Maintenance Management

Vibration Analysis

Vibration Analysis

Description of vibration

Shown in the diagram is the representation of a shaft with an out of balance in the form of a key. The graph plots the relative vertical displacement of a point on the disc.

The total vertical movement is called the Peak to Peak Displacement of the vibration. This is an indication of the amount of lateral movement of the machine and is a good indication of the amount of out of balance in a machine when the value is compared to a standard for that machine. This parameter is often used when balancing.

The Vibration Velocity is the speed of movement of this point, being highest as the point passes through its at rest position. It gives a good guide to the amount of energy being generated by the vibrating object. This energy usually results in wear and eventual failure. The amount of energy is proportional to the square of the velocity of vibration. Velocity, being a good indication of the amount of wear taking place in a machine is a used exclusively in monitoring systems.

For analysis purposes the r.m.s value is used.

For very low speed machines where the velocity is low the displacement may be used instead.

The Vibration Frequency is the time taken to complete one cycle. The shaft above is said to have a fundamental frequency equal to the shaft rotational velocity i.e.

R.P.M / 60 = Fundamental frequency = 1 / Periodic time

There is a formula for working out the frequency that a particular vibration is occurring from knowing only the displacement and the velocity.

Frequency = 0.45 x Vibration Velocity (mils/sec r.m.s)/ Vibration Displacement (mils peak to peak)

The equation is true only when the majority of the vibration occurs at one frequency. In reality machines vibrate in a much more complex way with vibration occurring at several frequencies. By analysis of the frequency at which each of the vibrations are occurring it is possible to ascertain whether they are being generated from with the or externally. By further analysis it is possible to locate the source of vibration within complex machinery.

Vibration phase can be defined as the angular relationship between the positions of maximum vibration and some fixed point on a rotating shaft at any instant.

It is useful during balancing.

Vibration measurement units

There are three different ways of expressing vibration measurements

they are related as follows

R.M.S. =Peak to Peak/2.83

Half Peak Values = Peak to Peak/2

Units may be in mils (1x 10-3 inches) or microns (1x 10-3 millimetres) and they may be converted as follows 1 mil =25.4 microns

Causes of vibration

Typical causes could be

The great majority of the above create a vibration at a multiple of the fundamental. The Vibrations source identification table allows identification of the cause.

Sequence of analysis

  1. Assemble equipment
  2. record operational parameters of machine- lubricating oil temperature, load, history of mal operation, work done
  3. Run machine until it reaches normal operating temperature
  4. Take readings at designated points. Analyse frequency of any high readings
  5. If possible measure vibration at different speeds
  6. Note changes in temperature, load etc. during measurement period
  7. If possible double check readings
  8. Determine source of vibration using identification table
  9. Remedy fault

Additional information can be gained by measuring vibration of the shaft itself. This may be done using a Teflon tipped pick up or a piece of hardwood.

Causes of vibration other than initial out of balance

Thermal effects may occur due to the following reasons.

  1. Non-homogenous forging of the rotor causing uneven bi-metallic expansion
  2. Uneven machining of the rotor forging
  3. Parts of the rotating element is restrained from expansion
  4. Friction effects due to parts rubbing
  5. Uneven ventilation

Compromise or thermal balancing may be used to help alleviate the problem but these should only be carried out by specialised personnel

Double frequency vibration can have many different sources such as

  1. Badly mating or worn gears giving very high frequencies
  2. Aerodynamic and hydraulic forces will produce high frequency vibrations. If a fan is the source then the frequency will be at blade number x fundamental and may be caused by

Determination of rolling element bearing wear using vibration acceleration as the parameter

The condition of rolling element bearings can be accurately determined by taking measurements of acceleration in terms of 'g' peak.

Irregularities in newly fitted bearings lead to dynamic load and vibration detectable as accelerations in a vibration monitor. It is the magnitude and frequency span that determines the condition of the bearing. Accelerations due to a failing bearing will fall between 1 - 5kHz.

When judging the condition of a bearing it is important to take into account the speed at which it is running. Acceleration is proportional to the square of the rotational frequency. Therefore a slow running machine would give accelerations lower then a higher speed running machine for the same bearing condition.

The following table can be used as a rough guide.

State of rolling element bearing  Level of acceleration 'g' peak (in range 1 - 5 kHz)  

                   Satisfactory                        1  

                   Bearing failing                     2 -5  

                   Renew bearing urgently        5+


This does not apply to journal, plain or sleeve bearings

Care must be taken with some the following machinery as they can naturally generate vibration in the 1 - 5 kHz range

Pattern of frequency of failing rolling element bearing.

