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 90^o; that is, it

              reaches its maximum ¼ cycle or 90^o before 

              displacement maximum

   •         Acceleration leads displacement by 180^o.

   •         Acceleration leads velocity by 90^o

   •         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