A brief introduction to vibration analysis of process plant machinery

A Brief Introduction to Vibration Analysis of Process Plant Machinery I Basic Concepts I Machinery Vibration is Complex Vibration of a machine is not usually simple • Many frequencies f

A Brief Introduction to Vibration Analysis of Process Plant Machinery (I)

Basic Concepts I

Machinery Vibration is Complex

Vibration of a machine is not usually simple

• Many frequencies from many malfunctions

• Total vibration is sum of all the individual vibrations

• Unfiltered overall amplitude indicates overall condition

• Displacement amplitude is not a direct indicator of vibration severity unless combined with frequency

• Velocity combines the function of displacement and frequency

• Unfiltered velocity measurement provides best overall indication of vibration severity

Characteristics of Vibration

Vibration is the back and forth motion of a machine part

One cycle of motion consists of

• Movement of weight from neutral position to upper limit

• Upper limit back through neutral position to lower limit

• Lower limit to neutral position

• The movement of the weight plotted against time is a sine wave

Simple Spring- Mass system Movement plotted against time

Free and Forced Vibration

When a mechanical system is subjected to a sudden impulse, it will vibrate at its natural

frequency

• Eventually, if the system is stable, the vibration will die out

Forced vibration can occur at any frequency, and the response amplitude for a certain force will

be constant

Relationship between Force and Vibration

• Forces that cause vibration occur at a range of frequencies depending on the malfunctions present

• These act on a bearing or structure causing vibration

• However, the response is not uniform at all frequencies It depends on the Mobility of the of the structure

• Mobility varies with frequency For example, it is high at resonances and low where damping is present

Various Amplitudes of a Sine Wave

• A = Zero to Peak or maximum amplitude – used to measure velocity and acceleration

• 2A = Peak to Peak = Used to measure total displacement of a shaft with respect to available bearing clearance

• RMS = Root Mean Squared amplitude - A measure of energy - used to measure velocity and acceleration – mainly used in Europe

• Average value is not used in vibration measurements

Characteristics of Vibration (2)

Time required to complete one cycle is the PERIOD of vibration

• If period is 1 sec then the number of cycles per minute (CPM) is 60

Frequency is the number of cycles per unit time – CPM or C/S (Hz)

• Peak to peak displacement is the total distance traveled from one extreme limit to the other extreme limit

• Velocity is zero at top and bottom because weight has come to a stop It is maximum at neutral position

• Acceleration is maximum at top an bottom where weight has come to a stop and must accelerate to pick up velocity

Root Mean Squared Amplitude

• RMS amplitude will be equal to 0.707 times the Peak amplitude if, and only if, the signal is a sine wave (single frequency)

• If the signal is not a sine wave, then the RMS value using this simple calculation will not be correct

Displacement, Velocity & Acceleration

• Displacement describes the position of an object

• Velocity describes how rapidly the object is changing position with time

• Acceleration describes how fast the velocity changes with time

• If Displacement d = x = A sin (wt) , then

• Velocity = rate of change of displacement

• Weight “C” and “D” are in “in step”

• These weights are vibrating in phase

• Weight “X” is at the upper limit and “Y” is at neutral position moving to lower limit

• These two weights are vibrating 90 deg “out of phase”

Displacement, Velocity and Acceleration Phase Relationship

• Velocity leads displacement by 90o; that is, it

reaches its maximum ¼ cycle or 90o before

displacement maximum

• Acceleration leads displacement by 180o

• Acceleration leads velocity by 90o

• Small yellow circles show this relationship clearly

Units of Vibration Parameters

English Metric Unit Conversion

Preferable to measure both in g’s because g is directly related to force

Conversion of Vibration Parameters Metric Units

• Displacement, Velocity and acceleration are related by the frequency of motion

• Parameters in metric units

Conversion of Vibration Parameters English Units

• Displacement, Velocity and acceleration are related by the frequency of motion

• Parameters in English units

– D = Displacement in mils (inch / 1000)

