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 timeFree and Forced VibrationWhen 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 outForced 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 velocityRoot 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•          v = dx / dt   = Aw cos wt = Aw sin (wt + 90o)     •          Acceleration = rate of change of velocity•          a = dv /dt = - Aw2 sin wt = Aw2 sin (wt + 180o)

 

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

Basic Concept IIConcept of Phase

•         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”

       

         •         Weight “A” is at upper limit and weight                   “B” is at lower limit         •          These weights are vibrating 180 deg                    “out-of-phase”

  Displacement, Velocity and Acceleration Phase Relationship

 

   •         Velocity leads displacement by 90o; that is, it              reaches its maximum ¼ cycle or 90obefore               displacement maximum   •         Acceleration leads displacement by 180o.   •         Acceleration leads velocity by 90o

   •         Small yellow circles show this relationship clearly

  Units of Vibration Parameters

•         Displacement–       Metric            - Micron        = 1/1000 of mm–       English           - Mil                = 1/1000 of Inch•         Velocity–       Metric            - mm / sec   –       English           - inch / sec•         Acceleration–       Metric                        - meter / sec2

–       English           - g  = 9.81 m/sec2 =  

English Metric Unit Conversion

•         Displacement                1 Mil = 25.4 Micron

•         Velocity                1 inch/sec = 25.4 mm/sec

•         Acceleration                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–       D = Displacement in microns (mm/1000)–       V = Velocity in mm/sec–       A = Acceleration in g’s–       F = Frequency of vibration in cycles /minute (CPM)•         V = D x F / 19,100•         A = V x F / 93,650•         Therefore,  F = V / D x 19,100

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 19100 CPM.

–        At frequencies higher than 19,100 CPM velocity will be higher than displacement•          A = V x F / 93,650–        This means that acceleration in g’s will be equal to velocity in mm/sec at a frequency of

93,650 CPM.–        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

 Velocity

The same data is now displayed using velocity. Note how the 300Hz component is more apparent

 Acceleration

The same data is now displayed using acceleration.  Note how the large lower frequency component is diminished and the higher frequency component 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 structuresPhysical 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

vibration measured 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 its axis 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.•           In metric units•           Very rough > 16 mm/sec•           Rough                     > 8 mm/sec•           Slightly rough > 4 mm/sec•           Fair              - 2 – 4 mm/sec  •           Good           - 1 – 2 mm/sec

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

Basic Concept V

Vibration Transducers 

•          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.

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 AccelerometersConverting 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 be used.•          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

 Refferensi Book1. Machinery Malfunction Diagnosis and Correction – Robert C Eisenmann – Prentice Hall

2. Fundamentals of Rotating Machinery Diagnostics – Donald E. Bently – Bently Pressurized Bearing Press

3. Vibration Vector4.5. • A vibration vector plotted in the transducer response plane

6. •  1x vector is 90 mic pp /220 o

7. •  Zero reference is at the transducer angular location

8. •  Phase angle increases opposite to direction of rotation9.

10.11.12.  Polar Plot13.

14.15.  • Polar plot is made up of a set of vectors at different speeds.16.17. •  Vector arrow is omitted and the points are connected with a line18.19. •  Zero degree is aligned with transducer location20.21. •  Phase lag increases in direction opposite to rotation22.23. • 1x uncompensated Polar Plot shows location of rotor high spot relative to

transducer24.25. •  This is true for 1x circular orbits and approximately true for 1x elliptical orbits26.27.28.29. Read more » 30. Posted by Fajar at 12:35 PM 1 comments 31. Email ThisBlogThis!Share to TwitterShare to Facebook

32. 8/06/2011

33. Shaft Orbit Plots (II) 34. Not- 1X Compensation of an Orbit35.36. • At Left orbit is the uncompensated orbit

37. • At right is the same orbit with the 1X component removed

38. • The remaining vibration is primarily 1/2X from a rub39.

40.41.42. Measurement of peak-to-peak amplitude of an Orbit43.44. X transducer measurement axis is drawn together with perpendicular lines that are

tangent to maximum and minimum points on the orbit

45.46.47. Direction of Precession in Orbits48.49. • In the orbit plot shaft moves from the blank towards the dot. In the plot on left the

inside loop is forward precession50. • In the right orbit the shaft has reverse precession for a short time at the outside

loop at bottom

51.52.53.54. Effect of Radial Load on Orbit Shape55.56. • Orbits are from two different steam turbines with opposite rotation. Both

machines are experiencing high radial loads57. •  Red arrows indicate the approximate direction of the applied radial load.

