A fully analytical nonlinear dynamic model of spindle-holder-tool system considering contact characteristics of joint interfaces

Abstract

The productivity, surface finish, and dimensional accuracy during machining are directly related to the vibration characteristics of tool tip. Moreover, the dynamics of tool tip is not only determined by the flexibility of tool, collet, holder and spindle, but also depends on the contact characteristics of joint interfaces. This paper proposes a fully analytical model of the spindle-holder-tool system considering the nonlinear contact characteristics of joint interfaces. The dynamics of spindle, holder, collet and tool are modeled applying Timoshenko beam theory considering the combined shear and rotational effects, in which the tapered sections of spindle, holder and collet are modeled using multi-stepped beam to account for the taper effect. Under highly dynamic cutting load, the variation in the spacing of joint interfaces will induce the changes in the contact characteristics due to the corresponding vibrations. Therefore, the contact behaviors of spindle/holder, collet/holder, collet/nut, and tool/collet interfaces are analytically modeled using the distributed nonlinear spring-damping layers. The fractal theory and the slicing method are applied to derive the vibration displacement-dependent stiffness matrix of nonlinear springs in joint interfaces considering the surface morphology, geometry, material properties, and locking force of joint interfaces. Furthermore, the five degree of freedom (DOF) nonlinear stiffness model of the spindle-bearing joint dependent on vibration displacement is also considered. The effectiveness of the established analytical dynamic model is verified through vibration testing and modal hammering experiments. The changes in the vibration characteristics by considering the connection ways of joint interfaces, the fractal parameters of joint interfaces and the rotation speed are also investigated. The developed model can provide some theoretical principles for the optimization at design stage without prototypes.