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Vibration Analysis

Dr./ Ahmed NagibNovember 9, 2015

Vibration Analysis Lectures

Chapter I Vibration Sources and Uses Chapter II Basic Machinery Vibrations Chapter III Data Collection and Analysis Chapter IV Machine Characteristics Chapter V Vibration Instruments Chapter VI Vibration Testing Chapter VII Basic Analysis Chapter VIII Vibration Severity

Vibration

Q: Will structure fail before the human body in a factory or vice versa?

Vibration

Sources of Vibration

Table 1.1. Sources of Vibration.Function

Inadequate DesignManufacturing Processes

InstallationWear and Abuse

Faulty Maintenance

Sources of Vibration - FunctionVibration by imposed motion

Sources of Vibration - Function

The two causes of vibration are imposed motions and forces. Imposed motions usually relate to the function of the machine. Cams, slider cranks (reciprocating compressors and engines), chain and sprocket cogging, and misalignment are examples of devices and conditions that generate vibrations by imposed motions. The imposed motion creates internal forces in the machine. In reality all vibration is essentially caused by forces that are generated internally or applied externally.

Sources of Vibration - Inadequate machine design can be responsible for excessive vibration because the machine enhances or is the cause of unnecessary pulsating or vibratory forces. For example, if a motor stator flexes as a result of electromagnetic forces, unnecessary vibration results.

Sources of Vibration – Manufacturing Process and Assembly poor quality machining and manufacturing or assembly errors. These conditions enhance background noise and, in some cases, will produce unacceptable vibration. • Gears cut with a poor hobbing tool will produce a high-frequency gear-mesh like vibration.

• Motors assembled with rotors that are not centered in the stator will cause unbalanced electromagnetic forces that excite vibration.

• Inadequate balancing causes excessive forces and vibration

Sources of Vibration – Manufacturing Process

Table 1.3. Vibrating Forces.Poor Quality Machining Assembly Errors Installation • misalignment • distortion • looseness Structural and Material Defects Thermal Distortion Lack of Lubrication Unbalance

Sources of Vibration – Installation Erroes

Misalignment, distortion (soft foot), and looseness (bolts not tight) are examples of conditions that cause excessive vibration; Figure 1.4. Normal wear, structural damage, and abuse can modify the function of a machine and so cause vibration.

Sources of Vibration – Installation Erroes

Sources of Vibration – Lack or Faulty maintinanceMachines become unbalanced, need lubrication, and require changing of worn parts. Some parts, such as vibration isolators, deteriorate over time, depending on the environment. Lack of or excessive lubrication is detrimental to the life of rolling element bearings as well as gears. Bolts must be tight, and properly torqued. Fits and clearances are important in assembly. Above all it is important to keep good records. Lack of good professional maintenance is an open invitation to machine vibration.

Harmonic Mass Unbalance

Periodic Misalignment

Impulsive Rolling Element Bearing, Gears tooth

Pulsating

Random Cavitation in Pumps

Types Vibration

Vibration Effect

Table 1.4. Vibration Effects.Catastrophic Failure

Fatigue FailureLoss of Product QualityHuman Annoyance

The weakest link in a machine exterior, its piping, ductwork, or supporting structure, can fail as a result of excessive vibration. Coupling, shaft and bearing failures occur in the rotating elements. Cracks, prior to failure, can occur in ductwork and foundations; piping can become overstressed and fail.

Uses of Vibration

Table 1.5. Uses of Vibration.Acceptance Testing

Predictive MaintenanceManufacturing

Predictive Maintinance Procedure

Table 1.6. Predictive Maintenance.Monitoring

Fault DiagnosisSeverity Evaluation

Measurement and Analysis

Schematic of Data Collection Instrument.


Data Acquisition


Data Acquisition with two sensors

Vibration Data

Vibration

Monthly Trend Plot of a Pump Motor for Peak Velocity.

Periodic Monitoring

data are acquired sequentially in a route from bearing to bearing and machine to machine. The data collector is preprogrammed and routes are uploaded in the computer to accept and store the data acquired from the machines in the route. After acquisition, the data are downloaded to the computer for trending and analysis.

Review

Sources of vibration include function, inadequate design, manufacturing processes, installation, wear, abuse and bad maintenance

Forces cause vibration Types of vibration include harmonic, periodic,

impulsive, pulsating, and randomEffects of vibration are component failures, loss of

product quality, and human annoyance Uses of vibration include acceptance testing,

predictive maintenance, and manufacturing Sensors are used to detect vibrations Analyzers are used to quantify the amplitude and

frequency of vibrations

Chapter II -Basic Machinery Vibrations

Table 2.1. Vibration UnitsThe basic units used in this book to describe vibratory forces and motions, from the English system, are pound (lb), inch (in.), and second (see).Amplitudes of vibrating motion are described using the following units:

displacement, mils-‐peak to peak (1,000 mils = 1 inch)velocity, in./sec-‐peak or rms (IPS-‐peak or rms)

acceleration, gs peak or rms (386.1 in./sec2 = 1 g)Frequencies are expressed in cycles/minute (CPM) or cycles/second (Hertz, Hz), or orders (multiples of operating speed).Speeds are expressed in revolutions/minute (RPM).

Vibration cause and effect

Vibration Measurement

Mechanical vibration is measured by a transducer (also called sensor) that converts vibratory motion to an electrical signal. The units of the electrical signal are volts (v) or, more typically, millivolts (mv). There are 1,000 millivolts per volt (mv/v)

Vibration

Example 2.2. Measurement Units400 mv-‐pk to pk was measured by a displacement transducer that has a scale factor of 200 mv/mil. Then the displacement amplitude equals

400 mv − pk to pk200 mv/mil = 2 mils pk − pk

Example 2.1. Voltage UnitsConvert 253 millivolts to volts123 45

6777 45/5 = 0.253 vConvert 0.342 volts to millivolts

0.342 𝑣 6777 455 = 342 mv

Proximity Probe

Proximity probes, also termed noncontactingeddy current displacement transducers, are attached to the bearing housing and measure shaft vibration relative to the mounting position of the probe. Two probes are usually mounted at a 90° angle to each other

Vibration

Magnetically Mounted Accelerometers on a Fan Pedestal.

Vibration motion

Three fundamental properties that describe vibration are frequency, amplitude, and phase. Frequency is defined as the number of cycles or events per unit time. It is expressed as cycles per second (Hertz, Hz), cycles per minute (CPM), or orders (multiples) of operating speed

Vibration motion

Amplitude is the maximum value of vibration at a given location on the machine. When the vibration is displayed as displacement and measured in mils (1 mil =1/ 1,000 in.), the amplitude measured is peak to peak.

Vibration motion

For example, in Figure 2.6, one cycle of vibration is made in 32.8 milliseconds (mSec) or 0.0328 sec. Therefore, one cycle divided by 0.0328 sec. equals 30.48 cycles per second. ).

Vibration motion

Example Period and FrequencyFrom Figure 2.6, Period (τ) = 32.8 mSec/cycle

τ = 31.= 4>?@6777 4>?@/A?@ = 0.0328 sec/ cycle

Frequency (f) = 6B?CDEF (H)

Then

f = 6H =6

7.731= A?@/@J@K? = 30.49 Hz(cycles/sec)

f = 30.49 Hz x 60 sec/min = 1,829 cycles/minute (CPM)

Vibration motion

For example, in Figure 2.6, Velocity equals 0.6 IPS-Peak.

