28 Electric and Hybrid Vehicles FIGURE 2.7 Forces acting on a vehicle. vehicle tractive force and the opposing forces are all in the x T - direction, and hence, the vector sign ‘-’ will not be used in the symbols for simplicity. The propulsion unit of the vehicle exerts the tractive force F TR to propel the vehicle forward at a desired velocity. The tractive force must overcome the opposing forces, which are summed together and labeled as the road load force F RL . The road load force consists of the gravitational force, rolling resistance of the tires and the aerodynamic drag force.
The road load force is F F RL = + gxT r F F oll A + D (2.1) where x T is the tangential direction along the roadway. The forces acting on the vehicle are shown in Figure 2.7. The gravitational force depends on the slope of the roadway. The force is positive when climb- ing a grade and is negative when descending a downslope roadway. The gravitational force to be overcome by the vehicle moving forward is F m gxT = g sin β (2.2) where m is the total mass of the vehicle, g is the gravitational acceleration constant and b is the grade angle with respect to the horizon. The rolling resistance is produced by the flattening of the tire at the contact surface with the roadway.
In a perfectly round tire, the normal force to the road balances the distributed weight borne by the wheel at the point of contact along the vertical line beneath the axle. When the tire flattens, the instantaneous center of rotation at the wheel moves forward from beneath the axle towards the direction of motion of the vehicle as shown in Figure 2.8. The weight on the wheel and the road normal force are misaligned due to the flattening of the tire and form a couple that exerts a retarding torque on the wheel. The rolling resistance force F roll is the force due to the couple, which opposes the motion of the wheel.
The force F roll is tangential to the roadway and always assists in braking or retarding the motion of the vehicle. The tractive force F TR must overcome this force F roll along with the gravitational force and the aerodynamic drag force. The rolling resistance can be minimized by keeping the tires as much inflated as possible. The ratio of the retarding force due to rolling Instantaneous center of rotation mg F roll mg FIGURE 2.8 Rolling resistance force of wheels. yT Froad FTR xT FAD Froll Roa β FgxT FgyT mg xT