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

Basic Concepts I

Machinery Vibration is Complex 

Vibration of a machine is not usually simple

•          Many frequencies from many malfunctions

•          Total vibration is sum of all the individual vibrations

•          Unfiltered overall amplitude indicates overall condition 

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

•          Velocity combines the function of displacement and frequency

•          Unfiltered velocity measurement provides best overall indication of vibration severity

Characteristics of Vibration

Vibration is the back and forth motion of a machine part 

One cycle of motion consists of

•           Movement of weight from neutral position to upper limit

•           Upper limit back through neutral position to lower limit

•           Lower limit to neutral position

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

 

             Simple Spring- Mass system                   Movement plotted against time

Free and Forced Vibration

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

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

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

Relationship between Force and Vibration

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

•          These act on a bearing or structure causing vibration

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

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

  
 Various Amplitudes of a Sine Wave

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

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

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

•           Average value is not used in vibration measurements 

 

 

Characteristics of Vibration (2)

Time required to complete one cycle is the PERIOD of vibration

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

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

                                                                                        

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

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

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

Root Mean Squared Amplitude

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

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

  

Displacement, Velocity & Acceleration

•          Displacement describes the position of an object

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

•          Acceleration describes how fast the velocity changes with time

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

•          Velocity = rate of change of displacement

•          v = dx / dt   = Aw cos wt = Aw sin (wt + 90^o)     

•          Acceleration = rate of change of velocity

•          a = dv /dt = - Aw² sin wt = Aw² sin (wt + 180^o)