Clauberg, J. and Huber, R., "Using Non-Smooth Mechanics and Parallelization Techniques for the Efficient Simulation of Different Types of Valve Springs," SAE Technical Paper 2013-01-1119, 2013, doi:10.4271/2013-01-1119.
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. By comparing the contact forces and surging liability the influence of the winding shape (cylindrical and beehive) on the entire valve train dynamic is investigated.More and more detailed simulation models, e.g. the use of the proposed dynamic spring model instead of a static force law, lead to increasing complexity and computational times. Beside others, parallelization is one of the most promising ways to reduce computational time. In this paper, the ability of multi-core computers is used to reduce the simulation time by applying parallelization methods for the equations of motion, for the calculation of the contact kinematics between adjacent coils and for the integration schemes.