For the EV drivetrain shown in Figure 9.8, Vt=50 V, Ra=0.7 ohm, k =1.3, and wg=7848N.

Gearbox gears are as follows: first GRi=2, second GR2=1, and rwh=wheel radius=7 in=0.178 m. Find the vehicle maximum % gradability for each gear.

FIGURE 9.7 Connection of a gear with the motor.
FIGURE 9.8 EV drivetrain for Example 9.1.


The torque-speed relationship is

FIGURE 9.9 Plots for Example 9.1. The relationship between FTR and Tout is

Ftr per rear wheel=torque per wheel/rwh=(1/2 Tout)/rwh Therefore,


In first gear, FTR=1043 N.


In second gear, FTR=521.7 N, and maximum grade=6.7%.

The steady state torque-speed characteristics for the separately excited DC motor connected to the gearbox for the first two gears are shown in Figure 9.9. The maximum percentage grades for the two gears are also shown in the figure.

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