toque (1) Joint initiative of IITs and IISc Funded by MHRD Page 18 of 8

19 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles engine speed atio defined as nn v nt ( ) whee max max n engine speed at max imum powe, also known as nomin al speed n n( T ) engine speed at max imum toque () Engine Toque T Powe P max P(T max ) T max T(P max ) Toque Engine Powe P n min n(t max ) n(p max ) Engine Speed Figue 4: Chaacteistic cuves of an intenal combustion engine The highe value of the poduct bette engine powe at low and medium engine speeds. This in tun means less fequent gea changing. Joint initiative of IITs and IISc Funded by MHRD Page 19 of 8

20 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Electic Moto The electic motos have ae ideal fo vehicle application because of the toque speed chaacteistics of the motos (Figue 5). Electic motos ae capable of deliveing a high stating toque. It is vey impotant to select pope type of moto with a suitable ating. Fo example, it is not accuate to simply efe to a 10 h.p. moto o a 15 h.p. moto, because hosepowe vaies with volts and amps, and peak hosepowe is much highe than the continuous ating. Powe Toque Speed Figue 5: Toque vs. speed and powe vs. speed chaacteistics of electic moto It is also confusing to compae electic motos to IC engines, since electic motos ae designed fo a continuous ating unde load and IC engines ae ated at thei peak hosepowe unde loaded condition. The commonly used motos in EVs ae: AC motos Pemanent magnet (PM) motos Seies wound DC motos Shunt wound DC motos Joint initiative of IITs and IISc Funded by MHRD Page 0 of 8

21 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The DC seies motos wee used in a numbe of pototype Electic Vehicle (EVs) and pio to that mainly due to the ease of contol. Howeve, the size and maintenance equiements of DC motos ae making thei use obsolete. The ecent EVs and Hybid Electic Vehicles (HEVs) use AC, PM and Switched Reluctance motos. A classification of motos used in EVs is shown in Figue 6. Electic Motos DC Motos AC Motos Self excited Sepaately excited Induction Synchonous PM Switched eluctance Seies Shunt Field excited PM excited Wound oto Squiel cage oto PM bushless dc PM Synchonous PM hybid Figue 6: Classification of electic motos used in EVs The AC Induction Moto (IM) technology is vey matue and significant eseach and development activities have taken place in the aea of induction moto dives. The contol of IM is moe complex than DC motos, but the availability of fast digital pocessos, computational complexity can easily be managed. The competito to the induction moto is the pemanent magnet (PM) moto. The pemanent magnet motos have magnets on the oto, while the stato constuction is same as that of induction moto. The PM motos can be suface mounted type o the magnets can be inset within the oto. The PM motos can also be classified as sinusoidal type o tapezoidal type depending on the flux density distibution in the ai gap. Pemanent magnet motos with sinusoidal ai gap flux distibution ae called Pemanent Magnet synchonous Motos (PMSM) and the with tapezoidal ai gap flux distibution ae called Bushless DC (BLDC) motos. Joint initiative of IITs and IISc Funded by MHRD Page 1 of 8

22 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles The need fo geabox Intenal combustion engines today dive most of the automobiles. These intenal combustion engines wok eithe on the pinciple of spak ignition o diesel pinciple. In addition to the many advantages of the intenal combustion engine, such as high powe to weight atio and elatively compact enegy stoage, it has two fundamental disadvantages: i. Unlike the electic motos, the intenal combustion engine cannot poduce toque at zeo speed. ii. The intenal combustion engine poduces maximum powe at a cetain engine speed. iii. The efficiency of the engine, i.e. its fuel consumption, is vey much dependent on the opeating point in the engine s pefomance map. With a maximum available engine powe P max and a oad speed of v, the ideal taction hypebola F ideal and the effective taction hypebola F effec can be calculated as follows: P Fideal v P Fideal v whee tot max max tot efficiency of the divetain (1) Hence, if the full load engine powe P max wee available ove the whole speed ange, the taction hypebolas shown in Figue 7 would esult. Howeve, the P max is not available fo the entie speed ange. The actual taction pofile of the ICE (F engine ) is shown in Figue 7. Fom Figue 7 it is evident that the entie shaded aea cannot be used. Adhesion Limit Without dive tain efficiency:ideal taction hypebola F ideal Tactive efot F z With dive tain efficiency:ideal taction hypebola F effec Intenal combustion engine taction available F engine Speed Figue 7: Taction foce vs. speed map of an intenal combustion engine without geabox Joint initiative of IITs and IISc Funded by MHRD Page of 8

