64 Electric and Hybrid Vehicles Traction Force, F TR F max1 Lower GR Higher GR Constant Torque Constant Power F max2 v max2 v max1 v rm2 v rm1 Vehicle Speed, v FIGURE 3.13 Electric motor torque–speed characteristics in terms of traction force and vehicle speed for two gear ratios. 1,000 rev/m for lightweight passenger vehicles. The transmission gear achieves this speed reduction in the range of ~ 10–15:1 typically in two stages of 3–4:1 of speed reduction. The gear sizing depends on whether the low- or the high-speed performance of the EV is more important based on the power rating determined for the EV.
The tractive force versus speed characteristics of the propulsion system can be widely different for two gear ratios as shown in Figure 3.13. Note that the rated speeds shown are for the drivetrain unit comprising of the electric motor and transmission system, and that the electric motor rated speed is different from these values. The electric motor speed can first be converted into drivetrain unit speed or vehicle wheel speed using the gear ratio as shown earlier. The motor rated speed at the wheel ω rm,wh in rad/s can be converted to linear vehicle speed using v r rm = ⋅ ω rm , wh wh , where r wh is the radius of the wheel.
The symbol v rm is referred to here as the equivalent electric motor linear speed after accounting for the transmission gear and the wheel radius. A higher wheel speed or vehicle speed can be attained with a smaller gear ratio, but the peak traction force that the drive- train can deliver will be smaller. The smaller traction force will limit the initial acceleration and maximum gradability capabilities of the vehicle. On the other hand, if a high gear ratio is used in the transmission for the same electric motor, the peak traction force available at the wheels will be higher, but the maximum vehicle speed v max will be limited.
Therefore, we can conclude that the gear ratio depends on the motor rated speed, vehicle rated speed, vehicle maximum speed, wheel radius and maximum gradability. It must be observed that a higher gear ratio entails a larger gear size. Therefore, the gear ratio and the electric motor rated speed must be selected simultaneously to optimize the overall size and performance requirements. In the following, the design of the electric motor will be discussed in view of the specified requirements of the initial acceleration, the rated velocity on a given slope, the maximum steady- state velocity and the maximum gradability. In the process, the following parameters will be used:
rated motor power P m , rated motor speed ω rm , rated wheel speed ω fwh , rated vehicle speed v f , vehicle total mass m , vehicle frontal area A F , rolling resistance coefficients C 0 and C 1 , and aerodynamic drag coefficient C D . The design process starts with a set of known parameters and some educated guess, and ends with the final design values that meet the requirements after several iterations. 3.5.1.1 Initial Acceleration The initial acceleration is specified as 0 to v f in t f s. v f is the vehicle rated speed obtained from v r f f = ⋅ ω wh wh .
The design problem is to solve for F TR starting with a set of parameters including vehicle mass, rolling resistance, aerodynamic drag coefficient, percent grade, wheel radius, etc., some of which are known, while others have to be assumed. The acceleration of the vehicle in terms of these variables is given by Equation 2.32, repeated here for convenience