分数阶阻尼裂纹转子的小波尺度谱分析方法研究

doi:10.3969/j.issn.1000-1093.2014.08.022

摘要/Abstract

摘要： 结合在分数阶微积分的基础上建立的裂纹转子系统模型和小波尺度谱，提出基于小波尺度谱的分数阶阻尼的转子裂纹故障诊断方法，并讨论了不同的裂纹深度下分数阶阻尼的裂纹转子系统的小波尺度谱和重分配尺度谱特性。仿真结果表明，分数阶阶次的改变对系统运动特性有很大的影响，在建立动力学模型时可以灵活调节分数阶阶次来改变转子系统的振动特性以达到诊断转子裂纹的最佳效果。提出的方法对裂纹故障敏感，能有效地提取裂纹转子系统中的故障信息。最后用实验进行了验证，实验结果与理论数值分析的结果相吻合，验证了文中建立的分数阶阻尼的裂纹转子系统模型的正确性。

关键词: 动力机械工程, 小波尺度谱, 分数阶微积分, 裂纹转子, 故障诊断

Abstract: A fault diagnosis method of cracked rotor system with fractional order damping based on wavelet scalogram is proposed through the model of cracked rotor system based on the fractional calculus and wavelet scalogram. The characteristics of wavelet scalogram and reassigned scalogram from different crack depth in rotor system with fractional order damping are discussed. The simulation results show that the derivative order of damping and the crack depth have great influence to the dynamics characteristics of rotor system. The optimal derivative order of damping can be determined by adjusting the fractional order. The proposed method is sensitive to crack fault, which can effectively extract the crack fault information in the rotor system. Finally, the effectiveness of the proposed method is verified through the experiment rig. The experimental results are very consistent with the simulation results, and the proposed model of cracked rotor system based on the fractional calculus is correct.

Key words: power machinery engineering, wavelet scalogram, fractional calculus, cracked rotor, fault diagnosis

中图分类号:

TH165.3

李志农，王海峰，何旭平，肖尧先. 分数阶阻尼裂纹转子的小波尺度谱分析方法研究[J]. 兵工学报, 2014, 35(8): 1281-1287.

LI Zhi-nong, WANG Hai-feng, HE Xu-ping, XIAO Yao-xian. Using Wavelet Scalogram Method to Analyze Cracked Rotor System with Fractional Order Damping[J]. Acta Armamentarii, 2014, 35(8): 1281-1287.

参考文献

［1］李志农, 丁启全, 吴昭同, 等. 转子裂纹的高阶谱分析［J］. 振动与冲击, 2002, 21(1): 60-62.
LI Zhi-nong, DING Qi-quan, WU Zhao-tong, et al. High-order spectrum analysis of cracked rotor［J］. Journal of Vibration and Shock, 2002,21(1): 60-62. (in Chinese)
［2］员险锋, 李志农, 林言丽. 基于非线性输出频率响应函数的裂纹故障诊断方法研究［J］. 机械强度, 2013, 35(2): 133-137.
YUAN Xian-feng, LI Zhi-nong, LIN Yan-li. Crack fault diagnosis method based on nonlinear output frequency response function［J］. Journal of Mechanical Strength, 2013, 35(2): 133-137. (in Chinese)
［3］ Li H，Zhang Y P，Zheng H Q. Application of Hermitian wavelet to crack fault detection in gearbox［J］. Mechanical Systems and Signal Processing, 2011, 25(4): 1353-1363.
［4］ Robert G. Dynamic behaviour of the Laval rotor with a transverse crack［J］. Mechanical Systems and Signal Processing，2008，22(4)： 790-804.
［5］ Stoisser C M, Audebert S. A comprehensive theoretical, numerical and experimental approach for crack detection in power plant rotating machinery［J］. Mechanical Systems and Signal Processing, 2008, 22(4): 818-844.
［6］ Sekhar A S. Crack identification in a rotor system: a model-based approach［J］. Journal of Sound and Vibration, 2004, 270(4/5): 887-902.
［7］陈雪峰, 向家伟, 董洪波, 等. 基于区间B样条小波有限元的转子裂纹定量识别［J］. 机械工程学报, 2007, 43(3): 123-127.
CHEN Xue-feng, XIANG Jia-wei, DONG Hong-bo, et al. Quantitative identification of rotor cracks based on finite element of B-spline wavelet on the interval［J］. Chinese Journal of Mechanical Engineering, 2007,43(3): 123-127. (in Chinese)
［8］刘长利, 周邵萍, 江君, 等. 双盘双呼吸型裂纹转子的非线性动力学特性［J］. 振动、测试与诊断, 2012, 32(4): 136-140.
LIU Chang-li, ZHOU Shao-ping, JIANG Jun, et al. Nonlinear dynamics analysis of double-disc rotor with two breathing cracks［J］. Journal of Vibration, Measurement & Diagnosis, 2012, 32(4): 136-140. (in Chinese)
［9］ Auger F, Flandrin P. Improving the readability of time-frequency and time-scale representations by the reassignment method［J］. IEEE Transacion on Signal Processing, 1995, 43(5) : 1068-1089.
［10］ Peng Z K, Chu F L, Tse P W. Detection of the rubbing-caused impacts for rotor-stator fault diagnosis using reassigned scalogram［J］. Mechanical Systems and Signal Processing, 2005, 19(2): 391-409.
［11］ Peng Z, Chu F, He Y. Vibration signal analysis and feature extraction based on reassigned wavelet scalogram［J］. Journal of Sound and Vibration, 2002, 253(5): 1087-1100.
［12］褚福磊, 彭志科,冯志鹏, 等. 机械故障诊断中的现代信号处理方法［M］. 北京：科学出版社, 2009.
CHU Fu-lei, PENG Zhi-ke, FENG Zhi-peng, et al. Modern signal processing method for mechanical fault diagnosis［M］. Beijing: Science Press, 2009. (in Chinese)
［13］ He Y Y, Liu Y. Experimental research into time-frequency characteristics of cavitation noise using wavelet scalogram［J］. Applied Acoustics, 2011, 72(10): 721-731.
［14］ Yesilyurt I. The application of the conditional moments analysis to gearbox fault detection-a comparative study using the spectrogram and scalogram［J］. NDT & E International, 2004, 37(4): 309-320.
［15］ Yesilyurt I. End mill breakage detection using mean frequency analysis of scalogram［J］. International Journal of Machine Tools and Manufacture, 2006, 46(3/4): 450-458.
［16］任朝晖, 马辉, 王德明, 等. 小波分析在转子裂纹故障中的应用［J］. 东北大学学报:自然科学版, 2007, 28(4): 545-548.
REN Chao-hui, MA Hui, WANG De-ming, et al. Application of wavelet transform to crack fault diagnosis for rotor systems［J］. Journal of Northeastern University:Natural Science, 2007, 28(4): 545-548. (in Chinese)
［17］ Torvik P J, Bagley R L. On the appearance of the fractional derivative in the behavior of real materials［J］. Journal of Applied Mechanics, 1984, 51(2): 294-298.
［18］曾复. 裂纹转子非线性振动机理及实验研究［D］. 杭州：浙江大学, 2001.
ZENG Fu. Research on mechanism of nonlinear vibration of cracked rotors and relative experiment［D］. Hangzhou:Zhejiang University, 2001. (in Chinese)
［19］李志农. 时序模型盲辨识在旋转机械故障诊断中的应用研究［D］. 杭州：浙江大学, 2002.
LI Zhi-nong. Blind identification of time series model and its application on fault diagnosis of rotating machinery［D］. Hangzhou:Zhejiang University, 2002. (in Chinese)

