53833762 vibration analysis rotating equipment

Vibration Analysis on Rotating Equipment

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The use of vibration analysis in the condition assessment of rotating equipment

Prepared by: Ron Frend

COPYRIGHT RONALD FREND 2002


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CONTENTS

VIBRATION ANALYSIS - AN INTRODUCTION -------------------------------------------9

Vibration Examples------------------------------------------------------------------------------------------------- 9 Imbalance--------------------------------------------------------------------------------------------------------------- 9 Misalignment ---------------------------------------------------------------------------------------------------------10 Looseness--------------------------------------------------------------------------------------------------------------11 Rolling Element Bearing Defects----------------------------------------------------------------------------------13

VIBRATION THEORY--------------------------------------------------------------------------- 15 Simple Harmonic Motion-------------------------------------------------------------------------------------------15 RMS vs. PEAK-------------------------------------------------------------------------------------------------------18 Time Domain ---------------------------------------------------------------------------------------------------------19 The Frequency Domain ---------------------------------------------------------------------------------------------19 What is an FFT?------------------------------------------------------------------------------------------------------20 The FFT Analyzer ---------------------------------------------------------------------------------------------------20 Advantages of FFT Analyzers -------------------------------------------------------------------------------------21 Frequency Spans -----------------------------------------------------------------------------------------------------21 Measurement Basics-------------------------------------------------------------------------------------------------21 Spectrum---------------------------------------------------------------------------------------------------------------21

Parameter Selection------------------------------------------------------------------------------------------------ 22 Selecting displacement, velocity or acceleration----------------------------------------------------------------22

How does it work? ------------------------------------------------------------------------------------------------- 22 Accelerometers -------------------------------------------------------------------------------------------------------24

Acceleration Amplitude Demodulation ------------------------------------------------------------------------ 25 Theory -----------------------------------------------------------------------------------------------------------------25 The Demodulation Process -----------------------------------------------------------------------------------------26 Resonance Sources---------------------------------------------------------------------------------------------------28 A.C. Motor Example.------------------------------------------------------------------------------------------------29

FAILURE MODES-------------------------------------------------------------------------------- 32

Induction Motors--------------------------------------------------------------------------------------------------- 32 Mechanical or Electrical Effects-----------------------------------------------------------------------------------32 Armature Related Problems ----------------------------------------------------------------------------------------32 Stator Related Problems --------------------------------------------------------------------------------------------33 Broken Rotor Bars ---------------------------------------------------------------------------------------------------34

DC Motors----------------------------------------------------------------------------------------------------------- 34 How DC Power Is Created. ------------------------------------------------------------------------------------34 DC Systems and Controls-------------------------------------------------------------------------------------------36 DC Control Firing Cards--------------------------------------------------------------------------------------------37 S.C.R. problems ------------------------------------------------------------------------------------------------------38 Example of a Firing Card Fault ------------------------------------------------------------------------------------38


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DC Control Comparitor Card --------------------------------------------------------------------------------------40 Example of a Comparitor Card Defect ---------------------------------------------------------------------------41 Importance of Exact RPM ------------------------------------------------------------------------------------------42 Example of Mechanical -v- Electrical Frequencies ------------------------------------------------------------43

Rotating Equipment ----------------------------------------------------------------------------------------------- 45 Imbalance--------------------------------------------------------------------------------------------------------------45 Vibration due to imbalance-----------------------------------------------------------------------------------------46 Misalignment ---------------------------------------------------------------------------------------------------------51 Looseness--------------------------------------------------------------------------------------------------------------54

Vibration due to aerodynamic forces--------------------------------------------------------------------------- 59 Aerodynamic cross coupling ---------------------------------------------------------------------------------------60 Surging-----------------------------------------------------------------------------------------------------------------60 Choking or Stone Walling ------------------------------------------------------------------------------------------61

Bearing Failures ---------------------------------------------------------------------------------------------------- 62 Elasto Hydrodynamic Lubrication --------------------------------------------------------------------------------62 First Stage of Bearing Failure--------------------------------------------------------------------------------------63 Second Stage of Bearing Failure ----------------------------------------------------------------------------------64 Third Stage of Bearing Failure-------------------------------------------------------------------------------------65 Fourth Stage of Bearing Failure -----------------------------------------------------------------------------------66 Bearing Defect Frequency Calculation ---------------------------------------------------------------------------67 Analysis of bearing defects -----------------------------------------------------------------------------------------70

Balancing ------------------------------------------------------------------------------------------------------------ 75 In-place Balancing ---------------------------------------------------------------------------------------------------75 Vibration Related to Imbalance------------------------------------------------------------------------------------78 How to Balance - Single Plane-------------------------------------------------------------------------------------79 Single Plane Vector Method of Balancing-----------------------------------------------------------------------80 Four-step Method of Balancing Single Plane -------------------------------------------------------------------82 Balancing in One Run -----------------------------------------------------------------------------------------------85

SINGLE CHANNEL ANALYSIS -------------------------------------------------------------- 87

Taking measurements --------------------------------------------------------------------------------------------- 87

POTENTIAL FAILURE ANALYSIS---------------------------------------------------------- 91

A methodology for objective set up ----------------------------------------------------------------------------- 91

Introduction --------------------------------------------------------------------------------------------------------- 91

The PFA Tree ------------------------------------------------------------------------------------------------------- 91 Base cause-------------------------------------------------------------------------------------------------------------91 Failure type------------------------------------------------------------------------------------------------------------91 External manifestation-----------------------------------------------------------------------------------------------92 Technology------------------------------------------------------------------------------------------------------------92 Parameter --------------------------------------------------------------------------------------------------------------92 Analysis----------------------------------------------------------------------------------------------------------------92 Interval-----------------------------------------------------------------------------------------------------------------92 Setup -------------------------------------------------------------------------------------------------------------------92


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Developing a Potential Failure Analysis for Rolling Element Bearings --------------------------------- 93 Stage 1 -----------------------------------------------------------------------------------------------------------------93 Stage 2 -----------------------------------------------------------------------------------------------------------------94 Stage 3 -----------------------------------------------------------------------------------------------------------------94 Stage 4 -----------------------------------------------------------------------------------------------------------------94

Including the Component Failure in the PFA Tree. --------------------------------------------------------- 95

Conclusion ----------------------------------------------------------------------------------------------------------- 96 Measurement Windows ---------------------------------------------------------------------------------------------99 Averaging ----------------------------------------------------------------------------------------------------------- 100 Real Time Bandwidth and Overlap Processing --------------------------------------------------------------- 101 Octave Analysis ---------------------------------------------------------------------------------------------------- 102

Analysis ------------------------------------------------------------------------------------------------------------ 103 Severity charts ------------------------------------------------------------------------------------------------------ 105

Two Channel Analysis------------------------------------------------------------------------------------------- 106 Two channel functions -------------------------------------------------------------------------------------------- 106

Advanced functions ---------------------------------------------------------------------------------------------- 108 Representation by complex numbers --------------------------------------------------------------------------- 108 Cascade & waterfall plots----------------------------------------------------------------------------------------- 109 Triggering ----------------------------------------------------------------------------------------------------------- 109 Bod plots ----------------------------------------------------------------------------------------------------------- 110 Orbits----------------------------------------------------------------------------------------------------------------- 110

INTRODUCTION TO RESONANCE ------------------------------------------------------ 114

What is resonance? ---------------------------------------------------------------------------------------------- 115

Natural Frequency ----------------------------------------------------------------------------------------------- 115 Mechanical ---------------------------------------------------------------------------------------------------------- 115 Liquids & pumping systems-------------------------------------------------------------------------------------- 118 Air & gases---------------------------------------------------------------------------------------------------------- 120 Karman Vortices --------------------------------------------------------------------------------------------------- 122

Critical Speed (Balance Resonance) -------------------------------------------------------------------------- 123

IDENTIFYING RESONANCE IN MECHANICAL SYSTEMS ----------------------- 126

Mode Shape ------------------------------------------------------------------------------------------------------- 126

Phase---------------------------------------------------------------------------------------------------------------- 127

The bump test ----------------------------------------------------------------------------------------------------- 129 Running machine Bump Test ------------------------------------------------------------------------------------ 130 Reverse Bump or Plucking the Suspect Part. --------------------------------------------------------------- 130