58. •  Red arcs represent the probable orientation of the bearing wall59.

60.61.62. Deflection Shape of Rotor Shaft63.64. • When keyphasor dots of simultaneous orbits at various bearings along the

length of the rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft can be obtained

65.  *   This is a rigidly coupled rotor system 66.

67.    

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70. 8/05/2011

71. Shaft Orbit Plots (I)

72.The Orbit73. • The orbit represents the path of the shaft centerline within the bearing clearance.

74. • Two orthogonal probes are required to observe the complete motion of the shaft within.

75. • The dynamic motion of the shaft can be observed in real time by feeding the output of the two orthogonal probes to the X and Y of a dual channel oscilloscope

76. • If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on the orbit itself

77. • The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery diagnosis

78.79. Precession80.81. Once a gyroscope starts to spin, it will resist changes in the orientation of its spin

axis. For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If atorque, or twisting force, is applied to the spin axis, the axis will not turn in the direction of the torque, but will instead move in a direction perpendicular to it. This motion is called precession. The wobbling motion of a spinning top is a simple example of precession. The torque that causes the wobbling is the weight of the top acting about its tapering point. The modern gyroscope was developed in the first half of the 19th cent. by the

82.83.  84. Construction of an Orbit85.86. • XY transducers observe the vibration of a rotor shaft

87. • A notch in the shaft (at a different axial location) is detected by the Keyphasor transducer.

88. • The vibration transducer signals produce two time base plots (middle) which combine into an orbit plot (right)

89.

90.91.92.  Probe Orientation and the Orbit Plot

93.

94.95. • On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and

oscilloscope display show the same view.96.97.98. •  On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are

automatically rotated99.100.101. •  The oscilloscope, however, must be physically rotated 45oCCW to

display the correct orbit orientation 102.103.104.105.106.107.108.

109.110.

111. Examples of 1X and Subsynchronous Orbits112.  

113. • Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor dots because the frequency is not a fraction of the running speed

114. • The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster indicating dominant 1X behavior 

115.  116.117. Slow Roll Vector Compensation of 1X Filtered Orbit118.

119.120. • Slow roll vector compensation can considerably change the amplitude

and phase of the orbit121.122. •  Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231 o 123.124.125.126.127.128.129.130. Slow roll Waveform Compensation of a Turbine Orbit131. Note how compensation makes the orbit (right) much clearer

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138. Full Spectrum Plots 139. Full Spectrum140.141. • Half Spectrum is the spectrum of a WAVEFORM

142. • Full Spectrum is the spectrum of an ORBIT

143. • Derived from waveforms of two orthogonal probes

144. – These two waveforms provide phase information to determine direction of precession at each frequency

145. – For phase accuracy they must be sampled at same time

146. • Calculated by performing a FFT on each waveform

147. • These FFT’s are subjected to another transform

148. – Data converted to two new spectra – one for each direction of precession – Forward or Reverse

149. – Two spectra are combined into a single plot150. Forward to the right, Reverse to the left

151. Calculation of Full Spectrum Plot152.

153.

154.155.156.  157. First158. Waveform and its half spectrum159.

160. Second161. Waveform and its half spectrum162.

163. Combined orbit and its full spectrum164.

  

165. Circular Orbits and Their Full Spectra 166.

167.168.

Forward Precession        169.          Spectrum on forward side of plot170.171.  <--    Reverse Precession172.          Spectrum on reverse side of plot173.          Direction of rotation – CCW174.175. <--   Forward Precession176.         Spectrum on forward side of plot177.         Direction of rotation – CW178.179. <--   Reverse Precession180.         Spectrum on reverse side of plot181.         Direction of rotation - CW182.183.184.185. Full Spectrum of Elliptical Orbit

186.187. Orbit is generated by two counter rotating vectors188.189. Forward spectrum length is twice the length of forward rotating vector190.191. Reverse spectrum length is twice the length of reverse rotating vector192.193. Major axis of ellipse = a +b194. Minor axis of ellipse = a - b195.196. Original orbit cannot be reconstructed from full spectrum because there is no

phase information.197.198. 3 possible orbits are shown199.