[1]	王伽豪，那文波，刘志威，昝琪，王铮. 双闭环比值控制系统传感器故障诊断方法[J]. 兵工学报, 2024, 45(4): 1252-1263.
[2]	吕卫民, 孙晨峰, 任立坤, 赵杰, 李永强. 一种基于TCN-LGBM的航空发动机气路故障诊断方法[J]. 兵工学报, 2024, 45(1): 253-263.
[3]	魏剑峰, 张发平, 卢继平, 杨向飞, 杨鹏楷. 基于高斯模型和RMSD-DS的火炮反后坐装置故障诊断方法[J]. 兵工学报, 2023, 44(10): 3101-3114.
[4]	黄文宽, 钱林方, 尹强, 刘太素. 基于迁移学习的供药装置故障诊断方法[J]. 兵工学报, 2023, 44(10): 2964-2974.
[5]	李良钰，苏铁熊，马富康，吴小军，徐春龙. 基于集合经验模态分解-支持向量机的高压共轨系统故障诊断方法[J]. 兵工学报, 2022, 43(5): 992-1001.
[6]	李泽东，李志农，陶俊勇，毛清华，张旭辉. 基于特征融合的注意力增强卷积神经网络的航空发动机滚动轴承故障诊断方法[J]. 兵工学报, 2022, 43(12): 3228-3239.
[7]	李炜，韩寅龙，孙晓静. 基于特征优选与深度学习的车载电源微小故障诊断方法[J]. 兵工学报, 2022, 43(11): 2935-2944.
[8]	李志农, 胡志峰, 毛清华, 张旭辉, 陶俊勇. 非线性调频模态分解-同步提取变换方法及其在滚动轴承故障诊断中的应用[J]. 兵工学报, 2021, 42(6): 1324-1330.
[9]	朱敏，许爱强，许晴，李睿峰. 基于改进多层核超限学习机的模拟电路故障诊断[J]. 兵工学报, 2021, 42(2): 356-369.
[10]	李佳蔚，崔涛，刘宇航，师帅楠，孙强. 基于排气温度动态模型的在线观测器研究[J]. 兵工学报, 2019, 40(8): 1562-1571.
[11]	郭伟超，赵怀山，李成，李言，汤奥斐. 基于小波包能量谱与主成分分析的轴承故障特征增强诊断方法[J]. 兵工学报, 2019, 40(11): 2370-2377.
[12]	翟禹尧，史贤俊，吕佳朋. 基于广义随机Petri网的导弹系统测试性建模与指标评估方法研究[J]. 兵工学报, 2019, 40(10): 2070-2079.
[13]	李文军，王潇楠，郑永军. 热电偶分数阶传递函数阶次和参数估计[J]. 兵工学报, 2018, 39(9): 1820-1828.
[14]	张伟，刘星，许爱强，平殿发. l_p范数约束的模拟电路3层多核故障诊断模型[J]. 兵工学报, 2018, 39(7): 1352-1363.
[15]	任海锋，潘宏侠. 基于多分形特征的枪械自动机裂纹故障诊断[J]. 兵工学报, 2018, 39(3): 457-462.