Set up for FFT-type analyzers --------------------------------------------------------------------------------- 130 Impact hammer ----------------------------------------------------------------------------------------------------- 131


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CALCULATING NATURAL FREQUENCY IN MECHANICAL SYSTEMS------ 135

Uniform Beams --------------------------------------------------------------------------------------------------- 135

Plates---------------------------------------------------------------------------------------------------------------- 137

DETUNING RESONANT STRUCTURES------------------------------------------------ 139

Vibration isolators ----------------------------------------------------------------------------------------------- 139 Springs --------------------------------------------------------------------------------------------------------------- 140 Rubber --------------------------------------------------------------------------------------------------------------- 142

Modifying the structure----------------------------------------------------------------------------------------- 145 Damping ------------------------------------------------------------------------------------------------------------- 145 Changing the Mass------------------------------------------------------------------------------------------------- 146 Changing the stiffness --------------------------------------------------------------------------------------------- 146

WHOLE BODY VIBRATION ---------------------------------------------------------------- 147

Sources of vibration---------------------------------------------------------------------------------------------- 147

Frequency ranges ------------------------------------------------------------------------------------------------ 147


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List of illustrations Figure 1 Velocity spectrum showing imbalance ______________________________________________ 9 Figure 2 - Velocity spectrum showing fan imbalance _________________________________________ 10 Figure 3 Velocity spectrum of misaligned fan - radial ________________________________________ 11 Figure 4 Velocity spectrum of misaligned fan - axial _________________________________________ 11 Figure 5 Velocity spectrum from a loose fan drive motor______________________________________ 12 Figure 6 Envelope spectrum of a fan drive motor with loose bearing ____________________________ 13 Figure 7 Enveloped acceleration spectrum of bearing - inner race defect _________________________ 14 Figure 8 Inner race spall_______________________________________________________________ 14 Figure 9 Simple Harmonic Vibration _____________________________________________________ 16 Figure 10 Integration from acceleration to velocity __________________________________________ 17 Figure 11 Integrating to displacement ____________________________________________________ 18 Figure 12 Peak -v- RMS _______________________________________________________________ 19 Figure 13 Compression mode accelerometer _______________________________________________ 24 Figure 14 Shear mode accelerometer _____________________________________________________ 24 Figure 15 Simple modulation example ____________________________________________________ 25 Figure 16 Bearing modulation example ___________________________________________________ 26 Figure 17 Demodulation process ________________________________________________________ 27 Figure 18 Enveloping process___________________________________________________________ 27 Figure 19 Fast Fourier Transform _______________________________________________________ 28 Figure 20 FFT - 3D view_______________________________________________________________ 28 Figure 21 Two channel time waveform - bearing defect_______________________________________ 29 Figure 22 High frequency waterfall ______________________________________________________ 30 Figure 23 Enveloped acceleration spectrum________________________________________________ 30 Figure 24 Comparison - velocity to envelope _______________________________________________ 31 Figure 25 The creation of DC power _____________________________________________________ 35 Figure 26 FFT spectrum of half wave rectification___________________________________________ 36 Figure 27 FFT spectrum of full wave rectification ___________________________________________ 36 Figure 28 Basic DC system circuit _______________________________________________________ 37 Figure 29 FFT spectrum full wave DC firing card frequencies _________________________________ 38 Figure 30 FFT spectrum after repair _____________________________________________________ 38 Figure 31 FFT spectrum showing half wave firing card frequencies _____________________________ 39 Figure 32 FFT spectrum of same motor (no load) ___________________________________________ 40 Figure 33 FFT spectrum showing comparitor card defect._____________________________________ 41 Figure 34 FFT after the comparitor card was replaced _______________________________________ 42 Figure 35 DC motor components ________________________________________________________ 42 Figure 36 FFT from a 5 HP motor - full wave rectified _______________________________________ 43 Figure 37 Same motor - speed lowered by 25% _____________________________________________ 44 Figure 38 Imbalance slide 1 ____________________________________________________________ 46 Figure 39 Imbalance slide 2 ____________________________________________________________ 46 Figure 40 Imbalance slide 3 ____________________________________________________________ 47 Figure 41 Imbalance slide 4 ____________________________________________________________ 47 Figure 42 Imbalance slide 5 ____________________________________________________________ 48 Figure 43 Imbalance slide 6 ____________________________________________________________ 48 Figure 44 Imbalance slide 7 ____________________________________________________________ 49 Figure 45 Imbalance slide 8 ____________________________________________________________ 49 Figure 46 Imbalance slide 9 ____________________________________________________________ 50 Figure 47 Misalignment slide 1__________________________________________________________ 51 Figure 48 Misalignment slide 2__________________________________________________________ 51 Figure 49 Misalignment slide 3__________________________________________________________ 52 Figure 50 Misalignment slide 4__________________________________________________________ 52 Figure 51 Misalignment slide 5__________________________________________________________ 53 Figure 52 Looseness slide 1 ____________________________________________________________ 54 Figure 53 Looseness slide 2 ____________________________________________________________ 54


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Figure 54 Looseness slide 3 ____________________________________________________________ 55 Figure 55 Looseness slide 4 ____________________________________________________________ 55 Figure 56 Looseness slide 5 ____________________________________________________________ 56 Figure 57 Looseness slide 6 ____________________________________________________________ 56 Figure 58 Looseness slide 7 ____________________________________________________________ 57 Figure 59 Looseness slide 8 ____________________________________________________________ 57 Figure 60 Looseness slide 9 ____________________________________________________________ 58 Figure 61 Aerodynamic forces __________________________________________________________ 60 Figure 62 Elasto-hydrodynamic lubrication ________________________________________________ 62 Figure 63 Loss of Lubricant - Ball Bearing Inner Race Courtesy of the Barden Corporation__________ 63 Figure 64 Loss of Lubricant - Roller Bearing Courtesy of the Torrington Company _________________ 64 Figure 65 Waterfall plot from a damaged motor bearing______________________________________ 65 Figure 66 Early Fatigue - Ball Bearing Courtesy of the Barden Corporation ______________________ 66 Figure 67 Developed Fatigue on Roller Bearing Courtesy of the Torrington Company ______________ 66 Figure 68 Ball Bearing Terminology _____________________________________________________ 68 Figure 69 Waterfall of early damage to a motor bearing collected every 1.5 hrs over 14 days_________ 69 Figure 70 Bearing damage severity assessment chart ________________________________________ 70 Figure 71 Demodulated acceleration spectrum from a dry bearing ______________________________ 70 Figure 72 Demodulated acceleration spectrum of a marked bearing_____________________________ 71 Figure 73 Demodulated acceleration spectrum from a slightly more heavily marked bearing _________ 72 Figure 74 Time waveform from a marked bearing.___________________________________________ 72 Figure 75 Time waveform from a heavily marked bearing _____________________________________ 73 Figure 76 Velocity spectrum from a spalled bearing _________________________________________ 73 Figure 77 Sources of imbalance _________________________________________________________ 75 Figure 78 Assembly tolerance stack up____________________________________________________ 76 Figure 79 Heavy spot _________________________________________________________________ 76 Figure 80 Units of measure of imbalance __________________________________________________ 77 Figure 81 Mass centre displacement______________________________________________________ 77 Figure 82 Force due to imbalance _______________________________________________________ 78 Figure 83 The vector diagram___________________________________________________________ 80 Figure 84 Simplified vector diagram______________________________________________________ 81 Figure 85 Additional corrections ________________________________________________________ 82 Figure 86 Direction to shift the weight ____________________________________________________ 83 Figure 87 Sample problem vector diagram_________________________________________________ 84 Figure 88 Determining the flash angle ____________________________________________________ 86 Figure 89 Typical tap block for mounting an accelerometer ___________________________________ 87 Figure 90 Accelerometer mounting techniques a-d___________________________________________ 89 Figure 91 Accelerometer mounting techniques e-g___________________________________________ 90 Figure 92 Overview of accelerometer mounting techniques ____________________________________ 90 Figure 93 PFA development for rolling element bearings _____________________________________ 93 Figure 94 PFA for a main motor_________________________________________________________ 95 Figure 95 General severity chart for vibration _____________________________________________ 105 Figure 96 Vector addition of 2 vibrations_________________________________________________ 108 Figure 97 Cascade of fan over 20mS ____________________________________________________ 109 Figure 98 Bode plots _________________________________________________________________ 110 Figure 99 Orbit showing misalignment___________________________________________________ 111 Figure 102 Harmonic series for the tone C. _______________________________________________ 120 Figure 103 Sonic vibration in a tube_____________________________________________________ 122 Figure 104 Karman vortices ___________________________________________________________ 123 Figure 107 Campbell Diagram _________________________________________________________ 125 Figure 109 Mode shape readings _______________________________________________________ 127 Figure 110 Phase relationships_________________________________________________________ 128 Figure 111 Phase / frequency relationships @ resonance ____________________________________ 129 Figure 112 Impact hammer response ____________________________________________________ 132 Figure 113 Impact hammer specification sheet_____________________________________________ 132


