70 Electric and Hybrid Vehicles engine, and to maintain charge sustaining operation at rated cruising velocity with the IC engine only. The electric motor, with its higher peak power capabilities, will be more heavily used during initial acceleration. The battery will be sized for peak power-handling only and not for continuous electric-only mode of operation. The IC engine and electric motor will be operated in the series mode for urban driving conditions. The electric generator will be sized to generate sufficient power with continuous operation during urban driving. 3.5.3.1 Total Power Required:
Initial Acceleration Power required during acceleration is usually sufficient to meet the maximum velocity and towing requirements. Therefore, the acceleration power which comes from the combined efforts of elec- tric drive motor and IC engine is calculated first, but later it has to be verified that the other power requirements are met by the two drive components. The initial acceleration requirements are met by operating the IC engine and electric motor at their peak torque capabilities until the power limit of the two is reached.
Therefore, the drivetrain can be assumed to be opearting with constant torque (i.e., constant force F TR ) acceleration initially, and then with constant power acceleration. In order to estimate the contant force required initially and the peak power requirement, three velocity profiles are considered and analyzed. These velocity profiles are with constant force F TR acceleration, unifrom acceleration and a third one termed smooth acceleration.
The velocity profile with constant force F TR acceleration is given by K v t ( ) = 1 tanh ( ) K K 1 2 t (3.4) K 2 where F K 1 0 = − TR gC − > mg sin 0 β m ρ K 2 1 = + C A D F gC > 0 2 m The velocity profile for constant acceleration is v t ( ) = at (3.5) where a is the constant acceleration. For 0–60 mph in 9 s, the constant acceleration is a = 2.98 m/s 2 The velocity profile for smooth acceleration is [8] t x v t ( ) = v f (3.6) t f The range of the exponent x is between 0.47 and 0.53 with lower values used for slow accelerating vehicles and higher values used for fast accelerating vehicles. We will take x = 0 . 5 for our initial analysis.
The 0–60 mph velocity profiles for the three types of acceleration are shown in Figure 3.16. A force of F TR = 6,000 N has been assumed for the constant force acceleration. The velocity profile