The Toyota Prius and the Ford Escape use similar powertrain transmissions, as shown in Figure 4.3 as well as in Figure 1.23. It has an engine, two electric machines, and a planetary gear train in the transmission. The engine is connected to the car
rier, electric motor MG2 is connected to the ring gear as well as the final drive, and the generator MG1 is connected to the sun gear. Hence, the speed and torque r elationships are
e s
r s g r
r s r
r e r
r s
g s e s
r s
shaft m
N
N N
N
N N
T T N
N N
T T T N
N N
T T T ir *1
(4.15)
where ωe, ωm, and ωg are the speeds of the engine, the motor and the generator, respectively, ωr is the ring gear speed, m r; s g; i1 = N2/N1 is the gear final drive ratio, and N1 and N2 are the gear teeth number of the final drive.
Since there is no clutch, the planetary gear is always running whenever the vehicle is moving. It can be seen from the above equation and the diagram of the powertrain that the speed of the motor MG2 is directly proportional to the linear speed of the vehicle through the radius of the front tires and the final drive ratio. The ring gear speed and the motor speed are identical.
OUTPUT MG1 MG2
Engine Battery
Figure 4.3 Toyota Prius transmission.
Advanced HEV Architectures and Dynamics of HEV Powertrain 77
There are four different operating modes:
● Mode 0: Launch and backup – the motor is powered from the battery; the vehicle is driven by the motor only:
T T
T i T
e g
shaft m
0 0
1
(4.16)
● Mode 1: Cruising, or e‐CVT mode 1:
T N
N N T
r r
r s e (4.17)
T N
N N T
g s
r s e (4.18)
Tout i T T1 r m (4.19)
PB 0; Pm m mT Pg g sT (4.20)
ICE
Power split Power split G
Battery
Final drive EM
ICE
G
Battery
Final drive EM Power split
Hybrid Electric Vehicles 78
● Mode 2: Sudden acceleration, e‐CVT mode 2:
T N
N N T
r r
r s e (4.21)
T N
N N T
g s
r s e (4.22)
Tout i T T1 r m ; Pm m mT P Pg B (4.23)
● Mode 3: Regenerative braking – MG2 is operating as a generator to produce electricity to charge the battery and at the same time to provide braking torque to the final drive.
This operation is the reverse of launch and backup operation.
During normal operation (e‐CVT or acceleration mode), the speed of the engine is con
trolled by the torque on the generator. Basically, the generator power is adjusted so that the engine turns at the desired speed. Hence, by adjusting the generator speed, the engine can operate at a relatively constant speed while the vehicle is driven at different speeds.
In the Prius, the engine is limited from 0 to 4000 rpm. The motor is limited from a small negative rpm for reverse and up to 6000 rpm (~103 mph or 165 km/h). The genera
tor is limited to ±5500 rpm. The ring gear and sun gear have 78 and 30 teeth respectively.
The four planetary gears each have 23 teeth. The final drive ratio is 3.93 and the wheel radius is 0.287 m. Hence, ωe = 0.7222ωm + 0.2778ωg.
The control strategy is as follows. For a given vehicle speed, and a desired output power determined by the drive cycle, or driver inputs, the desired operating point of the engine can be determined based on the maximum efficiency curve of the engine. From the vehicle speed and engine speed, the desired generator speed can then be calculated.
The generator speed is regulated through the inverter by controlling the output power of the generator (either as generator or motor). Motor torque is determined by looking at the difference between the total vehicle torque demand and the engine torque that is delivered to the ring gear. The battery provides power to the motors along with the electricity generated by the engine.
Example 4.1 Consider a planetary gear train based transmission with an engine ( carrier) providing 100 kW at 2000 rpm optimum operating point. The ring gear has 72 teeth and the sun gear has 30 teeth. The final drive ratio is 3.7865, and the wheel
ICE
G
Battery
Final drive EM Power split
Advanced HEV Architectures and Dynamics of HEV Powertrain 79
radius is 0.283 m. (1) For a vehicle speed of 45 mph or 20.6 m/s, the power demand under heavy acceleration at this speed is 120 kW. Find the speed and power for each compo
nent, assuming no losses. (2) For a vehicle speed of 70 mph, or 32.7 m/s, when cruising, the power demand is 70 kW. Calculate the speed and power of each component.
Solution
e r
r s r s
r s s r s
N
N N
N
N N 0 706. 0 294.
i) At 45 mph, the ring gear (same as motor speed) is calculated from the above to be 2632 rpm. Therefore, the sun gear (generator) speed needs to be 482 rpm in order to operate the engine at 2000 rpm:
Tc(engine) Pengine/ engine carrier( ) 477Nm
T N
N N T
r r
r s c
(ring gear) 0 706 477 337. Nm
T N
N N T
s s
r s c
(generator) 0 294 477 140. Nm Pc(engine) 100kW
Pr(ring gear) Tr r 337 2 2632 60 92 9/ . kW Ps(generator) Ts s 140 2 482 60 7 1/ . kW Pc(engine) P Pr s
Pvehicle 120 kW
Pm(motor) Pvehicle Pr 27 1. kW Pbat Pm Ps 20 kW
ii) At 70 mph, the ring gear (same as motor speed) is calculated from the above to be 4080 rpm. Therefore, the sun gear (generator) speed needs to be −2995 rpm in order to operate the engine at 2000 rpm:
Tc(engine) Pengine/ engine carrier( ) 477Nm
T N
N N T
r r
r s c
(ring gear) 0 706 477 337. Nm
T N
N N T
s s
r s c
(generator) 0 294 477 140. Nm Pc(engine) 100kW
Pr(ring gear) Tr r 337 2 4080 60 144/ kW
Hybrid Electric Vehicles 80
Ps(generator) Ts s 140 2 ( 2995 60)/ 44kW Pvehicle 70 kW
Pm(motor) Pvehicle Pr 74kW Pbat Pm Ps 30 kW