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Figure 114 Stress/strain diagram for steel ________________________________________________ 140 Figure 115 Stress/strain diagram for rubber ______________________________________________ 140 Figure 116 Resonance Curve __________________________________________________________ 141

List of Tables Table 1 Speed of sound in liquids _______________________________________________________ 118 Table 3 Natural frequency calculation of uniform beams_____________________________________ 135 Table 4 Standard values for uniform beams _______________________________________________ 136 Table 5 Damping ranges of vibration isolators_____________________________________________ 139 Table 6 Whole body vibration (frequency ranges) __________________________________________ 148

List of Equations Equation 3 Newton's 2nd law __________________________________________________________ 117 Equation 5 Differential equation of motion of a single-degree-of-freedom system _________________ 118 Equation 6 Velocity of sound in materials_________________________________________________ 119 Equation 7 Speed of sound in the ocean __________________________________________________ 119 Equation 8 General formula relating speed, wavelength & frequency ___________________________ 119 Equation 9 Newton-Laplace eq. for the speed of sound in a gas _______________________________ 121 Equation 10 Ratio of specific heats (gamma) ______________________________________________ 121 Equation 11 Speed of sound in a gas ____________________________________________________ 121 Equation 12 Karman vortices __________________________________________________________ 123 Equation 14 Amplitude magnification due to springs ________________________________________ 141 Equation 15 Natural frequency of a spring________________________________________________ 142 Equation 16 Modulus of elasticity for rubber ______________________________________________ 144


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Vibration Analysis - an introduction The study of noise and vibration phenomena dates back centuries. The first recorded incidence of such study was by Pythagoras in the sixth century B.C. who studied the origin of musical sounds and the vibration of strings. In 1638 Galileo described the vibrations of pendulums, the phenomenon of resonance and the factors influencing the vibration of strings. Euler in 1744 and Bernoulli in 1751 developed the equation for the vibrations of beams and developed the normal modes for various boundary conditions. In 1882 Hertz developed the first successful theory for impact. So we can see that vibration analysis itself is not new but some of the ways that we take the measurements and apply those measurements as machine health diagnoses are very new.

In this section we will briefly take a look at some vibration examples of typical defects suffered by fans and fan drives without delving too deeply into why!

Vibration Examples When the novice analyst first carries out vibration analysis he will usually rush out and take a vibration spectrum using the default parameters set up in the analyzer. We will carry on that noble tradition and look at some spectra that have been collected from real machines and show typical examples of common defects.

Imbalance

Figure 1 Velocity spectrum showing imbalance

Figure 1 shows a vibration spectrum that was taken at the sheave end of a centrifugal fan in the vertical direction. The fan was driven from the AC motor via a V-belt and rotated at about 720 rpm. The AC drive motor rotates at just under 1200 rpm. The spectrum is a simply a graph of the vibration frequency on the bottom axis with the amplitude at that frequency on the vertical axis. This spectrum is of velocity vibration so the amplitude units could be in


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mm/s or ips (inches/second). The frequency is in cpm (cycles/minute) but it could have been displayed in Hz (Hertz or cycles/second) or in orders (multiples of run speed). The spectrum was recorded from a vibration transducer which was mounted radial to the shaft (vertical in this case). Notice in the spectrum that there is one big spike which is labeled at 716.59 cpm and there are two much smaller spikes just to the right. The first spike to the right is at 1187 cpm which equates to the run speed of the motor and the second spike is at 1433.18 cpm which is exactly twice fan speed. Because the one spike is so dominant that is the one that we are concerned about. A check with a stroboscope confirmed that the fan was actually running at 717 rpm so the big spike of vibration is at exactly (within the precision of the strobe) run speed. At this stage we are not concerned about the physics of why a vibration at run speed is usually indicative of imbalance but we will look at our spectral explanation charts (see appendix 1) and have a fair degree of confidence that the fan needs balancing.

Figure 2 - Velocity spectrum showing fan imbalance

Figure 2 shows a similar problem on a different fan but we see that the spectrum looks very similar with one dominant spike at the run speed of the fan. Figure 1 amplitude was displayed with metric units and figure 2 with inch units but the shape of the spectrum is the same in both cases.

Misalignment

Probably 40% of all bearing and shaft failures are caused by misalignment of the components creating an extra axial thrust on the bearings.


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Figure 3 Velocity spectrum of misaligned fan - radial

In figure 3 we see what initially looks like an imbalance condition of the fan, although the amplitudes are relatively low.

Figure 4 Velocity spectrum of misaligned fan - axial

However, in figure 4 we are now looking at the vibration taken axial to the shaft. If the problem was simple imbalance of the fan we would expect all of the forces to be caused by centrifugal force and therefore acting in a direction which was radial to the shaft. Again, looking at our spectrum explanation charts we see that, on a belt driven train, a high axial velocity vibration relative to the radial vibration is almost always indicative of component misalignment to the belt.

Looseness

Looseness exists when the component is not directly attached to the structure or rotating element and has a relatively large clearance, allowing the component to rattle.


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Figure 5 Velocity spectrum from a loose fan drive motor

The above spectrum was recorded at the sheave end of the drive motor of an underground colliery main ventilation fan. The motor was running at 590 rpm and immediately we see the large family of harmonics of run speed. The amplitudes do not seem too high but the machine was massive and any vibratory forces have to move the mass before we see a vibration. In this case the structure of the bedplate was cracked causing parts of the structure to vibrate freely at the excitation frequency of the motor (speed). Whenever we see multiples or sub-multiples of run speed vibration frequencies we immediately consider the possibility of loose components.


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Figure 6 Envelope spectrum of a fan drive motor with loose bearing

The early stages of looseness can be detected in a similar manner, be looking for harmonics of run speed, and using demodulated or enveloped acceleration readings. Figure 6 shows the early stages of looseness of a bearing inside the fan drive motor. As the looseness deteriorates the envelope readings will decrease but then the velocity readings will start to increase.

Rolling Element Bearing Defects

The primary tool in assessing bearing condition is the use of enveloped acceleration readings.

Figure 7 shows the envelope spectrum from a bearing with a severe spall in the inner race. Notice that the spike at about 8,772 cpm is marked BPIR which stands for Ball Pass Outer Race. We will study bearing defects in detail later but notice that the main defects are not multiples of run speed. In other words they are non-synchronous.


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Figure 7 Enveloped acceleration spectrum of bearing - inner race defect

Figure 8 Inner race spall


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Vibration Theory The following section is meant as a primer to help the newcomer to vibration analysis understand some of the terms used and to develop an understanding of the concepts.

To understand the concept of vibration analysis, it is important to realize that the motion of the measured surface varies with time. The transducer converts the movement into an electrical signal which is passed to the spectrum analyzer which in turn converts that signal from the time domain into the frequency domain. The time domain waveform is composed of a machines response to many individual forces such as imbalance, misalignment, gear meshing forces, rotating electrical fields, and many other factors. When viewing the time domain data it can be quite difficult to separate these components of vibration. However, in the frequency domain it is much easier to separate these elements to determine the importance of each.

Vibration amplitude is measured using three different parameters, acceleration, velocity and displacement. The purpose of this section is to describe the relationship between each of these and how they are used on rotating machinery.

