Nonlinear bifurcation characterization of the herringbone gear transmission system based on topological modification time-varying meshing stiffness

Abstract

This research delved into the effects of topological modification on the nonlinear bifurcation properties of herringbone gear transmission system (HGTS). A model utilizing the potential energy method was initially developed to analyze the time-varying meshing stiffness (TVMS) of a herringbone gear following topological modification. Additionally, a dynamic model of a bending-torsion-axis-pendulum (BTAP) coupling of HGTS with 24 degrees of freedom (DOF) was established, which took into account various factors such as topological modification, meshing errors, TVMS, damping, backlash, and bearing clearance. The model employed the Runge-Kutta method to assess the pre-topological and post-topological modification nonlinear vibration responses and bifurcation characteristic, with a specific emphasis on backlash, and speed variations. The bifurcation diagram and maximum lyapunov exponent (MLE) graph were employed to elucidate these changes. Supplementary studies utilizing time domain diagram, frequency domain diagram, phase plane diagram, poincaré map analyses provided a comprehensive understanding of the HGTS’s nonlinear dynamics. The findings indicate that while the fundamental vibration and bifurcation trends persist post-topological modification, local bifurcation and vibration responses exhibit improvements. Specifically, an increase in backlash leads to a transition from single-periodic to multi-periodic, and then to chaotic regimes, the topological modification improves in reverting some chaotic behaviors to periodic, thereby reducing the extent of chaos. Increased rotational speeds result in periodic-chaotic-periodic sequences, but topological modification shifts bifurcation points, reducing chaos. Comparisons of experimental and theoretical data corroborate the model’s accuracy, demonstrating consistent trends.