Modal Analysis Approach on Vehicle Transient Behavior Considering Roll and Pitch Dynamics

Although the basis of vehicle dynamics is planar motion, accompanied roll and pitch motion also affect not only the planar motion but also the driver‘s subjective evaluation. Many studies indicate that the phase difference between roll and pitch during turn-in seemingly influences the driver‘s subjective evaluation. In a previous study conducted in 1971, R.S. Sharp performed modal analysis of the motorcycle's sprung mass rigid body motion, and classified the major oscillation mode as Capsize, Weave, and Wobble and the sensitivity analysis were conducted on the effect of speed and design specifications for each mode. These findings have become a fundamental theory in the design of motorcycle performance. On the other hand, in the vehicle dynamics analysis that consider roll and pitch, the characteristics have been understood through parameter studies and equivalent models, and the oscillatory and damping properties have been analyzed using characteristic roots. However, there have been very few studies that analyze vehicle behavior by decomposing the sprung mass motion into vibration modes. Therefore, fundamental insights into the vibration modes of vehicle dynamics - including roll and pitch - are still needed for theoretical performance design of transient behaviour of the sprung mass, especially in the area of four-wheel vehicles. In this report, the complex eigenvalue problem associated with a four-degree-of-freedom bicycle model that incorporates roll and pitch dynamics were formulated and analytically solved, consequently extracting the vibration modes that govern the vehicle’s transient behavior. Based on the knowledge that behaviour of vehicle sprung mass is a superposition of identified modes, the underlying mechanism of sprung mass behavior which has been remained insufficiently understood are clarified. (230 words)