A Comparison of Different Multibody System Approaches in the Modeling of Flexible Twist Beam Axles

One of the challenging issues in the area of flexible multibody systems is the ability to properly account for the geometric nonlinear effects that are present in many applications. One common application where these effects play an important role is the dynamic modeling of twist beam axles in car suspensions. The purpose of this paper is to examine the accuracy of the results obtained using four common modeling methods used in such applications. The first method is based on a spline beam approach in which a long beam is represented using piecewise rigid bodies interconnected by beam force elements along a spline curve. The beam force elements use a simple linear beam theory in approximating the forces and torques along the beam central axis. The second approach uses the well known method of component mode synthesis that is based on the linear elastic theory. Using this method the deformation of the beam, which is modeled as one flexible body, is defined using its own vibration and static correction mode shapes. The equations of motion are, in this case, written in terms of the system’s generalized coordinates and modal participation factors. The linear elastic theory is used again in the third approach using a slightly different technique called the sub-structuring synthesis method. This method is based on dividing the flexible component into sub-structures, in which, the method of component mode synthesis is used to describe the deformation of each substructure. The fourth approach is based on a co-simulation technique that uses a Multibody System (MBS) solver and an external nonlinear Finite Element Analysis (FEA) solver. The flexibility of any body in the multibody system is, in this case, modeled in the external nonlinear FEA solver. The latter calculates the forces due to the nonlinear deformations of the flexible body in question and communicates that to the MBS solver at certain attachment points where the flexible body is attached to the rest of the multibody system. The displacements and velocities of these attachment points are calculated by the MBS solver and are communicated back to the nonlinear FEA solver to advance the simulation. The four approaches described are reviewed in this paper and a multibody system model of a car suspension system that includes a twist beam axle is presented. The model is examined four times, once using each approach. The numerical results obtained using the different methods are analyzed and compared.