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

Abstract

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.

Analysis and optimization of the vehicle handling stability with considering suspension kinematics and compliance characteristics

“…Initially, the rotation of the joint around its axis is not considered. Since the unit matrix e k * of any position of the mechanism can be calculated by formula (13), the rotation amount of e k * can be determined by the outer product as:…”

“…In order to analysis the force and moment of suspension's ball joint and bushing, firstly, the position transformation of each connection point of the double wishbone suspension is analyzed. 13 The double wishbone suspension is composed of upper control arm, lower control arm, wheel knuckle, springs, shock absorbers and tie rods. The four bushes A 1 and A 2 , A 3 and A 4 in Figure 10 connect the upper and lower control arms to the vehicle body respectively.…”

Sliding mode control of double-wishbone active suspension systems based on equivalent 2-degree-of-freedom model

“…Their stiffness characteristics have considerable contribution to the automotive riding comfort and handling performances. 29 To better understand this issue, the effects of bushings and top mount on the identified parameters are analyzed in this part.…”

Topology Optimization and Performance Calculation for Control Arms of a Suspension

“…Space of the CA. Forces at the outer ball joint of the CA for 16 typical load cases can be tested or calculated using the methods proposed by the author of this paper [11]. Table 3 shows the 16 typical load cases and the calculated forces at the outer ball joint of the CA, where is the gravity acceleration.…”