Fault Diagnosis

MENG 475 – Fall 2010

Unbalance

Static unbalanceActing through the center of mass of the rotorCan be corrected at a single location (plane)Can be detected without spinning the rotorVibration measurements will be in-phase1X RPM always present and dominates spectrum

1X RADIAL

Unbalance

Couple unbalanceRotor is statically balanced, but dynamically unbalancedVibration measurements 180° out-of-phase1X RPM always present and dominates spectrum

1X RADIAL

Unbalance

Dynamic unbalanceCombination of static & couple unbalance1X RPM always present and dominates spectrumRadial phase can vary

1X RADIAL

Bearing Faults

Bearing Faults

Damaged inner ring Damaged rolling element Damaged outer ring

Bearing Faults

Measurement of “spikiness”:• Crest Factor (peak to RMS)• Kurtosis (4th power statistical average)

Amplitude Modulation: Sidebands

SidebandsHigh frequency (150 Hz)

signal modulated by a low

frequency (5 Hz) signal

Gear Vibration

When gear teeth go into and out of mesh, they create cyclic forces

and vibrations. These vibrations occur at the gear mesh frequency

(GMF), which is given by:

where N is the number of teeth and w is the angular velocity. For

example, a 40 tooth gear mounted on a shaft rotating at 3600 rpm

would have a GMF of (40×3600/60) = 2400 Hz. These periodic

forces produce harmonics in the spectrum according to the Fourier

series. Therefore, vibrations are expected to occur not only at the

GMF, but also at its harmonics.

GMF N

Amplitude ModulationThis occurs in gears with excessive backlash or eccentricity. The result is a

high-frequency vibration signal (carrier wave) whose amplitude is varying at a

lower frequency (modulating wave):

0 0.5 1 1.5 2 2.5 3-1.5

-1

-0.5

0

0.5

1

1.5

Variation in the amplitude of vibration, or amplitude modulation, can be caused by

varying loads, misalignment, improper backlash and eccentricity in the shaft, teeth or

gear. If one event occurs during each revolution, then the modulating frequency is

the speed of the problem gear.

Gear FaultsExample: Gear vibrations at the GMF of 150 rad/s, modulated by the speed of shaft

rotation of 5 rad/s. The time signal can be expressed as:

1 0.5cos 5 cos 150x t t

This time signal leads to distinctive sidebands in

the spectrum of gear vibration, as explained

here. Using the trigonometric identity:

1 12 2

cos cos cos cos

1 14 4

cos 150 cos 155 cos 145x t t t

0 0.5 1 1.5 2 2.5 3-1.5

-1

-0.5

0

0.5

1

1.5

GMF = N = 150 rad/s

= 5 rad/s

N

Gear Faults

The Fourier analysis reveals a spectrum that has

the GMF ± sidebands

1 14 4

cos 150 cos 155 cos 145x t t t

1N

1N

GMF N

Sideband Sideband

0 50 100 150 200 250 300 350 400 450 5000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

GMF

2GMF

SidebandsSidebands

These sidebands

also occur at the

harmonics of the

GMF

Gear Faults

Vibration Spectrum – Gear

1N 1N

N1st meshing

2nd meshing

2 1N 2 1N

2N

When two or more events occur during each revolution (such as tooth-to-tooth spacing

errors or eccentricity errors), the modulating frequency will be two or more times the

speed of rotation of the faulty gear, resulting in a family of sidebands around the GMF and

its harmonics.

… … … …

…

Misalignment

Vibration Orbit Patterns When the signals from two proximity

probes are combined together in a two-

channel oscilloscope or vibration

analyzer, the orbital motion of the shaft

can be observed. Misalignment appears

not only at the 1X frequency but also at

2X and 3X.

Angular Misalignment

1X2X

3X

AXIALAxial vibrationVibration measurements 180° out-of-phase across coupling

Parallel Misalignment

1X

2X

3X

RADIALRadial vibrationVibration measurements 180° out-of-phase across coupling

Fault Diagnosis

• Frequency analysis: tool for fault diagnosis

Frequency Spectrum Vs. Overall Level