This document covers the fundamentals of vibration analysis using time waveforms (TWF), emphasizing its advantages in situations where traditional FFT analysis falls short, particularly for low-speed applications and assessing impact severity. It provides detailed instructions on setting up TWF measurements, including selecting appropriate units, sampling periods, and utilizing various analysis techniques. The conclusion reiterates the importance of using TWF to enhance, rather than replace, spectral data in analyzing vibration irregularities.

1. VIBRATION ANALYSIS FOR CBM
BASIC CONCEPTS – UNIT 4
BY DIBYENDU DE

2. UNDERSTANDING TIME WAVEFORMS
1. Why? There are limitation of FFT process in analysis of vibration.
2. However, FFT information can be enhanced with time waveform
analysis.
3. How to practically set up, acquire and manipulate time waveform
data.
4. How to interpret the data including the time-frequency
relationship, symmetry, and pattern recognition of common
faults.

3. INTRODUCTION TO TIMEWAVEFORM (TWF)
Period (P) = Time taken for one complete
cycle
P is in seconds
Frequency of Vibration (f) = 1/P (Hz)
Or f = Hz x 60 = CPM (cycles per minute)

4. EXAMPLE OF TWF – SIMPLE
Pump running at 1785 RPM.
The time spacing between the impacts is
0.0337 seconds. (p)
Frequency f = 1/p = 1 / 0.0337 = 29.67 Hz
29.67 x 60 = 1780 CPM
This indicates that the impact is occurring
at a frequency of 1 x RPM

5. EXAMPLE OF TWF – COMPLEX
In complex TWF determination of
frequency components is extremely
difficult. Hence not recommended.
In such situations time waveform data is
best utilized by applying the principles of
pattern recognition and if necessary
calculating the frequency components of
the major events in the waveform
pattern.

6. WHEN TO USE TWF?
Time waveform can be used effectively to enhance spectral information in the
following applications:
• Low speed applications (less than 100 RPM).
• Indication of true amplitude in situations where impacts occur such as
assessment of rolling element bearing defect severity.
• Gears.
• Sleeve bearing machines with X-Y probes (2 channel orbit analysis)
• Looseness.
• Rubs.
• Beats

7. WHEN NOT TO USE TWF?
Time waveform can be applied to any vibration problem.
In some situations normal spectral and phase data provide better
indications as to the source of the problem without the added
complexity of time waveform data.
Examples:
• Unbalance on normal speed machines
• Misalignment on normal speed machines

8. SETUP FOR TWF?
• Unit of measurement
• Time period sampled
• Resolution
• Averaging
• Windows

9. UNITS OF MEASUREMENT
Amplitude measurement units should be generally selected based upon the
frequencies of interest. The plots show how measurement unit selection affects the
data displayed. Each plot contains 3 separate frequency components of 60Hz, 300Hz,
and 950 Hz.
This data was taken using Displacement
Note how the lower frequency at 60 Hz is
accentuated

10. UNITS OF MEASUREMENT.. CONTD…
Each plot contains 3 separate frequency components of 60Hz, 300Hz, and 950 Hz.
This data was taken using Velocity
Note how 300 Hz is more apparent

11. UNITS OF MEASUREMENT.. CONTD…
Each plot contains 3 separate frequency components of 60Hz, 300Hz, and 950 Hz.
This data was taken using Acceleration
Note how 950 Hz dominates and the
lower frequency vibration frequencies
disappear.

12. UNITS OF MEASUREMENT.. CONTD…
The unit of measurement in TWF should be the natural unit of the
transducer used.
For displacement, displacement transducer should be used.
E.g. – for data gathered from non-contact probes on sleeve bearings
displacement is used.
For modern data collectors acceleration will be the unit of choice.

13. TIME PERIOD SAMPLED
For most analysis work the instrument should be set up to see 6-10
revolutions of the shaft being measured.
The total sample period desired can be calculated by this formula:
Total sample period [seconds] = 60 x # of revolutions/desired RPM
E.g. Time period in seconds = 60 x 10/1500 = 0.4 sec
[# of revolution = 10 and RPM = 1500]

14. TIME PERIOD SAMPLED
Some instruments do not permit the setting of time period data when
acquiring time waveform data.
With these instruments it is necessary to set an equivalent FMAX setting.
The appropriate FMAX setting can be calculated by the following formula
FMAX [CPM] = Lines of Resolution x RPM /# Of Revolutions desired
E.g. Fmax (CPM) = (400 x 1500)/10 = 60,000 CPM
[Lines of resolution = 400; RPM = 1500; # of revolution desired = 10]

15. RESOLUTION OF TWF
For TWF analysis it is recommended that 1600 lines (4096 samples are
used).
This ensures that the data collected has sufficient accuracy and key events
are captured.

