工程科学学报，第39卷，第4期：604610,2017年4月 Chinese Journal of Engineering,Vol.39,No.4:604-610,April 2017 DOI:10.13374/j.issn2095-9389.2017.04.016:http://journals.ustb.edu.cn 迭代广义短时Fourier变换在行星齿轮箱故障诊断中 的应用 张 东，冯志鹏网 北京科技大学机械工程学院，北京100083 ☒通信作者，E-mail:fengzp@usth.cdu.cn 摘要短时Fourier变换(STFT)在分析非平稳信号的过程中，受调制系数的影响，时频分布图中的能量扩散至主导频率的 周围，降低了时频分布的可读性.运用STT分析瞬时频率缓变或恒定的信号时，调制系数的影响较小甚至可以忽略不计，而 得到能量聚集程度很高的时频分布.根据这一特点，提出了迭代广义短时Fourier变换(IG-STFT),该方法有效改善了时频图 的可读性.首先运用迭代广义解调分离出频率恒定的单分量成分，然后运用ST℉T分析信号的时频分布，最后依据ST℉T的分 析结果和相位函数得到原信号的时频分布.通过行星齿轮箱仿真信号和实验信号分析，验证了该方法在分析非平稳信号中 的有效性，准确诊断了齿轮故障. 关键词故障诊断：行星齿轮箱：傅里叶变换：广义解调：非平稳信号 分类号TH165.3 Application of iterative generalized short-time Fourier transform to fault diagnosis of planetary gearboxes ZHANG Dong,FENG Zhi-peng School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:fengzp@ustb.edu.en ABSTRACT Due to the effect of the modulation part,the energy diffuses around the surrounding area of dominating frequencies and diminishes the readability of the time-frequency representation when short-time Fourier transform (STFT)is used to process nonsta- tionary signals.However,when the instantaneous frequency slowly changes or is constant,the effect is small and can even be neglec- ted.Thus,the time-frequency representations have high-energy concentration.Based on this feature,a novel method called iterative generalized short-time Fourier transform (IG-STFT)was proposed,which improved the readability of the time-frequency representa- tion.First,the stationary mono-components are separated using iterative generalized demodulation.Then,the time-frequency repre- sentations of each mono-component are acquired using STFT.Finally,the time-frequency representation of the original signal is obtained according to the analysis results of STFT and the phase function.The analysis results of a planetary gearbox simulation signal and experimental signals verify the effectiveness of this method for analyzing nonstationary signals and diagnosing gear faults. KEY WORDS fault diagnosis:planetary gearbox:Fourier transform:generalized demodulation:nonstationary signal 行星齿轮箱在风力发电机组、直升机等设备中应机组运行过程中行星齿轮箱齿轮一旦出现故障，将会 用广泛，是传动系统中的关键部件四.实际运行中行 大大降低动力传递效率甚至导致设备停机，带来巨大 星齿轮箱的工作环境恶劣，各齿轮易于出现故障.在 的经济损失乃至人员伤亡四。故研究行星齿轮箱的故 收稿日期：2016-06-20 基金项目：国家自然科学基金资助项目(11272047,51475038)工程科学学报，第 39 卷，第 4 期: 604--610，2017 年 4 月 Chinese Journal of Engineering，Vol． 39，No． 4: 604--610，April 2017 DOI: 10． 13374 /j． issn2095--9389． 2017． 04． 016; http: / /journals． ustb． edu． cn 迭代广义短时 Fourier 变换在行星齿轮箱故障诊断中 的应用 张 东，冯志鹏 北京科技大学机械工程学院，北京 100083 通信作者，E-mail: fengzp@ ustb． edu． cn 摘 要 短时 Fourier 变换( STFT) 在分析非平稳信号的过程中，受调制系数的影响，时频分布图中的能量扩散至主导频率的 周围，降低了时频分布的可读性． 运用 STFT 分析瞬时频率缓变或恒定的信号时，调制系数的影响较小甚至可以忽略不计，而 得到能量聚集程度很高的时频分布． 根据这一特点，提出了迭代广义短时 Fourier 变换( IG-STFT) ，该方法有效改善了时频图 的可读性． 首先运用迭代广义解调分离出频率恒定的单分量成分，然后运用 STFT 分析信号的时频分布，最后依据 STFT 的分 析结果和相位函数得到原信号的时频分布． 通过行星齿轮箱仿真信号和实验信号分析，验证了该方法在分析非平稳信号中 的有效性，准确诊断了齿轮故障． 关键词 故障诊断; 行星齿轮箱; 傅里叶变换; 广义解调; 非平稳信号 分类号 TH165 + . 3 收稿日期: 2016--06--20 基金项目: 国家自然科学基金资助项目( 11272047，51475038) Application of iterative generalized short-time Fourier transform to fault diagnosis of planetary gearboxes ZHANG Dong，FENG Zhi-peng School of Mechanical Engineering，University of Science and Technology Beijing，Beijing 100083，China Corresponding author，E-mail: fengzp@ ustb． edu． cn ABSTＲACT Due to the effect of the modulation part，the energy diffuses around the surrounding area of dominating frequencies and diminishes the readability of the time--frequency representation when short-time Fourier transform ( STFT) is used to process nonsta￾tionary signals． However，when the instantaneous frequency slowly changes or is constant，the effect is small and can even be neglec￾ted． Thus，the time--frequency representations have high-energy concentration． Based on this feature，a novel method called iterative generalized short-time Fourier transform ( IG-STFT) was proposed，which improved the readability of the time--frequency representa￾tion． First，the stationary mono-components are separated using iterative generalized demodulation． Then，the time--frequency repre￾sentations of each mono-component are acquired using STFT． Finally，the time--frequency representation of the original signal is obtained according to the analysis results of STFT and the phase function． The analysis results of a planetary gearbox simulation signal and experimental signals verify the effectiveness of this method for analyzing nonstationary signals and diagnosing gear faults． KEY WOＲDS fault diagnosis; planetary gearbox; Fourier transform; generalized demodulation; nonstationary signal 行星齿轮箱在风力发电机组、直升机等设备中应 用广泛，是传动系统中的关键部件［1］． 实际运行中行 星齿轮箱的工作环境恶劣，各齿轮易于出现故障． 在 机组运行过程中行星齿轮箱齿轮一旦出现故障，将会 大大降低动力传递效率甚至导致设备停机，带来巨大 的经济损失乃至人员伤亡［2］． 故研究行星齿轮箱的故