Simple Harmonic Motion Simple harmonic motion can be visualized by many common examples such as a pendulum, a mass and spring combination, a rotating mechanism or a diving board- Figure 9 uses a pendulum. If the pendulum swings back and forth 100 times in one minute, then the frequency is 100 cycles per minute. Similarly if a machine is rotating 100 times in one minute, its speed is 100 revolutions per minute or 100 RPM.

The frequency of vibration is often expressed in terms of cycles per second or HERTZ after the German physicist Heinrich Hertz. However for predictive maintenance techniques where rotational speed is often the key to vibration peaks, cycles per minute are used in preference to Hertz.

In addition to frequency the amplitude is the other necessary quantity that must be known in order to characterize vibration. In figure 9 the points B and C represent the extreme position of the pendulum and the distance between them is the peak to peak displacement-

Amplitude meters are often calibrated to give the peak to peak value because it is the displacement extremes that are of interest. In vibration work, the displacement is often expressed in terms of mils or micron. One Mil is equal to 0.001 inch and one micron (m) is 0.001 mm. Since the pendulum is continuously moving, it has a velocity associated with each position and, like displacement, the velocity also varies between a positive peak and a negative peak.


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(48)

* FREQUENCY

* AMPLITUDE

... Displacement

... Velocity

... Acceleration

Vibration is described by its frequency and amplitude.The amplitude is expressed in units of either displacement,velocity or acceleration.

An oscillating system will produce a certain number ofcycles per unit time, called the frequency. Frequency is usuallyexpressed in terms of cycles per second, or Hertz.

A

BC

one cycle

Figure 9 Simple Harmonic Vibration

Figure 10 shows that at position B and C, the velocity is zero, and at position A the velocity is maximized, first to the right, then to the left. Since the peak positive velocity occurs 1/4 cycle before the peak positive displacement, velocity is said to lead displacement by 90. The 90 degree phase lead is shown in the diagram on figure 10. Velocity amplitude is expressed only in terms of zero to peak or zero to RMS.

The negative peak velocity differs only in direction, not magnitude. The rate of change of displacement is the velocity, therefore if D is expressed in terms of inches, instead of the usual mils, then the product 2pifD will be the velocity in inches per second which are the units used for velocity in vibration work.


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(49)

A

BC

Peak Peak

to

Peak

A B A C A

Figure 3. The distance between the extremes of motion is the peak-to-peak displacement. Displacement meters are often calibratedin peak-to-peak units. The amplitude is one half of the peak-to-peakvalue for a sine wave.

Figure 4. Velocity is highest where displacement is zero and is zerowhere displacement is maximum. Therefore a 90 phase shift existsbetween displacement and velocity. The velocity amplitude is directlyproportional to frequency for a given displacement.

o

Dis

p

A

BC

A B A C A

Disp

Vel

HighestVelocity

Figure 10 Integration from acceleration to velocity

As velocity is continuously changing, an acceleration is also associated with the velocity, this acceleration is also associated with the motion. Acceleration is the third way to express vibration amplitude. Figure 11 shows that at position B and C the acceleration is maximum. Just prior to point B, velocity is to the right and just after it is to the left. At B therefore the rate of change of velocity, the acceleration, is maximum. Conversely just prior to point A velocity is increasing and just after, it is decreasing. Therefore the rate of change of velocity (the acceleration) must be zero at A. Note that acceleration reaches its maximum at Points B and C just as displacement does, but at B acceleration is to the left whereas the displacement is to the right. The maximum acceleration to the right occurs 1/2 a cycle before the maximum velocity to the right and acceleration is said to lead displacement by 180. Acceleration leads velocity by 90.

The diagram in figure 11 shows these phase leads and also the acceleration amplitude relationship, A = (2pif)2D. This says that for any given value of displacement, the acceleration is proportional to the square of the frequency.

The unit of acceleration is the g which is equal to 9.81 m/sec2 and is derived from the acceleration due to earths gravity.


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(50)

A

BC

A B A C A

Disp

Vel

Acce

l

Figure 5. At B, acceleration is maximum to the left and displacementmaximum to the right, a 180 phase shift. Acceleration amplitude variesas the square of frequency for a given value of displacement.

o

Avg RMS

Peak

Peak

to

PeakTimeA

mpl

itude

Avg = 0.637 x PeakRMS = 0.707 x Peak

Figure 6. The simple relationships which exist between average, RMSand Peak amplitude values for sine waves are not valid forcombination or random waveforms.

Acceleration Acceleration

Figure 11 Integrating to displacement

RMS vs. PEAK The rms or root mean square value is calculated by breaking the waveform down into a number of points, squaring the amplitude value of each point, calculating the mean of the squared values and then finding the square root of the mean.

Using rms values can be compared to the use of rms in electrical circles i.e. stereo speakers power values are measured in rms values. Electrical (AC) voltage is also measured in rms. This, like vibration signals, is a continuously varying quantity, ranging from zero to a peak value. To measure only the peak value may be misleading since the voltage is actually at a peak for only a small portion of the cycle. During most of the cycle the value of the instantaneous voltage is somewhere between zero and peak.

RMS, then, is an attempt to apply a single quantitative value -which reflects the effective value of this varying function. This same logic applies to vibration. Velocity is a quantitative measure of the effective velocity and reflects the power or energy being used to vibrate the machine mass.

Peak value is the maximum amplitude seen during the measurement. When using FFT analyzers care should be taken when evaluating peak or rms severity as the peak amplitude in the spectrum is derived from a sine wave. True peak can be seen in the time waveform.


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Avg RMS

Peak

Peak

to

PeakTimeA

mpl

itude

Ampl

itude

Time

RMS

Peakto

Peak

Peak

Simple Sine Wave

Complex Waveform

(51)

Figure 12 Peak -v- RMS

Time Domain

The traditional way of observing signals is to view them in what is called the time domain. The time domain is a record of what happened to a parameter compared to time- Typically the signal would be displayed on an oscilloscope. With respect to machinery vibration, analysis of signals in the time domain can be very difficult and is far easier in the frequency domain

The Frequency Domain

If we now convert a time waveform to the frequency domain we will get a totally different picture. We now have axes of amplitude v frequency instead of amplitude -v- time. Every sine wave separated out by the FFT appears as a separate line. Its height represents its amplitude, its position represents its frequency.

The method most analyzers use to transform signals from the time domain to the frequency domain is called :-


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FFT (Fast Fourier Transform)

What is an FFT? The fast Fourier transform (FFT) is an algorithm for transforming data in the time domain to the frequency domain. Most analyzers have an FFT processor, which performs this transformation automatically and then stores the computed spectra into memory.

We cannot transform to the frequency domain in a continuous manner. We therefore must sample and digitize the time domain input. The number of samples determines the resolution (number of lines) of frequency.

Most analyzers offer resolutions of 100,200,400,800,1600,3200 or even 6400 Lines.

FFT Spectrum Analyzers take a time varying input signal, like you would see on an oscilloscope trace, and compute its frequency spectrum.

Fourier's theorem states that any waveform in the time domain can be represented by the weighted sum of sines and cosines. The FFT spectrum analyzer samples the input signal, computes the magnitude of its sine and cosine components, and displays the spectrum of these measured frequency components.

Many of these measurements were once done using analog spectrum analyzers. In simple terms, an analog filter was used to isolate frequencies of interest. The signal power, which passed through the filter, was measured to determine the signal strength in certain frequency bands. By tuning the filters and repeating the measurements, a spectrum could be obtained.

The FFT Analyzer

An FFT spectrum analyzer works in an entirely different way. The input signal is digitized at a high sampling rate, (2.56 x Fmax usually). Nyquist's theorem says that as long as the sampling rate is greater than twice the highest frequency component of the signal, then the sampled data will accurately represent the input signal. Certain analyzers pass the input signal through an analog filter, which attenuates all frequency components above Fmax by 90 dB to make sure that Nyquist's theorem is satisfied. This is the anti-aliasing filter. The resulting digital time record is then mathematically transformed into a frequency spectrum using an algorithm known as the Fast Fourier Transform or FFT. The FFT is simply a clever set of operations which implements Fourier's theorem. The resulting spectrum shows the frequency components of the input signal.