Vibration motion

Also, the velocity amplitude can be reported in root-mean-square (RMS) units. If the data are harmonic (one-frequency) as they are in Figure 2.7, then the RMS is equal to 0.707 times the peak or 0.424 IPS-RMS. If the data are not harmonic, no simple mathematical relationship holds between RMS and peak and an electronic circuit must be used to get the RMS. The advantage of the peak unit is that it always can be obtained from the time waveform.

Vibration

Vibration Measures.

Measure Units Description

displacement mils p-‐p*motion of machine, structure, or rotor; relates to stress

velocity in./sec, IPStime rate of motion;

relates to component fatigue

acceleration gs**relates to forces

present in components

*1 mil = 0.001 inch; p-‐p = peak to peak **1 g = 386.1 inches/sec2

Vibration

Displacement. Displacement (D) is the dominant measure at low frequencies and is related to stress in flexing members. It is expressed in mils peak to peak because the total excursions of the machine motions are measured. It is normally nonharmonic but periodic and will therefore yield different positive and negative peaks. Displacement is used as the measure for low-frequency vibration [less than 600 CPM (10 Hz)] on bearing caps and structures.

Vibration

Displacement is also commonly used to determine the relative motion between a bearing and its journal or between the machine casing and its shaft to assess whether or not rubbing may occur. Figure shows vibration data plotted in the displacement measure that is symmetrical originating from a harmonic force like mass unbalance.

Vibration

Velocity (V) is the time rate of change of displacement. Velocity cannot be sensed by touch - only changes in it. Basically, it is displacement times frequency and is a measure of fatigue in machines. The greater the displacement and/or frequency of vibration, the greater is the severity of machine vibration at the measured location.Velocity is used to evaluate machine condition in the frequency range from 600 CPM (10 Hz) to 60,000 CPM (1,000 Hz).

Vibration

Figure 2.8 is a plot of velocity versus time. The amplitude is measured in peak units positive or negative, whichever is larger. In Figure 2.8 the negative peaks are larger;; therefore, the peak velocity is 0.42 inches per second, IPS-peak.

Vibration

Acceleration is the dominant measure at higher frequencies. Because it is related to force it can be sensed by touch. It is proportional to the force on a machine component such as a gear and is used to evaluate machine condition when frequencies exceed 1,000 Hz (60,000 CPM) in gears and bearings. Acceleration is the time rate of change in velocity.

Vibration

Figure shows acceleration measured on a gearbox;; the peak amplitude is 10 gs.

Vibration

If the vibration is harmonic (one frequency), the amplitudes of the velocity and acceleration are directly related to displacement by frequency. If the frequency is known and, the measures-displacement, velocity, and acceleration - are related by frequency. If a measure and the frequency is known, the two other measures can be calculated using the formulas provided below.

V = 2𝜋fD and A=2𝜋fV

VibrationTo calculate velocity, displacement must be changed from mils-peak to peak to inches-peak. This requires division by two (2) and by one thousand (1,000 mils = 1 inch). To obtain acceleration in gs, divide the value in in/sec2 by 386.1 in/sec2 per g. For example, a vibration displacement of 5 mils-pk to pk becomes 5/2000 = 0.0025 inches-peak. For a frequency of 100 Hz, the velocity is V = 2 x 𝜋x 100 x 0.0025 in/sec-peak. V = 1.57 IPS-pk. The acceleration A = 2 x 𝜋x 100 x 1.57/386.1 = 2.55 gs-peak. A displacement of 6.4 mils-pk to pk relates to a velocity of 0.2 IPS-peak at 10Hz whereas the acceleration is only 0.03 gs peak.An acceleration of 3.2gs at 1,000 Hz relates to a displacement of 0.064 mils-pk to pk. Therefore, displacement and acceleration measures are restricted to low- and high-frequency applications respectively.

Vibration AnalysisThe basic vibration data (waveforms) collected by sensors and displayed by instruments must be broken down into frequency components in order to perform a detailed vibration analysis.

Vibration AnalysisVibration signals are usually composed of multiple frequency components with different amplitude. The amplitude of the lower plot (time waveform) is 3.6 mils peak-to-peak;; the period is 18.7 mSec (53.5 Hz). The upper plot, which is called a spectrum, is the breakdown of the time waveform in mils peak-to-peak versus frequency. The spectrum is obtained from the waveform using a mathematical procedure called an algorithm. This allows the analyst to determine the dominant source of the problem. The fundamental frequency, 53.3 Hz, of the data in Figure 2.10 is equal to the operating speed of the driven pump (3,198 RPM).

Vibration

The data shown in Figure 2.11 were obtained from a velocity sensor mounted on a generator exciter bearing with a magnet.

Vibration

The amplitude of the time waveform is 0.73 inch/second (IPS)-peak. The amplitude in the spectrum can be given in spectral component peaks (0.275 IPS at 60 Hz and 0.24 IPS at 120 Hz) or in overall root-mean-square (RMS), which is 0.283 IPS

VibrationThe RMS measure of a complex waveform cannot be obtained from the peak value. If the vibration waveform is not harmonic (one frequency), the RMS cannot be obtained by multiplying the peak value by 0.707 as shown in Example 2.4. Note that the two RMS peaks in the spectrum do not add up to the actual RMS values.

Example 2.4. Peak and RMS Measurements.From Figure 2.11

At 60 Hz RMS = 0.275 x 0.707 -‐ 0.194 IPSAt 120 Hz RMS = 0.24 x 0.707 -‐ 0.170 IPSTotal RMS in the spectrum -‐ 0.283 IPS

Excitation

The purpose of vibration analysis is to identify defects and evaluate machine condition. Frequencies are used to relate machine faults to the time-varying forces, termed forcing frequencies, that cause vibration. It is therefore important to identify the frequencies of machine components and machine systems before performing vibration analysis. The forces are often the result of defects or wear of components or are due to equipment design or such installation problems as misalignment, soft foot, and looseness.

VibrationExample Machine Forcing Frequencies.

Mass unbalance shaft rotational frequency (RPM)Misalignment two times RPMBent shaft RPM

Vane and blade number of vanes/blades x RPMElectromagnetic two times line frequency

NATURAL FREQUENCIES AND CRITICAL SPEEDS Natural frequencies are determined by the design of a machine or component. For example, the shape of a bell will determine its natural frequency. The sound of the bell when it is rung is its natural frequency. How long it rings is a measure of its damping. Natural frequencies are properties of a system and are dependent on the distribution of mass (material) and stiffness (elasticity). Every system has a number of natural frequencies. However, they are not multiples of the first natural frequency (with the exception of rare instances of simple components).

NATURAL FREQUENCIES AND CRITICAL SPEEDS Natural frequencies are not important in machine diagnostics unless a forcing frequency occurs at or close to a natural frequency or impacts occur within the machine. If a forcing frequency is close to a natural frequency, a resonance exists, and the vibration level is high because the machine absorbs energy easily at its natural frequencies. If the forcing frequency is an order of the operating speed of the machine, the resonance is termed a critical speed. Only natural frequencies in the range of forcing frequencies are of interest in the vibration analysis of machines.

REVIEW • Two important characteristics of vibration are frequency and amplitude. • The frequency is the number of cycles per unit of time. • The period is the time required for one cycle of vibration;; it is the reciprocal of frequency. • Amplitude is the maximum value of vibration at a given location on a machine. It is expressed in mils (displacement), in.!sec (velocity), or gs (acceleration). • The amplitude of vibration is expressed in units of peak, peak to peak, or rms. • Peak and rms are used with velocity and acceleration;; mils peak to peak are used with displacement. • The measures of vibration - displacement (stress), velocity (fatigue) and acceleration (force) - can be converted one to the other if the vibration is a single frequency (harmonic).

