高速薄辐板齿轮传动节径型振动位移与动应变时空变换方法

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

高速薄辐板齿轮传动功率密度高,在航空动力传动系统中应用广泛,但节径型共振模态密集、振动能量高,是高速薄辐板齿轮传动疲劳损坏的主要形式之一。节径型振动位移与试验动应变呈非正相关关系,振动响应与动应力之间缺少直接量化的纽带,为此,提出一种高速薄辐板齿轮节径型振动位移与动应变时空变换方法。综合考虑节径型振动下试验动应变与振动位移行波之间的空间向量关系,建立试验动应变与振动位移变换函数,并给出偏微分方程的时空离散解与动应变-振动位移变换方法;根据试验动应变时/频信号以及不同节径数下齿轮行波模态特性,获取振动位移时空离散解。理论与试验结果表明,某试验齿轮在3节径下出现明显行波共振,理论仿真的振动频率、转速与试验结果基本一致,验证了所提理论和方法的正确性与可行性。

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.