Now here's the interesting part. The original digital time record comes from discrete samples taken at the sampling rate. The corresponding FFT yields a spectrum with discrete frequency samples. In fact, the spectrum has less than half as many frequency points as there are time points (remember Nyquist's theorem). Suppose that you take 1024 samples at 2560 Hz. It takes 0.4 Seconds to take this time record. The FFT of this record yields 400 frequency points or lines, but over what frequency range? The highest frequency will be determined by the in-built ratio of Fmax to data sampling rate - 2.56. The lowest frequency is just the Fmax divided by the number of lines: Fmax = data sampling rate / 2.56

No. Of Lines = No samples / 2.56

Bin resolution = Fmax / No. of lines

= (2560 / 2.56) / (1024 / 2.56) = 2.5 Hz (the same as the lowest measurable frequency)


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Everything below 2.5 Hz (for this example) is considered to be DC. The output spectrum thus represents the frequency range from DC to 1000 Hz with points every 2.5 Hz.

Advantages of FFT Analyzers

The advantage of this technique is its speed. Because FFT spectrum analyzers measure all frequency components at the same time the technique offers the possibility of being hundreds of times faster than traditional analog spectrum analyzers. In the case of a 1000 Hz span and 400 resolvable frequency bins, the entire spectrum takes only 400 mS to measure. To measure the signal with higher resolution the time record is increased, but again, all frequencies are examined simultaneously, providing an enormous speed advantage.

Frequency Spans Before we continue, let's clarify a couple of points about our frequency span. We just described how we arrived at a DC to 1000 Hz frequency span using a 400 mS time record. Because the signal passes through an anti-aliasing filter at the input, the entire frequency span is not useable. A typical filter has a flat response from DC to 1000 Hz and then rolls off steeply from 1000 Hz to 2.56 kHz. The range between 1000 Hz and 2.56 kHz is therefore not useable and the actual displayed frequency span stops at 1000 Hz. There is also a frequency bin labeled 0 Hz (or DC). This bin actually covers the range from 0 Hz to 2.5 Hz (the lowest measurable frequency) and contains the signal components whose period is longer than the time record (not only DC). So our final displayed spectrum contains 400 frequency bins. The first covers 0 - 2.5 Hz, the second 2.5 - 5 Hz, and the 400th covers 997.5 - 1000 Hz.

The length of the time record determines the frequency span and resolution of our spectrum. What happens if we make the time record 800 mS or twice as long? Well, we ought to get 2048 time points (sampling at 2560 Hz) yielding a spectrum from DC to 1000 Hz with 1.25 Hz resolution containing 800 points. But the analyzer places some limitations on this. One is memory. If we keep increasing the time record, then we would need to store more and more points. (0.00125 Hz resolution would require 2,048,000 values.) Another limitation is processing time. The more points you take, the longer the processing time.

Measurement Basics

An FFT spectrum is a complex quantity, This is because each frequency component has a phase relative to the start of the time record. (Alternately, you may wish to think of the input signal being composed of sines and cosines.) If there is no triggering, then the phase is random and we generally look at the magnitude of the spectrum. If we use a synchronous trigger then each frequency component has a well-defined phase.

Spectrum The spectrum is the basic measurement of an FFT analyzer. It is simply the complex FFT. Normally, the magnitude of the spectrum is displayed. The magnitude is the square root of the FFT times its complex conjugate. (Square root of the sum of the real (sine) part squared and the imaginary (cosine) part squared). The magnitude is a real quantity and represents the total signal amplitude in each frequency bin, independent of phase.

If there is phase information in the spectrum, i.e. the time record is triggered in phase with some component of the signal, then the real (cosine) or imaginary (sine) part or the phase may be displayed. The phase is simply the arc tangent of the ratio of the imaginary and real parts of each frequency component. For vibration measurements phase is usually considered to be relative to the trigger pulse.


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Parameter Selection

Selecting displacement, velocity or acceleration As previously discussed, displacement amplitude is higher at lower frequencies. Therefore when motions are being measured a displacement measurement is in order because frequencies of interest on the shaft are limited to 20 or so orders of rotation. For a 3600 rpm machine, 20 orders is a frequency of 1200 Hz. At that frequency 0.5 in/sec is 0.13 mils pk-pk, very small but certainly a measurable value.

For higher frequencies however, significant vibration has a displacement value which -is too small to conveniently measure and velocity or acceleration is more appropriate. Velocity measurements are especially good for a number of reasons.

The most prominent advantage of a velocity measurement is that the value of rms velocity is related to the potential for mechanical damage, regardless of the frequency. The many published vibration severity charts are based on this principle. As an example suppose a displacement of 0.l mils is observed, is this severe? At 6 Hz this is not severe at all; at 60 Hz this is rough but at 200 Hz this is very rough and should not be permitted for machines up to the 100HP class. Now suppose a velocity of 0.6 in/sec (15mm/s) is observed. Is this severe? The answer is Yes, this is severe regardless of the frequency.

Newtons second law (F=ma) tells us that the acceleration of a body is directly proportional to the force applied to the body. In other words the acceleration vibration gives a good indication of impactive forces inside the machine such as bad bearings.

In summary, displacement measurements are good from 0 Hz to 500 Hz, velocity up to 1 kHz and acceleration from 2 Hz to 20 kHz depending on the design of the accelerometer. In applying this to rotating machinery displacement measurements are relative readings of the displacement of the shaft to a reference, usually the bearing. Velocity and acceleration measurements are usually made on the bearing cap or on the machine casing in way of a structural web to enhance the transmission of vibration to the pick-up point.

How does it work? Consider a rotating machine (a motor) which has, for example, an out of balance condition on the rotor so that for every revolution of that rotor the out of balance mass generates a centripetal (opp. to centrifugal) force. We place our transducer on the drive end of the motor in the vertical direction, as near as possible to the bearing and couple the transducer to a spectrum analyzer. The transducer sees the force once per rev. of the rotor as a simple harmonic motion. That is to say that the machine surface will cause the transducer to move in a downwards direction with the machine as the force itself is acting downwards and will cause the transducer to move upwards when the machine is moving up etc. The output of the transducer will depend on what type of transducer we are using.

Displacement transducers will give an output proportional to the linear displacement of the transducer in thousandths of a inch or micron.

Velocity transducers will give an output proportional to the linear speed (velocity) of the transducer in inches/second or millimeters/second.

An accelerometer will give an output which is proportional to the acceleration of the transducer in Gs or inches/second/second or meters/second/second.

For predictive maintenance purposes we use accelerometers almost exclusively so we will concentrate on them for now. According to Newtons Second Law

F=mx a


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where F = the force

m = the mass

a = the acceleration

So immediately we see that the output from the accelerometer is directly proportional to the internal forces acting on the machine. Newton also says that for a rotating body

F=m2r where = the rotational speed in radians/second

r = the radius at which the force is acting.

As we know that the acceleration is proportional to the force and we assume that the mass and radius of force of the machine stay constant, then we may safely say that the acceleration is also proportional to the square of the speed.

a=2r

The important point here is that the faster the machine goes, or the higher up the frequency range we go, the acceleration amplitudes must increase for a given force even if there is nothing wrong with our machine. However, we know that acceleration is simply the rate of change of velocity. So if we integrate our acceleration reading with respect to time we will get a velocity reading. Integrating acceleration will change our value from:

inches/second2

to

inches/second

effectively finding the square root of the acceleration (for time). We have already said that we have a concern that the acceleration increases with frequency, so if we need a value that is independent of frequency for severity analysis purposes we can use the velocity reading.

Back to our motor. If we plot the acceleration against time (time domain) we would see a sine wave which is the result of simple harmonic motion. This is the signal that is passed along to the analyzer. The analyzer will then convert this time domain signal into a frequency domain signal either as acceleration or as an integration from acceleration into velocity. Either way, the out of balance condition will show itself in the frequency domain as a single spike at a frequency which corresponds to the run speed of the machine. For example, if the motor is running at 1,200 rev/min the spike will have a frequency at 1,200 cycles/minute (cpm) or 20 Hertz (Hz).


