Chaos Analysis of Single-Stage Spur Gear System Considering Backlash Fractal

Abstract

Purpose: Considering the time-varying pressure angle and dynamic clearance, the effects of rotational speed, tooth surface friction, and tooth surface morphology on the system’s dynamic response are studied. Method: An improved gear nonlinear model is proposed, which considered nonlinear factors such as time-varying pressure angle, position angle, tooth surface morphology, and tooth surface friction. The time-varying dynamic backlash is deduced, and the nonlinear dynamic equation of the gear is established. The nonlinear dynamic response of the gear system is obtained based on Runge–Kutta method. Results: The influence of the rotational speed and tooth surface friction on single-stage spur gear system response is analyzed through the analysis of the bifurcation diagram, the three-dimensional spectrum diagram, the proportion of the meshing state, and the largest dynamic meshing force (LDMF). Dynamic response differences between the three different model are compared. In addition, by changing the tooth surface roughness and fractal dimension, the influence of tooth surface morphology on the dynamic response of the system is studied. Conclusion: Compared with the traditional model, when the dynamic center distance and dynamic pressure angle are considered, the system response may enter a chaotic state earlier. When the tooth surface friction is further considered, the chaotic state of the system response is suppressed. At the same time, the velocity of the dynamic transmission error is significantly reduced, and the fluctuation amplitude of the dynamic pressure angle is increased. The value of LDMF rose overall. The stability of the system response decreases with the increase of tooth surface roughness and fractal dimension. Compared with the fractal dimension, the tooth surface roughness has a more obvious effect on the dynamic response of the system.