# Dynamic coupling effects of geometric eccentricity on multi-stage gear transmission via stiffness modulation and error excitation

## TL;DR

This paper explores how geometric eccentricity affects vibrations in multi-stage gear systems through stiffness changes and error excitation, offering design guidelines for reducing unwanted vibrations.

## Contribution

The study introduces a novel analytical method for three-path stiffness modulation and identifies a dynamic performance-based design safety domain for low-vibration gear systems.

## Key findings

- Strong nonlinear coupling exists between eccentricity ratio and phase difference, amplifying vibrations under extreme asymmetry and anti-phase conditions.
- Symmetric eccentricity with phase optimization reduces oscillations effectively.
- Experimental validation confirmed the accuracy of the stiffness-error coupling mechanism in predicting vibration behavior.

## Abstract

This research investigates the dynamic mechanism arising from the coupling between multi-path stiffness modulation and geometric eccentricity in multi-stage gear transmission systems (MGTS) for high-end equipment. The study aims to address the critical challenges in vibration suppression and precision control for such systems. A lumped parameter model integrating translational and rotational degrees of freedom was established, and an analytical method for three-path stiffness modulation based on center distance fluctuation, pressure angle reconstruction, and contact ratio transition was proposed. The influence of geometric eccentricity on the dynamic characteristics via the combined action of stiffness excitation and displacement error was then systematically analyzed. It was found that a strong nonlinear coupling exists between the eccentricity ratio and the initial phase difference: the combination of extreme asymmetry and an anti-phase condition markedly amplifies the stiffness modulation amplitude, inducing severe vibration, while symmetric eccentricity coupled with phase optimization effectively mitigates these oscillations. The feasibility of the established model was verified experimentally. The simulated and measured frequency spectra showed good agreement at the meshing frequency and its major sidebands, thereby demonstrating the accuracy of the stiffness-error coupling mechanism. Ultimately, a dynamic performance-based “parameter design safety domain” was constructed, which explicitly defines a low-vibration design interval centered on the eccentricity ratio and phase difference. This work thereby not only deepens the theoretical understanding of the error-stiffness-vibration coupling mechanism in the MGTS but also provides theoretical support and a practical guide for the dynamic design, vibration suppression, and operational optimization of high-precision gear transmission systems.