23 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles In ode to utilize the shaded aea, shown in Figue 7, additional output convete is equied. The output convete must convet the chaacteistics of the combustion engine in such a way that it appoximates as closely as possible to the ideal taction hypebola (Figue 8). Adhesion Limit Taction foce available in second gea Taction equied fo 0% gadient Tactive efot F z 1 st gea nd gea 3 d gea 4 th gea Speed Figue 8: Taction foce vs. speed map of an intenal combustion engine with geabox The popotion of the shaded aea, i.e. the popotion of impossible diving states, is significantly smalle when an output convete is used. Thus, the powe potential of the engine is bette utilized. The Figue 8 shows how inceasing the numbe of geas gives a bette appoximation of the effective taction hypebola. Dive tain tactive effot and vehicle speed Afte having dealt with the configuation of the divetain, this section deals with the tactive effot. The toque tansmitted fom the powe plant to the diven wheels (T w ) is given by: T i i T o w g o t p whee ig gea atio of the tansmission (1) i gea atio of the fianl dive efficiency of the diveline fom the powe plant to the diven wheels T t p toque output fom the powe plant [ Nm] The tactive effot on the diven wheels (Figue 9) is expessed as Tw Ft whee amic adius of the tye [ m] () Joint initiative of IITs and IISc Funded by MHRD Page 3 of 8

24 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Substituting value of T w fom equation 1 into equation gives F T i i p g o t t (3) The total mechanical efficiency of the tansmission between the engine output shaft and diven wheels is the poduct of the efficiencies of all the components of the dive tain. The otating speed of the diven wheel is given by N w p N ii whee N p g o [ pm] (4) ottational speed of the tansmission [ pm] The otatational speed N p of the tansmission is equal to the engine speed in the vehicle with a manual tansmission and the tubine speed of a toque convete in the vehicle with an automatic tansmission. The tanslation speed of the wheel (vehicle speed) is expessed as N w V [ m / s] (5) 30 By substituting the value of N w fom equation 4 into equation 5, the vehicle speed can be expessed as N p V [ m / s] (6) 30ii g o Vehicle pefomance The pefomance of a vehicle is detemined by the following factos: maximum cuising speed gadeability acceleation Joint initiative of IITs and IISc Funded by MHRD Page 4 of 8

25 Tactive effo [Nm] NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Maximum Cuising Speed The maximum speed of a vehicle is defined as the constant cuising speed that the vehicle can achieve with full powe plant load on a flat oad. The maximum speed of a vehicle is detemined by the equilibium between the tactive effot of the vehicle and the esistance and maximum speed of the powe plant and gea atios of the tansmission. This equilibium is: T i i g 0 p g 0 t Mgf cos( a) acd AfV whee i i t p gea atio of the tansmission gea atio of the final dive 1 efficiency of the diveline fom the powe plant to the diven wheels T toque output of the powe plant [ Nm] equation 30 shows that the vehicle eaches its maximum speed when the tactive effot, epesented by the left hand side tem, equals the esistance, epesented by the ight hand side. The intesection of the tactive effot cuve and the esistance cuve is the maximum speed of the vehicle, Figue 9. (30) Tactive effot Resistance on gade F +F w +F g Speed [km/h] Figue 9: Tactive effot of an electic moto poweed vehicle with a single speed tansmission and its esistance Joint initiative of IITs and IISc Funded by MHRD Page 5 of 8

