measurement of vibration

8/2/2019 Measurement of Vibration

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Measurement of Vibration

A.Rama Rao

Vibration Laboratory SectionReactor Engineering Division

Bhabha Atomic Research CentreMumbai-400085

E-Mail: [email protected]

There are three quantities, which are of interest in vibration studies. In the case of

sinusoidal motion, the three quantities are related by the frequency of oscillation. The

instantaneous position or displacement of a body can be mathematically described as,

X = Xpeaksin( 2t/T) = Xpeaksin (2ft) = Xpeaksin(t)

where = 2f = angular frequency.

Xpeak=Maximum displacement.

f = 1/T and T = period of oscillation

As the velocity of motion is the time rate of change of motion, it can be expressed as,

v = dx/dt = Xpeakcos (t) = Vpeakcos(t) = Vpeaksin(t+ /2)

and acceleration which is again time rate of change of velocity, it can be express as,

a = dv/dt = dx2

/dt2

= - 2

Xpeaksin(t) = - Apeaksin(t) = Apeaksin(t+ )

It can be seen that the form and period of vibration remain the same except that the

velocity leads the displacement by a phase angle of 90 o and acceleration leads velocity

again by 90o

1.0 Amplitude quantification

Common sense says that vibration severity is indicated by correct measurement of

vibration amplitude. Figure 1 shows a sinusoidal signal with amplitude, period and phase.

The peak amplitude is used to describe for example the displacement of a shaft, which

helps in estimating the position of the shaft with respect to the clearance of the bearing

supporting the shaft. Whenever there is vibration of a body within a given clearance, peak

value measurement is advisable.


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Figure-1 A Periodic signal


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Figure-2 Amplitude Characteristics of a Periodic Signal

Measurement of Root Mean Square value of a signal has important significance in

expressing the power content of the vibration and hence the damage potential of

vibration. It gives the DC equivalent of oscillating or alternating signal. It is

mathematically expressed as

PEAKRMSXX

2

1

Other amplitude quantifications are Form factor (Ff) and Crest factor (Fc).

Ff= RMS/AVERAGE

Fc = PEAK/RMS

These factors give some indication of the wave shape. For example for pure harmonic

motion Ff= 1.11 and Fc = 1.41. Deviation from these numbers indicates that the signal is

not pure harmonic. Of the two factors, crest factor has important diagnostic importance.

For example, while monitoring health of bearings, if the crest factor shows an increasing

trend then it is considered to be an indication of impending damage to the bearing. This

happens for example when there is single vibration component caused by a faulty

bearing. This defect goes undetected by RMS measurement but crest factor easily picks

up the in defect in the bearing. Figure 2 illustrates the relative significance of these

measurement quantities.

2.0 Transducer specification

Transducers help us in making dependable measurement when their selection for a

particular type of measurement is carefully followed. A very common mistake made in

this regard is that one transducer is used for all types of measurement. During normal

operating condition this mistake may not be too costly but when vibration severity

increases, the error may be too big. For example, transducer tuned to measure machinery

vibration strictly cannot be used for assessing piping vibration. The error will be highly

non-conservative.


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2.1 Eddy Current Probes

Eddy current probes, which measure displacements with out contacting the vibrating

surface, have been standardized in terms of gap between the target and the probe, its

measurement range, sensitivity and the connecting electronics. The probe design that

follow standard API 610 give an out put of 8 V/mm for a three meter cable between the

probe and the proximeter that supplies to the probe the carrier signal for modulation

during vibration of the target. The proximeter also demodulates the measured signal and

gives voltage out put. The proximeter is supplied with external DC voltage of 18 to 24 V.

Figure 3 shows typical mounting details of the probe inside a bearing housing. Care must

be taken while positioning the tip of the probe with respect to the shaft. As shown in

Figure 4, no metal should be present within 4 mm of the probe face except the target

surface.


