Analytical Modeling of Vibration Signals from a Planetary Gear in Normal and Faulty Conditions
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This document summarizes analytical modeling of vibration signals from a planetary gear. It first introduces dynamic modeling of planetary gears from previous literature. It then describes modeling normal vibration signals by considering gear configurations and phase differences. Code is shown to simulate the signals. Modeling of faulty signals is also discussed by considering amplitude modulation and frequency modulation. The document concludes by noting the need to simulate developed faulty behaviors and validate with test data.
Analytical Modeling of Vibration Signals from a Planetary Gear in Normal and Faulty Conditions
- 1. Jungho Park, Ph. D. candidate Laboratory for System Health and Risk Management(SHRM) Department of Mechanical and Aerospace Engineering, Seoul National University hihijung@snu.ac.kr Analytical Modeling of Vibration Signals from a Planetary Gear in Normal and Faulty Conditions
- 2. CONTENTS 2016/12/23 Seoul National University 2 Introduction01 Analytical Modeling of Vibration Signals from a Planetary Gear 02 Concluding Remarks05 Planetary Gear in a Normal Condition Planetary Gear in a Faulty Condition
- 3. 01 2016/12/23 Seoul National University 3 INTRODUCTION
- 4. 2016/12/23 Seoul National University 4 INTRODUCTION Dynamic modeling of a Planetary Gear Inalpolat, Murat, and Ahmet Kahraman. "A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors." Journal of Sound and Vibration 329.4 (2010): 371-393. Google Citation : 98 Al-Shyyab, A., and A. Kahraman. "A non-linear dynamic model for planetary gear sets." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221.4 (2007): 567-576.Google Citation : 31
- 5. 2016/12/23 Seoul National University 5 INTRODUCTION Dynamic modeling of a Planetary Gear Motivation : The predicted signals of dynamic models could be different from vibration signals using accelerometers. Inalpolat, Murat, and Ahmet Kahraman. "A dynamic model to predict modulation sidebands of a planetary gear set having manufacturing errors." Journal of Sound and Vibration 329.4 (2010): 371-393. Google Citation : 98 Al-Shyyab, A., and A. Kahraman. "A non-linear dynamic model for planetary gear sets." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 221.4 (2007): 567-576.Google Citation : 31
- 6. 2016/12/23 Seoul National University 6 Inalpolat, Murat, and A. Kahraman. "A theoretical and experimental investigation of modulation sidebands of planetary gear sets." Journal of Sound and Vibration 323.3 (2009): 677-696. Google Citation : 161 INTRODUCTION Motivation & Objective ① ② ③ACC. • Motivation : The predicted signals of dynamic models could be different from vibration signals using accelerometers. • Objective : Literature review will be given with the codes that simulated the modulated vibration signals of a planetary gear.
- 7. 02 2016/12/23 Seoul National University 7 Analytical Modeling of Vibration Signals from a Planetary Gear
- 8. 2016/12/23 Seoul National University 8 Analytical Modeling of Vibration Signals from a Planetary Gear Configuration of a Planetary Gear Ring Gear Planet Gear Carrier Sun Gear Case (i) : Equally spaced planets and in-phase gear meshes Same loads at each planet Case (ii) : Equally spaced planets and sequentially phased gear meshes Benefits in reducing vibration and noises Case (iii) : Unequally spaced planets and in-phase gear meshes Case (iv) : Unequally spaced planets and sequentially phased gear meshes
- 9. 2016/12/23 Seoul National University 9 Analytical Modeling of Vibration Signals from a Planetary Gear Difference between Case (i) and (ii) Case (i) : Equally spaced planets and in- phase gear meshes Case (ii) : Equally spaced planets and sequentially phased gear meshes . ° • Example) Vr = 93, Vp=31 • Example Vr = 95, Vp=31, Vs=31, ° . ° 120° . ° 3 120°
- 10. 2016/12/23 Seoul National University 10 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals - 1 ∑ cos • First, the dynamic mesh force for ring-planet i mesh can be expressed in Fourier series as : The Fourier coefficient of j-th harmonic of the dynamic force : The phase angle of the j-th harmonic component : The phase angle between the ring gear meshes of planet i and planet 1 2 1 / • However, the modulation from measured vibration signals should be considered. 1 carrier rotation
- 11. 2016/12/23 Seoul National University 11 Analytical Modeling of Vibration Signals from a Planetary Gear cos ∑ Weighting function : (phase angle considered) Generalized Vibration Signals - 2 (i)th planet (i+1)th planet (i+2)th planet X X X • Combination of Hanning and step function to simulate weighted vibration signals measured from the accelerometer (phase angle not considered)
- 12. 2016/12/23 Seoul National University 12 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals - 3 (i)th planet (i+1)th planet (i+2)th planet X X X • Combination of Hanning and step function to simulate weighted vibration signals measured from the accelerometer (phase angle not considered)
- 13. 2016/12/23 Seoul National University 13 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals – 3 : code implementation - ① cos
- 14. 2016/12/23 Seoul National University 14 Analytical Modeling of Vibration Signals from a Planetary Gear ∑ Generalized Vibration Signals – 3 : code implementation - ②
- 15. 2016/12/23 Seoul National University 15 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals – 3 : code implementation - ③
- 16. 2016/12/23 Seoul National University 16 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals – 4 - ①: Case (i) (a) N=3, Zr=123 and Zs=72, (b) N=4, Zr=124 and Zs=72, (c) N=5, Zr=125 and Zs=70, (d) N=6, Zr=126 and Zs=72 • For this case, the equation can be simplified like a below equation as there are no phase differences between planets. 1 2 cos 1 4 cos 1 4 cos (a) (b) (c) (d)
- 17. 2016/12/23 Seoul National University 17 Analytical Modeling of Vibration Signals from a Planetary Gear Generalized Vibration Signals – 4 - ②: Case (ii) (a) N=3, Zr=125 and Zs=73, (b) N=4, Zr=126 and Zs=74, (c) N=5, Zr=126 and Zs=74, (d) N=6, Zr=122 and Zs=70 • The symmetry could be different due to the order of phase differences. (a) (b) (c) (d)
- 18. 2016/12/23 Seoul National University 18 Analytical Modeling of Vibration Signals from a Planetary Gear Modelling of Faulty Signals - 1 Feng, Zhipeng, and Ming J. Zuo. "Vibration signal models for fault diagnosis of planetary gearboxes." Journal of Sound and Vibration 331.22 (2012): 4919-4939. Google Citation : 96 • In the literature, AM and FM effects due to gear damage as well as transfer path were considered. 1 cos 2 . cos 2 sin 2 . AM by faulty gear rotation FM by faulty gear rotation , , In this case, the faults were simplified as abrupt local peaks.
- 19. 2016/12/23 Seoul National University 19 Analytical Modeling of Vibration Signals from a Planetary Gear Modelling of Faulty Signals - 2 • The ring gear local fault was simulated. • Faulty behaviors in the frequency domain are not obvious. Need to define health indices in the time domain, after using filtering techniques to remove noises.
- 20. 03 2016/12/23 Seoul National University 20 Concluding Remarks
- 21. 2016/12/23 Seoul National University 21 Concluding Remarks Concluding Remarks • Simulated the modulated vibration signals of a planetary gear in a normal and faulty conditions measured from an accelerometer. • Observed the difference between normal and faulty conditions in the time and frequency domain. • Need to simulate faulty behaviors developed in the previous literature, and validate using the test-bed data. ① ② ③