Friction dynamics analysis of crossed beveloid gear with considering tooth surface topography

The contact surfaces of beveloid gears have different topography features due to different machining methods, manufacturing accuracies, and surface wear, and they are not always smooth. As a consequence, in this study, a nonlinear dynamic model of a crossed beveloid gear was developed, considering tooth surface topography features and friction. The phase plane diagram, Poincare diagram, time-domain response diagram, bifurcation diagram, and spectrum diagram of the system response were obtained using the Runge–Kutta method to dissolve the differential equations of the system dynamics. The effect of parameters such as tooth roughness and time-varying friction on the dynamic response of a beveloid gear was then investigated, and the results show that the motion of the gear system denotes a simple harmonic with a period of 1 when the tooth surface roughness R a is <1.6 μm. And with the variation of tooth surface roughness, the motion state of the system presents a variety of response forms, such as single-period, multi-period, quasi-period, bifurcation, and chaos.