REVIEW • A force, or excitation, causes vibration. • Vibratory forces arise from process variable, improper design, bad installation, and defects. • Vibrations are analyzed in the time waveform and the frequency spectrum. • Natural frequencies are a property of a machine system and depend on mass and stiffness. • Resonance occurs when a forcing frequency is equal to or close to a natural frequency. • Vibration is amplified at resonance.

This chapter involves the acquisition of data which will be analyzed and used to make maintenance or acceptance decisions on the operability and efficiency of machines. Sources of data• physical observations of persons walking through the plant • periodic collection of vibration data, oil samples, and

thermography snapshots • continuous vibration monitoring with permanently

installed sensors • periodic or continuous acquisition of process data like

temperature, pressure, and flow • design and installation drawings and procedures • maintenance records

Chapter III – Data Collection

Vibration

The procedures and processes of obtaining data, types of data, sensors and instruments for collection of data, and computers for analyzing and displaying data will be discussed.

Any vibration analysis is only as good as the data collected.

This is a very important task and as such good procedures should be observed.

PHYSICAL OBSERVATIONS by Human Senses While there are several types of recorded data that form the basis for machine fault and condition analysis, among the most basic data are direct observations by the person doing the data collection based on human senses -hearing, sight, touch, smell, and taste. Human sensory capabilities, although not analytical, cannot be underestimated in the machine analysis process.

Noise

Unusual noises can indicate rubs, bearing defects, looseness, improper assembly, lack of lubrication, and any other metal to metal contact problems. A listening rod or screw driver can be used to detect a bearing defect or rubbing in a low speed machine. In pumps, a sign of flow problems is a noise that sounds like gravel in the piping. Motors and generators may emit high frequency whining noises when they are subject to excessive vibration due to casing distortion, misalignment, or coupling unbalance.

Noise

High pitched noise from new gears indicates bad construction and machinery quality or design (low contact ratio). Rubbing of guards by pulleys and belts will cause impacting and noise. Lack of lubrication in oil starved bearings or bearings with excessive clearance means that the bearing needs attention. Excessive noise is almost always an indicator of trouble. The experienced data collector will be able to enhance their analytical capability by learning to identify noise sources and associate the physical problem with them.

SightThe use of sight is an even more powerful tool for data collectors. Smoke, fire, and catastrophic failures need and get immediate attention. However, other mundane faults may go unnoticed for months. Foundation and bearing pedestal faults are the source of many cases of excessive vibration. A flashlight and feeler gage or knife help to root out these type problems. Squishing oil between joints is a certain clue of looseness.Cracks in ducting and piping and other machine components provide clues to the presence of excessive vibration. Vibration analysis will confirm these faults

SightVibration analysis will confirm these faults. The data collector may have to go off route to measure these cases.

Hammered and Torched to Fit.

Smell and Touch The senses of smell and touch are less important but should not be neglected. Unusual, abnormal odors are easily detected by the human sense of smell. Oil smoke can be smelled long before an oil fire. Ammonia and other chemical and gas leaks are best detected by the nose. Even small quantities can be detected. Hot bearings or other machine parts that are not normally operating above ambient temperature can be identified by touch. However, the data collector needs to exercise extreme caution. A steaming or red hot machine should not be touched. The water can confirm the temperatures are above 100⁰ C. The use of taste is not recommended in this work.

PERIODIC AND CONTINUOUS DATA COLLECTION

Periodic and continuous non-intrusive data collection provide current and trended information about the condition of a machine. The procedure involves the use of sensors to acquire data, meters to quantify the measured data, and instruments to store, manipulate, and present the data. Periodically acquired data provide an intermittent record of what is happening in the machine. Whereas continuous data monitoring and collection provides continuous surveillance along with the ability to protect the machine through data based automatic shutdown.


Measurement of vibration for analytical use is performed by a sensor, sometimes called a transducer or pickup, and is nonintrusive to the machine or process, Figure 3.2. The sensor transforms the vibration (mechanical motion) of the mounting location to an electrical voltage which varies with time, Figure 3.3.

Selecting a Measure A measure is a unit or measures of vibration are standard of measurement that provides a means for physical evaluation. Examples of measures are pounds for weight and feet for height. Three basic available displacement, velocity, and acceleration. Ideally the sensor would directly provide the selected measure. Unfortunately, sensor limitations do not always allow direct measurement of vibration in the proper measure. Other predictive maintenance based measures are temperature, pressure, and viscosity.

Selecting a Measure The measure is selected on the basis of the frequency content of the vibration present, the type of sensor, the design of the machine, the type of analysis to be conducted (e.g., faults, condition, design information), and the information sought.

Selecting a Measure Relative shaft displacement

which is measured with a noncontacting relative displacement sensor, proximity probe, shows the extent of bearing clearance taken up by vibration and is used over a frequency range as wide as the shaft speed. This permanently mounted probe measures the relative motion between the point of mounting and the rotor.

Selecting a Measure Absolute displacementwhich is used for low-frequency vibration (0 to 10Hz) measured on the bearing pedestal, relates to stress (shaft or structure) and is typically measured with a double integrated accelerometer. It is called seismic vibration. Absolute displacement of a shaft must be measured with either a contacting sensor or a noncontacting sensor in combination with a seismic sensor mounted on the bearing pedestal.

Selecting a Measure VelocityFor general machinery monitoring and analysis in the span from 10 Hz to 1,000 Hz, velocity is the default measure. Velocity as a time rate of change of displacement is dependent upon both frequency and displacement and related to fatigue. It has been shown to be a good measure in the span for 10Hz to 1,000 Hz because a single value for rms or peak velocity can be used in rough assessments of condition without the need to consider frequency. Most modem data collectors use accelerometers but the signal must be integrated to obtain velocity.

Selecting a Measure Acceleration is the measure used above 1,000 Hz;; it relates to force and is used for such high- frequency vibrations as gearmesh and rolling element bearing defects. Acceleration and velocity are absolute measures taken on the bearing housing or as close to the bearing as possible.

Selecting a Measure .

MeasureUseful

Frequency Span

Physical Parameter Application

Relative displacement (Proximity probe)

0 – 1000 HZ stress/motionrelative motions

in bearings/casings.

Absolute displacement (seismic)

0 – 10 Hz stress/motion machine condition

Velocity(seismic)

10 – 1000 Hz energy/fatigue

general machine, medium-‐frequency vibrations

Acceleration(seismic)

>1000 Hz force

general machine, medium-‐high-‐frequency vibrations

Selecting a Measure The rule of thumb for measure selection is that velocity is used for bearing pedestal measurement up to 2,000 RPM and acceleration is used above that machine speed. If the machine has permanent non-contacting displacement sensors, then displacement is acquired.

Selecting a Measure FREQUENCIES Bearing Frequencies

FTF =Ω2 1 −

BP cos CA

BPFI =N2 Ω 1 +

BP cos CA

BPFO =N2 Ω 1 −

BP cos CA

BSF =P2B Ω 1−

BP

1cos1 CA

FTF = fundamental train frequency CA = contact angle BPFI = ball pass frequency, inner race Ω = machine speed BPFO = ball pass frequency, outer race N = number of rolling elements BSF = ball spin frequency P = pitch diameter, in RPM = shaft speedB = ball or roller diameter, in Bearing defect frequencies are same units as machine speed

Selecting a Measure FREQUENCIES Bearing Frequencies

General Guideline Bearing Frequencies (for use in maximum Frequency selection ONLY) BPFO = 0.41 x RPM x N BPFI = 0.59 x RPM x N FTF = 0.41 x RPM BSF = 0.22 x RPM x N

FAN

blade pass frequency = no blades x RPM

Example 3.1. Measure and Sensor Selection -‐ Fan.

