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UNIVERSITY OF WINDSOR MECH 8000-3 Automotive Hybrid Powertrain Course Project Due: Monday, Jul 25, 6:00 pm (in class) and online Use TA office hours to get help if needed. Max Grade: 25 marks The Toyota hybrid system (THS) in the 1st generation Prius has power split device (PSD) as shown in Figure 1. A typical configuration of such a PSD is as under: a. The ring gear is directly connected to the shaft of MG2 and to the driving wheels through a final reduction gear with an overall ratio of 4. b. The engine is connected to the carrier gear and MG1 is connected to the sun gear. C. The teeth numbers for the ring and the sun gears are 78 and 30 respectively d. The wheel radius is 30 cm e. The total resistive force (rolling resistance + aerodynamic drag) on a level road is given by F= 300+ 0.25 v² (v in m/s). f. The engine is operating at WOT and its torque-speed curve is given by T-4.45×10 N2 +0.0317N +55.24, 1000<N<6000 rpm 1) 2) g. The maximum torque output of MG2 is 400 Nm. h. The vehicle has a mass of 1500 kg i. The front axle-to-vehicle weight ratio is 0.6 j. The tyre road adhesion coefficient is 0.9 k. The vehicle is accelerating from standstill with an engine idle speed of 1000 rpm in 'engine-only' mode. Battery MG2 IC Engine MG1 R с S Epicyclic gear unit Final drive axle Figure 1: Hybrid Powertrain with a PSD Assuming no power loss, calculate the vehicle and powertrain characteristics for a time duration of 10 secs and provide plots (vs time in s) for the following: the variation of vehicle speed in m/s vehicle acceleration in m/s² Page 1 of 5
3) 4) 5) 6) Assumptions Although the vehicle is in engine-only priority mode, circulating power is present and both motor/generator are involved. The initial condition of zero vehicle speed results in speed of MG2 equal to zero. Therefore, at the start of calculations, MG2 cannot absorb and deliver the circulation power to the wheels. It can be assumed that the traction force is at its maximum at time zero. With no power loss considered, we can use PF v at every time step (since vehicle is in engine-only mode). Speed of MG2 is directly related to vehicle speed, whereas speed of MG1 must be determined from the circulating power (which is also equal to MG1 power) 1) 2) 3) 4) total traction force in N component torques in Nm (Tout. To, TMG2, TR) component speeds in rpm (Ne, NMG1, NMG2) component powers in kW (Pe, PMG1,PMG2) 5) Solution Requirements and Procedure 1) All calculations must be done in MS Excel 2) To solve the following dynamic equation for vehicle acceleration using numerical integration, dv dt -- (²-²)-1 (²- = you have to use the 4th order Runge-Kutta Method with an initial value for vehicle speed, Vo = y(0) = 1 x 10-8 m/s at t=0 and a time step, h = 0.0001 s For a first order ordinary differential equation defined by 30 (to + 7) = y*(10) + k77/2 to progress from a point at t-te. y(to), by one time step, h. follow these steps (repetitively). k₁= f(y(lo), to) = y* (to)+k₁= ky-1 (3x (to + 2/7), 40 + 47) ks = 1 (20 (to + 47), tu + 7 ) 3/3 (to+h) y(to)+k₂h ka=f( -F-cv² where c = 0.5pA, Ca (to+h), to +h). 3 (to+h) y(to) + dy(t) de = (3/(t), t) approximate derivative at t= to intermediate estimate of function at t= to +h/2 (using k) estimate of slope at t-te+h/2 another intermediate estimate of function at t-to+h/2 (using ką) another estimate of slope at t-to+h/2 an estimate of function at t=to+h (using ka) estimate of slope at t-to+hi k₁ +2k₂ +2ks+k₁ estimate of y(to+ 6 Page 2 of 5
STEP 1: Integrate dv/dt term to find the vehicle velocity for 10 sec. The calculation procedure should be as follows: Calculate the constant values of gear ratio (i), maximum tractive force, (Fr.max), and at t=0, the initial values for MG2 speed (NMG2), MG1 speed (NMG), engine speed (N.), engine torque (T.), engine power (P.), MG1 torque (TMG), ring torque (TR), circulating power (Pair) With Vo = y(0) = 1 x 108 m/s at t=0 and a time step, h = 0.0001 s, use the 4th order Runge-Kutta method to estimate the vehicle speed at each time step for a total of 10 s. 3) a. b. C. d. e f. g. At first time step (to+h), estimate i. MG2 speed (NMG2) ii. MG1 speed (NMGI) iii. engine speed (N.) iv. engine torque (T₂) engine power (P.). V. vi. vii. viii. ix. X. xi. xii. xiii. circulating power (Pair) tractive effort (F), first estimate 1. If F> Fix, then F = F,x output torque (Tu), first estimate ring torque (TR) MG1 torque (TMG) MG2 torque (TMG2) 1. If TMG2>TMG2.max, then a. TMG2 = TMG2.MAX b. Recalculate final output torque (Tout) c. Recalculate final tractive effort (F) total resistance force (FR) acceleration (dv/dt) Use these values to find the value of vehicle velocity at current time step, (to+h) using 4th order RK method Repeat the procedure at all subsequent time steps using the calculated vehicle velocity from previous step to estimate the values for next step Repeat this till t= 10 sec. You will have 100,000 values (step size of 0.0001 s) STEP 2: Down sample the vehicle velocity vs time data. i. Select every 50th point from the time and velocity columns to get a down- sampled velocity profile with a time step of 0.005 s Page 3 of 5
h. i. j. ii. You will have 2000 velocity values for t= 0 to t=10 sec STEP 3: Reconstruct all information with the final down-sampled velocity vs time dataset. At each time step, calculate i. ii. iii. iv. V. vi. vii. viii. ix. X. xi. xii. xiii. xiv. XV. MG2 speed (NMG2) MG1 speed (NMGI) engine speed (N₂) engine torque (T.) ring torque (TR) MG1 torque (TMG) engine power (P.) tractive effort (F), first estimate 1. If FF, then F= F output torque (T), first estimate MG2 torque (TMG2) 1. If TMG2>TMG2.max, then a. TG2 = TMG2,x b. Recalculate output torque (Tout) c. Recalculate final tractive effort (F₁) circulating power (P) total resistive force (FR) acceleration (dv/dt) MG1 power (PMGI) MG2 power (PMG2) Repeat the procedure at all subsequent time steps using the calculated values from previous step to estimate the values for next step Repeat this till t = 10 sec. You will have 2000 values with a time step of 0.005 s. Page 4 of 5
Requirements for Project Submission 1) Project report should have a standard cover page with group # and names/student ID of all group members 2) Each figure should be on a separate page (Landscape) with 1" margins 3) Create figures in separate charts in Excel. 4) Font size for all figures should be Arial, 18 point 5) All figures should have axes titles with units. 6) STEPS 1 & 2 should be completed in a separate Excel file (22S MECH80003_PrjGp#_Steps1_2.xlsx) and the file provided with first 20 rows of the calculations. 7) STEP 3 should be completed in another Excel file (22S MECH80003_PrjGp#_Step3.xlsx) and the file provided with first 20 rows of the calculations. 8) Create a pdf file of the requirements and name the file as 22S MECH80003_PrjGp#_Report.pdf 9) The 3 files should be zipped together as "22S_MECH80003_PrjGp#.zip" and the single zip file should be uploaded through Blackboard no later than pm on July 25, 2022. 10) Print the file (22S MECH80003_PrjGp#_Report.pdf) and submit the printed project report in class on July 25, 2022. 11) 1 submission per group. Page 5 of 5