Development of a total variance handling dynamics evaluation index for three-axle coach based on residue theorem

This paper develops the unique total variance evaluation index to analyze the effect of suspension on coach handling dynamics. The residue theorem was introduced to compute the integral of analytic function on the closed contour and general result was given. The three-axle coach model derivations were established to calculate the mathematical yaw rate transfer function considering the series of roll steer. According to the theorem of Plancherel, the energy of system total variance in the time domain is equal to the energy in the frequency domain. By residue theorem, the total variance evaluation index can be calculated as sum of the residues and the mathematical expression was developed to account for any arbitrary three-axle vehicle. The total variance index considers vehicle inertia parameters, tire cornering stiffness, and the complex three-axle series of suspension roll steer. It can be immediately available for computation without having to resort to Newton’s Second Law and summing forces and moments. This approach was validated with the simulation of 3DOF model. And the relationship between the total variance and the traveling speed with influence of suspension roll steer was analyzed. This work simplifies the analysis of studying comprehensive performance with effect of suspension on handling characteristics. The vehicle designer could use this approach to get optimization design parameters.