Contact characteristic analysis of spindle–toolholder joint at high speeds based on the fractal model

Due to the influence of centrifugal force, accurate contact stiffness model of spindle–toolholder joint at high speeds is crucial in predicting the dynamic behavior and chatter vibration of spindle–toolholder system. In this paper, a macro–micro scale hybrid model is presented to obtain the contact stiffness of spindle–toolholder joint in high speeds. The hybrid model refers to the finite element model in macro-scale and three-dimensional fractal model in micro-scale. The taper contact surface of spindle–toolholder joint is assumed flat in macro-scale and the finite element method is used to obtain the pressure distribution at different speeds. In micro-scale, the topography of contact surfaces is fractal featured and determined by fractal parameters. Asperities in micro-scale are considered as elastic and plastic deformation. Then, the contact ratio, radial and torsional contact stiffness of spindle–toolholder joint can be calculated by integrating the micro asperities. Experiments with BT40 type toolholder–spindle assembly are conducted to verify the proposed model in the case of no speed. The reasonable intervals of spindle speed and drawbar force can be obtained based on the presented hybrid model, which will provide theoretical basis for the application and optimization of the spindle–toolholder system.