[4D4] Non-linear dynamic behaviour of spiral bevel gear by considering the torsional shaft stiffness
M Molaie¹, R Ebrahimnejad¹, A Zippo¹, G Iarriccio¹, F Pellicano¹ and F Samani¹,²
¹University of Modena and Reggio Emilia, Italy
²Shahid Bahonar University of Kerman, Iran
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 recognised 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 an SBG, time-dependent mesh stiffness and non-smooth non-linearity caused by backlash is considered. The employed dynamical system is a three-degrees-of-freedom model, integrating rotational shaft stiffness to investigate the dynamic behaviour of SBGs. Through the utilisation of various analysis tools, such as a bifurcation diagram, the Fourier spectrum, a 3D-phase diagram and a Poincaré map, an amplitude-frequency diagram is generated, revealing the presence of periodic, quasiperiodic and chaotic responses in specific regimes. This research provides an in-depth understanding of the dynamic behaviour of an SBG system, contributing to the characterisation and prediction of the non-linear phenomena, which is vital for the optimisation and design of gear mechanisms across various engineering applications.
