Development of an Empirical Spring Aid Model for Automotive Applications

Spring aids are used to provide additional stiffness at the end of bump travel, preventing metal to metal contact. Commonly they are represented by nonlinear stiffness depending on displacement; however the main drawback of this approach is that it does not show any hysteretic behavior, hence they do not produce realistic force predictions differentiating between loading and unloading and energy absorbed is not calculated. Although introducing damping as a function of velocity generates some hysteresis, it does not generate realistic results for quasi-static and dynamic events; and measured data proves that velocity does not have a significant influence in the width of the loop. An empiric model can be build combining nonlinear stiffness and viscous damping, as a function of velocity, and also adding an additional term accounting for structural damping. This structural damping, implemented similar to a friction element, is nonlinear depending on displacement and velocity; and it is capable of representing realistically the hysteresis present in the component behavior. The three terms work in parallel, stiffness and structural damping capture the amplitude dependency of the spring aid; whereas viscous damping represents the strain rate dependency. Although measured data and previous studies suggest the strain rate dependency is not critical, viscous damping provides a fine tuning element generating more realistic results for the range of velocities tested. The parameters used are obtained from measured Force-Displacement data, considering quasi-static and different velocity conditions. The process starts using the quasi-static curve, deriving the stiffness term from the centerline, then structural damping is obtained based on the hysteresis loop width; and finally viscous damping is calculated at different velocities to capture the strain rate dependency.