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Figure-3 Eddy Current Probe Mounting within the Bearing Housing

Figure 4 Schematic of Proper installation of Eddy Probe.

Eddy probes are also available to measure the nano micron deflection of the outer race of

the ball bearings. These probes are highly sensitive and also require special mounting

within the bearing housing. Figure 5 shows high sensitivity probe to measure nano level

deflection of outer race of a bearing.


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Figure-5. High Sensitivity Eddy current Probe

The probe tip diameter basically decides the range of measurement. They normally are in

the range of 6mm to 12mm. The magnetic field generated at the tip of the probe need to

be directed towards the target with out much of loss. If 12 mm probe is used for

measuring vibration of 30 mm shaft then there is a possibility of error in measurement.

The orbit plot has very high potential in machinery diagnosis. For example, figure 6

shows the orbit plot of a shaft measured in x-y direction as shown in figure 3.


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Figure-6 Orbit plot or X-Y from Eddy Probes

Figure 6 shows some of the orbit shapes indicating severity of misalignment between to

coupled rotors and figure 7 shows 3-D plot along with orbit plot used for recognizing

resonance during start trial of a machine.


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Figure-7 Orbit plots indicating severity of misalignment

Figure-8 3-D plot and orbit plot.

2.2 Accelerometers

As brought out earlier, accelerometers are widely used for measuring all the three

vibration quantities. Piezoelectric based accelerometers are widely used type of sensors.

The piezo material develops charge when subjected to force. Quartz and Rochelle salt are


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when excited from low frequency up to its resonance frequency. Normally for

general-purpose accelerometers the resonance frequency is in the range of 30

to 90 KHz. As a thumb rule the upper limit of the useful range is taken as 1/3rd

the resonance. That is 10 to 30 KHz. Figure shows the band useful frequency

range. Accelerometers are not capable of a true DC response. The

preamplifier decides the lower limit of the frequency.

Figure-10 Frequency response of an Accelerometer

Up to 1 Hz is normally considered acceptable without any amplitude or phase

distortion. If a measurement involves higher frequencies than 30 KHz, then

accelerometers with resonance frequency higher than 100 KHz must be used

and if low frequency measurement is to be carried out involving low

displacements, then accelerometers are not suitable. Double integration of

acceleration signal for estimating low displacement gives unreasonably high

displacement, which is due to noise in the integration. This is one commonly

made mistake and so there is a need to exercise caution.

2.2Sensitivity: It is the magnitude of voltage developed across its outputterminals when subjected to certain acceleration. This is specified as V/m/s

2


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or pico coulomb/ m/s2. Ideally, the general feeling that higher the sensitivity

the better suits low level of acceleration. However for measurements

involving vibration and intermittent shock for example in automobile on a

bumpy road, high sensitivity could lead to saturation of input signal and hence

distortion. High sensitivity accelerometer normally has limited high frequency

range and accelerometers suited for high frequency measurement are of lower

sensitivity. What is important is to make an estimation of what is the likely

level of voltage that may be received from the accelerometer. Based on this

the electronics, and other condition for storage device may be adjusted.

2.3Dynamic Range: When it is required to measure abnormally low and highvibration levels, the dynamic range needs to be considered. Now-a-daysaccelerometers are available with dynamic range from 60dB to 100 dB.

Dynamic range of 60 dB measures from says 1mm/s2 to 1000 mm/s2and 100

dB range measures up to 100,000 mm/s 2. The dynamic range must be seen in

combination with sensitivity to assess the performance of the sensor in the

lower or upper range of the amplitude. Figure 11 shows the illustration of

dynamic range.

Figure-11 Illustration of dynamic range of accelerometer


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Upper limit of the dynamic range is determined by structural strength of the

accelerometer. Accelerometers are available to measure up to 100,000 g,

which is well into the range of mechanical shock.