If the peak appears to be isolated then other possible sources such as gear teeth should be investigated.
If the vibration occurs over a broad band then it is probably due to bearing failure. Cavitation can be determined as the source by checking the locality of the source. Whether bearing housing or pump casing. Also the discharge valve may be partially closed which should reduce the cavitation and the vibration.

Method for assessing condition of rolling element bearing.

  1. Measure radial acceleration at each bearing in vertical and horizontal directions and record the lowest value
  2. evaluate condition of bearing against set levels
  3. If over 1 ( minimum that can be reliably analysed) then use harmonic analyser to check frequency range
  4. put harmonic analyser in 'fine' mode and check spread of vibration, if over 500 Hz the probably bearing failure
  5. Repeat as check '4' on velocity mode

The effect of main engine revolutions on vibration readings
Generally the increase in vibration will be small, their are some cases however were a noticeable rise occurs. This may be due to a flexible bed plate or harmonics.

Example-Engine room supply fan

Vibration velocity (mils)



Initial vibration


Trial weight in position 1


Trial weight in position 2


Trial weight in position 3

Balancing using a vibration analyser

The three point method of balancing.

  1. Measure vibration and record (use analyser to ensure only fundamental frequency is used
  2. Drill three holes in a suitable place, say in the motor fan. These should be as close to 120o as possible. Each hole should be labelled 1,2 or 3 corresponding to three angles of the polar diagram. Place the calibration weight, which should be small especially for high speed motors, in the three positions and take vibration readings from the same point
  3. Plot the points on the polar diagram. Looking at the highest reading the scale of the polar diagram can then be determined.
  4. Join the first point to the second point and bisect this line. Join the second point to the third point and bisect the line, etc.
  5. From the points of bisection of the lines, draw perpendiculars so that they intersect.
  6. Using the point of intersection as the centre, draw a circle to cut each of the plotted measured points. This circle indicates the level of vibration that can be made by moving the weight around the circle
  7. The point at which the circumference of the circle is nearest to the centre of the polar diagram is the point at which the balance weight needs to be fixed
  8. The amount of weight (ASSUMING THAT THE TRIAL WEIGHT WAS TOO SMALL) is given by;
  1. Trial Weight x Initial Vibration Level / (Initial Vibration Level -Vibration Level At Best Position On Circle)
  1. Repeat process if required.


Final weight position : 15o from position 3 (Towards position 2)

Final weight = Trial weight x 300 / (300-190)
=2.7 x Trail weight

Note: It is possible to divide the balancing weight if it is not practical to fit one large piece. In the example above we could fit 7/8 at position 3 and 1/8 at position 2

Vibration source identification





Unbalanced Rotating Components

1 x F

Velocity and displacement highest in radial direction. Proportional to size of out of balance

Common cause of vibration due to dirt build up on rotating element or wear. In-Situ balancing following cleaning/repairs gives best results

Misalignment of coupling and bearings

2xF usual also 1&3F

Velocity and displacement large in axial directions

Common cause of vibration. Flex couplings should not be relied upon to make up misalignement

Damaged Ball / roller Bearings

High 5kHz

Acceleration level high in rolling element bearings. Distinguished by wide history

Often first component to show vibration though cause may be elsewhere

Work, Damaged or poor bearings

Very high, gear teeth x F

Use velocity measurement. Acceleration may be too high

Often vibration accompanied by noise

Resonance, Loose component

1&2 and Higher x F

Velocity and displacement can be very high. Big variation at joints

A common cause of vibration. Resonance readings may be reduced by strengthening foundations/bearings supports


1&2 x F

Velocity and displacement can be high. Often large in axial direction

Check shaft bend with clock gauges. Check shaft material correct for operating temperatures, no rubbing at seals

Electromagnetic effects in stator/rotor

Poles x F

Vibration disappears with power switched off

Unequal thermal effects

1 x F

Varies with load

Fundamental problem not met often. Compromise balance sometimes helps

Hydrodynamic forces

Impeller blades x F

Velocity can be high if associated pipework resonant

Not common, stiffening pipework supports may help. Cavitation causes very high freq vibrations


Fan blades x F

Velocity high if support structure/casing resonant

No Common

Bad Belt Drives

Varing x F

Velocity erratic

Can be checked using stroboscope. Examine belts and pulley for wear

Oil Whirl

½ x F

Displacement and Velocity unstable and increasing with time. Can be very High

Can create alarming vibrations. Occurs on on high speed plain bearing machines.