42 Electric and Hybrid Vehicles over the contact patch is shown to have generated the traction force. In addition, there is normal stress due the weight borne at the axle of wheel which works in the vertical y -direction. The verti- cal or normal pressure shifts forward due to the deformation of the tire at the tire–road interface. Consequently, the centroid of the normal road reaction force is shifted forward and is not aligned with the spin axis of the wheel. This results in the rolling resistance force F roll . Figure 2.18 also shows the normal stress distribution over the contact patch area of the rolling tire.
The normal stress distribution integrated over the contact patch area results in the normal road reaction force F gyT . The normal force F gyT plays a strong role in determining the traction force limit, which is addressed later in the section. 2.7.3 f orce T ransmission aT T ire –r oad i nTerface The tire–road interface can be thought of a gear mechanism responsible for the generation of the traction force. The conversion of rotary motion of the wheels to linear motion of the vehicle can be compared to the ball-screw arrangement shown in Figure 2.19, which is a gear mechanism used for force transmission along with conversion of rotary motion to linear motion.
Let us consider that power is being transmitted from the rotary gear to the linear gear with the latter held stationary. The rotary gear is driven along its spin axis by a rotary motor, which enables the rotary system of motor and gear to move along the linear gear train. In this system, when torque is applied by the rotary motor friction force is developed in the gear train that helps the rotary system move forward or backward. This type of friction force enables vehicle propulsion along the road surface except that a pneumatic tire and a paved surface is used for developing the friction force which has been labeled as traction force F TR .
Two mechanisms contribute to the friction coupling at the tire–road interface in a vehicle; these are adhesion and hysteresis [3]. Adhesion and hysteresis friction forces generated at the tire–road interface due to the vehicle propulsion torque are shown in Figure 2.20. Adhesion to the road results FIGURE 2.19 Ball-screw gear arrangement for converting rotary motion to linear motion. Tire Adhesion Distributed pressure T TR F gyT F TR Hysteresis Road aggregate and binder FIGURE 2.20 Forces at tire–road interface on a rolling tire.