Contact Transformation for the Prediction of Structural Wears

Abstract

In prediction of structural wears with the finite element (FE) approach, the geometry of FE model must be updated constantly to imitate the nonlinear wear behaviors which need a great amount of computational time. Improvement of efficiency of wear simulations becomes increasingly important due to the design requirements. In the current study, an alternative and efficient FE approach by introducing the approach of contact surface transformation is proposed to improve the simulation efficiency of structural wear. The FE model of pin-on-plate wear problem is demonstrated and wear result presented is comparable to available simulation data. The result shows that the computational time is comparatively reduced and numerical precision is increased. It is believed that the current method can offer superior performance for larger and complex structures. Introduction Wear is the most significant factor in reducing the service life of mechanical components. In order to improve the service life of components, understanding of the wear behavior of mechanical components is a significant task for engineering design. The FE model has been developed using Archard’s wear law [1] in order to simulate large or complex structures and provide more valuable information of structural wear for engineering design [2-5]. In the FE model of wear prediction, the geometry of contact regions between components is variable and the wear behavior is generally nonlinear. The geometry at the end of each sliding motion needs to be updated dynamically [3] and much more computational time in the iterative procedures is required. Several ideas have been offered in an attempt to reduce computational time of the wear simulation. Podra and Andersson [2] proposed an incremental formulation with an optimal time step (such as scaling approach) to obtain more computational efficiency for the pin-on-plate wear simulation. Sfantos and Aliabadi [6] indicated that BEM can reduce the number of unknowns in wear simulation, making updating of the worn components relatively fast and easy. However, BEM uses an asymmetric matrix, which is more complicated than approaches using a symmetric matrix. Recently, Mukras et al. [7] proposed parallel computation using nonlinear FE analysis in order to minimize the computational time with the accuracy and stability of wear prediction. However, the computational time of matrix operations were still longer, especially in the large structures. Bae et al. [8] used a substructure method to develop an FEM based approach to wear simulation that can reduce a large number of the unknowns required by traditional FEM, significantly reducing computational time, but the matrix of overall structures needs to change repeatedly in the iterative procedures. Therefore, reducing the computation time of wear simulation remains worthy of study. Wear formulation. The wear depth is of more interest from the viewpoint of engineering, and can be expressed as: ( ) = = p p p p w n j p c c k F x dS dV dh A A . (1) International Conference on Intelligent Systems Research and Mechatronics Engineering (ISRME 2015) © 2015. The authors Published by Atlantis Press 2179 where superscript { , } = p a b is the component index, j is the index of the contact point, h the wear depth, S the sliding distance, w k is the wear coefficient in units of mm /N-m, which can be determined via experiment, ( ) n j F x is the normal force on contact point j x , and c A is the contact area. Contact formulation. During the wear motion, the geometry and the normal forces on the contact region change, but the contact force throughout the contact region must always be at equilibrium. A modified localized Lagrange multiplier method (MLLM) is defined. It consists of a governing equation for the contact problem and constrains conditions on the contact region as follows: + = + = a a a a a c ext b b b b b c ext K u B λ F K u B λ F . (2)