考虑静摩擦的两圆柱体分形接触强度模型研究

Research on contact strength calculation of two cylinders based on by static friction by fractal theory

为了研究两圆柱体结合面之间静摩擦力对接触强度的影响,文章通过引入静摩擦影响系数,在分形理论的M-B接触模型、静摩擦因数预测模型和Gelinck数学模型基础上,修正结合面之间真实接触面积计算方法,并推导考虑静摩擦影响的两圆柱体结合面分形接触强度模型。通过Matlab仿真分析发现:静摩擦因数对接触强度的影响呈现复杂的非线性关系,无法通过单一的调节润滑黏度、接触速率等因素改变接触强度;与传统接触强度模型相比,该文所用模型计算的接触强度有所降低,且随着分形维数的减小接触强度呈现非线性增大。研究结果为进一步探讨摩擦对齿轮等实际产品的接触强度影响提供了一定的理论基础。

In order to obtain the influence of the static friction force between two cylinders on the con- tact strength, and by introducing the influence coefficient of static friction, the fractal contact strength model considering the static friction was derived after modifying the methodology of calculating the real area of joint face based on M-B fractal contact model, static friction factor prediction model and Gelinck model. The results of the simulation of the models in Matlab show that the static friction coefficient and contact strength interact with each other and their relationship shows complex nonlinearity; the contact strength cannot be changed by only adjusting the value of lubricating viscosity and the contact velocity separately; the analysis result of contact strength by the model in this paper is consistent with that of the traditional methodology, but the former value is a little smaller; the contact strength increases nonlinearly with the decrease of fractal dimension. The investigation in the paper can help to further analyze the influence of friction on calculating the contact strength of gears.