Contact stiffness of spindle-tool holder based on fractal theory and multi-scale contact mechanics model

Abstract

Abstract The contact stiffness of the spindle/tool holder is essential for the cutting stability of the spindle system because the elastic connection of the spindle/tool holder interface determines the dynamic characteristics of the spindle system. To predict the dynamic characteristics of the spindle system at the design stage, an analytical model of the contact stiffness of the spindle/tool holder interface was proposed based on the fractal theory and the multi-scale contact mechanics model to consider the combined effect of the cutting force and drawbar force on the contact stiffness. The fractal theory was used to characterize the micro-morphology of rough surfaces and the fractal parameters were identified by the power spectrum method. For the contact of two rough curved surfaces, the surface contact coefficient was introduced into the multi-scale contact mechanics model to correct the contact stiffness, the actual contact area and the contact stress. To verify the validity of the method, the experiments were conducted and the results showed that the modeling error of the contact stiffness was reduced from 25.13% to 4.72% by the proposed method. Finally, the effect of such factors as the cutting force, the mean roughness, the material properties, the preload and the temperature variation on the contact stiffness was discussed. The contact stiffness of spindle/tool holder interface increased with the cutting force and the drawbar force and that the contact stiffness decreased with the mean roughness. Moreover, the shear contact stiffness increased with the equivalent elastic modulus, the interference fit and the temperature. The conclusion was drawn that the model can be used to predict the contact stiffness of the spindle/tool holder interface at the design stage.