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 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 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 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 II Concept 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 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 • Displacement – Metric - Micron – English - Mil • = 1/1000 of Inch Velocity – Metric - mm / sec – English - inch / sec • = 1/1000 of mm Acceleration – Metric – English - meter / sec2 - g = 9.81 m/sec2 = English Metric Unit Conversion • Displacement Mil = 25.4 Micron • Velocity 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 = 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 plots illustrate how measurement unit affects the data displayed Each of the plots contain 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 Balancing of an FD Fan at a Refinery Presented by Troy Feese There are several commercially available software packages, such as SMS Star and ME’Scope, that can be used to perform operating deflection shape (ODS) measurements This article provides a case history of a forced draft (FD) fan that experienced high vibration due to unbalance and an impeller resonance near the operating speed The common balancing method of influence coefficients was unsuccessful due to varying phase data However, vibration was reduced to an acceptable level using the four-run method without phase data Background The FD fan supplied air for a boiler and was driven by a steam turbine through a speed-reducing gearbox as shown Figure Refinery personnel reported high vibration several days after replacing the fan roller bearings In an attempt to reduce the vibration, a second set of replacement bearings was installed; however, the vibration remained high Initial vibration data were acquired with a hand-held analyzer The predominant vibration was in the horizontal direction and occurred at 1× running speed of 1745 RPM (29 Hz) of the fan Test Procedure High vibration at 1× running speed is a typical indication of unbalance However, other factors can cause vibration problems, as described in the reference paper1 Therefore, the refinery requested that more detailed testing be performed before attempting to field balance the FD fan.The test procedure included the following steps: • Measured operating deflection shape (ODS) while running at 1745 RPM with load • Monitored bearing housing vibration while reducing air flow to boiler • Inspected the fan while it was down • Performed impact tests of bearing pedestals and fan rotor • Created vibration waterfall and Bode plots during coastdown • Balanced the fan using the four-run balance method to reduce vibration • Performed a final check of fan vibration with maximum air flow Operating Deflection Shape (ODS) There are several commercially available software packages, such as SMS Star and ME’Scope, that can be used to perform operating deflection shape (ODS) measurements First, a simple wire-frame model was created from basic dimensions of the FD fan The undeformed representation of the bearing housings, bearing pedestals, and concrete foundation is shown in Figure as dashed lines While operating the unit at constant speed and load, a tri-axial accelerometer was moved to 18 different locations to measure vibration in three orthogonal directions Phase angles were determined from a stationary reference accelerometer The software was then used to animate the measured vibration (amplitude and phase) at 1× running speed The highest vibration occurred at the top of the bearing housings in the horizontal direction Figure shows the rocking motion in which both ends (air inlet and coupling) were moving inphase The maximum vibration was approximately mils p-p at 1× running speed (29 Hz) Vibration on the concrete foundation was - mils p-p, which was also considered excessive However, no significant separation was found between bearing housings, pedestals, and concrete foundation Therefore, looseness was ruled out as a possible cause of the high vibration Reduced Air Flow to Boiler As the fan was unloaded, the air flow reduced from 70,000 lb/hr to zero with the louvers closed, which caused the speed to increase from 1745 to 1760 RPM During this time, the vibration levels of the fan bearings were monitored, and no change in 1× vibration was observed This demonstrated that the vibration was not caused by aerodynamic forces Both bearings still had approximately the same level of vibration, which pointed to a static unbalance condition of the fan impeller and not coupling unbalance Fan Inspection During the inspection, five balance weights of various sizes were found already welded around the periphery of the fan impeller This indicates previous trouble balancing the fan The fan impeller was covered with a thin layer of dirt, so it was difficult to tell if a balance weight had possibly come loose No obvious signs of damage were found, and no foreign objects were found inside the fan housing The amount of dirt would have been similar before and after the bearing replacements Therefore, the inspection did not explain the change in vibration after installation of the new roller bearings Other items to verify included: the speed rating of the roller bearings, bearing clearances, and proper lubrication Impact Tests