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Accelerometers

Figure 13 Compression mode accelerometer

Looking at the figure above we see a schematic of an accelerometer. Modern accelerometers are available as compression mode or shear mode. Generally speaking the shear mode accelerometer offers better axial sensitivity with much better mechanical integrity. In other words the shear mode accelerometer is not as affected by thermal transients and gives better accuracy for the axis in which it is mounted.

Figure 14 Shear mode accelerometer

Many low cost industrial accelerometers are now shear mode. For off-line measurements the accelerometer will probably be connected to a magnet and the magnet positioned at a pre-determined point every time a reading is taken. However, the response from the accelerometer is better if it is permanently mounted.

Permanently mounting an accelerometer should be done with care. The way the accelerometer is mounted will affect the resonant frequency and, hence, the useable frequency range. By far the best way to mount an accelerometer is to spot face the subject surface and drill and tap it to accept the stud for the accelerometer. However, on a motor it is usually not practical to drill into the motor frame for obvious reasons. The best


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alternative to stud mounting is to have tap blocks made with a tapped hole that will accept the accelerometer stud.

Acceleration Amplitude Demodulation

Theory

But before we look at any case histories using DEMODULATION we should be clear in our mind about exactly what is MODULATION.

Figure 15 Simple modulation example

A signal may be said to be amplitude modulated if the amplitude of that signal is changing over a period of time because of the influence of another signal. The example above was taken from a large steam turbine running at 3600 rpm. The run speed signal is being MODULATED by a signal at 4 Hz which is probably a foundation resonance. This type of modulation is commonly found in maintenance applications but consider the example below.


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Figure 16 Bearing modulation example

Here we see a vibration at 2 kHz which has been modulated slightly more than three times within the time period (50 mS which equates to 1 revolution of the inner race). The 2 kHz vibration is the resonance of the bearing which is being excited by the bearing outer race frequency (3.07 x run speed). The excitation of the 2 kHz frequency by the bearing defect on the outer race causes the 2 kHz amplitude to be changed like the roller coaster example above. In other words the bearing outer race frequency is modulating the bearing resonance frequency. The demodulation process extracts the modulating frequency to produce a time waveform which can be handled by the F.F.T. process.

When we DEMODULATE the above reading we are not interested in the 2 kHz frequency but we are interested in the outer race defect frequency which is:

(1000/50*3.07) Hz = 61.4 Hz. As can be seen from Figure 2, the modulation is at this frequency. In vibration terms, demodulation is a way of extracting the rate of occurrence of high frequency resonances.

The Demodulation Process

The time waveform of a machine with a bearing in the early stages of deterioration will look like the top plot below. The bearing excitation resonance is shown as small, high frequency pulses sitting on top of the high amplitude, low frequency vibration.


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Figure 17 Demodulation process

The demodulator circuit now passes the signal through a high pass filter to give the time waveform shown in the lower section of the plot.

Figure 18 Enveloping process

With the time domain signal in this format the F.F.T. conversion would give a single spike in the frequency domain at the resonant frequency which we have earlier said is not what we want. To modify the signal so as to be suitable for F.F.T. we must envelope (figure above) each parcel of energy by first rectifying and then passing the signal through a smoothing R-C (resistance-capacitive) circuit.


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Figure 19 Fast Fourier Transform

The signal is NOW passed through the F.F.T. and we get a spike in the frequency domain at the bearing defect frequency (figures above and below).

Figure 20 FFT - 3D view

Resonance Sources When taking a demodulated reading we must first decide on which filter setting to use that will allow the carrier signal to pass without allowing the low frequency, high amplitude noise to pass. Conventional thinking will tell you that the resonance frequency which we are using as the carrier wave is always the resonant frequency of the bearing; while this is often the case it is not always so. For vibration readings, the accelerometer which we will use to detect the signal will probably be sitting on top of a magnet which will give a structural resonance in the 1.5 to 4 kHz range (typically). The bearing housing will have its own


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resonance, the machine structure will have its own resonance. In short, the carrier wave signal resonance could be coming from any part of the mechanical structure.

If we are taking a reading with a non-vibration parameter we will probably be utilizing a different carrier signal so we may have to use a different high pass or band pass filter. Ultra-sound data are heterodyned to the audible range so demodulating at 5 to 8 kHz gives acceptable results while A.C. electric current should be demodulated from the A.C. frequency of 60 Hz or 50 Hz.

A.C. Motor Example. This plot shows the signal from the inboard bearing of a 35 H.P. A.C. motor operating a belt-driven fan.

Figure 21 Two channel time waveform - bearing defect

The 2 upper plots are the time domain signal in two planes over a period of 640 mS. The lower plots show the time domain (left) and frequency domain (right) over a 50 mS period of the lower 640 mS plot. Note that the frequency spectrum shows spikes at 2 kHz and 3 kHz while the time domain plots show an angel fish pattern which is classic of a bearing defect. Note also that the lower left portion of the plot is a zoom of the windowed part of the long time record. This shows a detail of the one angel fish and the amplitude can be seen to be passing from positive to negative and back again many times during the life of a single angel fish - i.e. a high frequency oscillation. This leads us to the conclusion that this is the frequency of 2 and/or 3 kHz seen in the spectrum and one or both of these frequencies are the result of impacts and subsequent ring down and they are occurring at the resonant frequency of part of the mechanical structure.


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Figure 22 High frequency waterfall

The plot above shows a time/frequency cascade of the same time interval cropped below 0.001G. This clearly shows the modulation of the 2 kHz frequency while the 3 kHz frequency is static. The modulation has been calculated to be equal to the bearing outer race defect frequency of the motor inboard bearing. Every time one of the bearing balls passes a defect on the outer race, the ball impacts on the defect causing the 2 kHz vibration to suddenly rise and then ring down. The 2 kHz is the resonant frequency and the bearing defect frequency (outer race) is the modulating frequency. The figure below shows the demodulated spectrum on the left with waterfall plot on the right above a trend of the defect frequency.

Figure 23 Enveloped acceleration spectrum

Note that the demodulated spectrum is clean and extremely easy to analyze. The spikes occur at the bearing defect frequency (outer race) with multiple harmonics but there is no sign of the resonant frequency because this high frequency has been removed during its use in the demodulation process. The frequency range of


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the spectrum is such that the frequency of the impacts is clearly visible but we do not need to see the resonant frequency. The last spectrum in the waterfall is lower than the previous spectrum due to greasing of the motor bearings which lowered the amplitude at which the impacts caused the bearing to vibrate at resonance.

Figure 24 Comparison - velocity to envelope

This figure shows a similar defect on another machine but here the velocity spectrum (left) is displayed alongside the demodulated spectrum (right). Note that the demodulated spectrum is much cleaner and easier to analyze.


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Failure Modes

Induction Motors

Mechanical or Electrical Effects

Vibration of electrical motors can be either mechanical or electrical in origin. Mechanical problems may include imbalance, misalignment, defective bearings and looseness. Vibration caused by electrical problems are normally the result of unequal magnetic forces acting on the rotor or stator. The unequal magnetic forces may be due to open or shorted windings, broken rotor bars, unbalanced phases, unequal air gap and other similar problems. Generally, the largest component frequency of vibration resulting from these electrical problems will be 1 x RPM and, this will appear similar to imbalance. A common way to check for electrical vibration is to observe the change in vibration amplitude the instant electrical power is disconnected from the unit.

If the vibration disappears the instant the power is shut off, the vibration is likely to be due to electrical problems. If this is the case conventional electrical testing procedures can be carried out to pinpoint the true cause of vibration. On the other hand, if the vibration amplitude decreases only gradually after power is disconnected, the problem is more likely to be mechanical in nature. Perhaps an even better indication of the contribution of electrical problems is by observing the time waveform of the vibration as power is disconnected.

Electrical problems with induction motors will often cause the motor load current ammeter to swing or pulsate in a cyclic manner. If phase readings are taken, or if the motor has a strobe light flashed at run speed, it will be seen that the phase is erratic and instead of the strobe freezing the rotor, the rotor will appear to swing back and forth. This pulsating vibration common with induction motors will either be a single frequency whose amplitude is being modulated or it will be a beat between two frequencies of vibration which are very close together. If the nature of the pulsating vibration can be determined, this can help significantly to identify the specific problem as discussed in the following paragraphs.

