vibration-based health monitoring of damaged bevel...

MSC Software Confidential MSC Software Confidential

Vibration-based Health Monitoring of

Damaged Bevel Gears Using ADAMS 2012 Regional User Conference

Presented by Brian Fang, Xi Wu

May 7, 2013

MSC Software Confidential

• Detection of problems with gears is important for maintenance

• Methods for non-destructive detecting cracks in gear systems

have generally fallen short of the required performance

• A simple pair of gears involves sophisticated mathematics and it

cannot accurately simulate the gear train’s practical dynamic

behavior

• In 2008, MSC developed ADAMS software to realistically simulate

the dynamics behavior of gears

Background

2


• Acoustic and vibrational sensors used to detect

issues.

• Past Approaches:

– Time-Frequency

– Wavelet Transform

Past Methods

3


• The housing of gears tends to vibrate strongly at the gear mesh

frequency

• 𝐺𝑀𝐹 = 𝑁𝑝Ω𝑝 = 𝑁𝐺Ω𝐺

– 𝑁𝑝 and 𝑁𝐺 number of teeth on the pinion and gear respectively

– Ω𝑝 andΩ𝐺 angular velocity of the pinion and gear respectively

Gear Mesh Frequencies (GMF)

4


• A quick algorithm recently developed to assess the health of a

gear system using just FFT

𝑆𝐸𝑅 = 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒𝑖6𝑖=1

𝑐𝑒𝑛𝑡𝑒𝑟 𝑚𝑒𝑠ℎ 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒

• Note that actual fluctuations can be quite complex in actual

damaged gear system.

• Magnitude of sideband peaks is compared to that of the center

frequency peak.

• Large ratios are indicative of damage system while ratios of

around 1 or less are indicative of healthy systems

Sideband Energy Ratio

5


• The center frequency is the gear mesh frequency and we expect

the strong responses at those frequencies.

• The SER will be large for damaged systems.

• The location of accelerometers will play role in collecting

consistent data.

Hypotheses

6


Experiment

• The gear system was run at 5

frequencies

– Motor Shaft Speed: 10hz,

15hz, 20hz, 25hz, and 30hz

• An oscilloscope was used to

calculate the input shaft

speed

• In previous experiments

bearing and gears were

intentionally damaged.

7


Experiment (continued)

• Four PCB accelerometers

were used

• Accelerometers 1, 3 and 4

were placed along the shafts

• Accelerometer 2 was placed

above the gears

• Dactron® acquisition system

was used recorded output

from accelerometers and

plotted FFT

8


Experimental Results

• FFT of the data

collected from

accelerometer

2 at an input

shaft speed of

15Hz

9

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 90 180 270 360 450 540 630

Acc

ele

rati

on

(m

/s^

2)

Frequency (Hz)

15Hz Accelerometer 2

ORBP

GMF 2*GMF 3*GMF


Experimental Results (continued)

• FFT of the data

collected from

accelerometer

2 at an input

shaft speed of

30Hz

10

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 180 360 540 720 900 1080 1260 1440 1620

Acc

ele

rati

on

(m

/s^

2)

Frequency (hz)

30Hz Accelerometer 2

GMF 3*GMF

2*GMF

ORBP


• SER to be 2.975 to 3.269 with 99% Confidence*

• Consistency depended on location of sensor. The most consistent

Experimentally Determined SER

11

Locations Speed

10 Hz 15 Hz 20 Hz 25 Hz 30 Hz

Accelerometer 1 3.058 3.849 3.172 3.583 2.98

Accelerometer 2 3.059 3.5003 2.444 3.07 2.428

Accelerometer 3 3.556 3.886 1.602 3.378 3.323

Accelerometer 4 3.261 4.31 1.648 4.403 2.691


• Two systems

– Perfect gear system

– Damaged Gear system

ADAMS Simulation

12


Parameters Value

Stiffness K 1.8 x 105 N-mm

Force Exponent e 2.2

Damping c .27 N-s/mm

Penetration dc 1 x 10-3 mm

Young's Modulus E 2.07 x 1011 Pa

Poisson's Ratio ν 0.29

Density ρ 7801 kg/m3

ADAMS Simulation Parameters

Parameters Value

Backlash B 0.05 mm

Module m 3 mm/tooth

Pressure Angle Φ 20 deg

Face Width F 10mm

Pinion Zp 13 Teeth

Gear Zg 26 Teeth

13


• Constant angular velocity on pinion

• Resistance torque of 10N-mm added to Gear

• Revolute joints at the center of the gears

Simulation Constraints

14


Perfect Gear System

0

2

4

6

8

0 100 200 300 400 500 600 700 800

Fo

rec (

N)

Frequency (Hz)

15Hz Perfect Gearing System


Perfect Gear System

0

1

2

3

4

5

0 500 1000 1500

Fo

rce (

N)

Frequency (Hz)

30Hz Perfect Gearing System


Damaged Gear System

-1

1

3

5

7

9

0 100 200 300 400 500 600 700 800

Fo

rce (

N)

Frequency (Hz)

15hz Damaged Gearing System


Damaged Gear System

0

1

2

3

4

5

0 200 400 600 800 1000 1200 1400 1600

Fo

rce (

N)

Frequency (Hz)

30Hz Damaged Gearing System


Simulation Determined SER

• For Undamaged system, the mean was 0.970

• For Damaged system, the mean was 2.55

SER Indicator

Speed

10 Hz 15 Hz 20 Hz 25 Hz 30 Hz

SER for a perfect

gearing system 0.99 0.68 1.07 1.07 1.04

SER for a damaged

gearing system 2.95 3.71 1.62 1.81 2.66


Conclusion

• ADAMS Simulation does vary quite a bit, but it is able to follow

the pattern and theory of SER

• SER relatively simple way to detect problems and their severity;

more difficult to predict exact issue


Further Study

• Do experiment with a healthy gear system

• Make a more complex gear system model by :

– Adding in bearings in ADAMS

– Using vibration package

– Include friction

– Include housing

MSC Software Confidential 22

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