16. AVERAGING OF TWF
In most data collectors averaging is performed during the FFT process.
For TWF use synchronous time averaging. Removes unwanted ‘noise’
Overlap averaging should be disabled.
Synchronous time averaging can be useful on gears where broken teeth are
suspected to assist in the location of the defective teeth relative to a
reference mark. It is also useful on reciprocating equipment to “time“
events to a particular crank angle.

17. AVERAGING OF TWF

18. WINDOW OF TWF
Various windows can be applied to TWF prior to performing FFT.
The purpose is to shape the spectrum and minimize leakage errors.
Some instruments can apply these windows to time waveform data.
This would force the data to zero at the start and end of the time
sample potentially losing data.
To eliminate this effect a uniform or rectangular window should be
applied.

19. TWF PATTERNS – UNBALANCE

20. TWF PATTERNS
TWF in acceleration distorts the signal. High
frequency superimposed on the low frequency
signal.

21. TWF PATTERNS – MISALIGNMENT

22. TWF PATTERNS – MISALIGNMENT
In this pattern the relative phase between 1 x RPM and 2 x RPM was changed
90 degrees resulting in a very different pattern.

23. TWF PATTERNS – MISALIGNMENT
The pattern originates when the 1 x, & 2 x, vibrations are 0 degrees apart.

24. TWF PATTERNS – EVEN MOTION – SYMMETRICAL
Symmetrical data indicates that the machine motion is even on each side of the
centre position. Non-symmetrical data indicates rubs or constraints.

25. TWF PATTERNS – NON– SYMMETRICAL IN (Y) BUT
SYMMETRICAL WITH TIME AXIS (X)
The amplitudes below the line are significantly higher than those above the
line. In this case a misalignment condition was the source. The markers on
the plot indicate 1 x RPM.
With 1 x RPM
markers
present it can
be noted that
the waveform
pattern
although
complex is
repetitive with
1 x RPM. This
indicates that
the vibration is
synchronous to
RPM.

26. TWF PATTERNS – NON-SYMMETRY OF TIME AXIS
The waveform pattern indicates a non-repetitive pattern characteristic of nonsynchronous
vibration. Indicates instability.

27. TWF PATTERNS – HARMONICALLY UNRELATED
2 frequency sources that are not harmonically related. (58 Hz and 120 Hz) This is the kind of signal
that could be created when a 2-pole motor has an electrical hum problem.
Higher frequency
wave does not
always start at the
same part of the
lower frequency
cycle and therefore
appears to “ride” on
the other wave
causing symmetry
to be lost.

28. EXERCISE – IS THIS TWF SYMMETRIC?

29. EXERCISE – TWF OF A SLOW SPEED BEARING
Is the spacing synchronous?
Is the amplitude changing?
What might be the nature of the defect?

30. TWF PATTERNS – BEATS AND MODULATION
Often these phenomena are audible. The time span for data
collection should be set to capture 4-5 cycles of the beat.
The time period = 0.5 s.
Frequency = 120 CPM.
It is the frequency
difference between 2 source
frequencies
In this case the beat was
caused by interaction
between a 2 X RPM
vibration source and a 2 x fL
vibration source on an
induction motor.

31. TWF PATTERNS – IMPACTS
This TWF shows several random impacts with magnitudes over 6 g pk. The cause of this signal
was a failed rolling element bearing. The shape of the waveform often appears to be a large spike
followed by a “ring down”.
When the FFT
process is applied to
a signal that contains
impacts the true
amplitude of the
vibration is often
greatly diminished.

32. TWF PATTERNS – IMPACTS
The previous TWF pattern in FFT -
When the FFT
process is applied to
a signal that contains
impacts the true
amplitude of the
vibration is often
greatly diminished.

33. TWF PATTERNS – IMPACTS
Amplitude of
impact in FFT less
than 0.02 ips.
Amplitude of
impacts in TWF
exceeds 0.15 ips.

34. CONCLUSION ON TWF – 1 OF 3
• Use Time waveform for the following selected analysis situations to enhance FFT
information
• Low speed applications (less than 100 RPM).
• Indication of true amplitude where impacts occur -- rolling element bearing defect.
• Gears.
• Sleeve bearing machines with X-Y probes (2 channel orbit analysis)
• Looseness.
• Rubs.
• Beats
• Impacts

35. CONCLUSION ON TWF – 2 OF 3
• Use an appropriate measurement unit
• Rolling element bearings, gears, looseness, rubs, impacts …acceleration
• Sleeve bearing machine with x-y probes…displacement

36. CONCLUSION ON TWF – 3 OF 3
• Initially set up to observe 6 –10 revolutions of the shaft in question
• Study the following symptoms in the waveform
• Amplitude
• Amplitude Symmetry
• Time Symmetry (use RPM markers)
• Beats / Modulation
• Impacts (shape and amplitude)
• Remember use time waveform to ENHANCE not REPLACE spectral data.

37. THANK YOU FOR COMPLETING UNIT 4
CONTACT: FOR FACILITATED TRAINING
DIBYENDU DE, EMAIL ID: DDE337@GMAIL.COM