Armature Related Problems

Typical problems associated with the rotor or armature of an induction motor which cause electrical vibration include:

Broken rotor bars This type of defect is best discovered by the use of motor current analysis and comparing the height of the slip * No. of poles sidebands around line frequency to previous levels.

Wound rotor windings Defects in the rotor will cause a modulation of rotor bar pass or stator slot passing frequencies at run speed. In other words these frequencies will have sidebands of 1x. If the machine has a beat at slip frequency this is usually due to a defect in one rotor winding phase such as a broken conductor or bad brush.

A bowed rotor This defect usually occurs on very large, horizontal motors where the motor has sat idle for an extended period and the weight of the rotor causes a sag in the middle of the rotor. In vibration readings this will look very like imbalance with a small axial component. If bowing of the rotor is suspected then the condition can usually be corrected by slow rolling the motor for up to two days to reset the sag.

An eccentric rotor The variable air gap this produces between the rotor and stator give a vibration at 2 x line frequency with sidebands at pole pass frequency as well as sidebands around run speed of pole passing frequency.


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Out of magnetic center This is almost always caused by improper fitting of the bearings. This causes to motor to run out of magnetic center which gives a vibration at run speed. There will be a phase difference in the vibration between energized and de-energized

Stator Related Problems Electrical problems in the stator of an induction motor can also result in vibration with a pulsating amplitude. However, in this case the pulsation is the result of a beat between two separate frequencies of vibration which are very close together. Common stator related problems which can be expected include:

Stator windings Phasing problems such as a loose connector in the stator windings or supply will cause a modulation or sideband of the reciprocal of the number of pairs of poles x line frequency (e.g. 60 x 1/3 for a 1200 rpm motor) around 2 x line frequency. A defect in the windings themselves will also cause an unequal magnetic flux around the motor although is usually very small except in severe cases.

Windings insulation Gradual degradation of the insulation of the windings will result in a fall off of the insulation to ground resistance which should be at least 1.5 M for a main drive motor.

Imbalanced phases A difference in the supply voltage or power factor of the three phases will cause a vibration of 2 x line frequency (120 Hz) around rotor bar passing frequency. If demodulated spectra are used this will show up as very high spikes at 120 Hz (100 Hz in Europe) in the frequency domain.

In the case of a stator related problem, to produce a vibration whose amplitude pulsates in a cyclic fashion it is necessary that two frequencies of vibration be present. One of these vibration frequencies may be the result of some imbalance or misalignment occurring at the running speed of the armature. The other vibration will probably be an electrical vibration which occurs at the rotating speed of the magnetic field powering the motor. If any of the above stator problems are encountered a mechanical vibration will occur at the rotating speed of the magnetic field. Since the mechanical and electrical vibrations are relatively close in frequency their amplitudes will alternately add together and subtract at a rate equal to the difference between their frequencies. The result will be noticeable steady pulsation or beat of the vibration amplitude.

Observing the pulsating vibration in time waveform on an oscilloscope or spectrum analyzer can be useful in identifying the beat frequency characteristics of stator related induction motor problems. The phase relationship between the two individual vibration frequencies is constantly changing producing a resultant vibration whose amplitude increases and decreases in a periodic fashion.

Electric motors have inherent vibration due to torque pulses. Torque pulses are generated as the rotating magnetic field of the motor energizes the stator poles. Since each motor pole is essentially energized twice for each cycle of AC current, the vibration resulting from torque pulses will be two times the line frequency powering the motor. Thus, if an AC line frequency is 60 Hz or 3600 cpm, torque pulse frequency will be 120 Hz or 7200 cpm. This vibration is rarely troublesome except where extremely low vibration levels are required, or if the torque pulses should happen to excite a resonance condition in the machine or structure. Torque pulses have also been known to excite loose rotor bars and loose stator windings at frequencies of 2x, 3x, and even 4x torque pulse frequency. Care should be taken if a significant 7,200 cpm vibration is seen in velocity vibration readings as this can also be caused by stator distortion brought on by a severe misalignment or a soft foot condition.

Demodulated readings will demodulate the frequencies above the high pass filter or inside the band pass filter. This range will usually also include the rotor bar pass and slot pass frequencies. A modulation of the rotor bar or slot passing frequencies by 2 x line frequency is not uncommon and does not necessarily mean that there is a defect in the motor. It is the authors experience that inequalities in the power factor at each of the three phases will cause very large changes in this modulation. If frequencies at 120 Hz (7,200 cpm) are apparent in your demodulated spectrum, the first thing to check is the individual phase power factor.


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Broken Rotor Bars

AC induction motors experience a wide range of mechanical problems common to most machinery such as misalignment, looseness, bad bearings etc. However, they also have their own unique set of problems that are often linked to the electro-magnetically generated fields in the stator and the rotor. Frequency analysis of the motor load current has been consistently proven to be able to detect the presence of broken rotor bars, end ring resistances and cast rotor blow holes. Each of these three problems give the same effect to the motor - variations in current draw, as the defective bar cuts the lines of flux. In the 1960s Aberdeen University in Scotland carried out a joint research project with Shell Exploration & Production on several off-shore oil and gas production facilities in the North Sea. The object of the project was to determine a reliable and repeatable method for the evaluation of broken rotor bars on A.C. induction motors. The driving force for this project was the large number of motor failures suffered at these production facilities. The project concluded that the presence of sidebands at the motor slip multiplied by the number of poles around the line supply frequency indicated not only the presence of broken rotor bars (or equivalent) but also how many bars were affected. The quantitative analysis of the number of broken rotor bars relies heavily on the height of the sideband compared to the height of the line frequency spike (generally expressed in dB Amps) at a fixed speed and a steady load of at least 50% during the measurement. To identify the separate spikes clearly the spectrum must have a fine line resolution. These measurements are usually taken with 1600 or 3200 lines with a bandwidth of 80 Hz (for 60 Hz line supplies) or 65 Hz (for 50 Hz line supplies). A 3200 line spectrum with a bandwidth of 80 Hz will take 40 seconds to collect during which time the load and speed of the motor under test must not vary significantly.

DC Motors

How DC Power Is Created. Direct current is created by taking three phase alternating current and converting it through a bank of silicon controlled rectifiers (SCRs) into direct current. AC is supplied in the United States at 60 cycles per seconds or 60 Hz (Hertz). Industrial power in the United States is supplied in a three phase 60.Hz format. This means there are three individual alternating current waveforms being supplied simultaneously at 60 Hz but 120 degrees out of phase. The three waveforms are identical in amplitude and duration; thus, a one second snapshot of three phase AC will reveal 180 positive and 180 negative amplitude peaks

When AC is rectified to DC these peaks are electronically processed to allow only positive peaks to remain in the wave form. These peaks, although no longer alternating, create a pulsing which is detectable through vibration analysis.

When three SCRs (half-wave rectified) are used to convert AC to DC then a pulsing or frequency equal to the 180 Hz is created in the DC drive System. When six SCRs are used to convert the AC to DC, (full-wave rectified or High Efficiency System) then a pulsing or frequency of 360 Hz (6 x 60 Hz) is created in the DC drive system.

Those who are more comfortable using cpm (Cycles Per Minute), rather than Hz, need only multiply the frequency in Hz by 60 seconds.

Thus 180 Hz x 60 sec. = 10,800 cpm and 360 Hz x 60 sec. = 21,600 cpm.


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Figure 25 The creation of DC power

Single phase alternating current frequency is 60 Hz

or 60 Hz x 60 see. = 3,600 cpm

Three phase alternating current frequency is 180 Hz or 3 x 60 Hz x 60 sec. = 10,800 cpm and also has 180 positive and 180 negative amplitude peaks per second.

Half-wave rectified direct current (3 SCRs) is 3 x 60 Hz @ 180 Hz or 180 Hz x 60 sec. @ 10,800 cpm

Full-wave rectified direct current ( 6 SCRs ) is 6 x 60 Hz = 360 Hz or 360 Hz x 60 sec. = 21,600 cpm

A half-wave rectified DC drive system will then have a dominant electrically related frequency of 10,800 cpm and a full-wave rectified system will have a dominant electrically related frequency of 21,600 cpm When these frequencies exist within their respective systems they should be considered normal unless amplitudes greater than 0.1 in./sec. peak are detected. This usually means that there is an electrical control problem.