Select a measure and sensor for a fan operating at 950 RPM. The fan has seven (7) blades and fifteen (15) rolling elements in its bearings. The frequencies of interest are operating speed and orders, blade pass frequency and multiples, and rolling element fault frequencies, and multiples.

operating speed frequency = ]27 ^_à7 = 15.83 Hz and ordersblade pass frequency = no blades x RPM

blade pass frequency = ]27 ^_à7 ×7 = 110.8 Hz and multiples ball pass frequency of inner race = 0.6 x no. balls x RPM

bearing fault frequency = ]27 ^_à7 ×0.6×15 = 142.5 Hz and multiplesThe majority of the frequency activity is between 150 and 1425 Hz, if ten multiples are used. Therefore, velocity measure will provide the best information. An integrated accelerometer or velocity sensor can be used to acquire the data.

Example 3.2. Measure Selection -‐ Low Speed Roll

Select measure(s) for low-‐speed 200 RPM dryer roll. The multi-‐ton roll is mounted on large rolling element (26) bearings. Because the roll operates at such a low speed, mass unbalance is not a major consideration since the force is small. The highest rolling element bearing frequency is the ball pass frequency of the inner race. It can be estimated as BPFI = (0.6) (RPM) (N)BPFI = (0.6) 200 (26) = 3,120 CPM (52 Hz)Therefore, the frequency span is 520 Hz if ten multiples are used. This value is within the velocity range (see Table 3.1).

Example 3.3. Measure Selection -‐ Motor

Select measure(s) for a 200 HP-‐four pole induction motor with eight rolling elements in the bearings. The operating speed vibrations have a frequency of 1,800 CPM (30 Hz) and a frequency span of300 Hz, which is within the velocity range. For ten multiples, the bearing frequency span is (BPFI) (10) = (0.6) (8) (1,800) (10) = 86,400 CPM (1,440 Hz)Because the majority of the activity is in the velocity range, a velocity transducer can be used even though some activity is above 1,000 Hz. The useful frequency spans of all measures overlap. Therefore, the measure should be selected from the predominant portion of the frequency activity of the component. For example, if the default frequency span for the bearing had been 2,880 Hz (16 rolling elements), acceleration would have been selected as the measure for the bearings. Unfortunately, the shaft vibration frequency span of300 Hz remains within the velocity range. Therefore, two measures, velocity and acceleration, are required.

Vibration Sensors

Magnitude, frequency, and phase between two signals are used for evaluation. Sensor selection is based on sensitivity, size required, selected measure, frequency response, and machine design and speed. The sensor should be mounted as close to the source of vibration as possible.

Proximity probes

The proximity probe (non-contacting eddy current displacement transducer) shown in Figure 3.5 measures static and dynamic displacement of a shaft relative to the bearing housing. It is permanently mounted on many large (greater than 1,000 HP) machines for monitoring (protection and trending) and analysis.

Proximity probes

The probe generates a negative DC voltage proportional to the distance of the shaft from the sensor (gap). The typical gap is 40 mils or at 200 mv/mil, 8 volts. The negative voltage decreases as the shaft gets closer to the probe. The probe generates an AC voltage proportional to the vibration with a scale factor of 200 mv/mil. Therefore, the voltage measured is divided by the scale factor to obtain the vibration level (Example 3.4). The probe does require an 18 or 24 volt power supply.

Example 3.4

Assuming the data on Figure 3.3 were taken from a proximity probe with a scale factor of 200 mv/mil (0.20 Volts/mil), the peak to peak displacement would be 1.58 volts divided by 0.2 volts per mil or 7.9 mils-pk to pk. If the measured gap voltage was 7.6 volts, then the gap (distance from the probe to the shaft) would be 7.6 volts divided by 0.2 Volts/mil or 38 mils.

Velocity transducers

Velocity transducers. The velocity transducer (Figure 3.6) is a seismic transducer (i.e., it measures absolute vibration) that is used to measure vibration levels on casings or bearing housings in the range from 10 Hz to 2,000 Hz. The transducer is self-excited - that is, it requires no power supply. The self-generated signal can be directly passed to an oscilloscope, meter, or analyzer for evaluation. A typical velocity transducer generates 500 mv/(in./sec).

Velocity transducers

Accelerometers

Accelerometers are used to measure vibration levels on casings and bearing housings;; they are the transducers typically supplied with electronic data collectors. An accelerometer (Figure 3.7) consists of a small mass mounted on a piezoelectric crystal that produces an electrical output proportional to acceleration when a force is applied from the vibrating mass.

Accelerometers

The size of an accelerometer is proportional to its sensitivity. Small accelerometers (the size of a pencil eraser) have a sensitivity of 5 mv/g (1 g = 386.1 in./sec2) and a flat frequency response to 25 kHz. A 1,000 mv/g accelerometer, which is used for low-frequency measurement, may be as large as a velocity sensor;; however, the limit of its usable frequency span may be to 1,000 Hz. The analyst should be aware of the properties of each accelerometer being used.

Accelerometers

Accelerometers

If vibration velocity is desired, the signal is usually integrated, which electronically converts acceleration to velocity, before it is recorded or analyzed;; an analog integrator/power supply is shown in Figure 3.8.

Analog Integrator and Power

Accelerometers

Accelerometers are recommended for permanent seismic monitoring because of their extended life and because their cross sensitivity is low. (Cross sensitivity means that the transducer generates a signal in horizontal direction from vibration in the vertical direction.) However, cable noise, transmission distance, and temperature sensitivity of the accelerometer must be carefully evaluated. Excellent guidelines are available from vendors for accelerometer use.

Sensor Selection

Important considerations in sensor selection include frequency response, signal-to-noise ratio, size, thermal and amplitude sensitivity of the sensor, and the strength of the signal being measured. The frequency range of the sensor must be compatible with the frequencies generated by the mechanical components of the machine. Otherwise, another transducer must be selected and the signal converted to the proper measure. For example, if the velocity measure is desired at frequencies above 2,000 Hz, an accelerometer integrated to velocity should be selected to obtain the signal. If the time waveform of the velocity measure is desired, the signal must be acquired from a velocity pickup or analog integrated signal from an accelerometer, either within or external to the data collector.

Sensor Selection

The cable that transmits the signal to the data collector can cause erroneous readings. Many standard cables are specially wound cords that are more convenient than the standard coaxial construction. But, because many conductors are flexible at the core, individual strands may fail at stress points as a result of handling or packing in a carrying case. In addition, the terminals must be handled carefully.

Sensor Mounting

The method used to mount a vibration sensor can affect the frequency response because the natural frequency of an accelerometer can decrease, depending on the mounting method used - hand-held, magnetic, adhesive, threaded stud (Figure 3.9).

Method Frequency LimitHand Held 500 HzMagnet 2,000 HzAdhesive 2,500-‐4,000 HzBees Wax 5,000 HzStud 6,000-‐10,000 Hz

Approximate Frequency Spans for 100 mv/g Accelerometers.

Sensor Location

The key to accurate vibration measurement is placement of the sensors at a point that is responsive to machine condition. In any event the sensor should be placed as close to the bearing as is physically possible and in the load zone. Figure 3.10 shows the optimum points for mounting sensors for data acquisition in a normal bearing mounting

Sensor Location

The horizontal and vertical locations at the bearing centerline are shown. These locations are used to sense the vibrations from radial forces such as mass unbalance. Vibrations from axially-directed forces such as gearmeshand bearing faults are measured in the axial direction in the load zone.

