Author(s)

N. Str¨omberg & J. F. Massana

Abstract

Today, high-performance machine components are often improved by coatings. For instance, thin layers can increase the life-time by reducing friction and wear. An example of this is the spline joint in the suspension system of a truck. This joint, which is placed at the output of the gearbox, allows relative translation in the axial direction. In order to improve performance, this spline can be coated with a thin layer of polyamide. In such a manner, the life-time of the joint is increased by decreasing friction and wear. This type of coatings may be optimized by performing finite element contact analysis. However, when performing such an analysis, it can be difficult to obtain a good mesh due to the very thin layer. An approach to avoid this difficulty is to instead include the elastic properties of the coating in the contact formulation. Such a soft contact formulation is suggested and solved in this paper. The formulation is obtained by adding an elastic part to the free energy corresponding to Signorini’s contact conditions. In such a manner a new soft contact law is derived by taking the subdifferential of the free energy. In this law two new constitutive parameters appear. The first parameter describes the elastic response of the thin layer and the second one is taken to be equal to the thickness of the layer. In the event, when the layer is completely penetrated, hard contact is developed following a classical Lagrange formulation of Signorini.A numerical method for solving the new contact formulation is also developed. The method is obtained by following the augmented Lagrangian approach. In such a way an equivalent setting of equations is derived which in turn is solved by using a non-smooth Newton method. The method is implemented in a Matlab toolbox. The method is robust and produces accurate results. This is shown by comparing numerical results with solutions obtained by using a penalty formulation in Abaqus. Keywords: soft contact, finite elements, Newton’s method.

Keywords

soft contact, finite elements, Newton’s method.