2.4Mass: Normally accelerometers are lightweight and compact in design.However when they are used in large numbers say on aeroplane wings or

panels, the mass loading could be an issue. Additional mass changes the level

response and the frequency of the structure thus invalidating the measurement

results. The change in the response can be corrected with the following

formula.

as = am (ms+ma)/ms and fs =fm {(ms+ma)/ms }

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where

as = acceleration with out mass loadingfs = frequency with out mass loading

ms = effective mass of the structure

ma = mass of accelerometer

As a general rule, mass of the accelerometer should not be greater than one

tenth of the effective (dynamic) mass of the structure.

2.5Transient Response: Accelerometers are also used for measuring shortduration shocks caused by impact of two bodies or say during drop testing of

packages etc. The two shock parameters that need to be accurately measured

are time duration of shock and the amplitude of shock. The shock duration

could be smaller than the natural period of the system. The most likely error

could be in estimating the time duration due to retention of charge by the

accelerometer when shock is suddenly applied and in estimating the amplitude

when the resonance of the accelerometer is excited. The supplier provides the

safe lower and upper limit of shock measurement.

2.6Temperature limits: Since property of the piezo material is dependent on thetemperature, it is advisable to stick to the specified limit. Beyond the limit the

piezo material depolarizes causing permanent loss or change in sensitivity.


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Some times heat sinks (finned washer) or mica washers are used to reduce

heat transmission. Sensitivity versus temperature curves is provided by the

suppliers to estimate the error in measurement due to temperature effect.

2.7Phase Response: Any shift in the phase between mechanical input andresulting electrical output of the accelerometer indicates time delay between

input and output and hence distortion of the mechanical input. At frequencies

below the mounted resonance there should be no phase shift. Figure 12

illustrated the phase and amplitude relationship.At resonance frequency, the

motion of the seismic mass inside the accelerometer lags that of the base

resulting in phase distortion

Figure-12 Phase and amplitude relation

2.8 Environmental condition: Most of the accelerometers withstand accumulated

gamma radiation dose of 2 M Rad with out significant degradation. For

permanent installation under nuclear radiation, accelerometers to withstand

accumulated dose of 100 M Rad is available. Magnetic sensitivity of piezo

sensors is very low. Measurements on power generators and magnetic devices


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are possible with out distortion. Acoustic noise present in the machine is not

sufficient to induce any error in the measurement.

3.0 Piezoelectric Accelerometers

Since accelerometers are widely used in the industry, let us understand its

working. Figure 13 shows a general arrangement of measurement using an

accelerometer.

Figure-13 General scheme of measurement using accelerometer

The output impedance of a piezo element is very high and so cannot be directly

connected to a read out device, which normally have low input impedance. When

connected, it can greatly reduce the sensitivity as well as its frequency range. To

eliminate this connectivity problem, the accelerometer out put is connected to a

pre amplifier, which has high input impedance and low output impedance. Figure

14 shows the equivalent circuit diagram of an accelerometer, which is basically a

charge generator q coupled with an internal capacitance C. e is the voltage

across the capacitor. Figure 15 show the equivalent diagram of accelerometer plus

cable plus charge amplifier.

Figure-14 Equivalent circuit for an Accelerometer

Vibration Preamplifier Analyzer Recorder

Pick-up


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Figure-15 Equivalent diagram for an Accelerometer + Cable + Charge Amplifier

The pre amplifiers are either voltage type in which the out put voltage is

proportional to input voltage from the sensor or charge type in which the out put

voltage is proportional to input charge. When voltage amplifier is used, the

overall system is very sensitive to changes in cable capacitance that is changes in

the cable length between the sensor and the pre amplifier. However, with charge

pre amplifiers the out put remains unaffected by the length of the cable. Hence

one has to be careful in knowing the type of preamplifiers before the

measurement or even while specifying for purchase of vibration equipments.

Some preamplifier includes integrators to convert acceleration signal to velocity

or displacement proportional signal.