200. Circular & Elliptical 1x Orbits201.

202.203. • Direction of precession is indicated by dominant line of “Forward” and

“Reverse” components. 204.205. •  Flatness of ellipse is determined by the relative size of forward and reverse

components206.207. •  When orbit is circular there is only one spectrum line

208.209. •  When orbit is a line the spectrum components are equal.

210.211. •  Therefore, the smaller the difference between components, the more

elliptical the orbit. 212.

213. Orbit and Spectrum of a ½x Rub214.215. • Orbit and spectrum of  a steam turbine with a ½ x rub

216. •  Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their harmonics.

217. •  From the ratio of forward ad reverse components

218. •  1x is the largest, forward and mildly elliptical

219. •  ½ x and 2x orbits are nearly line orbits

220. •  Small component of 3/2 x is third harmonic of ½ x fundamental

221.  222.223. Half and Full Spectrum Display of a ½ x Rub

224.225.226.  227. Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots228. • Half and full spectrum display of a ½ x rub (red data) and fluid induced

instability (blue data)229. • Note similarity in appearance of the two half spectrum plots

230. • The full spectrum plots clearly show the difference in the subsynchronous vibration

231. – The ½ x rub orbit is extremely elliptical – small difference between forward and reverse components

232. – The fluid induced instability orbit is forward and nearly circular – large difference between forward and reverse 1x and ½ x components.

233. • The unfiltered orbits are at the bottom

234. Full Spectrum Cascade Plot of Machine Start Up

235.236. • Horizontal axis represents precession frequency

237.238. •  Rotor speed is to the left and amplitude scale is on the right

239.240. •  Order lines drawn diagonally from the origin show vibration frequencies that

are proportional to running speed241.

242.243.244. • Display of spectra plots taken at different speeds during start up

245. •  Base of each spectrum is the rotor speed at which the sample was taken

246. •  Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted

247. •  Resonances and critical speed can be seen on 1x diagonal line

248. •  Sudden appearance of ½ x indicates rub which can produce harmonics.

249. •  Phase relationships cannot be seen on cascade plot.

250. •  Many harmonics at low speed usually due to scratches on shaft

251.

252.253.  254. Horizontal ellipse shows rub second balance resonance (critical)255.256. Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight

shift to right is due to stiffening of rotor system from rub contact.257.258.259.260.261.262. Full Spectrum Waterfall Plot

263.264. • Displays spectra with respect to time

265.266. • Used for correlating response to operating parameters

267.268. •  Time on left and Running Speed on right. Amplitude scale is at extreme right

269.270. •  Plot of compressor shows subsynchronous instability whenever suction

pressure is high (red). 1x component is not shown on plot. 271.

272. •  Full spectrum shows subsynchronous vibration is predominantly forward.

273.274.275.276.277. Waterfall of Motor with Electrical Noise Problem278.

279.280.281. • High vibration at mains frequency (60 Hz) during start up (red). 1x is low.

282.283. •  Vibration reduces when normal speed and current are reached (green)

284.285. •  When motor is shut down (blue) 60 Hz component disappears suddenly.

286.287. •  1x component reduces gradually with speed.

288.289.290.

291. Summary292.293.  • Conventional spectrum is constructed from the output waveform of a single

transducer294. • Full Spectrum is constructed from the output of a pair of transducers at right

angles.295. – Displays frequency and direction of precession

296. – Forward precession frequencies are shown on right side

297. – Reverse Precession frequencies are shown on left side

298. • Full spectrum is the spectrum of an orbit

299. – Ratio of forward and reverse orbits gives information about ellipticity and direction of precession

300. – However, there is no information about orientation of orbit

301. • Cascade and Waterfall plots can be be constructed either from half or full spectra

302.303.

304. Posted by Fajar at 10:54 AM 3 comments 305. Email ThisBlogThis!Share to TwitterShare to Facebook

306. 8/03/2011

307. Half Spectrum Plots 308. Spectrum Plot-1309. • Machines can vibrate at many different frequencies simultaneously  1x,

2x, 3x, vane passing etc.310. • Timebase  and orbit have frequency information but only a couple of

harmonics can be identified – impossible to identify nonsynchronous frequencies311. • Using an analog tunable analyzer the amplitude and phase at each

individual frequency can be identified but only one at a time. 312. – All frequencies cannot be seen simultaneously.

