A multi-scale model of real contact area for linear guideway based on the fractal theory

Abstract

High precision, efficiency and reliability are the unremitting pursuits of machinery manufacturing industry. As one of the pivotal function parts of high-end NC machine tool, precise linear guideway determines the machining precision and operation performance. Accurate evaluation and prediction of surface topography are the crucial effects on the matching performance of linear guideway. In this paper, the real contact area is regarded as a key parameter, a multi-scale method with the fractal theory is proposed. First, the contact area of a single asperity was obtained with Hertz contact theory. Afterwards, the contact area between rough surfaces was deduced by the fractal theory. Finally, using the proposed multi-scale contact mechanics model, the real contact area between rough plane and cylinder was obtained by integral solution. Compared with the former fractal model and GW model, the proposed model on the real contact area calculation of linear guideway is more accurate and comprehensive. The effect factors of load, fractal parameter and friction were discussed, the increasing rate of real contact area of smoother surface is greater as load increases. The proposed model may provide practical guidance for assembly accuracy and surface quality requirements at design stage.