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.

高精度，高效率和可靠性是机械制造业的不懈追求。精密线性导轨作为高端数控机床的关键功能部件之一，决定了加工精度和操作性能。表面形貌的准确评估和预测是线性导轨匹配性能的关键因素。本文以实际接触面积为关键参数，提出了一种基于分形理论的多尺度方法。首先，利用赫兹接触理论获得单个粗糙表面的接触面积。然后，通过分形理论推导出粗糙表面之间的接触面积。最后，使用所提出的多尺度接触力学模型，通过积分解获得了粗糙平面与圆柱体之间的实际接触面积。与以前的分形模型和GW模型相比，该模型在直线导轨实际接触面积计算上更加准确，全面。讨论了载荷，分形参数和摩擦的影响因素，随着载荷的增加，光滑表面的实际接触面积的增加率越大。所提出的模型可以为设计阶段的组装精度和表面质量要求提供实用指导。