GM Volt - Vehicle, Motor, Road, and Enironmental Parameters: Enable Generator Only Mode Gear Ratio, Inefficiencies: GR 8 η Max Motor Power: Power max 111 kw.9 axle.9 Battery Energy: Energy P Generator 53 kw Power max P Generator.9 bat 16 kw hr 7. Max Motor Torque: Tm 73 ft lbf Tm = 37.138 N m Tire Radius*: r tire in 195/55R1 Tm Max Force, Fm Fm GR η Fm = 1.773 1 3 lbf RPM n axle Power max = 133.968 hp r tire ω max 1 RPM Power max ω CP n Constant Power ω CP RPM RPM CP.577 1 3 CP = Motor Torque, ω: Tm π Power max Constant Power k 1 3 CP CP = 8.337 mph Tm = 37.138 N m ehicle elocity, Fm CP : Aerage Wind Velocity: Shape Correction Factor: Drag Coeff: Cross Wind Drag Coff: Air Density: Road Rolling Resist: Rotational Inertia Coeff: k m 1.8 Passenger Weight: Gross Weight: M M gross 3.31 1 3 gross M curb + Passengers = lb Motor Breaking Force in g: MotorBrake g GR Tm ( k m M gross r tire g M curb WeightToHP Vehicle Dynacs Equations: Power max Road Resistance, Ft: Aerodynac Loss, Fa: Opposing Force, Fo: Tractie Force: Third Law of Motion: (a is acceleration End 3 GM VOLT PERFORMANCE SIMULATION http://www.leapcad.com/transportation/gm_volt_simulation.mcd Vw mph Power max = 99.9 kw SCF.85 Cd.8 Cd cw.14 gm ρ 1.93 1.3 gm liter liter RR road. Ft( M gross g d t ( t F( ( t Fo( ( t Gien = d k m M gross acc g ( t a( elocity( t sec P m ω Rolling Resistance Per Tire: RR tire.7 Tire Hysteresis, Th: Th sec θ (radians: (Aerage % road grade θ atan( Curb Weight: M curb Th sin( θ + ( RR tire + RR road cos( θ + sin( θ ( x Fa(.5 ρ Af ( + Vw Cd + Cd cw.5 + V cw Fo( Fa( + Ft( Power max F( if CP, Fm, η axle T F( Fo( ω ω a( ( T ω ( ω k Effectie Cross Wind V: Frontal Area*: Frontal Area Corrected: ( = ( T ω k π ω RPM kw 314 lb Passengers M batt 3lb MotorBrake g =.539 WeightToHP = elocity 17 lb 3.438 lb hp T( F( r tire GR π r tire GR RPM k m M gross P( F( Applying maximum motor torque, find the elocity starting from initial elocity = mph. V cw Afg.16 m Af Fo( 6 mph = 83.544 lbf mph Afg SCF Af = 1.836 m P( 6 mph = 13.51 hp Odesole( t, End elocity( 3 = 11.8 x mph s m Time sec time( root( elocity( Time, Time Time to Accelerate from 4 to 6 mph: time( 6 mph = 8.167 s time( 6 mph time( 4 mph = 3.818 s
Dyno Motor Torque, Power (kw G M V O L T P E F O R M A N C E S I M U L A T I O N C U R V E S: Dyno Motor Force T ω ( ω lbf ft P m ( ω NS o ( 5 mph NumStarts, P o, S Dyno Torque and Power s. RPM Cures 3 5 15 1 5 16 F( mph 1 lbf 8 4 Time ssr 3n Power dissloss (, P o NSo and NS are iteratie conerging estimates of NumStarts ( floor ( Cruise_Range, P o, S Constant Power 1 3 4 5 6 7 8 9 1 11 1 ω Dyno Motor Speed (RPM * 1 Dyno Force Cure 4 6 8 1 1 Dyno elocity (mph Find the Single Charge (@SOC = 5% Cruise Range for a gien Velocity Driing Pattern/Profile: Gien we cruise at constant speed and Time for start, stop, and regen breaking, Time ssr = eery 15 nutes. Drie Train Power Efficiency - Battery Loss to Force Commanded Vehicle Velocity: State of Charge for generator is SOC gen. SOC gen is 5% for recharge. 