313. – Trend changes in individual frequencies cannot be followed

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

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

316.317. Spectrum Plot-2  318. • Spectrum plot is the basic display of a Spectrum Analyzer. It the most

important plot for diagnosis319. • Spectrum plot displays the entire frequency content  of complex vibration

signals in a convenient form.320. – It has frequency on X-axis and amplitude on Y-axis

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

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

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

324.

Periodic motion with more than one frequency

325.

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

326.327.  328. Illustration of how the previous signal can be described in terms of a

frequency spectrum.329. Left        - Description in time domain330. Right      - Description in frequency domain 331.332.333.334.  335. Spectrum Frequency as a Function of Pulse Shape

336.337.

Construction of Half Spectrum Plot - 1

338. • Raw timebase signal (red) is periodic but complex.

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

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

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

342. •  We can see components’ amplitude, frequency and phase 

343.344.   

Construction of Half Spectrum Plot - 2

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

346. •  Component signals now appear as  series of vertical lines.

347. •  Each line represents a single frequency

348. •  Unfortunately, the phase of the components is now hidden.

349. •  It is not possible to see phase relationships  in spectrum plot.350.

351.352.   353. These plots show why it is impossible to guess the frequency content from the

waveform.354. Vertical lines in top plot show one revolution355. It is clear that 2x and higher frequencies are present356. But 3x and 6x could not be predicted from the waveform.357. A Fourier spectrum shows all the frequencies present

358.359.360. Linear and Logarithmic Scaling

361. • Amplitude scaling can be Linear or Logarithmic

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

363. – Will display all signals and the noise floor also

364. • However, when applied to rotating machinery work

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

366. • Linear scaling shows only the most significant components.

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

368. • Most of our work is done with linear scaling369.

370.371.   372. Illustration of Linear and Log scales 373. •  Log scale greatly amplifies low level signals

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

375. •  It is very easy to read 0.1% signals on the log scale376.377. Limitations of Spectrum Plots

378. • FFT assumes vibration signal is constant and repeats forever.

379. • Assumption OK for constant speed machines .

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

381. • FFT calculates spectrum from sample record

382. – Which has specific number of digital waveform samples

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

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

385. – This introduces noise or leakage into the spectrum

386. • This problem is reduced by “windowing”

387. – Forces signal smoothly to zero at end points

388. – Hanning window best compromise for machinery work389.390. Effect of Windowing

391.392. • Figure shows a timebase plot with a mixture of 1/2x and 1x frequencies. 393. Two examples of half spectrum plots are shown below394.

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

396. •  This “leakage” is due to discontinuity at sample record ending397.

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

399. •  Noise floor at base is almost gone.

Half Spectrum PlotsSpectrum Plot-1

•          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

 Illustration of how the previous signal can be described in terms of a frequency spectrum.Left        - Description in time domainRight      - Description in frequency domain 

 Spectrum Frequency as a Function of Pulse Shape

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 revolutionIt is clear that 2x and higher frequencies are presentBut 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 higherFull Spectrum PlotsFull Spectrum

•          Half Spectrum is the spectrum of a WAVEFORM•          Full Spectrum is the spectrum of an ORBIT•          Derived from waveforms of two orthogonal probes–        These two waveforms provide phase information to determine direction of precession at

each frequency–        For phase accuracy they must be sampled at same time•          Calculated by performing a FFT on each waveform•          These FFT’s are subjected to another transform–        Data converted to two new spectra – one for each direction of precession – Forward or

Reverse–        Two spectra are combined into a single plot

Forward to the right, Reverse to the left

Calculation of Full Spectrum Plot

 FirstWaveform and its half spectrum

SecondWaveform and its half spectrum

Combined orbit and its full spectrum

  

Circular Orbits and Their Full Spectra

Forward Precession                 Spectrum on forward side of plot

 <--    Reverse Precession         Spectrum on reverse side of plot         Direction of rotation – CCW

<--   Forward Precession        Spectrum on forward side of plot        Direction of rotation – CW

<--   Reverse Precession        Spectrum on reverse side of plot        Direction of rotation - CW

Full Spectrum of Elliptical Orbit

Orbit is generated by two counter rotating vectors

Forward spectrum length is twice the length of forward rotating vector

Reverse spectrum length is twice the length of reverse rotating vector

Major axis of ellipse = a +bMinor axis of ellipse = a - b

Original orbit cannot be reconstructed from full spectrum because there is no phase information.

