Non-linear dynamic behaviour of spiral bevel gear by considering the torsional shaft stiffness

Abstract

Spiral bevel gears (SBGs) play a crucial role in developing silent power transmissions for non-parallel shaft applications, offering advantages such as improved motor allocation flexibility and space reduction. While SBGs have been recognized for reducing vibration magnitude in high-speed gearboxes compared to straight bevel gears, complete vibration suppression remains elusive, leading to potential challenges such as teeth contact loss and complex dynamic scenarios. To construct the dynamical model of SBG, time-dependent mesh stiffness and non-smooth nonlinearity caused by backlash is considered. The employed dynamical system is a three-degree-of-freedom model, integrating rotational shaft stiffness, to investigate the dynamic behavior of SBGs. Through the utilization of various analysis tools such as bifurcation diagram, Fourier spectrum, 3D-phase diagram, Poincaré map, and amplitude-frequency diagram are generated, revealing the presence of periodic, quasiperiodic, and chaotic responses in specific regimes. This research provides an in-deep understanding of the dynamic behavior of SBG system, contributing to the characterization and prediction of nonlinear phenomena, which is vital for the optimization and design of gear mechanisms across various engineering applications.