Acoustic signal analysis of the resonance frequency region for planetary gearbox fault diagnosis based on high-order synchrosqueezing transform
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摘要: 建立了非平穩運行工況下行星齒輪箱共振頻帶內的聲音信號解析模型，揭示了齒輪故障特征在聲音信號共振頻帶內的分布規律。根據共振頻率不隨轉速變化的特點定位了齒輪箱共振頻率，為在共振頻帶內提取齒輪故障特征奠定基礎。針對傳統時頻分析方法時頻分辨率低的缺陷，研究了基于高階同步壓縮變換的時變故障特征提取方法。通過數值仿真和實驗信號分析，驗證了所提出的聲音信號模型與行星齒輪箱故障特征分布規律的正確性，以及利用高階同步壓縮變換方法提取共振頻帶內行星齒輪箱故障特征的有效性。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 analysis 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 frequency in frequency direction, time–frequency representation by synchrosqueezing transform achieves a high time–frequency resolution. The high-order interpretation of instantaneous frequency further improves the capability to capture the time–frequency details. The acoustic signal model and corresponding fault characteristics of the planetary gearbox in the resonance frequency region are verified by both numerical simulations and laboratory experiments. The gear defect within the planetary gearbox is successfully diagnosed via the high-order synchrosqueezing transform.
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Key words:
- resonance /
- synchrosqueezing transform /
- nonstationary /
- planetary gearbox /
- fault diagnosis
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圖 1 仿真信號。（a）波形；（b）Fourier頻譜；（c）STFT時頻分布；（d）Wigner?Ville分布；（e）FSST；（f）FSST4
Figure 1. Simulation signal: (a) waveform; (b) Fourier spectrum; (c) time–frequency representation(TFR) by STFT; (d) Wigner–Ville distribution; (e) time-frequency representation by FSST; (f) time-frequency representation by FSST4
圖 2 實驗裝置。1—電動機；2—定軸齒輪箱；3,5—行星齒輪箱；4—聲壓傳感器；6—磁粉制動器；7—太陽輪故障
Figure 2. Test rig: 1—motor; 2—fixed-shaft gearbox; 3, 5—planetary gearbox; 4—microphone; 6—magnetic powder brake; 7—sun gear fault
圖 3 正常狀態聲音信號分析。（a）STFT時頻分布；（b）FSST4時頻分布
Figure 3. Acoustic signal analysis under normal conditions: (a) TFR by STFT; (d) TFR by FSST4
圖 4 太陽輪故障狀態聲音信號分析；（a）STFT時頻分布；（b）FSST4時頻分布
Figure 4. Acoustic signal analysis under sun gear fault conditions: (a) TFR by STFT; (b) TFR by FSST4
表 1 齒輪箱主要參數
Table 1. Main parameters of gearboxes
Gear Gear teeth number Gear Gear teeth number Gear fault frequency First stage Second stage Input 32 — Sun 20 ${f_{\rm{s}}}{\rm{(}}t{\rm{) = }}(20/27){f_{\rm{d}}}{\rm{(}}t{\rm{)}}$ Intermediate 96 16 Planet 40 (4) ${f_{\rm{p}}}{\rm{(}}t{\rm{) = }}(5/54){f_{\rm{d}}}{\rm{(}}t{\rm{)}}$ Output — 48 Ring 100 ${f_{\rm{r}}}{\rm{(}}t{\rm{) = }}(4/27){f_{\rm{d}}}{\rm{(}}t{\rm{)}}$ Note: the number in the parentheses indicates the number of planet gears. 
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