– V = Velocity in inch/sec

– A = Acceleration in g’s

– F = Frequency of vibration in cycles /minute (CPM)

• V = D x F / 19,100 – same as for metric units

• A = V x F / 3,690 – metric value / 25.4

Relative Amplitude of Parameters

• V = D x F / 19,100 in metric units

– This means that velocity in mm/sec will be equal to displacement in microns at a frequency of

– At frequencies higher than 93,650 CPM acceleration will be higher than velocity

Selection of Monitoring Parameters

• Where the frequency content is likely to be low (less than 18,000 CPM) select displacement – Large, low speed, pumps and motors with sleeve bearings

– Cooling tower fans and Fin fan cooler fans Their gear boxes would require a higher frequency range

• For intermediate range frequencies ( say, 18,000 to 180,000 CPM) select Velocity

– Most process plant pumps running at 1500 to 3000 RPM

– Gear boxes of low speed pumps

• For higher frequencies (> 180,000 CPM = 3 KHz) select acceleration

– Gear boxes

– Bearing housing vibration of major compressor trains including their drivers

• Larger machines would require monitoring more than one parameter to cover the entire

frequency range of vibration components

• For example, in large compressor and turbines

– The relative shaft displacement is measured by permanently installed eddy current displacement probes

– This would cover the frequency range of running speed, low order harmonics and subharmonic components

– To capture higher stator to rotor interactive frequencies such as vane passing, blade passing and their harmonics, it is necessary to monitor the bearing housing acceleration

• Monitoring one parameter for trending is acceptable

• However, for detailed analysis, it may be necessary to measure more than one parameter

Example in Selecting Units of Measurement

• Amplitude measurement units should be selected based upon the frequencies of interest

• Following 3 plots illustrate how measurement unit affects the data displayed Each of the plots contain 3 separate component frequencies of 60 Hz, 300 Hz and 950 Hz

Displacement

This data was taken using displacement Note how the lower frequency at 60 Hz is accentuated

A Brief Introduction to Vibration Analysis of Process Plant Machinery (III)

Basic Concepts III Forced Vibration

• Exciting Force = Stiffness Force + Damping Force + Inertial Force

• Stiffness

– Stiffness is the spring like quality of mechanical elements to deform under load

– A certain force of Kgs produces a certain deflection of mm

– Shaft, bearing, casing, foundation all have stiffness

• Viscous Damping

– Encountered by solid bodies moving through a viscous fluid

– Force is proportional to the velocity of the moving object

– Consider the difference between stirring water versus stirring molasses

• Inertial Forces

– Inertia is the property of a body to resist acceleration

– Mainly weight

Physical Concept of Vibration Forces

• Stiffness determines the deflection of a rotor by centrifugal forces of unbalance

– Determined by the strength of the shaft

• Damping force is proportional to velocity of the moving body and viscosity of the fluid

– Damping is provided by lube oil

• Inertial forces are similar to those caused by an earthquake when acceleration can be very high.– Acceleration is related to the weight of the rotor

– It can cause distortion of structures

Physical Concept of Vibration Parameters

• Displacement

– Displacement is independent of frequency

– Displacement is related to clearances in machine

– If displacement exceeds available clearances, rubbing occurs

• Velocity

– Velocity is proportional to frequency

– Velocity is related to wear

– In machines higher the velocity, higher the wear

• Acceleration

– Proportional to square of frequency

– Acceleration is related to force

– Excessive acceleration at the starting block can strain an athlete’s leg muscle

– Acceleration is important for structural strength

Stiffness Influence

• Stiffness is measured by the force in Kgs required to produce a deflection of one mm

