# Nonlinear dynamics of curve-face gear transmission systems in two-parameter plane

## TL;DR

This paper studies how curve-face gear systems behave dynamically, focusing on how key parameters influence their motion patterns and transitions.

## Contribution

A novel 6-DOF bending-torsional coupling model and two-parameter co-simulation method are introduced to analyze nonlinear dynamics in curve-face gears.

## Key findings

- Transitions between non-impact and tooth-impact vibrations occur via grazing bifurcation.
- Period-doubling bifurcation governs transitions between adjacent tooth-impact motions.
- Increased meshing damping reduces existence domains of tooth-impact and chaotic motions.

## Abstract

To systematically investigate the nonlinear dynamic characteristics of curve-face gear transmission systems and the influence of key parameters on their dynamic behavior, this study established a 6-degree-of-freedom bending-torsional coupling dynamic model. A two-parameter co-simulation numerical method was employed to explore the pattern types and existence regions of periodic motions within the two-parameter plane composed of key parameters. The transition mechanisms between non-impact vibrations and tooth-impact vibrations, as well as between adjacent fundamental periodic motions, were systematically revealed. Furthermore, the effects of parameter variations on the types and existence regions of periodic motion patterns were analyzed. The research results demonstrate that the transition between non-impact vibrations and tooth-impact vibrations occurs through grazing bifurcation, while transitions between adjacent tooth-impact motions are governed by period-doubling bifurcation. When the backlash exceeds 0.4125, variations in backlash values do not alter the types or existence regions of periodic motion patterns but only affect the displacement of the meshing pair. Increasing the meshing damping ratio significantly reduces the existence domains of tooth-impact periodic motions and chaotic motions in the two-parameter plane. This study provides theoretical foundations and practical references for the dynamic characteristic analysis and optimal design of curve-face gear transmission systems.