机床螺栓结合部等效材料法向接触弹性模量的分形模型

Fractal model for normal contact elastic modulus of machine tool bolt joint equivalent material

根据赫兹接触理论首次提出了单个微凸体的正应力-正应变本构关系,给出了两个微凸体之间互相作用的法向接触弹性模量。考虑表面粗糙度和载荷分布的不均匀性,根据MB模型给出了结合部等效材料的总法向接触条件弹性模量、总条件法向载荷的解析解。在弹性范围内,结合部等效材料的总法向接触弹性模量是以下10个输入参数:两接触表面的2个弹性模量、2个泊松比、表观压应力、表观面积、较软材料的硬度、较软材料的屈服强度、分形粗糙度参数、分形维数的复杂函数。总法向接触弹性模量基本上线性地随总法向表观压应力的增加而增加,还非线性地随分形维数的增加而增加,但非线性地随表面粗糙度的减小而增加。

According to Hertz contact theory, a constitutive relation of normal stress and strain was presented for the first time for an individual asperity. Also, the solution for normal contact elastic modulus of two interacting asperities was derived. Surface roughness and the non-homogeneity of load distribution taken into account, the analytic expressions for joint equivalent material total normal contact elastic modulus with a certain condition and total normal load with a given one were deduced from MB model. Joint equivalent material total normal contact elastic modulus is a complicated function depending on such 10 input parameters as two elastic moduli, two Poisson ratios of two contacting surfaces, apparent pressure, apparent area, the hardness, yield strength of the softer material, fractal roughness parameter and fractal dimension in the elastic regime. When the total normal apparent pressure is increased the total normal contact elastic modulus linearly increases in all. In addition, the total normal contact elastic modulus increases in a nonlinear way as fractal dimension increases and fractal roughness parameter decreases.