Time-space Transformation Method of Vibration Displacement and Dynamic Strain in Nodal-diameter Vibration of High-speed Thin-walled Gear

High-speed thin walled gear has high-power density and is widely used in aviation power transmission system. However, the node-diameter type resonance has dense resonant modes and high vibration energy, which is one of the main forms of fatigue damage of high-speed thin walled gear. Due to the non-positive correlation between dynamic strain and vibration displacement of nodal diameter vibration, there is no direct quantitative link between dynamic response and dynamic strain. Therefore, a time-space conversion method of node-diameter displacement and dynamic strain of high-speed thin walled gear is proposed. Considering the space vector relationship between the measured strain and the displacement traveling wave of the strain gauge, the conversion function of dynamic strain and vibration displacement is established, and the time-space discrete solution of the partial differential equation and the strain displacement conversion method are given. Then, based on the time-frequency signal of the test strain and the gear modal characteristics under different nodal diameters, the time-space discrete solution of the vibration displacement is obtained. Based on the comparison between the theoretical and experimental results, the test spur gear has obvious resonance at 3 nodal diameters. And the theoretical simulation vibration frequency and speed are basically consistent with the experimental results, which validates the feasibility of the proposed theory and method. © 2024 Chinese Mechanical Engineering Society. All rights reserved.