3 possible orbits are shown

Circular & Elliptical 1x Orbits

•         Direction of precession is indicated by dominant line of “Forward” and “Reverse” components. 

•          Flatness of ellipse is determined by the relative size of forward and reverse components

•          When orbit is circular there is only one spectrum line

•          When orbit is a line the spectrum components are equal.

•          Therefore, the smaller the difference between components, the more elliptical the orbit. 

Orbit and Spectrum of a ½x Rub

•         Orbit and spectrum of  a steam turbine with a ½ x rub•          Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their

harmonics.•          From the ratio of forward ad reverse components•          1x is the largest, forward and mildly elliptical•          ½ x and 2x orbits are nearly line orbits•          Small component of 3/2 x is third harmonic of ½ x fundamental

 

Half and Full Spectrum Display of a ½ x Rub

 Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots

•         Half and full spectrum display of a ½ x rub (red data) and fluid induced instability (blue data)

•         Note similarity in appearance of the two half spectrum plots•         The full spectrum plots clearly show the difference in the subsynchronous vibration–        The ½ x rub orbit is extremely elliptical – small difference between forward and

reverse components–        The fluid induced instability orbit is forward and nearly circular – large difference

between forward and reverse 1x and ½ x components.•         The unfiltered orbits are at the bottom

Full Spectrum Cascade Plot of Machine Start Up

•         Horizontal axis represents precession frequency

•          Rotor speed is to the left and amplitude scale is on the right

•          Order lines drawn diagonally from the origin show vibration frequencies that are proportional to running speed

•         Display of spectra plots taken at different speeds during start up•          Base of each spectrum is the rotor speed at which the sample was taken•          Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted•          Resonances and critical speed can be seen on 1x diagonal line•          Sudden appearance of ½ x indicates rub which can produce harmonics.•          Phase relationships cannot be seen on cascade plot.•          Many harmonics at low speed usually due to scratches on shaft

          Horizontal ellipse shows rub second balance resonance (critical)

         Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight shift to right is due to stiffening of rotor system from rub contact.

Full Spectrum Waterfall Plot

•         Displays spectra with respect to time

•         Used for correlating response to operating parameters

•          Time on left and Running Speed on right. Amplitude scale is at extreme right

•          Plot of compressor shows subsynchronous instability whenever suction pressure is high (red). 1x component is not shown on plot. 

•          Full spectrum shows subsynchronous vibration is predominantly forward.

Waterfall of Motor with Electrical Noise Problem

•         High vibration at mains frequency (60 Hz) during start up (red). 1x is low.

•          Vibration reduces when normal speed and current are reached (green)

•          When motor is shut down (blue) 60 Hz component disappears suddenly.

•          1x component reduces gradually with speed.

Summary

 •         Conventional spectrum is constructed from the output waveform of a single transducer

•         Full Spectrum is constructed from the output of a pair of transducers at right angles.–        Displays frequency and direction of precession–        Forward precession frequencies are shown on right side–        Reverse Precession frequencies are shown on left side•         Full spectrum is the spectrum of an orbit–        Ratio of forward and reverse orbits gives information about ellipticity and direction of

precession–        However, there is no information about orientation of orbit•         Cascade and Waterfall plots can be be constructed either from half or full spectra

Vibration Vector

• A vibration vector plotted in the transducer response plane

•  1x vector is 90 mic pp /220 o

•  Zero reference is at the transducer angular location

•  Phase angle increases opposite to direction of rotation

 Polar Plot

 • Polar plot is made up of a set of vectors at different speeds.

