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 behavior of SBGs is inherently nonlinear 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 nonlinear 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 nonlinear MS function is incorporated into the governing equations of motion to analyze 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 nonlinear 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 behaviors, and the influence of varying stiffness on vibration characteristics. Results indicate that neglecting nonlinear MS can lead to significant deviations in predicted system behavior, 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 characterization of nonlinear gear interactions, this research contributes to the development of improved design and maintenance strategies for SBGs in high-performance applications.
Zippo et al. (Wed,) studied this question.