Research on axial nonlinear vibration characteristics of ball screw feed system considering segmented restoring force

Taking the ball screw feed system as the research object, the two degree of freedom axial dynamic model of the system is constructed firstly. Based on Hertz contact theory, when the ball screw pair adopts variable lead self-preloading to eliminate the assembly clearance between the ball and raceway, considering the nonlinear segmented axial elastic recovery force generated by the uneven contact deformation between the ball and raceway under the action of external excitation force, further derive the nonlinear dynamic equation group of the system. Next, the fourth-order Runge-Kutta method was used to numerically solve the equation system, obtaining the system’s two and three-dimensional phase diagrams, Poincaré sections, time-domain waveform diagrams, frequency spectra, and bifurcation diagrams. Then, the effects of damping constant, initial contact angle between ball and raceway in ball screw pairs, and number of balls on the system’s response characteristics were analyzed, and the influence of external excitation forces on system stability was further studied. Finally, it was verified through experiments that the axial vibration of the system is indeed nonlinear vibration, providing a theoretical basis for the study of the dynamic characteristics of the ball screw feed system.