Resulting the Non-Linear Vibrational Behavior of Spiral Bevel Gears Resulting From Angular Misalignment
Authors: Estahbanati Mahdi , Samani Farhad S. , Pellicano Francesco , Molaie Moslem , Zippo Antonio 
Published: January 2025

Abstract
Spiral Bevel Gears (SBGs) stand as pivotal components within transmission systems, facilitating the transfer of power between intersected shafts, particularly in scenarios demanding elevated levels of torque or speed. Despite their operational advantages over straight bevel gears, SBGs are not immune to challenges, with misalignment emerging as a significant concern attributable to assembly errors and shaft stiffness. This research embarks on an exploration of the intricate interplay between misalignment-induced chaos and the vibration response of SBGs, leveraging a Finite Element Method (FEM) model constructed within Calyx software. A fundamental aspect of SBGs lies in their design featuring curved oblique teeth, fostering smooth meshing akin to helical gears and resulting in quieter operations. However, this design trait also engenders heightened tooth pressure, accentuating the importance of addressing misalignment issues. The study’s primary objective revolves around comprehensively investigating chaos within an eight-degree-of-freedom (8-DOFs) system, a domain hitherto unexplored. Key aims encompass the determination of mesh stiffness for this system and the elucidation of chaotic behavior in the presence of angular misalignment, along with identifying conditions conducive to severe inconsistencies.
Central to this investigation is the meticulous examination of angular misalignment’s influence on gear behavior, facilitated by a comprehensive 8-DOFs model. Research findings underscore a direct correlation between angular misalignment levels and transmission error, with heightened misalignment yielding proportional increases in vibrational response, ultimately culminating in escalated chaos. Noteworthy is the exclusive focus on vibrations originating solely from SBGs, excluding other system components, and emphasizing high-speed operational scenarios. Elastic properties of the gear pair remain within the linear elastic range throughout, preempting plastic deformation. The nonlinear nature of the gear set, primarily attributed to backlash — indicative of clearance between pinion and gear teeth — constitutes a critical aspect shaping system behavior. Assumptions regarding small deformations ensure structural integrity while facilitating comprehensive chaos analysis. Time-varying mesh stiffness for both front and rear contacts is meticulously determined, leveraging Calyx software and the finite element method.
Within the confines of this study, chaos in the vibration response of the 8-DOFs system is systematically explored across various angular misalignments, including zero misalignment, along with misalignments of ±0.25 mm and ±0.5 mm. Findings illuminate a progressive escalation of chaos with increasing angular misalignment, underscoring the profound influence of misalignment on system dynamics. In summary, this research provides invaluable insights into the complex dynamics governing SBGs under angular misalignments, shedding light on emergent chaos phenomena and underscoring the imperative of mitigating misalignment to ensure system stability and performance.