基于基底长度的粗糙表面分形接触模型的构建与分析

Construction and Analysis of Fractal Contact Mechanics Model for Rough Surface Based on Base Length

为建立更为精确的粗糙表面接触模型,根据微凸体变形特征、分形理论以及摩擦的作用,从微观角度基于基底长度建立了粗糙表面分形接触模型.通过与其他粗糙表面接触模型和实验数据的比较,验证了本文模型的正确与合理,并由数值仿真分析了分形维数、接触载荷与真实接触面积之间的相互关系.分析结果表明:特征尺度一定时,要维持一定的真实接触面积,分形维数越大,所需要的力也越大;分形维数与特征尺度一定时,随着载荷的增加,接触面积也在增加;特征尺度与接触力一定时,随着分形维数的增大,真实接触面积在减小.该模型的建立为进一步研究粗糙表面的摩擦、磨损与润滑提供了理论依据.

To establish a contact mechanics model of rough surface with better accuracy,the fractal contact mechanics model considering asperity's deformation properties,fractal theory and friction effect was established from micro perspective based on base length. Using other contact models of rough surface and experiment data as references,the proposed model was investigated. The relationship of fractal dimension,contact force and real contact area was studied by using numerical simulation analysis. The results indicate that the force increased with the increase of fractal dimension to maintain a certain real contact area when the characteristic length scale was fixed. Real contact area increased with the increase of force when fractal dimension and characteristic length scale were fixed. Real contact area decreased with the increase of fractal dimension when characteristic length scale and force were fixed. This model provided a foundation to research friction,wear and lubrication of rough surface.