Sensor Location

The sensor must be placed as close to the bearing as possible, even though placement is restricted by such components as housings, coupling guards, and fan covers.In general, radial readings are taken on radial bearings;; that is, any antifriction bearing with a contact angle of 0°. Radial bearings are used in electric motors, in medium- to light-duty fans, and in power transmission units not subject to axial loading. Angular contact bearings or any bearing absorbing thrust have a radial-to-axial coupling that requires an axial measurement for accurate condition monitoring.

Review

Measure: a unit or standard of measurement Frequency Span: Fmax or frequency range in the

spectrum Sensor: device that senses mechanical

vibration and emits an electrical signal

Frequency Response: amplitude out of an electrical device such as a sensor as a function of frequency

Chapter 4 – Machine Characteristics

The design and function of machines and their peripheral equipment determine the basic vibration characteristics encountered in machine condition monitoring and diagnostics. Manufacturing and installation quality may alter the vibrations of newly installed equipment. These mechanisms determine the amplitude and frequency of vibrations measured under a baseline condition.

Chapter 4 – Machine Characteristics

As the machine continues in service, defects due to fatigue and wear appear as part of the aging process. The severity of these defects is dependent on load, lubrication, contamination, and machine speed. These defects often cause vibrations at unique frequencies and increases in the amplitudes of vibrations at existing frequencies such as operating speed and its orders.

General Characteristics

It is important to know the connection between measured vibrations and the function and operating mechanisms of the machine. By knowing how the machine works and what can go wrong the analyst can better determine what a measured vibration pattern means. Vibrations are generated by forces which are caused by mechanisms involved in the design, manufacturing, installation, and wear and structural failures of the machine.

General Characteristics

The more information available about the machine design, construction, supports, operational responses, and defect responses, the easier will be the diagnosis of defects and malfunctions. All service equipment should be cataloged and the following data listed.

General Characteristics• broad characteristics such as rotational frequencies, gear mesh, vane pass, and bearing defect frequencies. • vibration, temperature gradients, or pressure initiated by an operating component or system. • vibration responses to process changes. • characteristics identified with the specific machine type. • known natural frequencies and mode shapes. • sensitivity to vibration from mass unbalance, misalignment, distortion, and other malfunction/defect excitations. • sensitivity to instability from wear or changes in operating conditions.

SOURCES OF VIBRATION

Source Design and Function

Manufacturing Installation Defects

mass unbalance

• • •

eccentricity • • • •misalignment • • •looseness • • •distortion • • •cogging •gear defects • • •bearing defects

• • •

electrical • • • •flow noise •

SOURCES OF VIBRATION

Source Design and Function

Manufacturing Installation Defects

natural frequency

• •

thermal • •bad grout • •reciprocating •flexible • •oil whirl • • •excessive clearance

• • • •

poor quality • •overstressed •hydrodynamic • • •acoustic • • •machining • • •

Design and Function

Mass unbalance occurs when the mass center of a rotating part is not located at the geometric center. However, it may result from unsymmetrical design of a part such as a coupling hub. Normally components and parts would have a symmetrical design to avoid this problem. The frequency of mass unbalance is the shaft operating speed and the amplitude is dependent on the mass unbalance and speed squared.

Design and Function

Mass unbalance . However, mechanisms such as the cam in Figure are likely to be unbalanced because the mass center is not at the geometric center.

Design and Function

Cogging of chain links of a sprocket, Figure 4.4, occurs because of the intermittent forces generated from the sprocket teeth entering and exiting the chain. The cogging frequency is the number of sprocket teeth times the RPM of the sprocket. Similarly, the frequency of a timing belt is the number of grooves in the pulley times the RPM of the pulley.

Design and Function

Flow noise is normally generated from inlet conditions (mixed flow from elbows, reducers, or increasers) or operating off the best efficiency point, BEP, of the pump. Straight flow is usually ensured by having at least ten (10) pipe diameters of straight, constant diameter pipe prior to the pump inlet. BEP operation is designed into the system by proper system design. Too little back pressure causes cavitation while too high back pressure causes recirculation of the flow at the inlet. Both conditions cause random noise and vibration and sound like gravel circulating in the pump.

Design and Function

Certain responses (Table 4.2), including vibration, temperature, and pressure can be related to components of the system

Design and Function Component Frequency

antifriction bearings ball pass frequency, outer raceball pass frequency, inner racefundamental train frequency

rotating unit frequencyball spin frequency

hydrodynamic journal bearings frictional frequency, whirl frequenciesgears rotating unit frequency

gear-‐mesh frequencies and harmonics harmonics of gear-‐mesh frequencies

assemblage frequencies system natural frequencies (gear-‐

tooth defects)Blade wheels and impellers Rotating unit frequencies

vane and blading frequencies harmonics of vane and blading

frequencies

Design and Function Component Frequency

rotors trapped fluid rotational frequency directional natural frequencies

higher harmonicscouplings and universal joints orders of rotating frequencyreciprocating mechanisms rotating frequency and its orders

Electric motor rotors sidebands at no poles x slips

Chapter 5 – VIBRATION INSTRUMENTS

The sensor which changes the mechanical motion of the machine to an electrical signal is connected to an instrument which provides an analytical read out and/or print out. The read out can be as simple as a single number from a meter or a waveform from an oscilloscope. More elaborate analyzers provide spectra (amplitude versus frequency) and digital time waveforms. Data collectors provide overall values, filtered values, phase readings, spectra, and time waveforms.


Figure 5.1. Time Waveform


Figure 5.2. Spectrum (Top) and Waveform (Bottom).


Figure. Trend on Three Bearing Pedestals.

Data Collectors and Analyzers The data collector (and analyzers are all Fast Fourier Transform (FFT) based calculated off a digitized waveform that is obtained from a sensor.

Data Collectors and Analyzers The spectrum of Figure 5.10 (upper plot) has 400 lines (bins) and a frequency span of 1,000 Hz. Therefore, there are 400 divisions across the horizontal frequency scale where data can be located. Any frequency between these lines is included in the closest adjacent bin.

Chapter 6 – VIBRATION TESTING

Basically there are four types of vibration tests that the machine analyst conducts• periodic monitoring• fault and condition analysis• Acceptance• design.


Periodic monitoringserves a predictive maintenance program by acquiring vibration data on a routine basis on organized routes with data point specific collector setups. The data collected on the route are compared against previous data and alarm settings to evaluate the machine's change in condition. Data are downloaded into a computer for trending and analysis.


Machine analysis

is conducted when trended data exceed alarm levels. Frequencies and amplitudes are evaluated to determine the fault and severity of the problem.


Acceptance testing

is used to determine whether a new or repaired machine meets the specification in the purchase agreement. Usually decisions are made on the basis of agreed upon measurements and vibration levels according to specified procedures.


Design testing

Basic tests for design characteristics are conducted to determine machine dynamic properties such as natural frequencies, damping, and critical speeds.

PERIODIC MONITORING

Periodic monitoring of machine vibrations is one of the principal components of any predictive maintenance program because it provides information that allows decisions to be made on production scheduling, minimizes the occurrence of catastrophic equipment failures, and provides rational management of assets and resources. By using the electronic data collector, an individual can effectively monitor many machines for signs of equipment malfunction, wear, and failure during production.

PERIODIC MONITORING

Machine Knowledge The person collecting data should have a working knowledge of the machines being monitored. This knowledge involves internal construction, supports, foundations and piping as well as how the machine works internally (Chapter 4). The experienced data collector will be aware of and report unusual physical behavior (Chapter 3) through senses of touch, sound, sight, and smell.