4.0 Cables

The signal carrying cables are one of the loose links in the chain of vibration

measuring setup. They have to be correctly and carefully used for dependable

diagnostics. There are many instances wherein bad cables have given wrong

reading. In spite of standardized connecting cables, over the years of use,connecting errors creep in. Since accelerometers are high impedance device,

certain problem may also arise due to cable noise. The noise can originate either

from mechanical motion of the cable, also called tribo-electric effect or from

the ground loop. Mechanical motions of the cable during the measurements result

in change in the charge. Such an effect disturb cause disturbance in the low


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frequency range. This can be avoided by the practice of clamping the cable firmly

to arrest relative movement between several layers of insulation in the cable as

shown in figure 16.

Figure-16 Illustration of fastening cables to eliminate triboelectric noise

The second source of noise is the hum picked up from the mains supply by

ground loop in the chain of measuring device. Ground loop currents flow in the

shielded layer of the cables because of slight difference in the electrical potential

of grounding points such as at the accelerometer base and the electrical ground of

the read out device. The best way to eliminate ground loop is to ensure that the

entire system is grounded at one point meaning electrically isolate the base of the

accelerometer as shown in figure 17.

Figure-17 Proper connection to avoid Ground loop


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Electromagnetic noise can also pose problem when the cable is laid in the vicinity

of running electrical machinery. If this cannot be avoided, then at least double

shielded cable must be used to reduce the pick up noise.

5.0 Mounting the accelerometer

Selection of the correct mounting arrangement plays a significant roll in the use of

vibration measurement as its mounting decides the mounted resonance frequency

and hence its useful frequency range of measurement.The popular methods are

stud mounted, wax mounted magnet mounted, adhesive mounted and hand probe

type. The mounting type also depends on the size of the accelerometers and

position of measurement. For example big size accelerometer cannot be mounted

with wax when it has to be used for measuring on inclined or vertical plane of a

machine for the fear of dislodging or slipping downward. However miniature

sensors can be mounted with wax in any plane. The most popular method is probe

type mounting because it needs minimum preparation and is quick to use.

However it is most error prone especially when the measurement involves high

frequency. Probe type mounting drastically reduces the useful frequency range.

Figure-18 Illustration of Probe type and Stud Mounting


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Figure-19 Change of Response of Accelerometer for different type of mounting

Figure 18 and 19 illustrate the two extreme mounting methods of accelerometer

and its effect on the frequency response. Looking at the reduction of high

frequency response during probe type of mounting of accelerometers, one has to

be careful. Due to ease of measurement with probe type of mounting, there is a

tendency to make error especially while monitoring high frequency vibration say

in a bearing.

6.0 Accelerometer Calibration

Accelerometer calibration is to ensure the accuracy, reliability and repeatability of

measurement. Calibration helps to trace measured vibration values to the physical

standard. There are several reasons for performing a calibration. The most

important being the contractual reasons as an evidence of the accuracy of the

sensor, possibly with reference to international standards. At times calibration is

required to when performance of the sensor in a particular environment has not


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been documented. System checking also forms an important part of the calibration

process, particularly in measurement systems consisting of many instruments.

The most common question raised by users is how often the sensor should be sent

for calibration. While the manufacturers say that ideally accelerometers do not

need calibration for several years if they are used as per the manufactured

specification. However, we know that the accelerometers are subject to rough

handling in shop floor. If not the sensor per se, at least the connected cables,

connectors, switches in the readout meters get bad. At least for the system as a

whole recalibration is required. Then the question is how often the calibration

should be done. This is best judge is the user himself. Depending on the usage and

duty cycle of the accelerometer and its electronics, recalibration can be carried at

least once in year or earlier.

There are different levels of calibration possible such as primary, secondary, and

working reference type. In primary calibration, the sensitivity of the

accelerometer is established in terms of fundamental or derived units for physical

quantities of SI systems. Such transducers are kept in National Standard Institutes.

measurement of vibration

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