An efficient spring model based on a curved beam with non-smooth contact mechanics for valve train simulations

The valve train plays a huge role in the performance of internal combustion engines by controlling the combustion process and is therefore one starting point to increase the efficiency of combustion engines. Considering the dynamics, the valve spring is the component with the lowest natural frequency in the motor and therefore plays a crucial role in the overall dynamics of the valve train. The spring force must be high enough to close the valve reliably and prevent the valves from bouncing of the seating due to surge modes after they have closed. Conversely, the spring force affect the friction level in the engine and therefore fuel consumption. For this reason the spring forces should be kept as low as possible. Modelling valve springs it has to be taken into account, that the dynamic response of the spring is substantially different from the static response. The internal dynamics of the spring like the moving masses of the coils, contacts between the windings leading to a non-linear spring characteristic and coil clash must be considered. Consequently, for the design and optimization of modern valve trains sophisticated valve spring models considering the internal dynamics are needed. In this paper a new valve spring model for efficient multi-body simulations of vale trains is presented. The approach is to approximate the spring wire as a curved beam and derive the equations of motion yielding hyperbolic partial differential equations. These equations are discretized using finite element methods and integrated in a multi-body simulation approach. The interactions between the windings are included using the Augmented Lagrangian Method and non-smooth contact mechanics. Compared to a multi-mass-model approach the presented method allows reducing the degrees of freedom and the stiffness of the resulting differential equations. Therefore the computational effort can be minimized at slightly increased accuracy, yielding an appropriate model for multi-body simulation. Using a test rig, the model is validated in the frequency and time domain with experimental data. Furthermore, the presented new model is compared to existing models like multi-mass-models.