26 NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Fo some vehicles, no intesection exists between the tactive effot cuve and the esistance cuve, because of a lage powe plant. In such a case the maximum speed of the vehicle is detemined by the maximum speed of the powe plant. This maximum speed is given by V max whee i g min i 0 n T p max p n 30ii pmax 0 g min min imum gea atio of the tansmission gea atio of the final dive max imum speed of the powe plant ( moto o engine)[ pm] toque output of the powe plant [ Nm] amic adius of the tye [ m] Gadeability Gadeability is defined as the gade angle that the vehicle can negotiate at a cetain constant speed. Fo heavy commecial vehicles the gadeability is usually defined as the maximum gade angle that the vehicle can ovecome in the whole speed ange. When the vehicle is diving on a oad with elatively small gade and constant speed, the tactive effot and esistance equilibium can be expessed as T i i 1 Mgf C A V Mgi (3) p 0 g t a D f Hence, Tpi0 igt / Mgf 1/ acd AfV i d f (33) Mg whee Tpi0 igt / 1/ acd AfV d (34) Mg The facto d is called the pefomance facto. When the vehicle dives on a oad with a lage gade, the gadeability of the vehicle can be calculated as (31) d f 1 d f sin( a) 1 f (35) Joint initiative of IITs and IISc Funded by MHRD Page 6 of 8

27 Acceleation (m/s ) NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Acceleation Pefomance The acceleation of a vehicle is defined by its acceleation time and distance coveed fom zeo speed to a cetain high speed on a level gound. The acceleation of the vehicle can be expessed as dv Ft Ff Fw Tpi0 igt / Mgf 1/ acdafv g a ( d f ) (36) dt M M whee is the otational inetia facto taking into account the equivalent mass incease due to the angula moments of the otating components. This mass facto can be witten as I 1 M I I w p i i I w 0 g p M total angula inetial moment of the wheels total angula inetial moment of the otating components associated with the powe plant To detemine the value of, it is necessay to detemine the values of the mass moments of inetia of all the otating pats. In case the mass moments of inetia ae not available then, the otational facto ( ) can be appoximated as: 1 ii g 0 The acceleation ate along with vehicle speed fo a petol engine poweed vehicle with a fou gea tansmission and an electic moto poweed vehicle with a single gea tansmission ae shown in Figue 10 and Figue 11 espectively. 5 (37) (38) 4 1 st gea 3 nd gea 3 d gea 1 4 th gea Speed [km/h] Figue 10: Acceleation ate of a petol engine poweed vehicle with fou geas Joint initiative of IITs and IISc Funded by MHRD Page 7 of 8

28 Acceleation (m/s ) NPTEL Electical Engineeing Intoduction to Hybid and Electic Vehicles Figue 11: Acceleation ate of an electic machine poweed vehicle with a single gea Fom equation 36, the acceleation time t a and distance S a fom a lowe speed V 1 to a highe speed V can be expessed as t a and S a M V dv (39) V 1 Tpigi0 t / Mgf 1/ acd AfV MV Speed [km/h] V dv (40) V 1 Tpigi0 t / Mgf 1/ acd AfV The powe plant toque T p in equation 39 and equation 40 is a function of speed of the powe plant. The speed of the powe plant is in tun a function of the vehicle speed and gea atio of the tansmission. Hence, analytical solution of equation 39 and equation 40 is not possible. Numeical methods ae usually used to solve these equations. Suggested Reading [1] I. Husain, Electic and Hybid Electic Vehicles, CRC Pess, 003 [] G. Lechne and H. Naunheime, Automotive Tansmissions: Fundamentals, Selection, Design and Application, Spinge, 1999 Joint initiative of IITs and IISc Funded by MHRD Page 8 of 8