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

doi:10.3901/JME.2024.05.070

机械工程学报 ›› 2024, Vol. 60 ›› Issue (5): 70-80.doi: 10.3901/JME.2024.05.070

扫码分享

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

魏静¹, 刘指柔¹, 魏海波², 徐子扬¹

1. 重庆大学机械传动国家重点实验室重庆 400044;
2. 重庆大学航空航天学院重庆 400044

收稿日期:2023-03-01 修回日期:2023-09-25 出版日期:2024-03-05 发布日期:2024-05-30
通讯作者: 魏静，男，1978年出生，博士，教授，博士研究生导师。主要研究方向为机电传动系统动力学与振动噪声控制。E-mail：weijing_slmt@163.com
作者简介:刘指柔，女，1993年出生，博士研究生。主要研究方向为高速航空齿轮振动控制。E-mail：20200701023@cqu.edu.cn；魏海波，男，1989年出生，博士，助理研究员。主要研究方向为高速航空齿轮振动控制。E-mail：haibwei@163.com；徐子扬，男，1994年出生，博士研究生。主要研究方向为高速航空齿轮振动控制。E-mail：slmt_xuzy@cqu.edu.cn
基金资助:
国家自然科学基金资助项目(52275048)。

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

WEI Jing¹, LIU Zhirou¹, WEI Haibo², XU Ziyang¹

1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044;
2. College of Aerospace Engineering, Chongqing University, Chongqing 400044

Received:2023-03-01 Revised:2023-09-25 Online:2024-03-05 Published:2024-05-30

摘要/Abstract

摘要： 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。

关键词: 薄辐板齿轮, 节径振动, 振动位移, 动应变, 时空变换方法

Abstract: 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.

Key words: thin-walled gear, nodal diameter vibration, vibration displacement, dynamic strain, time-space transformation

中图分类号:

TG156

魏静, 刘指柔, 魏海波, 徐子扬. 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[J]. 机械工程学报, 2024, 60(5): 70-80.

WEI Jing, LIU Zhirou, WEI Haibo, XU Ziyang. Time-space Transformation Method of Vibration Displacement and Dynamic Strain in Nodal-diameter Vibration of High-speed Thin-walled Gear[J]. Journal of Mechanical Engineering, 2024, 60(5): 70-80.

参考文献

[1] 杨广雪，安钱钱，李爽，等．高速列车齿轮箱动应力分布特性研究[J]. 机械工程学报，2022, 58(10)：152-159.YANG Guangxue，AN Qianqian，LI Shuang，et al. Research on dynamic stress distribution characteristics of high speed train gearbox[J]. Journal of Mechanical Engineering，2022，58(10)：152-159.
[2] 魏静，姜东，张爱强，等．时变位姿下行星齿轮传动系统动应力计算模型及其参数影响研究[J]. 机械工程学报，2021，57(21)：150-159.WEI Jing，JIANG Dong，ZHANG Aiqiang，et al. Dynamic stress calculation model of planetary gear transmission system under time-varying posture and its parameter influence research[J]. Journal of Mechanical Engineering，2021，57(21)：150-159.
[3] LI Shuting. Diaphragm stress analysis and fatigue strength evaluation of the flex-spline，a very thin-walled spur gear used in the strain wave gearing[J]. Mechanism and Machine Theory，2016，104(6)：1-16.
[4] ZHENG Xingyuan，LUO Wenjun，HU Yumei，et al. Analytical approach to mesh stiffness modeling of high-speed spur gears[J]. International Journal of Mechanical Sciences. 2022，20(5)：1-27.
[5] KONG Xiannian，TANG Jinyuan，HU Zehua，et al. Dynamic modeling and vibration analysis of spur gear system considering thin-walled gear and hollow shaft[J]. Mechanism and Machine Theory，2022，181(12)：94-114.
[6] 曲建俊，田秀，孙凤艳. 行波型超声波电动机摩擦材料的寿命预测模型[J]. 机械工程学报，2011，47(1)：96-101.QU Jianjun, TIAN Xiu, SUN Fengyan. Life prediction model for friction material of traveling wave ultrasonic motor[J]. Journal of Mechanical Engineering，2011，47(1)：96-101.
[7] 王有懿，赵阳，马文来. 耦合梁中高频抖动的行波分析与主动控制[J]. 机械工程学报，2013，49(22)：185-191.WANG Youyi，ZHAO Yang，MA Wenlai. Travelling wave analysis and active control of jitter in the median and high frequency regions for coupled beam[J]. Journal of Mechanical Engineering，2013，49(22)：185-191.
[8] KONG Xiannian，HU Zehua，TANG Jinyuan，et al. Effects of gear flexibility on the dynamic characteristics of spur and helical gear system[J]. Mechanical Systems and Signal Processing，2022，184(8)：3270-3294.
[9] 栾孝驰，赵宇，沙云东，等. 弧齿锥齿轮参数调节状态下行波共振特性及其影响规律研究[J]. 中国机械工程，2021，32(24)：2899-2914.LUAN Xiaochi，ZHAO Yu，SHA Yundong，et al. Research on traveling wave resonance characteristics of spiral bevel gears and its influence laws under parameter adjustment[J]. China Mechanical Engineering，2021，32(24)：2899-2914.
[10] 王勖成. 有限单元法基本原理和数值方法[M]. 北京：清华大学出版社，1997.WANG Xucheng. Fundamentals and numerical methods of finite element method [M]. Beijing：Tsinghua University Press，1997.
[11] RAGHUWANSHI N K，PAREY A. Experimental measurement of mesh stiffness by laser displacement sensor technique[J]. Measurement，2018，128(6)：63-70.
[12] LUAN Xiaochi，LIU Gongmin，SHA Yundong，et al. Experiment study on traveling wave resonance of fatigue fracture of high-speed bevel gear in aero-engine based on acoustic measurement method[J]. Journal of Sound and Vibration，2021，511(7)：345-360.
[13] MIRZAEI M，RIPKA P，MACHAC J，et al. Design and modeling of an axisymmetric eddy current sensor for speed measurement of nonmagnetic rods[J]. Sensors and Actuators A: Physical，2022，344(7)：728-737.
[14] GUO Xiaozhong，SHI Zhaoyao，YU Bo，et al. 3D measurement of gears based on a line structured light sensor[J]. Precision Engineering，2020，61(10)：160-169.
[15] RAGHUWANSHI N K，PAREY A. Experimental measurement of gear mesh stiffness of cracked spur gear by strain gauge technique[J]. Measurement，2016，86(3)：266-275.
[16] SANCHEZ-ESPIGA J，FERNANDEZ-DEL-ROMCON A，IGIESIAS M，et al. Numerical evaluation of the accuracy in the load sharing calculation using strain gauges: Sun and ring gear tooth root[J]. Mechanism and Machine Theory，2022，175(5)：94-114.
[17] LIU Zimeng，HUANGFU Yifan，MA Hui，et al. Traveling wave resonance analysis of flexible spur gear system with angular misalignment[J]. International Journal of Mechanical Sciences，2022，232(8)：617-640.

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

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

编辑推荐

Metrics

本文评价

[1]	徐子扬, 魏静, 魏海波, 戚勍, 信琦, 刘指柔, 张玉杰. 薄辐板齿轮柔性化动力学模型与行波共振表征[J]. 机械工程学报, 2024, 60(11): 296-308.
[2]	曲永志, 王泽超, 周祖德. 动应变与加速度在机械系统动力学描述中的关联与比较[J]. 机械工程学报, 2022, 58(8): 79-87.