A transient non-linear finite eleme

A transient non-linear finite element (FE) model is developed in this paper to calculate the natural frequencies of a high-speed beehive spring and simulate its dynamic responses at different engine speeds, with consideration of material damping, internal vibration and coil collision. A 3D scanning technique is used to obtain an accurate geometry of the spring model for the simulation. To validate the FE model, a conventional analytical model with varying stiffness is also developed for the same spring. By comparing the results of both models with the experimental results of engine head tests, it is shown that the FE model can successfully simulate the dynamic responses of the spring under different speeds. Especially, the FE model can predict the erratic force spikes of the spring at high testing speeds, which cannot be predicted by the conventional analytical model. Based on the analysis, the dynamic deformation mechanisms of the high-speed beehive spring are summarised and discussed.