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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.

In this paper, a spring model based on a curved beam is used for the simulation of cylindrical, conical and beehive valve springs. The internal dynamic are described by hyperbolic partial differential equations which are discretized by the finite element method. The contacts between adjacent windings are included using the Augmented Lagrangian method and non-smooth contact mechanics. For smooth contact modeling, spring and damper elements are used to minimize penetration of the bodies coming into contact. Rigid or non-smooth contact forces are subject to set-valued force laws describing the condition of non-penetration. Both contact models are compared. The derived spring models for all three types of winding shapes are validated in the frequency and time domain with experimental data. In the second part, a multi-body simulation model of an entire valve train including the derived spring model is presented.