PERIODIC MONITORING

Machine Knowledge These signs of deterioration are often vital in the process of non-intrusive monitoring. Knowledge of speeds and characteristics common to individual machines (Chapter 4) is absolutely essential. There are many texts and magazines on machine function which can heIpthe data collector continuously expands machine knowledge. Viewing the machine being repaired or having a background as an operator, millwright, or mechanic provide invaluable experience.

PERIODIC MONITORING

Data Collection Procedures The data collection route can be based on plant layout, machine train, machine type, or data type. Whatever the criterion used for route design, it should allow efficient movement of the data collector from machine to machine and data point to data point. Figure 6.1 shows a route for a 4,000 HP motor driven boiler feed pump while Figure 6.2 shows a schematic diagram of the location of measurements.

PERIODIC MONITORING

Figure 6.1. Example of a

Route for Motor Driven Boiler Feed Pump

PERIODIC MONITORING

Figure 6.2. Location of Measurement Points.

PERIODIC MONITORING

Transducer Positioning and Mounting. While collecting data on a route, the data collector programming should be consistent with transducer positioning and mounting - the measured position relates to the data collector recorded position. For this reason, the machine measurement positions should be permanently marked.

PERIODIC MONITORING

Transducer Positioning and Mounting. Magnet mountings require some care in attaching the transducer. The transducer needs to be mounted so that it does not rock or is not loose - this may cause erroneous, noisy data. It is a good idea to try to move the transducer after it is magnetically attached. If it rocks, turn it until it does not move when you put a minor force on it.

PERIODIC MONITORING Some general recommendations should be considered when vibration is sampled on equipment with known faults: 1. Never stand next to drive couplings or other locations where components would likely come out in the event of failure.

2. If temporary test equipment is setup for extended monitoring, locate the equipment on the end of the machine train, usually on the drive end.

3. Plan an escape route when approaching the machine. 4. Determine a threshold vibration level above which continued testing will not be performed. Discuss this level with plant personnel prior to testing if necessary so that appropriate action can be quickly taken to shut the machine off if the threshold values are exceeded.

5. Be prepared at all times to stop testing, move to a lower risk area, and possibly shut the machine down if conditions change so that noise or vibration levels obviously increase.

PERIODIC MONITORING Some general recommendations should be considered when vibration is sampled on equipment with known faults:

6. NEVER stay around a machine that has known faults with increasing severity. 7. NEVER continue testing once the pre-‐determined safe vibration threshold has been identified to be exceeded on any sample point.

8. NEVER continue operating a machine with an obvious mechanical fault such as loose hold down bolts, coupling element progressing damage (rubber material falling under coupling), metal shavings or bolts failing from the machine, etc.

PERIODIC MONITORING

Figure. Possible Unsafe Data Acquisition Locations

PERIODIC MONITORING

Screening and Trending The central tasks of periodic monitoring are screening and trending. Screening is the process of routine data sampling and comparison of that data to alarms to determine if the condition of the machine has changed.

PERIODIC MONITORING

PERIODIC MONITORING

Screening and Trending This process typically involves amplitude changes using overall peak or RMS values of velocity or acceleration. Changes in vibration levels can be attributed to long- and short-term changes in machine speed, production conditions, mechanical defects, thermal conditions, product buildup, and alignment and foundation function.

PERIODIC MONITORING

Screening and Trending A change in measured value of two to two and one-half usually indicates a genuine change in condition leading to more detailed analysis, more frequent monitoring, shut down for inspection or parts replacement. The severity of the problem and management procedures dictate what combination of these actions will be followed.

PERIODIC MONITORING

PERIODIC MONITORING

Screening and Trending Unfortunately, there are cases where trending of overall amplitude values of vibration does not work. Typically, the problem is either lack of signal strength (very low amplitudes), noise problems, or masking of the low amplitude important data by normal vibration levels. For example, low amplitude rolling element bearing defect frequencies may be sending a very important message about an impending bearing failure. However, there is a much higher amplitude component of vibration due to mass unbalance or gearmesh present (Figure 6.8).

PERIODIC MONITORING

Bearing Frequencies Masked by Gearmesh and Mass Unbalance Frequencies.

PERIODIC MONITORING

Screening and Trending Changes in overall amplitude due to the bearing defect may be a small percentage of the existing vibration amplitude. Trending of overall amplitude values in this case is useless. Bearing failures will be missed. There are three ways of dealing with this problem.

PERIODIC MONITORING

Screening and Trending The first method involving moderately low (0.05 IPS-peak) bearing defect frequency amplitudes uses RMS trending of band filtered values (Figure 6.8) which eliminate the higher amplitude normal vibration levels. In other words, only the data important to failure are being trended. In actual point of fact, usually band (filtered) trending is an adjunct to overall trending. For example, a trend chart like Figure 6.7 would be recorded for Bands 2,4, and 6 in Figure 6.7.

PERIODIC MONITORING

Bearing Frequencies Masked by Gearmesh and Mass Unbalance Frequencies.

PERIODIC MONITORING

Screening and Trending The second method involves routine high resolution spectrum analysis where important bearing defect frequency amplitudes are very low (less than 0.02 IPS-peak). Here the severity of the problem is defined by the presence of frequencies (defect frequencies and sidebands, Figure 6.8).

PERIODIC MONITORING

Screening and Trending The third and last method of dealing with low amplitude signals involves the use of procedures that filter out low frequency high amplitude portions of the vibration data prior to processing. The peakness and enveloping methods depend on high frequencies to carry the failure oriented information to the analyst. Because of transducer mounting uncertainties and design natural frequency variance, these methods in general do not yield trendableresults or indicate the severity of the problem. They do, however, indicate the presence of a problem.

PERIODIC MONITORING

Screening and Trending Therefore, providing a message to management to analyze further or go into the machine and determine the severity. These methods will indicate where the problem is located so that minimum energy will be exhausted.

MACHINE ANALYSIS

Machine testing for in-depth analysis has two levels• Fault analysis - what and where is the problem (Chapter 7)

• Condition evaluation - what is the severity of the problem (Chapter 8).

MACHINE ANALYSIS

Fault analysis In the time waveform, the data sample is essentially unprocessed raw data that has information about the condition of the machine. The analyst obtains an overview of what is at fault and the severity of the problem from the periodicity, shape, and amplitude of the time waveform, Figure 6.9 - lower plot.

MACHINE ANALYSIS

MACHINE ANALYSIS

Fault analysis The waveform contained in Figure 6.9 shows a shape and periodicity that indicates vibration of one and two times operating speed (small peak within the period) is present. The amplitude of 1.39 IPS indicates that it is a serious problem.

MACHINE ANALYSIS

Fault analysis For more analytical details, the spectrum, amplitude versus frequency - Chapter 7, is examined. Frequencies in the spectrum, Figure 6.9 - upper plot, confirm that the frequencies of operating speed and twice operating speed are present. Since this is a generator where vibration generated by two times operating speed (mechanical) and two times line frequency (electrical) can be present, the fault cannot accurately be defined through the use of frequency matching without further in- depth analysis.

MACHINE ANALYSIS

Fault analysis Most spectrum analysis is done through frequency matching - known machine frequencies such as operating speed are matched to frequencies present in the vibration spectrum. The problem in Figure 6.9 is that the frequencies of twice operating speed 7,200 cpm - 120 Hz (mechanical- indicating misalignment) and twice line frequency (electrical -indicating air-gap or stator faults) are equal. Thus one or the other or both faults could be present.

MACHINE ANALYSIS

Condition Evaluation Condition Evaluation is the process of determining the severity of the vibration and what it means in terms of machine condition. Most condition evaluation is done with charts and graphs where overall RMS or peak values of vibration are matched against the standard chart. For example, the value of 1.39 IPS on Figure 6.9 (lower plot) time waveform would be compared to a chart.

