43 Vehicle Mechanics from the intermolecular bonds between the rubber and road surface aggregates. In the microscopic level, the road surface is not smooth but has the peaks and valley of the surface aggregates as shown in Figure 2.20. The adhesion friction dominates in dry pavements, but the contribution decreases under wet conditions. The hysteresis is the deformation of the rubber when it is sliding over the road aggregates; the friction component comes from the energy loss due to hysteresis. Water does not affect hysteresis friction significantly; tires with improved wet traction are designed with high- hysteresis rubber in the tread.
The friction forces of adhesion and hysteresis depend heavily on the deformation of the tire at the tire–road interface due to the tire properties and the interaction of forces. This tire deformation results in the vehicle longitudinal slip, and the vehicle slip itself is fundamental to vehicle traction. The slip determines the traction force that the tire–road interface can support. Therefore, some slip is essential for vehicle traction, but too much slippage reduces the traction force limit. 2.7.4 Q uarTer c ar m odel The study of the laws of motion often starts from the consideration of a quarter car, i.e., one quarter of the vehicle. The quarter car model is shown in Figure 2.21.
The quarter car model allows analyz- ing separately the behavior of driving (powered) wheels and trailing (unpowered) wheels. Moreover, as the chassis and wheel dynamics are treated separately, this model is especially useful to study suspension dynamics if vertical components of forces are taken into account.
Using the same assumptions as in Section 2.3, the x -component of Newton’s second law of motion applied to the chassis is F F − − F F − = dv Rw AD gxT Rr m (2.26) dt where F Rw is the reaction force exchanged between the wheel and the chassis, m is the mass of a quarter of the chassis and F Rr is the reaction force between the front and the rear portions of the car, as shown in Figure 2.22. The components on the y -axis are omitted as suspension dynamics will not be analyzed here. FIGURE 2.21 Quarter car model. T TR F AD F gxT F Rr b F Rw F Rw F roll F gyT FIGURE 2.22 x -Axis force components of chassis and forces and torques of wheels in the quarter car model.