Keywords: valve spring, valve train simulation, multibody dynamics, nonsmooth dynamics, contact modelling, numerical integration.

In the first part of this paper an overview of smooth and non-smooth multibody dynamics is given. Therefore, the equations of motion for non-smooth uni- and bilateral contraint systems with impacts are introduced [1,2]. Also the constitutive laws governed by set-valued force laws and special integration schemes for non-smooth mutlibody systems with impacts, namely time stepping integrators, are described.

The second part of the paper deals with the derivation of a new continuous valve spring model and its validation. First the main characteristics of valve springs are treated and the advantages and disadvantages of commonly used dynamic valve spring models: modal model, multi mass model, and multi beam model, are shown. Then the new valve spring model based on the approximation of the spring as a curved beam is presented [3]. This approach leads to hyperbolic partial differential equations, which are discretized using the finite element method. The spring model is implemented and integrated in a multibody-simulation-environment and this facilitates the efficient simulation of the most common valve spring forms (cylindrical, conical and beehive). The main advantages of this model over the commonly used ones are fewer degrees of freedom together with contact modelling between the coils. Finally the model presented is validated using model adaptations in the static and dynamic case that are carried out for a commercially available cylindrical, a conical and a beehive valve spring. Great compliance between the simulations and measurements is shown.

The third part describes the integration of the presented continuous spring model in a valve train comprising twelve valve unit mechanisms. Taking this example into account, the efficiency of the proposed valve spring model is shown by comparing it to a common multi mass spring model. It can be concluded that the continuous model is about 50% faster than the multi-mass model. Furthermore, smooth and non-smooth contact mechanics and their corresponding integration schemes are applied to the valve train simulation model. It is shown that non-smooth contact mechanics is about 50% faster than smooth-contact mechanics for this application.

1

F. Pfeiffer, "Mechanical System Dynamics", in "Lecture Notes in Applied and Computational Mechanics", Springer, Berlin, 2005.

2

M. Förg, "Mehrkörpersysteme mit mengenwertigen Kraftgesetzen - Theorie und Numerik", Dissertation, Technische Universität München, 2008.

3

R. Huber, J. Clauberg, H. Ulbrich "An Efficient Spring Model Based on a Curved Beam with Non-Smooth Contact Mechanics for Valve Train Simulations", in "SAE World Congress 2010", Detroit, USA, 2010.

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