• Stiffness of a shaft is

– Directly proportional Diameter4 and Modulus of Elasticity

– Directly proportional to Modulus of Elasticity

– Inversely proportional to Length3

• Typical Stiffness values in pounds / inch

– Oil film bearings – 300,000 to 2,000,000

– Rolling element bearings – 1,000,000 to 4,000,000

– Bearing Housing, horizontal – 300,000 to 4,000,000

– Bearing housing, vertical – 400,000 to 6,000,000

– Shaft 1’ to 4” diameter – 100,000 to 4,000,000

– Shaft 6” to 15” diameter – 400,000 to 20,000,000

Damping Influence

• Damping dissipates energy

• Rotor instability can be related to lack of damping

• System Damping controls the amplitude of vibration at critical speed

• With low damping there is poor dissipation of energy and amplitude is high

Amplification factor Q through resonance is an indicator of damping

Relationship between Displacement, Velocity and Acceleration (For British Units)

Acceleration Varies as the Square of Frequency

• Acceleration is negligible at low frequencies

• It predominates the high frequency spectrum

• Measure displacement at low frequency, velocity at medium frequencies and acceleration at high frequencies

A Brief Introduction to Vibration Analysis of Process Plant Machinery (IV)

Basic Concepts IV Basic Rotor and Stator System

• Forces generated in the rotor are transmitted through the bearings and supports to the foundation

• Displacement probe is mounted on the bearing housing which itself is vibrating Shaft vibrationmeasured by such a probe is, therefore, relative to the bearing housing

• Bearing housing vibration measured by accelerometer or velocity probe is an absolute

measurement

Type of Rotor Vibration

• Lateral motion involves displacement from its central position or flexural deformation Rotation

is about an axis intersecting and normal to the axis of rotation

• Axial Motion occurs parallel to the rotor’s axis of rotation

• Torsional Motion involves rotation of rotor’s transverse sections relative to one another about itsaxis of rotation

• Vibrations that occur at frequency of rotation of rotor are called synchronous vibrations

• Vibrations at other frequencies are nonsynchronous vibrations

The Relationship Between Forced and Vibration

• Forces generated within the machine have may different frequencies

• The mobility of the bearings and supports are also frequency dependent Mobility = Vibration / Force

• Resultant Vibration = Force x Mobility

Alternative Measurements on Journal Bearings

• Relative shaft displacement has limited frequency range but has high amplitude at low frequencies – running speed, subsynchronous and low harmonic components

• Accelerometer has high signal at high frequencies – rotor to stator interaction frequencies – blade passing, vane passing

Types of Machine Vibration

• Casing Absolute is measured relative to space by Seismic transducer mounted on casing

• Shaft relative is measured by displacement transducer mounted on casing

• Shaft Absolute is the sum of Casing Absolute and Shaft Relative

Shaft Versus Housing Vibration

Shaft Versus Housing Vibration

(Selecting the Right Parameter)

• Shaft vibration relative to bearing housing

– Machines with high stator to rotor weight ratio ( For example in syngas comp the ratio may exceed 20)

– Machines with hydrodynamic sleeve bearings

– Almost all high speed compressor trains

• Bearing housing vibration

– Machines with rolling element bearings have no shaft motion relative to bearing housing.– Rolling Element bearings have zero clearance

– Shaft vibration is directly transmitted to bearing housing

• Shaft absolute displacement

– Machines with lightweight casings or soft supports that have significant casing vibration

Bearing Housing Vibration

• Shaft-relative vibration provides

– Machinery protection

– Low frequency (up to 120,000 CPM) information for analysis

• Many rotor- stator interactions generate high frequency vibrations that are transferred to the bearing housing

– Vane passing frequency in compressors

– Blade passing frequency in turbines

– These frequencies provide useful information on the condition and cleanliness of blades and vanes

• These vibrations are best measured on the bearing housing using high-frequency

accelerometers

– Periodic measurements with a data collector

Shaft Rotation and Precession

• Precession is the locus of the centerline of the shaft around the geometric centerline

• Normally direction of precession will be same as direction of rotation

• During rubbing shaft may have reverse precession

IRD Severity Chart

• Values are for filtered readings only – not overall

• Velocity is expressed in peak units (not RMS units)

• Severity lines are in velocity

• Displacement severity can be found only with reference to frequency

• Transducer is a device that converts one form of energy into another

• Microphone - sound (mechanical) to electrical energy

• Speaker - electrical to mechanical energy

• Thermometer - thermal to electrical energy

• Vibration is mechanical energy

• It must be converted to electrical signal so that it can easily be measured and analyzed

