Three-Dimensional Dynamic Simulation of Helical Compression Springs

The dynamic equations for general helical springs are solved and classified according to the number of energy terms used to formulate them. Solutions of several sets of dynamic equations, each with a different number of energy terms, are compared with experimental data. It is found that at higher compression speeds the numerical solution with a traditional, fixed boundary represents a physically impossible situation. A moving boundary technique is applied to improve the numerical solution and bring it into agreement with physical reality. Since a convergence proof for a numerical algorithm for nonlinear partial differential equations with a moving boundary is not available, a grid study has been performed to demonstrate convergence. The agreement between the solutions of different grid sizes and the experimental data is taken to show that the numerical algorithm was convergent. This three dimensional spring simulation model can be used in the simulation of high-speed mechanical machinery utilizing helical springs, and in particular, for design optimization of automotive valve springs.