The effect of nonlinear suspension kinematics on the simulated pitching and rolling dynamic behavior of cars

This paper compares the behavior of two modeling methods for independent suspensions. Both versions are based on the CarSim™ vehicle model, with equations created by the AutoSim™ symbolic multibody code generator. A fully nonlinear model uses the complete kinematical and dynamical multibody equations for the wheel spindle as it moves through the range of the suspension travel. Tables that specify longitudinal movement, lateral movement, steer, inclination, and dive define the 3D vertical motions of the spindle. In the other method, the spindle follows a straight line angled to match the full 3D motion for small displacements. This approach has historically been taken for math models created by hand, to help control the equation complexity. Those motions are combined with nonlinear algebraic corrections for inclination and steer, to obtain proper inputs for the tire model. The fully nonlinear model requires about 20% more overall computation time relative to the simpler “straight-line” model. On a 1.8 GHz PC, the simpler model runs about ten times faster than real-time, and the nonlinear model runs about eight times faster than real time. The models agree closely for moderate levels of braking, acceleration (throttle), and cornering. When the trajectory of the vertical movement of the wheel spindle curves significantly, as it does for most automobiles, the nonlinear model gives better predictions of roll and pitch.