•  Vector arrow is omitted and the points are connected with a line

•  Zero degree is aligned with transducer location

•  Phase lag increases in direction opposite to rotation

• 1x uncompensated Polar Plot shows location of rotor high spot relative to transducer

•  This is true for 1x circular orbits and approximately true for 1x elliptical orbits

Read more »

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8/06/2011

Shaft Orbit Plots (II)Not- 1X Compensation of an Orbit

• At Left orbit is the uncompensated orbit

• At right is the same orbit with the 1X component removed

• The remaining vibration is primarily 1/2X from a rub

Measurement of peak-to-peak amplitude of an Orbit

X transducer measurement axis is drawn together with perpendicular lines that are tangent to maximum and minimum points on the orbit

Direction of Precession in Orbits

• In the orbit plot shaft moves from the blank towards the dot. In the plot on left the inside loop is forward precession

• In the right orbit the shaft has reverse precession for a short time at the outside loop at bottom

Effect of Radial Load on Orbit Shape

• Orbits are from two different steam turbines with opposite rotation. Both machines are experiencing high radial loads

•  Red arrows indicate the approximate direction of the applied radial load.

•  Red arcs represent the probable orientation of the bearing wall

Deflection Shape of Rotor Shaft

• When keyphasor dots of simultaneous orbits at various bearings along the length of the rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft can be obtained

 *   This is a rigidly coupled rotor system

   

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8/05/2011

Shaft Orbit Plots (I)

The Orbit

• The orbit represents the path of the shaft centerline within the bearing clearance.

• Two orthogonal probes are required to observe the complete motion of the shaft within.

• The dynamic motion of the shaft can be observed in real time by feeding the output of the two orthogonal probes to the X and Y of a dual channel oscilloscope

• If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on the orbit itself

• The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery diagnosis

Precession

Once a gyroscope starts to spin, it will resist changes in the orientation of its spin axis. For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If atorque, or twisting force, is applied to the spin axis, the axis will not turn in the direction of the torque, but will instead move in a direction perpendicular to it. This motion is called precession. The wobbling motion of a spinning top is a simple example of precession. The torque that causes the wobbling is the weight of the top acting about its tapering point. The modern gyroscope was developed in the first half of the 19th cent. by the

 

Construction of an Orbit

• XY transducers observe the vibration of a rotor shaft

• A notch in the shaft (at a different axial location) is detected by the Keyphasor transducer.

• The vibration transducer signals produce two time base plots (middle) which combine into an orbit plot (right)

 Probe Orientation and the Orbit Plot

• On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and oscilloscope display show the same view.

•  On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are automatically rotated

•  The oscilloscope, however, must be physically rotated 45oCCW to display the correct orbit orientation 

Examples of 1X and Subsynchronous Orbits

 

• Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor dots because the frequency is not a fraction of the running speed

• The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster indicating dominant 1X behavior 

 

Slow Roll Vector Compensation of 1X Filtered Orbit

• Slow roll vector compensation can considerably change the amplitude and phase of the orbit

•  Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231 o

Slow roll Waveform Compensation of a Turbine Orbit

Note how compensation makes the orbit (right) much clearer

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8/04/2011

Full Spectrum PlotsFull Spectrum

• Half Spectrum is the spectrum of a WAVEFORM

• Full Spectrum is the spectrum of an ORBIT

• Derived from waveforms of two orthogonal probes

– These two waveforms provide phase information to determine direction of precession at each frequency

– For phase accuracy they must be sampled at same time

• Calculated by performing a FFT on each waveform

• These FFT’s are subjected to another transform

– Data converted to two new spectra – one for each direction of precession – Forward or Reverse

– Two spectra are combined into a single plot

Forward to the right, Reverse to the left

Calculation of Full Spectrum Plot

 First

Waveform and its half spectrum

SecondWaveform and its half spectrum

Combined orbit and its full spectrum

  

Circular Orbits and Their Full Spectra

Forward Precession        

         Spectrum on forward side of plot

 <--    Reverse Precession         Spectrum on reverse side of plot

         Direction of rotation – CCW

<--   Forward Precession

        Spectrum on forward side of plot

        Direction of rotation – CW

<--   Reverse Precession

        Spectrum on reverse side of plot

        Direction of rotation - CW

Full Spectrum of Elliptical Orbit

Orbit is generated by two counter rotating vectors

Forward spectrum length is twice the length of forward rotating vector

Reverse spectrum length is twice the length of reverse rotating vector

Major axis of ellipse = a +b

Minor axis of ellipse = a - b

Original orbit cannot be reconstructed from full spectrum because there is no phase information.