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Figure 26 FFT spectrum of half wave rectification

Figure 27 FFT spectrum of full wave rectification

DC Systems and Controls Direct current drive systems use rectified alternating current to power an electric motor. This DC source can be varied through system controls to change the running speed of the motor. This can be controlled manually or be adjusted automatically by allowing the control system to monitor the motor speed through the use of a tachometer, self adjusting the power source to achieve the desired speed. The self controlled systems or closed loop systems use low voltage control components to fire or open the pathways which allow the full DC power to be supplied to the motor. This allows the motor to run at the desired speed or


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desired rate of speed change to meet the needs of the driven system. The electrical problems associated with these systems are:

AC power supply

AC to DC rectification components

DC control components and

DC motor component failure

Figure 28 Basic DC system circuit

The system operates by DC power being supplied to the motor which creates a magnetic field and causes the motor armature to rotate at a speed proportional to the DC power supplied. As the motor turns, the tachometer (tach.) also turns which creates a low voltage proportionate to its speed. The tach. low voltage is compared to a constant or predetermined voltage variance by the comparitor card. The comparitor card, based on the voltage differential between the constant voltage pot and the tach. low voltage, signals the firing cards. There is a firing card or order for each SCR which controls the power flow through the SCR. The SCRs fire or open to create and supply DC power to the motor which either speeds or slows the motor to the appropriate speed determined by the pot. This is a very basic explanation of a DC motor circuit but should be sufficient to give an understanding of the concept of how the various components interact.

DC Control Firing Cards The firing cards, which control the opening and closing of the SCRs, must perform correctly to allow the system to function normally. Because there is one firing order per SCR there is a potential for one or more of the SCRs to perform erratically or not at all if the firing card malfunctions.

Vibration analysis has been used to determine malfunction on this card or SCRs based on frequencies which have sub multiples of the DC dominant frequency present. DC power frequencies will always be constant at 21,600 cpm on a full-wave system or 10,800 cpm on a half-wave system. If one sees a frequency of 3,600 cpm and frequency separation of 3,600 cpm between existing spectrum peaks or a frequency of 7,200 cpm and frequency differences of 7,200 cpm then faulty firing cards or SCRs may be the cause.


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1S.C.R. problems

Figure 29 FFT spectrum full wave DC firing card frequencies

Figure 30 FFT spectrum after repair

Example of a Firing Card Fault Vibration analysis was requested on a 300 HP DC motor which was critical to a production system. One day prior to the request for analysis the system would not maintain the expected speed and the motor was pulsing. A mechanical problem within the gearbox or drive train was initially suspected because the electrical system appeared to be functioning normally. The motor was uncoupled from the drive train and a visual inspection performed on the motor when run under a no load condition. The pulsing was still apparent even under a no load condition, however, the motor did start and run. A motor bearing then seemed the next logical failure point. The production system was critical to the plant operation, as previously mentioned, and a decision to recouple the motor and operate until a vibration analysis could be performed to determine bearing wear or failure seemed the best alternative. The analysis was performed

1 Thanks to Bill Rinehart for his permission to use this data


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revealing the FFT spectrum in figure 26. The dominant frequencies are 7,200 cpm, 14,400 cpm and 21,600 cpm. These frequencies are related to DC ELECTRICAL problems; not bearings or mechanical defects

When an FFT appears with dominant 1/3 frequencies of the DC full pulse frequency (21,600 for a full wave, six SCR system), then suspect firing card or SCR problems in the DC control. This DC control system uses three firing cards to control six SCRs which is typical of many DC control systems. When one firing card is not functioning then 1/3 of the power is lost. Dominant frequencies of 7,200 cpm and 14,400 cpm or frequencies equivalent to multiples of 1/3 of 21,600 cpm are representative of this situation. The firing cards were examined and a loose connection on one card was found and repaired. The FFT spectrum in figure 27 was taken after the repair. The 7,200 cpm and 14,400cpm frequencies are now gone. The 21,600 cpm frequency is the normal frequency of a full wave system and should be present.

Figure 31 FFT spectrum showing half wave firing card frequencies

Half-wave rectified AC power sources will tend to have 1/3 multiples of 10,800 cpm or frequency separations of 3,600 cpm. Full-wave rectified AC power sources can also have frequency separation of 3,600 cpm if the system has:

One firing card for each SCR, and one card is out

A three card system and one card is partially disabled

One SCR is not functioning

The FFT spectra directly above and below also show the difference between the firing card frequency amplitudes of a motor that is uncoupled and running under no-load (below) and the same motor coupled and running under a load (above). Although the frequencies are the same in each spectrum the amplitudes are considerably load dependent. The amplitude at 7,200 cpm on the spectrum below is only 0.00847 in/sec peak while the amplitude of the spectrum above at 7,200 cpm is 0.3037 in/sec peak, yet each spectrum represents the same firing card malfunction.

Another possible reason for seeing these 1/3 multiples would be if one phase of the AC power source was not present. This would affect one-third of the system power and virtually render one bank of SCRs inactive. A simple voltage test of the three incoming AC phases should confirm this situation if present.


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Figure 32 FFT spectrum of same motor (no load)

DC Control Comparitor Card The comparitor card is another low voltage control component which is responsible for determining the difference between the system actual speed and the set or predetermined speed performance. When this component malfunctions it has been observed that there are side-bands present around DC frequencies. These side-bands are not of a particular set frequency but are always equally spaced from the DC frequencies. it has also been observed that these side-bands will grow or diminish as the motor RPM is varied, however, they will remain equally spaced. It has not yet been determined if these side-bands are related to the RPM fluctuation or hunting which often accompanies comparitor card problems or if the constant collapsing and regenerating of the magnetic field of a system that is hunting is the cause. The side-bands do, however, exist regardless of the cause and should be considered a warning of this component failure. These side-bands may occur at small cpm increments as shown below and may require a high resolution FFT to differentiate them from the dominant frequencies.

To resolve side bands related to comparitor card malfunctions a FFT spectrum of 3200 lines of resolution at Bandwidth of 24,000 cpm is suggested.

Another possible reason to see these FFT characteristics could be a faulty or malfunctioning tachometer which would corrupt the voltage going to the card. Testing the voltage output of the tach. should confirm this situation.


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0.0872

5000 16,000

Figure 33 FFT spectrum showing comparitor card defect.

Example of a Comparitor Card Defect Vibration analysis was requested on a 125 HP DC motor which was thought to be vibrating heavily. The motor had been uncoupled from the belt to see if the motor vibrated when running solo.

The first set of spectra was collected under these conditions and revealed the above spectrum. A RPM check using a digital tach. also revealed that the motor was fluctuating or hunting approximately 30 cpm at an RPM of 1440. The tach. voltage was then checked but seemed to be consistent with the operating speed and fluctuations. Based on the side-bands a recommendation was made to change the comparitor card (also called the control card). There was not a spare card available at this time but there were spare firing cards. The firing cards were changed but did not solve the problem. A spare comparitor card was eventually located and the replacement accomplished. The speed fluctuations stopped and another set of spectra collected revealing the spectrum below.

DC motors are different from AC motors because of their power supply which requires different components. The most obvious of these is the tachometer which extends, usually, from the back of the motor. These units usually have small bearings which can be monitored in the same manner as any bearing.

Caution: Never Place A Magnetic Accelerometer Mount On A Tachometer These devices use magnets to generate the voltage which the control system monitors to determine the motor speed. Placing a powerful magnet on or near the tach may alter or destroy the voltage output causing the motor to literally speed up until it destroys itself.


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Figure 34 FFT after the comparitor card was replaced

Figure 35 DC motor components

The commutator is the device which transfers the DC power to the motor armature. Brushes, usually made of a carbon alloy, ride against the commutator and supply the DC power to the commutator. It has been observed that as these brushes wear, readings at one times the motor RPM will rise in amplitude, When the brushes arc it has been observed that these one times RPM readings will increase dramatically, sometimes reaching 0.3 ins./sec. peak or even higher in extreme cases. Another frequency associated with

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