• Commonly used Vibration Transducers

• Noncontact Displacement Transducer

• Seismic Velocity Transducer

• Piezoelectric Accelerometer

• Transducers should be selected depending on the parameter to be measured

Proximity Displacement Probes

• Proximity probes measure the displacement of shaft relative to the bearing housing

• They observe the static position and vibration of shaft

• By mounting two probes at right angles the actual dynamic motion (orbit) of the shaft can be observed

Non Contact Displacement Probes

(Eddy Current Proximity Probe)

• Measures the distance (or “lift off”) of a conducting surface from the tip of the probe

• Measures gap and nothing else.

• Coil at probe tip is driven by oscillator at around 1.5 MHz

• If there is no conducting surface full voltage is returned

• Conducting surface near coil absorbs energy

• Therefore, voltage returned is reduced

• Proximitor output voltage is proportional to gap

Eddy Current Proximity Probe System

Eddy Current Proximity Probe System Calibration

•

Eddy current “lift off” output is parabolic – not linear

• Proximitor has a nonlinear amplifier to make the output linear over a certain voltage range

• For a 24 Volt system the output is linear from 2.0 to 18.0 volts

Proximity Probe Advantages

•

Measures shaft dynamic motion

• Only probe that can measures shaft position – both radial and axial

• Good signal response between DC to 90,000 CPM

• Flat phase response throughout operating range

• Simple calibration

• Rugged and reliable construction

• Suitable for installation in harsh environments

• Available in many configurations

• Multiple machinery applications for same transducer – vibration, position, phase, speed

Proximity Probe DisAdvantages

• Sensitive to measured surface material properties like conductivity, magnetism and finish– Scratch on shaft would be read as vibration

– Variation in shaft hardness would be read as vibration

• Shaft surface must be conductive

• Low response above 90,000 CPM

• External power source and electronics required

• Probe must be permanently mounted Not suitable for hand-holding

• Machine must be designed to accept probes – difficult to install if space has not been provided

Seismic Velocity Pick-Up IRD 544

• Permanent magnet is attached to the case Provides strong magnetic field around suspended coil

• Coil of fine wire supported by low-stiffness springs

• Voltage generated is directly proportional to velocity of vibration

• When pick up is attached to vibrating part magnet follows motion of vibration

• The coil, supported by low stiffness springs, remains stationary in space

• So relative motion between coil and magnet is relative motion of vibrating part with respect to space

• Faster the motion higher the voltage

Velocity Pick-Up - Suspenped Magnet Type

•

Coil fixed to body, magnet floating on very soft springs

• All velocity pick ups have low natural frequency (300 to 600 CPM)

• Therefore, cannot measure low frequencies in the resonant range

• Their useful frequency range is above - 10 Hz or 600 CPM

Advantages of Velocity Pick-Up

• Measures casing absolute motion

• It is a linear self generator with a high output

– IRD 544 pick up – 1080 mv 0-pk / in/sec= 42 mv / mm/sec

– Bently pick up – 500 mv 0-pk / in/sec = 19.7 mv / mm/sec

• High voltage Output

– Can be read directly on volt meter or oscilloscope

– Therefore, readout electronics is much simplified

– Since no electronics needed in signal path, signal is clean and undistorted High signal to noise ratio

• Good frequency response from 600 to 90,000 CPM

• Signal can be integrated to provide displacement

Easy external mounting, no special wiring required

Disadvantages of Velocity Pick-Up

• Mechanically activated system Therefore, limited in frequency response – 600 to 90,000 CPM

• Amplitude and phase errors below 1200 CPM

• Frequency response depends on mounting

• Large size Difficult to mount if space is limited

• Potential for failure due to spring breakage

• Limited temperature range – usually 120oC

– High temperature coils available for use in gas turbines but they are expensive