3 possible orbits are shown

Circular & Elliptical 1x Orbits

• Direction of precession is indicated by dominant line of “Forward” and “Reverse” components. 

•  Flatness of ellipse is determined by the relative size of forward and reverse components

•  When orbit is circular there is only one spectrum line

•  When orbit is a line the spectrum components are equal.

•  Therefore, the smaller the difference between components, the more elliptical the orbit. 

Orbit and Spectrum of a ½x Rub

• Orbit and spectrum of  a steam turbine with a ½ x rub

•  Full spectrum clarifies the complex orbit which is a sum of ½ x, 1x and their harmonics.

•  From the ratio of forward ad reverse components

•  1x is the largest, forward and mildly elliptical

•  ½ x and 2x orbits are nearly line orbits

•  Small component of 3/2 x is third harmonic of ½ x fundamental

 

Half and Full Spectrum Display of a ½ x Rub

 

Differentiating ½ x Rub and Fluid Instability from Full Spectrum Plots

• Half and full spectrum display of a ½ x rub (red data) and fluid induced instability (blue data)

• Note similarity in appearance of the two half spectrum plots

• The full spectrum plots clearly show the difference in the subsynchronous vibration

– The ½ x rub orbit is extremely elliptical – small difference between forward and reverse components

– The fluid induced instability orbit is forward and nearly circular – large difference between forward and reverse 1x and ½ x components.

• The unfiltered orbits are at the bottom

Full Spectrum Cascade Plot of Machine Start Up

• Horizontal axis represents precession frequency

•  Rotor speed is to the left and amplitude scale is on the right

•  Order lines drawn diagonally from the origin show vibration frequencies that are proportional to running speed

• Display of spectra plots taken at different speeds during start up

•  Base of each spectrum is the rotor speed at which the sample was taken

•  Diagonal lines are “Order” lines. Usually 1x, 2x and ½ x are plotted

•  Resonances and critical speed can be seen on 1x diagonal line

•  Sudden appearance of ½ x indicates rub which can produce harmonics.

•  Phase relationships cannot be seen on cascade plot.

•  Many harmonics at low speed usually due to scratches on shaft

 

Horizontal ellipse shows rub second balance resonance (critical)

Vertical ellipse shows ½ x rub frequency is almost equal to first critical. Slight shift to right is due to stiffening of rotor system from rub contact.

Full Spectrum Waterfall Plot

• Displays spectra with respect to time

• Used for correlating response to operating parameters

•  Time on left and Running Speed on right. Amplitude scale is at extreme right

•  Plot of compressor shows subsynchronous instability whenever suction pressure is high (red). 1x component is not shown on plot. 

•  Full spectrum shows subsynchronous vibration is predominantly forward.

Waterfall of Motor with Electrical Noise Problem

• High vibration at mains frequency (60 Hz) during start up (red). 1x is low.

•  Vibration reduces when normal speed and current are reached (green)

•  When motor is shut down (blue) 60 Hz component disappears suddenly.

•  1x component reduces gradually with speed.

Summary

 • Conventional spectrum is constructed from the output waveform of a single transducer

• Full Spectrum is constructed from the output of a pair of transducers at right angles.

– Displays frequency and direction of precession

– Forward precession frequencies are shown on right side

– Reverse Precession frequencies are shown on left side

• Full spectrum is the spectrum of an orbit

– Ratio of forward and reverse orbits gives information about ellipticity and direction of precession

– However, there is no information about orientation of orbit

• Cascade and Waterfall plots can be be constructed either from half or full spectra

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8/03/2011

Half Spectrum PlotsSpectrum Plot-1

• 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

 

Illustration of how the previous signal can be described in terms of a frequency spectrum.

Left        - Description in time domain

Right      - Description in frequency domain 

 

Spectrum Frequency as a Function of Pulse Shape

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

Shaft Orbit Plots (I)

The Orbit

• The orbit represents the path of the shaft centerline within the bearing clearance.

• Two orthogonal probes are required to observe the complete motion of the shaft within.

