Investigation of Vertical and Pitch Road Vehicle Dynamic Responses to Improve the Critical Speed Using Controllable Semi-Active PID Suspensions

Abstract

Vertical and pitch dynamic responses are investigated and examined to improve the critical speed of a road vehicle. The objective of this paper is to improve the road vehicle critical speed by using new design of semi-active PID suspension equipped with conical spring stiffness installed at front and rear wheels which has variable magnitudes of spring stiffness that will depress the oscillations effectively. A numerical full road vehicle simulation model comprising mathematical differential equations of operation with (9) degrees of freedom and passive PID suspensions with helical shaped spring is constructed. Mathematical differential equations of operation contain all rectilinear and angular displacements of a road vehicle such as vertical displacements of road vehicle carbody with the front and rear wheels. Also roll, pitch, yaw, and lateral dynamic responses are included in the mathematical differential equations while a special technique is used to transform these second order differential equations into first order to reduce the computational time. Computer-aided simulation model with Matlab Program is adopted at different speeds and different sudden step steer angles. In order to satisfy the reliability of the adopted road vehicle simulation model, an experimental work using Hyundai-Tucson 2009 is carried out to examine the lateral and vertical dynamic responses of the road vehicle carbody. In the present simulation model the critical speed of a road vehicle is improved by 13.4% using semi-active PID suspension which is equipped with conical shaped spring at front and rear wheels.