• High cost compared to accelerometers

– Accelerometer cost dropping velocity pick up increasing

Note - Velocity transducers have largely been replaced by accelerometers in most applications

A Brief Introduction to Vibration Analysis of Process Plant Machinery (VI)

Basic Concept VI

Piezoelectric Accelerometers

• Piezoelectric crystal is sandwiched between a seismic mass and outer case

• Preload screw ensures full contact between crystal & mass

• When mounted on a vibrating surface seismic mass imposes a force equal to mass x

acceleration

• Charge output of piezo crystal is proportional to applied force

• Since mass is constant, output charge is proportional to acceleration

Piezoelectric Accelerometers

Converting Charge to Voltage

• The output of accelerometers is charge Usually expressed as picocoulomb / g (pc/g)

• Electronic charge amplifier is required to convert charge signal to voltage signal

– Impedance of accelerometer is high Cannot be connected directly to low impedance instruments– Charge amplifier has high input impedance and low output impedance so that long cables can beused

• Charge amplifier can be external or internal

– In bigger accelerometers amplifier can be located inside

– In small, high frequency units amplifier is located outside

– Also located outside in high temperature accelerometers

Accelerometers Mounting

• Mounted resonance of accelerometer drops with reduction in mounting stiffness

– This causes a reduction in the upper frequency range

• Ideal mounting is by threaded stud on flat surface

– Maximum stiffness, highest mounted resonance

– Resonant frequency 32 KHz Usable range 10 KHz

• Magnet mounting simpler but lower response

– Resonant frequency drops to 7 Khz Usable range 2 KHz

• Handheld probe convenient but very low frequency response

– Due to low stiffness of hand resonant frequency < 2 KHz

– Frequency response < 1 KHz

Accelerometers Resonance & Frequency Response

•

Frequency response depends on resonance frequency

• Higher the resonance frequency, higher the useful range

• Maximum useable frequency range is 1/3rd of resonance

• Resonance frequency, however, depends on mounting

Frequency Response - Screw Mount

• Screw mount has the highest resonance and, therefore the highest frequency response

• This film of silicon grease improves contact

• Make sure bottom of accelerometer contacts measured surface

Frequency Response - Magnet Mount

•

Weight of magnet determines the mounted resonance

• Smaller the magnet higher the frequency response

Use the smallest magnet that holds the accelerometer without slipping Use a machined surface for the best grip

Frequency Response Hand Held

•

Poor high frequency response - < 1 KHz

• Response may change with hand pressure

• Repeatability is poor when high frequencies are present

• Hand holding accelerometers should be avoided except for low frequency work

Filtering Necessary for Accelerometers

• Any high frequency vibration in the resonant range will be highly amplified

– Amplification can be up to 30 dB or almost 1,000 times

– Filtered amplitudes will be highly distorted

• Resonant frequency highly depends on mounting

– By previous example – 32 KHz for screw mount Only 2 KHz for handholding

• Therefore, resonance range should be filtered out

– For screw mount low pass filter should be set at 10 KHz

– For hand holding filter should be set at 1 KHz

– Analyst must know frequency response of accelerometer used for different mounting conditions

Filtering can be done in FFT Analyzer by setting maximum frequency correctly.

Advantages of Accelerometers

• Measures casing or structural absolute motion

• Rugged and reliable construction

• Easy to install on machinery, structures, pipelines

• Small size, easiest to install in cramped locations

• Good signal response from 600 to 600,000 CPM

• Low frequency units can measure down to 6 CPM

• High freq units can reach 30 KHz (1,800,000 CPM)

• Operates below mounted resonance frequency

• Flat phase response throughout operating range

• Internal electronics can be used to convert acceleration to velocity – Bently Velometer

• Units available from a cryogenic temperature of minus 200oC to a high temperature of > 600oC

Disadvantages of Accelerometers

• Sensitive to mounting and surface conditions

• Unable to measure shaft vibration or position

• Not self generating – Need external power source

• Transducer cable sensitive to noise, motion and electrical interference

• Low signal response below 600 CPM (10 Hz)

• Temperature limitation of 120oC for ICP Acceleroms

• Double integration to displacement suffers from low frequency noise – should be avoided

• Signal filtration required depending on mounting

• Difficult calibration check

Machine With Both Shaft and Bearing Housing Vibration Monitoring

• Machines can vibrate at many different frequencies simultaneously 1x, 2x, 3x, vane passing etc.