• The dynamic motion of the shaft can be observed in real time by feeding the output of the two orthogonal probes to the X and Y of a dual channel oscilloscope

• If the Keyphasor output is fed to the Z axis, a phase reference mark can be created on the orbit itself

• The orbit, with the Keyphasor mark, is probably the most powerful plot for machinery diagnosis

Precession

Once a gyroscope starts to spin, it will resist changes in the orientation of its spin axis. For example, a spinning top resists toppling over, thus keeping its spin axis vertical. If atorque, or twisting force, is applied to the spin axis, the axis will not turn in the direction of the torque, but will instead move in a direction perpendicular to it. This motion is called precession. The wobbling motion of a spinning top is a simple example of precession. The torque that causes the wobbling is the weight of the top acting about its tapering point. The modern gyroscope was developed in the first half of the 19th cent. by the

 

Construction of an Orbit

• XY transducers observe the vibration of a rotor shaft

• A notch in the shaft (at a different axial location) is detected by the Keyphasor transducer.

• The vibration transducer signals produce two time base plots (middle) which combine into an orbit plot (right)

 Probe Orientation and the Orbit Plot

• On the left side, when the probes are mounted at 0o and 90oR, the orbit plot and oscilloscope display show the same view.

•  On the right, when the probes are mounted at 45oL and 45oR, the orbit plots are automatically rotated

•  The oscilloscope, however, must be physically rotated 45oCCW to display the correct orbit orientation 

Examples of 1X and Subsynchronous Orbits

 

• Orbit at left shows subsynchronous fluid-induced instability. Note the multiple keyphasor dots because the frequency is not a fraction of the running speed

• The orbit at right is predominantly 1X. The keyphasor dots appear in a small cluster indicating dominant 1X behavior 

 

Slow Roll Vector Compensation of 1X Filtered Orbit

• Slow roll vector compensation can considerably change the amplitude and phase of the orbit

•  Slow roll vectors of X= 1.2 mil pp /324oand Y= 1.4 mil pp /231 o

Slow roll Waveform Compensation of a Turbine Orbit

Note how compensation makes the orbit (right) much clearer

Not- 1X Compensation of an Orbit

•          At Left orbit is the uncompensated orbit•          At right is the same orbit with the 1X component removed•          The remaining vibration is primarily 1/2X from a rub

Measurement of peak-to-peak amplitude of an Orbit

X transducer measurement axis is drawn together with perpendicular lines that are tangent to maximum and minimum points on the orbit

Direction of Precession in Orbits

•          In the orbit plot shaft moves from the blank towards the dot. In the plot on left the inside loop is forward precession

•          In the right orbit the shaft has reverse precession for a short time at the outside loop at bottom

Effect of Radial Load on Orbit Shape

•          Orbits are from two different steam turbines with opposite rotation. Both machines are experiencing high radial loads

•           Red arrows indicate the approximate direction of the applied radial load.•           Red arcs represent the probable orientation of the bearing wall

Deflection Shape of Rotor Shaft

•          When keyphasor dots of simultaneous orbits at various bearings along the length of the rotor are joined an estimate of the three dimensional deflection shape of the rotor shaft can be obtained

 *   This is a rigidly coupled rotor system

Bode and Polar PlotVibration Vector

•          A vibration vector plotted in the transducer response plane•           1x vector is 90 mic pp /220 o •           Zero reference is at the transducer angular location•           Phase angle increases opposite to direction of rotation

 Polar Plot

 •          Polar plot is made up of a set of vectors at different speeds.

•           Vector arrow is omitted and the points are connected with a line

•           Zero degree is aligned with transducer location

•           Phase lag increases in direction opposite to rotation

•          1x uncompensated Polar Plot shows location of rotor high spot relative to transducer

•           This is true for 1x circular orbits and approximately true for 1x elliptical orbits

Bode Plot and Polar Plot Show the Same Detail

•          Bode’ Plot displays the same “vibration vector data” as the Polar Plot •           Vibration amplitude and phase are plotted separately on two plots       with speed on the

horizontal axis.

 Effect of Slow Roll Compensation

•          Slow roll compensation removes slow roll runout from filtered vibration•            What remains is mainly the dynamic response•           Compensated vector has zero amplitude at the compensation speed

Detecting Resonance with Bode & Polar Plots

•          In a Bode plot balance resonance is indicated by peak amplitude and sharp, significant change of phase at the frequency of the peak. On Polar plot rotor modes will produce large, curving loops.Small system resonances are more easily visible as distinctive small loops