工程科学学报.第42卷.第8期：1048-1054.2020年8月 Chinese Journal of Engineering,Vol.42,No.8:1048-1054,August 2020 https://doi.org/10.13374/j.issn2095-9389.2019.07.18.002;http://cje.ustb.edu.cn 基于高阶同步压缩变换的行星齿轮箱声音信号共振频 带特征提取 张郑武，冯志鹏，陈小旺四 北京科技大学机械工程学院，北京100083 ☒通信作者，E-mail:chenxw@ustb.edu.cn 摘要建立了非平稳运行工况下行星齿轮箱共振频带内的声音信号解析模型，揭示了齿轮故障特征在声音信号共振频带 内的分布规律.根据共振频率不随转速变化的特点定位了齿轮箱共振频率，为在共振频带内提取齿轮故障特征奠定基础.针 对传统时频分析方法时频分辨率低的缺陷，研究了基于高阶同步压缩变换的时变故障特征提取方法.通过数值仿真和实验 信号分析，验证了所提出的声音信号模型与行星齿轮箱故障特征分布规律的正确性，以及利用高阶同步压缩变换方法提取共 振频带内行星齿轮箱故障特征的有效性. 关键词共振：同步压缩变换；非平稳：行星齿轮箱：故障诊断 分类号TG142.71 Acoustic signal analysis of the resonance frequency region for planetary gearbox fault diagnosis based on high-order synchrosqueezing transform ZHANG Zheng-wu,FENG Zhi-peng.CHEN Xiao-wang School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China Corresponding author,E-mail:chenxw@ustb.edu.cn ABSTRACT Planetary gearboxes have one or several planet gears rotating around the sun gear while revolving along their axle.This unique gear structure results in the simultaneous meshing of the planet gear with both sun and ring gears.Because of the high transmission ratio and large bearing capacity of its compact structure,planetary gearboxes have been extensively used in a variety of industrial applications.Therefore,planetary gearbox fault diagnosis is essential to ensure safe and efficient industrial manufacturing. Acoustic signal analysis provides an effective and noninvasive method for detecting potential faults in the planetary gearbox.However, the theoretical foundation of planetary gearbox fault signatures in acoustic signals is ambiguous.In this work,the planetary gearbox acoustic signal model of the resonance frequency region under the nonstationary state is structured by amplitude and frequency modulation,and the gear fault characteristics of the acoustic signals are explicitly derived.Given that resonance frequency is independent of rotational speed,the resonance frequency can be distinguished from speed-related frequency components.This lays the foundation for extracting the gear fault characteristics of the resonance frequency region.Moreover,the planetary gearbox often runs under time-varying speed conditions,and the fault frequency components are time-varying.To overcome the limitations of the traditional time-frequency analysis method in limited time-frequency resolution or cross-term interferences,the appropriate time-frequency ana- lysis method is essential.In this work,the high-order synchrosqueezing transform is exploited to identify the time-varying fault characteristics of the planetary gearbox acoustic signal.Owing to the step of squeezing the energy distributed along instantaneous 收稿日期：2019-11-19 基金项目：国家重点研发计划资助项目(2018YFC0810500):国家自然科学基金资助项目(51875034)：中央高校基本科研业务费资助项目 (FRF.TP.18-057A1):中国博士后科学基金资助项目(2019M650481)基于高阶同步压缩变换的行星齿轮箱声音信号共振频 带特征提取 张郑武，冯志鹏，陈小旺苣 北京科技大学机械工程学院，北京 100083 苣通信作者，E-mail：chenxw@ustb.edu.cn 摘    要    建立了非平稳运行工况下行星齿轮箱共振频带内的声音信号解析模型，揭示了齿轮故障特征在声音信号共振频带 内的分布规律. 根据共振频率不随转速变化的特点定位了齿轮箱共振频率，为在共振频带内提取齿轮故障特征奠定基础. 针 对传统时频分析方法时频分辨率低的缺陷，研究了基于高阶同步压缩变换的时变故障特征提取方法. 通过数值仿真和实验 信号分析，验证了所提出的声音信号模型与行星齿轮箱故障特征分布规律的正确性，以及利用高阶同步压缩变换方法提取共 振频带内行星齿轮箱故障特征的有效性. 关键词    共振；同步压缩变换；非平稳；行星齿轮箱；故障诊断 分类号    TG142.71 Acoustic signal analysis of the resonance frequency region for planetary gearbox fault diagnosis based on high-order synchrosqueezing transform ZHANG Zheng-wu，FENG Zhi-peng，CHEN Xiao-wang苣 School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China 苣 Corresponding author, E-mail: chenxw@ustb.edu.cn ABSTRACT    Planetary gearboxes have one or several planet gears rotating around the sun gear while revolving along their axle. This unique gear structure results in the simultaneous meshing of the planet gear with both sun and ring gears. Because of the high transmission ratio and large bearing capacity of its compact structure, planetary gearboxes have been extensively used in a variety of industrial applications. Therefore, planetary gearbox fault diagnosis is essential to ensure safe and efficient industrial manufacturing. Acoustic signal analysis provides an effective and noninvasive method for detecting potential faults in the planetary gearbox. However, the theoretical foundation of planetary gearbox fault signatures in acoustic signals is ambiguous. In this work, the planetary gearbox acoustic signal model of the resonance frequency region under the nonstationary state is structured by amplitude and frequency modulation, and the gear fault characteristics of the acoustic signals are explicitly derived. Given that resonance frequency is independent of rotational speed, the resonance frequency can be distinguished from speed-related frequency components. This lays the foundation for extracting the gear fault characteristics of the resonance frequency region. Moreover, the planetary gearbox often runs under time-varying speed conditions, and the fault frequency components are time-varying. To overcome the limitations of the traditional time–frequency analysis method in limited time–frequency resolution or cross-term interferences, the appropriate time–frequency ana￾lysis method is essential. In this work, the high-order synchrosqueezing transform is exploited to identify the time-varying fault characteristics of the planetary gearbox acoustic signal. Owing to the step of squeezing the energy distributed along instantaneous 收稿日期: 2019−11−19 基金项目: 国家重点研发计划资助项目（2018YFC0810500）；国家自然科学基金资助项目（51875034）；中央高校基本科研业务费资助项目 （FRF-TP-18-057A1）；中国博士后科学基金资助项目（2019M650481） 工程科学学报，第 42 卷，第 8 期：1048−1054，2020 年 8 月 Chinese Journal of Engineering, Vol. 42, No. 8: 1048−1054, August 2020 https://doi.org/10.13374/j.issn2095-9389.2019.07.18.002; http://cje.ustb.edu.cn