• Timebase and orbit have frequency information but only a couple of harmonics can be identified – impossible to identify nonsynchronous frequencies

• Using an analog tunable analyzer the amplitude and phase at each individual frequency can be

identified but only one at a time

– All frequencies cannot be seen simultaneously

– Trend changes in individual frequencies cannot be followed

– Each frequency sweep may take one minute during which short duration transient events may be missed

• A Spectrum Plot by a FFT Analyzer shows all frequencies instantaneously.

Spectrum Plot-2

• Spectrum plot is the basic display of a Spectrum Analyzer It the most important plot for diagnosis

• Spectrum plot displays the entire frequency content of complex vibration signals in a convenient form – It has frequency on X-axis and amplitude on Y-axis

– It is constructed from sampled timebase waveform of a single transducer – displacement, velocity or acceleration

• Fast Fourier Transform (FFT) calculates the spectrum from the sample record which contains a specific number of waveform samples

• Spectrum plots can be used to identify harmonics of running frequency, rolling element bearing defect frequencies, gear mesh frequencies, sidebands

Periodic motion with more than one frequency

Above waveform broken up into a sum of harmonically related sine waves

Construction of Half Spectrum Plot - 1

• Raw timebase signal (red) is periodic but complex

• Fourier transform is equivalent to applying of a series of digital filters

• Filtered frequency components are shown as sine waves (blue)

• Phase for each signal can be measured with respect to trigger signal

• We can see components’ amplitude, frequency and phase

Construction of Half Spectrum Plot - 2

• If we rotate the plot so that the time axis disappears we see a two dimensional spectrum plot of amplitude v/s frequency

• Component signals now appear as series of vertical lines.

• Each line represents a single frequency

• Unfortunately, the phase of the components is now hidden

• It is not possible to see phase relationships in spectrum plot

These plots show why it is impossible to guess the frequency content from the waveform Vertical lines in top plot show one revolution

It is clear that 2x and higher frequencies are present

But 3x and 6x could not be predicted from the waveform

A Fourier spectrum shows all the frequencies present

Linear and Logarithmic Scaling

• Amplitude scaling can be Linear or Logarithmic

• Logarithmic scaling is useful for comparing signals with very large and very small amplitudes.

– Will display all signals and the noise floor also

• However, when applied to rotating machinery work

– Log scale makes it difficult to quickly discriminate between significant and insignificant components.

• Linear scaling shows only the most significant components.

– Weak, insignificant and low-level noise components are eliminated or greatly reduced in scale

• Most of our work is done with linear scaling

Illustration of Linear and Log scales

• Log scale greatly amplifies low level signals

• It is impossible to read 1% signals in linear scale

• It is very easy to read 0.1% signals on the log scale

Limitations of Spectrum Plots

• FFT assumes vibration signal is constant and repeats forever

• Assumption OK for constant speed machines

– inaccurate if m/c speed or vibration changes suddenly.

• FFT calculates spectrum from sample record

– Which has specific number of digital waveform samples

– FFT algorithm extends sample length by repeatedly wrapping the signal on itself

– Unless number of cycles of signal exactly matches length of sample there will be discontinuity at the junction

– This introduces noise or leakage into the spectrum

• This problem is reduced by “windowing”

– Forces signal smoothly to zero at end points

– Hanning window best compromise for machinery work

Effect of Windowing

• Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies

Two examples of half spectrum plots are shown below

• Without window function the “lines” are not sharp and widen at the bottom

• This “leakage” is due to discontinuity at sample record ending

• When “Hanning” window is applied to the sample record 1/2x spectral line is narrower and higher

• Noise floor at base is almost gone