3V HV battery idle power is Po. 1V battery gies Accessory Power. The Traction Inerter x motor Efficiency - TInE, HV Power Electronics at Idle Efficiency - IPEE, and Gear Power Efficiency - GPE are 9%, 95%, and 97%, respectiely. Brake Regen efficiency of kinetic energy is 69% @ deacceleration =.315g. Then the number of starts per hour as a function of elocity, NS, NumStarts(, Po, is TInE.9 Fo( + ( NS, P o, S IPEE.95 P o watt IPEE Vehicle elocity (mph Dyno Motor Power (hp Energy bat ( 1 S NS o ( ( Energy bat ( 1 S NS, P o, S elocity( t mph acc g ( t 1 g P( mph hp ( Energy bat ( 1 S NumStarts, P o, S Energy accel ( ( Time ssr Power dissloss, P o GPE.95 Regen.69 SOC gen.5 USABC Round Trip Battery Energy Efficiency RTEff.9 Energy accel ( Power max time( 8 6 4 18 16 14 1 1 8 6 4 Energy accel ( ( Power dissloss, P o \Velocity & Acceleration (gx1 Cure 1 4 6 8 1 1 14 16 18 Energy accel ( ( Time ssr Power dissloss, P o t time (sec Dyno Motor Power Cure 4 6 8 1 1 Dyno elocity (mph Regen M gross Regen M gross Regen M gross
Velocity Range,.. 8 Cruise Range (les ( Cruise_Range mph, 5, SOC gen ( Cruise_Range mph, 1, SOC gen 1 9 8 7 6 5 4 3 Single Charge Highway Cruise Range Estimate ( = 44.83 Cruise_Range 55 mph, 5, SOC gen Single Charge Cruise Mileage Range 1 3 4 5 6 7 8 elocity (mph Specsmanship: Twice as much range at 3 mph than 7 mph. Conclusion: I need a bigger or a better battery! Cruise Range as a Function of Traction Battery Idle Power, Po Cruise_Range( 15 mph, 5,.3 = 19.854 Cruise_Range( 55 mph, 5,.5 = 44.83 13 Single Charge Cruise Mileage Range Cruise Range (les Cruise_Range( mph, 5,.3 Cruise_Range( mph, 5,.4 Cruise_Range( mph, 5,.5 Cruise_Range( mph, 1,.3 Cruise_Range( mph, 1,.4 Cruise_Range( mph, 1,.5 1 11 1 9 8 7 6 5 4 3 5 1 15 5 3 35 4 45 5 55 6 65 7 75 8 elocity (mph
Note: The Volt generator's output is 54 kw. This allows it produce a net charge up to 8 mph cruise. i.. 5 Ft g, θ θ i. i Phill, θ Find the Power to Maintain Constant Velocity at Road Grades Power cruise, P o ( Power dissloss (, P o ( k watt n P n cruisen Power cruise mph, 1 n ( ( M gross g Th sin( atan( θ + ( RR tire + RR road cos( atan( θ + sin( atan( θ Ft ( ( g (, θ + Fa( P hilln i ( Phill mph, θ, n i Power (hp@ Grade,, 4, 6, 8, 1 (% Cruise Power Loss s. Road Grade, Speed 7 65 6 55 5 45 4 35 3 5 15 1 5 1 3 4 5 6 7 8 9 1 elocity (mph Cruising Power (kwatts Cruise Power@ 1W Acc, Cd.5 s.8 45 4 35 3 5 15 1 5 1 3 4 5 6 7 8 9 1 elocity (mph AER Gien Three Different Driing Schedules FP1 HY1 US6F READPRN ("http://www.leapcad.com/transportation/ftp1hz.txt" READPRN ("http://www.leapcad.com/transportation/hwy1hz.txt" READPRN ("http://www.leapcad.com/transportation/us6profile.txt" The US6 cycle represents an 8.1 le (1.8 km route with an aerage speed of 48.4 les/h (77.9 km/h, maximum speed 8.3 les/h (19. km/h, and a duration of 596 seconds. The Federal Test Procedure(FTP is composed of the UDDS followed by the first 55 seconds of the UDDS. It is often called the EPA75. FP1 is a 1 Hz Sampling. HY1 is the 1 Hz Highway schedule. t ft FTPF FTP FTPF 1 rows( FTP = 1.875 1 3 UDDS UDDSF 1 rows( UDDS = 1.37 1 3 time US6F US6 US6F 1 n 6.. 598 HWY HWYF 1 R hwy rows( HWY mean( FTP = 1. Read US6 and FTP Driing Profile Files http://www.epa.go/nfel/testing/dynamometer.htm FTPF READPRN ("http://www.leapcad.com/transportation/fedtestproc.txt" UDDSF HWYF READPRN ("http://www.leapcad.com/transportation/uddscol.txt" READPRN ("http://www.leapcad.com/transportation/hwycol.txt" FTP1V submatrix( FP1,, rows( FP1, 1, cols( FP1 HWY1V submatrix( HY1,, rows( HY1, 1, cols( HY1
