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

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.