Abstract
The sidebands spaced around the gear meshing content and its harmonics are the commonly used fault indicator in the gear fault diagnosis under the constant rotational speed condition. However, when the gear works under the run-up condition, the variable rotational speed causes smearing to the frequency spectrum, which makes it difficult to recognize the sidebands caused by the local gear fault. This paper proposed a method which combines Fractional Fourier Transform (FrFT) and the Hilbert Transform (HT) to identify the sidebands of signal measured under the run-up process. The HT is utilized to construct the analytic representation of the measured signal, which has a better energy concentration than the measured signal in the fractional domain. Thus, the ability of extracting weak sidebands of FrFT is enhanced. Simulation case study and experimental case study are carried to verify the effectiveness of the proposed method. Tooth cracks of different depth are manufactured artificially to simulate the local fault of different severity. The results show that the weak sidebands which is invisible in the time-frequency representation can be identified by the proposed method. The amplitude of gear meshing content and its sidebands ascends with the growth of the crack depth.
This project is supported by National Natural Science Foundation of China (Grant No. 51775394), Hubei Province Major Science and Technology Innovation Plan (2018AAA024).
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References
Hong, L., Dhupia, J.S.: A time domain approach to diagnose gearbox fault based on measured vibration signals. J. Sound Vib. 333, 2164–2180 (2014)
Li, G., Li, F., Liu, H., Dong, D.: Fault features analysis of a compound planetary gear set with damaged planet gears. Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci. 232, 1586–1604 (2018)
Wen, L., Li, X., Gao, L., Zhang, Y.: A new convolutional neural network-based data-driven fault diagnosis method. IEEE Trans. Ind. Electron. 65, 5990–5998 (2018)
Zhao, R., Wang, D., Yan, R., Mao, K., Shen, F., Wang, J.: Machine health monitoring using local feature-based gated recurrent unit networks. IEEE Trans. Ind. Electron. 65, 1539–1548 (2018)
Xu, X., Qiao, Z., Lei, Y.: Repetitive transient extraction for machinery fault diagnosis using multiscale fractional order entropy infogram. Mech. Syst. Signal Process. 103, 312–326 (2018)
Mei, J., Jia, J., Zeng, R., Zhou, B., Zhao, H.: A multi-order FRFT self-adaptive filter based on segmental frequency fitting and early fault diagnosis in gears. Measurement 91, 532–540 (2016)
Li, Z., Wu, Z., He, Y., Fulei, C.: Hidden Markov model-based fault diagnostics method in speed-up and speed-down process for rotating machinery. Mech. Syst. Signal Process. 19, 329–339 (2005)
Luo, J., Yu, D., Liang, M.: Application of multi-scale chirplet path pursuit and fractional Fourier transform for gear fault detection in speed up and speed-down processes. J. Sound Vib. 331, 4971–4986 (2012)
Li, Z., He, Y., Chu, F., Han, J., Hao, W.: Fault recognition method for speed-up and speed-down process of rotating machinery based on independent component analysis and Factorial Hidden Markov Model. J. Sound Vib. 291, 60–71 (2006)
Feng, Z., Chen, X., Liang, M.: Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mech. Syst. Signal Process. 52–53, 360–375 (2015)
Chen, X., Feng, Z.: Iterative generalized time-frequency reassignment for planetary gearbox fault diagnosis under nonstationary conditions. Mech. Syst. Signal Process. 80, 429–444 (2016)
Feng, Z., Chen, X., Liang, M.: Joint envelope and frequency order spectrum analysis based on iterative generalized demodulation for planetary gearbox fault diagnosis under nonstationary conditions. Mech. Syst. Signal Process. 76–77, 242–264 (2016)
Wang, S., Chen, X., Selesnick, I.W., Guo, Y., Tong, C., Zhang, X.: Matching synchrosqueezing transform: a useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis. Mech. Syst. Signal Process. 100, 242–288 (2018)
Sun, R., Yang, Z., Chen, X., Tian, S., Xie, Y.: Gear fault diagnosis based on the structured sparsity time-frequency analysis. Mech. Syst. Signal Process. 102, 346–363 (2018)
Zhao, M., Lin, J., Wang, X., Lei, Y., Cao, J.: A tacho-less order tracking technique for large speed variations. Mech. Syst. Signal Process. 40, 76–90 (2013)
Chen, R., Wang, Y.: Efficient detection of chirp signals based on the fourth-order origin moment of fractional spectrum. Circ. Syst. Signal Process. 33, 1585–1596 (2014)
Almeida, L.B.: The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42, 3084–3091 (1994)
Ozaktas, H.M., Arikan, O., Kutay, M.A., Bozdagt, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44, 2141–2150 (1996)
Press, W.H.: Numerical Recipes 3rd Edition: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)
McFadden, P.D.: Examination of a technique for the early detection of failure in gears by signal processing of the time domain average of the meshing vibration. Mech. Syst. Signal Process. 1, 173–183 (1987)
Samuel, P.D., Pines, D.J.: A review of vibration-based techniques for helicopter transmission diagnostics. J. Sound Vib. 282, 475–508 (2005)
Chen, Z., Shao, Y.: Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depth. Eng. Fail. Anal. 18, 2149–2164 (2011)
Li, Y., Ding, K., He, G., Lin, H.: Vibration mechanisms of spur gear pair in healthy and fault states. Mech. Syst. Signal Process. 81, 183–201 (2016)
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Zhou, Q., Wu, C., Fan, Q. (2020). Gear Fault Diagnosis Under the Run-Up Condition Using Fractional Fourier Transform and Hilbert Transform. In: Tan, J. (eds) Advances in Mechanical Design. ICMD 2019. Mechanisms and Machine Science, vol 77. Springer, Singapore. https://doi.org/10.1007/978-981-32-9941-2_77
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