1. Vibration Analysis (cont)
Adam Adgar
School of Computing and Technology

2. The FFT Process
Based upon principle that any periodic signal (e.g. measured vibration signal) can be broken down into a series of simple sinusoids
Combining these sinusoids will generate the periodic signal we have just analyzed
FFT process can generate a spectrum from a time domain signal
By plotting amplitude versus frequency (instead of time), it becomes far easier to analyze.
Plot displays a certain number of amplitude values (400, 800, 1600, etc.) over a range of frequencies.

3. The FFT Process

4. FFT Terminology Commonly used terms include: Fundamental Frequency
1x rpm
But remember that a belt drive, for instance, has three fundamental frequencies
Dominant Frequency
Frequency at which the highest amplitude occurs
Synchronous Vibration
Vibration harmonically related to a fundamental frequency
Non-synchronous Vibration
Vibration not harmonically related to a fundamental frequency
Sub-synchronous Vibration
Vibration occurring at a frequency below the fundamental frequency

5. What Does Frequency Tell Us ?
Synchronous Vibration
Machines generate mechanical vibration at multiples (harmonics) of running speeds.
For example:
An unbalanced rotor causes a force that moves the bearing (causes vibration) in any direction (plane) at exactly once per revolution (1x RPM)
A pump with 5 vanes on the impeller can generate hydraulic pulses (which can be measured as mechanical vibration) at exactly 5 times per rev (5x rpm)
Different mechanical problems tend to generate their own characteristic vibration patterns.
Non-Synchronous Vibration
Other vibration generators may not be tied specifically to the machine's rotational speed. 
For example:
Bearing problems and electrical problems tend to generate vibrations at specific frequencies other than exact multiples (harmonics) of running speed.
Source of the problem can be identified by correctly linking the frequency to the various possible sources,

6. Trend Plot Y-Axis Units: Amplitude
X-Axis Units: Time (typically days or months)
Plot of a number of overall amplitude values - snapshots of the total vibration (vibration at all frequencies) - over a period of time
Interval between readings is time elapsed between those readings. Could be anything from months to milliseconds depending on the specifics of the vibration program and system(s) involved
Trend plots offer limited analysis tools (no identification of specific frequencies) but can be an important indicator of developing problems

7. Spectrum Plot Y-Axis Units: X-Axis Units:
Amplitude
X-Axis Units:
Frequency
Plot of many amplitude measurements over a range of frequencies
Uses “Fast Fourier Transform”, or “FFT”.
Most commonly used analysis tool
Allows for preliminary identification of the source of the vibration by enabling frequency identification

8. Envelope Spectra Y-Axis Units: X-Axis Units:
Amplitude (acceleration)
X-Axis Units:
Frequency
Enveloping spectra is sensitive to impact related events, not sinusoidal motion as processed by FFT
Allows quantification of both the frequency of impacts and their intensity
Impacts are destructive forces - normally indicate developing problem.
Most typically, this plot is used to detect bearing defects.
Signal processing focuses on the transient, impact type events (spikes on the time domain signal) that the FFT process misses
Looks for a consistent period between impacts (i.e. the impacts are occurring at a regular interval)
Similar in appearance (amplitude vs. frequency) to a conventional spectrum but displays different information
Filters used to help process the signal and focus on any impacts that may be occurring.

9. Interpretation of Spectra
Examples of Fault Types
Unbalance
Misalignment
Rolling Element Bearings
Gears

10. Unbalance Very common and simplest problem to diagnose
Unbalance caused by centrifugal force
Pure sinusoid signal when single fault exists
Hence generates peak at 1× rpm
Single-Plane Unbalance Symptoms:
Radial vibration at 1× rpm.
Little or no phase shift across bearings
Two-Plane Unbalance Symptoms:
Axial vibration at 1× rpm.
Significant phase shift (> 60°) across bearing
One of the only problems that does not distort the signal shape in some manner

11. Misalignment Most common vibration problem
Unlike unbalance, no single vibration symptom. As a result, it should always be considered as a possibility
Perfect alignment - Shaft centrelines are parallel and intersect
Types of misalignment (always a combination):
Angular - Shaft centerlines intersect but are not parallel
Offset - Shaft centerlines are parallel but do not intersect
General Symptoms
High axial vibration at 1× rpm, possible harmonics at 2× and 3× .
2× rpm axial vibration may be as high or even higher than at 1×.
Combination of angular/offset gives wide variation of symptoms

12. Rolling Element Bearings
One of most important areas of CbM
Vibration symptoms can vary greatly but are fairly predictable
Requires
Preferably acceleration spectra covering frequency range between 30,000 and 120,000 cpm
Enveloped spectra
Time domain show the impacts better than spectrum - especially on slow speed equipment

13. Early Stage RE Bearing Defects
Generates frictional or impact-related high frequency vibration
Shows up earliest on the enveloping spectra
Time signal being collected will contain the impact spikes showing up at an interval equal to the defect frequency
Acceleration spectrum shows high frequency peaks far more clearly than velocity spectrum
The defect frequency harmonics can be very low amplitude (not even noticeable) in the early stages
There will typically be no peak at 1× defect frequency on the velocity or acceleration FFTs in the defect's early stages

14. Gears and Gear Trains
Gears generate vibration under normal circumstances
The most common frequency generated is the number of teeth x RPM
This is known as 'gear mesh frequency' (GMF)
Consider 2 mating gears where one is eccentric. At one point during that gear's rotation, it will bottom out with the mating gear and the vibration at GMF will be very high
This causes modulation of the amplitude at gear mesh frequency.
Also it goes from its minimum amplitude to its maximum and back again to its minimum at a rate of once per shaft revolution - 1x rpm.
From this signal, the FFT generates a peak at GMF with sidebands at 1x rpm.
A limited amount of amplitude modulation on a gear train is normal
The number of and size of the sidebands should be closely monitored.
Even more significant can be the development of an amplitude peak at the natural frequency of the gear or gears. Wear or impacting due to problems such as backlash can cause the excitation of the natural frequency of a gear.

15. Further Work Read the Application Note Look at the web resources
Detecting Faulty Rolling Element Bearings
Look at the web resources