With the fan shut down, impact tests were performed using an instrumented hammer containing a load cell The results showed that the bearing housings did not have any natural frequencies near running speed However, a natural frequency of the fan impeller was measured at 28 Hz and appeared to be more sensitive in the axial direction, as shown in Figure This natural frequency could be a wobble mode of the impeller and could increase in frequency during operation due to gyroscopic effects The EPRI paper by Smith2 gives an example of a wobble mode There is an insufficient separation margin between the 28 Hz natural frequency of the impeller and the operating speed of 29 Hz For reliable operation, a separation margin of at least 10% is recommended Therefore, the fan vibration could be amplified due to the resonant condition, and the fan would be sensitive to even small amounts in unbalance A change in unbalance condition could be caused by dirt build-up, a lost balance weight, or insufficient press fit of the impeller on the shaft allowing the impeller to shift slightly Vibration Plots Taken During Coastdown Vibration waterfall (Figure 4) and Bode (Figure 5) plots showed that two peaks occurred during the coastdown It was unknown if the second peak was caused by a sudden change in speed as the steam was cut off to the turbine or if this might be a critical speed of the fan The phase shift confirmed a resonance In addition, the vibration is amplified above the expected speed squared relationship due to pure unbalance Balancing During the inspection, previous balancing locations were found all around the fan impeller This indicated trouble balancing the fan using the typical influence coefficient method Because the fan was running near a resonance, the phase angles could vary significantly at slightly different operating speeds The speed of the steam turbine could not be held absolutely constant as would a motor The refinery was willing to start and stop the fan multiple times, so it was decided to try the fourrun balance method The four-run method is best for balancing near a resonance because it does not rely on phase data Dennis Shreve discussed this simple balancing procedure in the paper.1 Therefore, the four-run procedure will not be repeated here To prepare for the four-run balance, the fan blades were numbered to 11 (opposite direction of rotation) An optical tach and strobe light were used to ensure that all balance runs were performed at approximately the same speed of 1745 RPM For the trial weight, a washer weighing 3.2 ounces was selected A general rule of thumb for determining an appropriate trial weight is that the resulting unbalanced force should not exceed 10% of the rotor weight Table summarizes the vibration data Since the vibration readings were slightly higher on the inlet end, these values were used to construct the diagram shown in Figure The four-run balancing method uses circles to represent vibration amplitudes from each run The approximate intersection point of the circles indicates the final balance weight location, which was near blade The calculated amount was 2.7 ounces, which was slightly less than the trial weight of 3.2 ounces The trial weight was removed, and the 2.7-oz correction weight was installed As shown in Table 1, the vibration was higher than Run In an effort to further reduce the vibration, a larger weight of 4.0 ounces was tried at blade As shown in Table 1, the vibration readings with the 4-oz weight were similar to Run Therefore, it was decided to leave the 4-oz weight installed and to stop balancing All of the vibration levels shown in Table were for no-load conditions Figure compares the “before and after” vibration readings while operating the fan at 1745-1750 RPM with air flow Conclusions This case history demonstrates how the four-run balance method was used in a real-world application If the fan would have continued operation with high vibration, the new roller bearings could have been damaged due to the excessive unbalanced forces At the time of the field study, the fan was scheduled to be replaced in approximately one year Therefore, the manager of the refinery was satisfied with the short-term solution of field balancing to reduce the fan vibration to an acceptable level With one or two natural frequencies near the operating speed, the fan was still very sensitive to small amounts of unbalance due to dirt build-up, etc For long-term reliability, natural frequencies of the fan rotor, impeller, and foundation should have a separation margin of at least 10% from the operating speed range The refinery maintenance department reports that this fan was always difficult to balance and has now been replaced with a new one, which is more reliable References Feese, T D and Grazier, P E., “Balance This! Case Histories from Difficult Balancing Jobs,” 33rd Texas A&M Turbomachinery Symposium, Houston, Texas, September 2004 Smith, D R and Wachel, J C., “Controlling Fan Vibration - Case Histories,” EPRI Symposium on Power Plant Fans: The State of the Art, Indianapolis, Indiana, October 1981 Shreve, Dennis, “Balancing Without Phase,” Uptime Magazine, January 2011 ... 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... 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... 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