机床地脚低速滑动界面法向刚度分形模型及试验验证

Fractal Model of Normal Stiffness for Slow Sliding Surface in Machine Tool Ground Foot and Experimental Confirmation

按照一个弹性微凸体的平均接触压强构筑微凸体顶端接触变形。计及动摩擦因数计算微凸体最初屈服的临界平均压强。采用以无阻尼自然角频率为自变量的功率谱密度函数,给出识别界面分形维数、特征长度的理论和试验方法。仿真结果表明:微凸体最初屈服的临界平均压强随着动摩擦因数的增加而变小;分形区域扩展因数随着分形维数的增加而减小;微凸体最大结合面积随着分形维数的增加呈现线性减小;增加动摩擦因数、面积比和特征长度都将衰减法向接触刚度;法向接触刚度随着分形维数、接触面积的比率、法向接触载荷或微凸体最大结合面积的增加而增强。按照有限元模拟对界面法向接触参数识别结果进行证明。考虑界面参数的有限元模型得到的动柔度、法向接触刚度数据与试验数据一致。

The contact deflexion at the tip of the asperity is deduced from the medial contact pressure at an elastic microcontact. The critical mean pressure for an asperity initial yield is computed comprising the dynamic friction coefficient. The theoretical and experimental ways to identify the surface fractal dimension and characteristic length are achieved adopting the power spectrum density function about the undamped natural angular frequency as a variable. The emulation results reveal that an increase in dynamic friction coefficient causes an attenuation in critical average pressure for an asperity initial yield. The fractal domain extension factor diminishes with the augmentation of fractal dimension. When the fractal dimension adds, the asperity maximum combination area reduces linearly. The normal contact stiffness will all attenuate by extending kinetic friction coefficient, area ratio and characteristic length. The normal contact stiffness is strengthened with the enhancing fractal dimension, contact area ratio, normal contact load or asperity maximum combination area. The finite element simulation is applied to demonstrate the normal contact parameters identification results in surface. The dynamic compliance and normal contact stiffness data from finite element model are in accordance with the experimental ones thinking over surface parameters.