An analytical formula of driver RMS acceleration response for quarter-car considering cushion effects

In this paper, a 3-DOF (degree-of-freedom) model of quarter-car coupled with driver and cushion is used to derive an analytical formula, which can describe the driver RMS (root-mean-square) acceleration response with cars under random excitation generated by road irregularities. The study starts with the 3-DOF model. Based on the vehicle random vibration theory, using the residue theorem, the analytical formula of driver RMS acceleration considering cushion effects is obtained. Then, the driver RMS acceleration values calculated from the measured data and from the analytical formulae of the 3-DOF and the classical 2-DOF model are compared. The results show the analytical formula for the 3-DOF model provides a more reasonable approximation of the real response of the test car. Having obtained the analytical formula, the effects of vehicle parameters on driver RMS acceleration are studied. Finally, to provide critical foundations for the selection of the cushion damping, the optimal damping ratio of driver-cushion system is deciphered from the analytical formula. To uncover how each dynamic parameter effects the optimal damping ratio, the analysis of influencing factors is performed and some important conclusions are obtained. The derived analytical formula can be also conveniently used either during preliminary design or for other special purposes.