[5D3] Non-linear dynamic analysis of spiral bevel gears: Hertzian stiffness effects under varying torque conditions
A Zippo, F Pellicano and M Molaie
University of Modena and Reggio Emilia, Italy
Spiral bevel gears (SBGs) are essential components in transmission systems, enabling efficient power transfer between intersecting shafts operating under high torque or speed conditions. The dynamic behaviour of SBGs is inherently non-linear due to multiple factors, including bearing clearances, backlash and variations in mesh stiffness (MS). Among these, the Hertzian effect plays a crucial role in altering the torque-deflection relationship, introducing a non-linear dependency of MS on both time and dynamic mesh torque (DMT). As a result, traditional linear models fail to accurately capture the dynamic response of SBGs under varying operating conditions. This study proposes a methodology to determine MS as a function of time and DMT by integrating finite element analysis (FEA) with polynomial regression techniques. The obtained non-linear MS function is incorporated into the governing equations of motion to analyse its effects on gear system dynamics. Two different gear systems operating under distinct torque conditions, nominal torque and low-level torque, are examined to assess the impact of non-linear MS compared to average MS models. The dynamic response is evaluated through amplitude-frequency and bifurcation analyses, offering insights into system stability, periodic and chaotic behaviours and the influence of varying stiffness on vibration characteristics. Results indicate that neglecting non-linear MS can lead to significant deviations in predicted system behaviour, particularly in terms of resonance frequencies and stability regions. The study highlights the necessity of continuously updating MS in dynamic simulations to enhance the accuracy of vibration predictions and reliability assessments. By providing a more precise characterisation of non-linear gear interactions, this research contributes to the development of improved design and maintenance strategies for SBGs in high-performance applications.
