A calculation method of joint forces for a suspension considering nonlinear elasticity of bushings

The forces and/or moments applied to a ball joint and a bushing in one suspension are important loads for the design or fatigue tests of control arms, trailing bars and steering knuckles. Taking a double wishbone suspension as one studying example, a modeling and calculation method for obtaining the forces applied to the ball joints and the bushings, and moments applied to the bushings are proposed and developed in this article. In modeling of a suspension, a bushing is modeled with three translational stiffness and three torsional stiffness along and around three orthogonal axes. The force (moment) versus displacement (angle) along (around) one axis is nonlinear and is simplified as piecewise linear at five sections. The joint forces and moments for ball joints and bushings of a double wishbone suspension system are calculated with the proposed method in this article, and compared with that obtained using two conventional methods (method I and method II) when a vehicle runs in typical and extreme driving conditions. Conventional method I simplifies the connections between the control arm and body as rigid link. Conventional method II assumes that the control arm links with the body using bushings, in which the bushings are modeled as three linear stiffness along three orthogonal axes. The calculation and comparison demonstrate that the bushing nonlinear and rotational stiffness must be modeled for precise calculation of ball joint force and moments, especially when a vehicle runs in extreme driving conditions.