MACHINE ANALYSIS

Condition Evaluation Unfortunately, this provides only a rough assessment of condition and more detailed analysis is usually required because these charts are not machine specific. However, some charts do have adjustments of allowable values for type, mounting, and size of machines.

MACHINE ANALYSIS

ACCEPTANCE TESTING Acceptance testing of new and repaired equipment provides some assurance of the quality of workmanship provided the purchase specification is properly written. The acceptance test is based on a purchase specification that includes procedures, measurement locations, process conditions, measures and how they are processed, and acceptable levels of vibration. Acceptance testing may be conducted in the shop prior to equipment release or it may be conducted in the field.

MACHINE ANALYSIS

ACCEPTANCE TESTING Due to mounting, process activation, and other differing conditions, levels of vibration will differ in these methods. If no specification exists, a baseline test should be conducted and the data compared with general vibration standards. The baseline test should reflect the operating conditions of the machine and its environment to the best extent possible.

MACHINE ANALYSIS

ACCEPTANCE TESTING The purchase specification should include testing procedures as well as acceptable levels of vibration;; that is, it should be similar to ISO, IEC, or OM standards. For example, ISO 10816 contains information about equipment mounting, the measures to be used, transducer locations, and acceptance levels.

MACHINE ANALYSIS

Procedure for Acceptance Testing1. Read the specification and determine what is legally required for acceptance. 2. If no specification exists, determine what the owner expects. 3. Based on available information determine the measurement locations, type of data to be evaluated, data processing if any, machine speeds, and process conditions.

4. Select transducers and set up the data collector, analyzer or tape recorder to acquire data. 5. Check the mounting conditions -‐make sure loose bolts or safety issues do not exist. 6. Conduct the machine test keeping records of data acquired. 7. Evaluate the data for acceptance and give reasons if the machine should not be acceptance. 8. Write a brief report.

MACHINE ANALYSIS

DESIGN TESTINGDesign characteristics of the machine such as natural frequencies, critical speeds, and damping levels are important factors in vibration analysis. Specialized tests have been designed to determine this information because of the influence of design on vibration severity. Abnormally high vibration levels cause bearing failures, rubs, and shaft and structural fatigue failure. In addition, high vibration levels may affect process quality - imaging and printing are two examples

MACHINE ANALYSIS

DESIGN TESTINGResonance - matching natural frequencies to forcing frequencies - cannot be tolerated in most machines. Therefore, special vibration tests have been devised to determine the common design parameters -natural frequencies and critical speeds. These advanced tests will be covered in subsequent books at advanced levels.

Chapter 7 – BASIC ANALYSIS

Vibration analysis is conducted to determine the origin of the vibration. Vibration sources include mechanical and electrical defects, normal functioning of the machine or its process, installation problems, and faulty design. These sources all involve the generation of forces which cause vibrations.

SPECTRUM ANALYSIS

Basic vibration analysis is about matching frequencies - that is known machine frequencies are related to those of the measured vibration. The typical vibration analyzer provides the vibration waveform (usually called the time waveform) and a spectrum - a plot of vibration level versus frequency. Figure 7.1 (lower plot) shows a data sample obtained by a sensor from a generator exciter pedestal measurement.

SPECTRUM ANALYSIS

SPECTRUM ANALYSIS

The lower plot, called the time waveform, shows the data as it was acquired from the exciter by the sensor. It has a period (repeat cycle) of 16.7 mSecor 0.0167 see per cycle of vibration. by using the formula f = 1/T = 60 Hz = 3600 RPM.

Note the time waveform in Figure 7.1 has a second peak in between the principal peaks. This indicates that another vibration frequency is present.

SPECTRUM ANALYSIS

The spectrum, upper plot, is required because the relative size (amplitude) of the two peaks cannot be readily determined from the time waveform.

The spectrum displays the amplitude and frequency of each vibration component is required for analysis. In this case the frequency of the second vibration component is 120 Hz or exactly twice the first vibration component which is equal to operating speed.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS The spectrum (a plot of amplitude versus frequency - upper plot of Figure 7.1) is computed from the time waveform by a numerical process called an algorithm. The process commonly used is the fast Fourier transform.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS When the analyst is setting up the analyzer, three decisions have to be made. 1. Fmax is the maximum frequency measured -1,250 Hz in Figure 7.1.

2. The number of lines which is tied to the number of data points - 400 lines in Figure 7.1.

3. The window which is related to the type of analysis - Hanning in Figure 7.1.

The number of lines and window are not shown on the plot.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS FmaxThe Fmax should be set for the maximum frequency desired but should not be excessively high;; however, it must cover the frequency range of spectral activity. The Fmax is determined from the design of the machine.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS The number of lines determines the detail of the spectrum. The fact that Figure 7.1 has 400 lines means 400 discrete points are plotted across the frequency axis - no information is provided between the lines. If a frequency does not fall on a line, then it will be included in the closest line with an amplitude error dependent on the window used. If two vibration components are close together and fall in the same bin (the area around the line - Figure 7.2), they are summed and a true picture is not obtained.

SPECTRUM ANALYSIS

Figure 7.2. Bins and Lines.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS However, the penalty for more lines is data acquisition time. Thus it takes more time to acquire data when using a large number of lines.

Data Acquisition Time = ef4g?C Eh iDj?A (e) klmn

For example, in the spectrum of Figure 7.1 (upper plot), the data acquisition time per sample was 400 lines/1,250 Hz or 0.32 sec. Ten averages were made - thus the total data acquisition time for the spectrum was 3.2 sec (3,200 mSec).

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS Without the window, the resolution (ability to resolve and display closely spaced frequencies) would be the Fmax divided by the number of lines or Fmax/N= 3.125 Hz/line in Figure 7.1. But the window, which is required because the FFT process degrades the resolution by spreading vibration component energy into adjacent bins, lowers the ability to resolve closely spaced frequencies. The amount of actual resolution then is equal to two times the Fmax and the window factor divided by the number of lines as shown below.

SPECTRUM ANALYSIS

FAST FOURIER ANALYSIS

Resolution (Hz) =

The Hanning window which was used in Figure 7.1 has a window factor (WF) of 1.5.

2 ×Fmax (Hz)

N ×WF

ANALYSIS TERMINOLOGY

Operating Speed and Orders The frequency of operating speed is the foundation of spectrum analysis of mechanically generated vibrations. Many other frequencies in the spectrum are related to the operating speed - being multiples (orders) or non-multiples.


Figure 7.3 shows a spectrum from a generator pedestal with one component (0.263 IPS-peak) at 60 Hz - the frequency of operating speed.


Vibrations shown in Figures 7.3 is symptomatic of mass unbalance


Figure 7.4 shows a spectrum with operating speed vibrations 60 Hz and a second order 120 Hz.


Vibrations shown in Figures 7.3 is symptomatic of misalignment


Electrical Frequencies Line frequency is the basic frequency of AC electric power and electrically generated vibration. Line frequency is 60 Hz in North America and 50 Hz in the remainder of the world. Line frequency will not be 60 Hz when variable frequency drives are analyzed. In each case the base frequency must be obtained prior to analysis.

ANALYSIS TERMINOLOGY Figure 7.5 shows data from a motor operating at 3,588 RPM.

ANALYSIS TERMINOLOGY The second order is dominant (upper plot) but may contain mechanical (2x operating speed) and/or electrical (2x line frequency) vibration.

ANALYSIS TERMINOLOGY The lower plot of Figure 7.5, which is a zoom (increased resolution) of the data on the upper plot, shows mechanical (119.6 Hz) and electrical (120 Hz) symptoms.

