Bifurcation and chaos analysis of cutter head-spindle system of VH-CATT gear machine tool considering time-varying stiffness

The stability of power system in variable hyperbolic circular arc tooth trace (VH-CATT) gear machine tool determines the surface accuracy and mechanical properties of the VH-CATT gear. Due to the existence of several time-varying parameters, the power system is a typical nonlinear dynamic system. To study the influence of the design parameters of the spindle and cutter head on the motion stability of the power system, a nonlinear dynamic model of the cutter head-spindle system is established based on the cutting principle, which considers the time-varying stiffness, clearance and excitation. According to the potential function and phase portrait, the existence of intersect homoclinic orbit is proved, and the concrete expression is derived. The threshold values of the parameters for occurrence of the homoclinic bifurcation are obtained by means of Melnikov method. The analytical predictions have been verified through numerical simulations, and good agreement is observed, which presents the dynamic behaviors of the system include 1 T-periodic, nT-periodic, and chaotic motion. Additionally, combined with bifurcation diagrams, time histories, phase portraits, Poincaré sections, and power spectra, the global bifurcation of the system and the transition between various motion states are revealed. The research results offer reference for the parameter selection of the cutter head-spindle system and also provide a theoretical basis for the subsequent experimental analysis.