Automobile plane-motion model including roll motion: Second report (Taking into consideration phase difference of cornering forces between front and rear wheels)

Abstract

The roll motion of the vehicle has an effect on the yaw natural frequency. Because the yaw natural frequency formula considering this effect is the solution to a quartic equation, the expression of the formula is thought to be complex and incomprehensible. Accordingly, a seemingly comprehensible approximate formula was suggested in the former paper. In this approximation process, it was assumed that the cornering forces of the front and rear wheels are generated simultaneously. On the other hand, a later report have indicated that the yaw resonance when the vehicle drives at a certain speed has a cornering forces phase difference of 90 degrees between the front and rear wheels. Therefore this paper formulates the yaw natural frequency and yaw damping ratio assuming the phase difference to be 90 degrees. As results of that, qualitatively, the design variables that dominate the characteristic equation are appropriately included in the yaw natural frequency and yaw damping ratio formulas, and quantitatively, the approximation error is reduced. Consequently, these formulas are believed to be more appropriate than the previously proposed formulas. These formulas indicate that, when the load distribution ratio of the front wheels becomes larger, the yaw natural frequency decreases and the yaw damping ratio increases. In addition, this paper also indicates the scope of these approximate formulas quantitatively.