Jungho Park, Ph. D. candidateLaboratory 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

CONTENTS

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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

01

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INTRODUCTION

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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

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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

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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.

02

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Analytical Modeling of Vibration Signals from a Planetary Gear

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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

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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°

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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

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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)

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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)

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Analytical Modeling of Vibration Signals from a Planetary Gear

Generalized Vibration Signals – 3 : code implementation - ①

cos

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Analytical Modeling of Vibration Signals from a Planetary Gear

∑

Generalized Vibration Signals – 3 : code implementation - ②

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Analytical Modeling of Vibration Signals from a Planetary Gear

Generalized Vibration Signals – 3 : code implementation - ③

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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.

12 cos

14 cos

14 cos

(a) (b)

(c) (d)

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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)

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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.

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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.

03

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ConcludingRemarks

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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