Real-Time Capable Calculation of Reaction Forces of Multibody Systems Using Optimized Bushings on the Example of a Vehicle Wheel Suspension

This paper presents an object-oriented modeling method capable of simulating the dynamics including the reaction forces of multibody systems with kinematic loops in hard real-time, called RTOOM. The modeling method describes the system by explicit equations, which can be solved numerically stable with a standard explicit numerical integrator with fixed step size. By knowing the application and the desired accuracy, the model can be adapted to fit the problem. Algebraic loops are resolved with low-pass filters parameterized for the frequency range of the application. Bushings with optimized spring and damping constants are used to avoid iterative methods for solving kinematics loops. For the optimization, a high accurate, non-manipulated and non-real-time multibody model is used. The optimization targets are stability, computing time and accuracy. The double wishbone suspension of the Formula Student racing car A40-02 of the University of Duisburg-Essen is used as an example. It has been successfully proven that a simulation up to 30 Hz with a required step size of 1 ms can be achieved. The simulation results show a very good accuracy up to 15 Hz with a deviation of the force below 4% and the acceleration below 7%. If the parameterization of the bushings remains the same, the accuracy is still acceptable even at higher frequencies.