COMMON MACHINE FAULTS

Table 7.4. Common Machine Faults.• Resonance and critical speeds • Mass unbalance • Misalignment • Looseness • Distortion • Beats • Rolling element bearing defects • Gear defects • Motor faults • Pumps • Fans

Resonance and Critical Speeds

All systems have natural frequencies that are not active unless they are excited by some force. When a forcing frequency such as operating speed is close to or equal to a natural frequency, the condition of resonance occurs and the vibration is amplified beyond what would normally be obtained for that force. When the rotor of the system excites the natural frequency, the frequency of the rotor that matches the natural frequency of the system is called a critical speed.

Resonance and Critical Speeds Figure 7.8 is an example of a resonance in a vertical pump support structure.

Figure 7.8. Vertical Pump Resonance.

Resonance and Critical Speeds

The operating speed of the pump is close to the natural frequency of the pump frame and support. This is a common problem with pumps driven by variable frequency driven motors. It is difficult to design a system where no natural frequencies will occur in a wide speed range.Natural frequencies usually respond directionally. Therefore, if the vibration level is high in one direction but not 90° from it, that is an indication that it may be resonant.

Mass Unbalance

Mass unbalance occurs when the geometric center (shaft centerline) and the mass center of a rotor do not coincide. Unbalance is a once-per-revolution fault - that is, it creates vibration at the frequency of rotor speed.

Mass Unbalance it creates vibration at the frequency of rotor speed

Figure 7.9. Mass Unbalance of a Generator.

Mass Unbalance

This can be done with phase analysis because the nature of the forces is different. The spectrum for mass unbalance normally has a high amplitude component at a frequency of operating speed (Figure 7.9 - 3,600 RPM) and low amplitude orders of operating speed. Mass unbalance appears to be similar to resonance;; however, by moving the sensor 90° the vibration should be similar in amplitude.

Misalignment

The magnitude of the resulting vibration is dependent on the radial stiffness of the components (bearings, shafts, seals, couplings) in the system.It is characterized by two peaks at 1x and 2x.The second order component of vibration in cases of severe misalignment can exceed the first order. High first-order axial vibration is also a symptom of misalignment.

Misalignment

Figure 7.9. Generator Misalignment.

Looseness Excessive bearing clearances and untightened bolts cause impacts that can be identified in the spectrum as once-per-revolution vibration plus orders of operating speed

Figure 7.11. Fan

Looseness.

Rolling Element Bearing Defects When a rolling element passes over a bearing defect in the races or cages (Figure 7.14), pulse-like forces are generated that result in one or a combination of bearing frequencies. This causes pulses in the time waveform and bearing frequencies and harmonics in the spectrum (Figure 7.15) at nonsynchronous (not an order of operating speed) frequency and resonance.

Rolling Element Bearing Defects

Figure 7.14. Nomenclature of Rolling Element Bearings.


Figure 7.15. Rolling Element Bearing Defects.

Rolling Element Bearing Defects Figure 7.15 shows the spectrum from a bearing supporting a felt roll (530 RPM)). It has a fundamental ball pass frequency of the outer race of 56.25 Hz or 6.37 times operating speed. The bearing frequencies would be calculated using the above formulas or would be given by the bearing manufacturer as a multiple of operating speed - in this case BPFO = 6.37 x operating speed. In Figure 7.15 the third harmonic has sidebands (small peaks) at operating speed frequency (530 RPM/60 = 8.83 Hz).

Rolling Element Bearing Defects • ball pass frequency of the outer race (BPFO);; generated by balls or rollers passing over defective outer races. • ball pass frequency of the inner race (BPFI);; generated by balls or rollers passing over defective inner races. • ball spin frequency (BSF);; generated by ball or roller defects. • fundamental train frequency (FTF);; generated by cage defects or improper movements. • ∅ = contact angle;; angle between lines perpendicular to the shaft and from the center of the ball to the point where the arc of the ball and the race make contact (Figure 7.14c). • N = number of rolling elements (balls or rollers). • P = pitch diameter, in. • B = ball or roller diameter;; average value for tapered bearings, in. • RPS = speed of rotating unit in revolutions per second.


Ω = RPM/60 = RPS

FTF =Ω2 1 −

BP cos∅

BPFI =N2 Ω 1 +

BP cos∅

BPFO =N2 Ω 1 −

BP cos∅

BSF =P2B Ω 1 −

BP

1

cos1 ∅

Gear Defects Gearboxes generate high-frequency vibrations as a result of the gearmeshing function of the box. The greater the number of gear teeth in mesh at any instant the smoother the performance of the box. Gearbox faults fall into two categories - gear meshing and broken teeth. Gearmesh frequency is number of teeth on the pinion times speed of the pinion or number of teeth on the gear times gear speed. These frequencies will be equal.

The gearmeshing problem occurs because of uneven local wear, pitting, roughness, and/or machine gear tooth quality. As the teeth go through mesh the vibration varies because the surface quality of the teeth vary. This causes vibration with amplitude modulation (change) which results in gearmesh frequency and sidebands in the spectrum

Gear Defects

FansOn fans, pumps, and other bladed machines, look for frequencies that are multiples of operating speed that relate to the number of blades or vanes. Figure shows data from a six (6) bladed fan.

FansThe spectrum (upper plot) shows vibration at 92.8 Hz which is close to six (6) times the operating speed (15.6 Hz). This vibration is generally caused by the blades passing the discharge duct.

CHAPTER 8- VIBRATION SEVERITYBEARING HOUSING EVALUATIONTable 8.2 shows peak and RMS velocity levels for machine vibrations based on evaluation of operating speed faults.

MACHINE CONDITION ACCEPTABLE LEVELS (IPS)RMS PEAK

Acceptance less than 0.08 less than 0.16Normal less than 0.12 less than 0.24Surveillance 0.12 to 0.28 0.24 to 0.7Unacceptable more than 0.28 more than 0.7

Table 8.2. Acceptable Levels of Machine Vibrations for Operating Speed Faults.

CHAPTER 8- VIBRATION SEVERITYBEARING HOUSING EVALUATIONFigure 8.1 shows vibration data acquired from a lobed blower operating at 3,563 RPM.

CHAPTER 8- VIBRATION SEVERITYBEARING HOUSING EVALUATIONFigure 8.1 shows vibration data acquired from a lobed blower operating at 3,563 RPM. The peak velocity from the time waveform (lower plot) is negative 0.962 IPS-peak. When judging zero to peak (peak) values always use the time waveform and select the largest value of velocity whether it is positive or negative. The RMS level 0.488 IPS-RMS in Figure 8.1 was calculated from the energy on the spectrum (upper plot). These two levels will be compared against acceptable levels provided in Table 8.2 for operating speed faults - e.g. mass unbalance, looseness, and misalignment.

MACHINE CONDITION ACCEPTABLE LEVELS (IPS)RMS PEAK

Acceptance less than 0.08 less than 0.16Normal less than 0.12 less than 0.24Surveillance 0.12 to 0.28 0.24 to 0.7Unacceptable more than 0.28 more than 0.7

CHAPTER 8- VIBRATION SEVERITYSHAFT VIBRATIONS The measurement of shaft vibrations is more direct than the measurement of pedestal/bearing housing vibration and therefore produces a more accurate picture of the severity of machine vibration and how it reflects on condition

CONDITION R/C3,600 RPM 10,000 RPM

Normal 0.3 0.2Surveillance 0.3-‐0.5 0.2-‐0.4Shut down at next convenient time

0.5 0.4

Shutdown immediately 0.7 0.6

Table 8.3. Evaluation of Relative Shaft Vibration Using Bearing Clearance and Speed.

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