A Physical Analytical Model to Study the Elasto-Kinematic Behaviour of a MacPherson Suspension

This paper describes a physical analytical model able to characterize the elasto-kinematic behaviour of a MacPherson suspension for automotive applications. The presented model allows to determine the position and the orientation of the wheel upright as a function of the generalized three-dimensional loads applied to the center of the tire-road contact patch, and consequently to determine the variation of the characteristic suspension parameters of main interest: wheel base, track, camber and toe. All the steps carried out to build the model are described, starting from the kinematic analysis, ongoing with the static and finally with the elasto-kinematic ones, describing how compliance has been taken into account in equilibrium conditions. The kinematic and static analyses have been validated by comparing the results with the ones of a multibody model. In order to obtain the desired elasto-kinematic curves it is possible to act both on the geometry of the suspension, and on the stiffness of the bushings and of the arms, which cause compliance, modifying the positions of the various elements of the suspension and ultimately of the hub. By means of the proposed model it is possible to rapidly evaluate the effects of these variations. Numerical examples relative to a suspension for the front axle of a vehicle are presented.