Calculate All Electric Range, AER, for Driing Profile Velocity/Time File, P and Sampling Rate, Hz Regen Efficiency Cure s Decel (g: REff ( g ( 91.35 85 77.1 1 e 7.19 g 8.48 Gg mph sec g AER( P, Hz Ebat E diss old n 1 N rows( P while E diss < 8 n = n n n + 1 t P t mod( n, N (.5 ag + old mph Hz k m M gross ( old ag mph sec P accel if > old mph Hz P accel k m M gross ( old ag mph REff old sec ( sec Power dissloss ( mph, 1 + P accel E diss E diss + kw hr Hz old Ebat E n diss ( Hz Gg otherwise n R m = R ( P + P mod( m, N mod( m+ 1, N mph sec Hz r1.. rows( HY1 1 Calculated AER(Miles: EPA Federal Test Procedure and Highway Driing Profiles AER( FTP, 1 = 39.93 AER( HWY, 1 = 38.416 AER( US6, 1 = 5.648 EPA 85 Cycle MPG Fuel Economy Least Squares Fit Regression for AER 1 MPG city 1.1853.359 + AER( FTP, 1 MPG city = 9.889 1 MPG hwy.1376 + 1.3466 AER( HWY, 1 X 1 4 MPG epa.55 MPG city +.45 MPG hwy MPG epa = 8.79 r r.. rows( FTP Distance r max( Distance = 11.414 r = FTP r 1 6 6 rr rr.. rows( US6 Distance.rr max( Distance. = 8.8 rr = US6 rr 1 6 6
Plot EPA Driing Profiles WRITEPRN ("EFTP.PRN" AER( FTP, 1 4 WRITEPRN ("EUS6.PRN" AER( US6, 1 4 WRITEPRN ("EHWY.PRN" AER( HWY, 1 4 E FTP E US6 E HWY READPRN ("EFTP.PRN" READPRN ("EUS6.PRN" READPRN ("EHWY.PRN" ( X ( X ( X max E FTP = 39.1 max E US6 = 5.65 max E HWY = 38.45 Speed (mph, Dist (Mile/1, E (kw*4 US6 Distance. E US6 1 9 8 7 6 5 4 3 1 US6 Drie Cycle: Distance, E(Bat Drain 5 1 15 5 3 35 4 45 5 55 6 time Time (seconds Speed (mph, Dist (Mile/1, E (kw*4 FTP Drie Cycle: Distance 11 1 9 8 FTP 7 UDDS 6 Distance 5 4 3 1 1 3 4 5 6 7 8 9 1 11 1 13 14 15 16 17 18 19 t ft Time (seconds r.. rows( HWY r Distance r r = HWY r 1 6 6 time HWYF mean( HWY = 48.4 max( HWY = 59.9
Speed (mph, Dist (Mile/1, E (kw*4 HWY Distance E HWY 11 1 9 8 7 6 5 4 3 1 HWY Drie Cycle: Distance, E(Bat Drain 5 1 15 5 3 35 4 45 5 55 6 65 7 75 8 time Time (seconds
Compare Volt Sustaining (Dotted s. Generator Only (Solid Mode: Volt For Comparison to Prius See: http://www.leapcad.com/transportation/macro%model%performance%comparison%-%- Volt%EREV%s%Prius.pdf For Comparison to Corolla See (Page 5: http://www.leapcad.com/transportation/corolla_simulation.pdf Read Charge Depletion Mode Data READPRN ("VoltGenOnly_tVelwMAgTPmFP.prn" Store Variables n.. 3 time Volt Volt 5 T w ( lbf ft TW( ω T ω ( ω lbf ft Volt 1 P w Volt 6 VV( t Read Charge Sustaining Mode Data (Disabled Data Format in File: Time, Vel, Angular Speed, MPH, Accel(g, Torque(rpm, Power (rpm, Force(, P( Volt ω Volt F Volt 7 elocity( t mph READPRN ("VoltSus_tVelwMAgTPmFP.prn" mph Volt 3 P Volt 8 AG( t g Volt 4 acc g ( t 1 g P cruisev Volt 9 Plot Compare Sustaining (Dotted s. Generator Only (Solid Mode: Dyno Motor Torque, Power (kw Dyno Torque and Power s. RPM Cures 3 5 Constant Power 15 1 5 1 3 4 5 6 7 8 9 1 11 1 Dyno Motor Speed (RPM * 1 Vehicle elocity (mph Vehicle Velocity & Accel(gx1 Cure 1 8 6 4 4 6 8 1 1 14 16 18 time (sec Dyno Motor Force Dyno Road Force Cure 16 1 8 4 4 6 8 1 1 Dyno elocity (mph Dyno Motor Power (hp Dyno Motor Power Cure 18 16 14 1 1 8 6 4 4 6 8 1 1 Dyno elocity (mph