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established and was initially applied to obtain non-intrusive measurements in fluid flows.Although the use of LDV for solid surface velocity measurement was recognized at an earlystage, its development in this area received little attention compared with the effort in fluidmechanics.

Accordingly, the measurements of vibration was still extensively achieved withaccelerometers or other forms of transducer which rely on contact with the measurementsurface for successful operation. There are, however, many cases of engineering interestwhere this approach is either impractical or impossible. Typical examples are the

measurement of very hot or light surfaces, such as exhaust pipes or loudspeakers, andmeasurement on rotating surfaces which preclude their use. In the latter area themeasurement of torsional vibration of rotating components presented a particularlydifficult measurement problem.

When designing rotating machinery components, an engineer must be careful tosuppress torsional oscillations, since incorrect or insufficient control may lead to fatiguefailure, rapid bearing wear, gear hammer, fan belt slippage and can produce associatedexcessive noise problems. Torsional oscillations are a particular problem in enginecrankshaft design where torsional dampers are commonly used to maintain oscillations atan acceptable level over the working speed range of the engine.

Torsional transducers have formerly included optical, seismic and mechanicaltorsiographs, strain gauges and slotted discs. The latter system has found common use in

the automotive industry and consists of a slotted disc fixed to the end of the crankshaft.A proximity transducer monitors the slot passing frequency, which is then demodulatedto provide a voltage analogue of the crankshaft speed and hence torsional oscillations, butwithin a limited frequency range. Strain gauges and associated telemetry or slip ringsystems are notoriously difficult to fix, calibrate and use successfully. In summary, themeasurement of torsional oscillations presented difficult problems for contactingtransducer technology and, of course, necessitated machinery downtime and specialarrangements being made for fitting, calibration, etc. Very often, the cost of this machinerystoppage would preclude a measurement being attempted, even though the vibration

engineer had concluded that it was vital if a design improvement is to be made.There was therefore a real need for a torsional vibration transducer which was userfriendly and could provide data immediately in on-site situations. It was not until theadvent of laser technology that a solution was found and, in what follows, the laser

torsional vibrometer is described, which allows the engineer to point low powered laserbeams at a rotating target component and obtain torsional vibration information.

2. LASER VIBROMETRY

2.1.

Laser Doppler velocimetry (LDV) or laser doppler anemometry (LDA) is now awell-established technique, which is used primarily for non-intrusive measurement in fluid

flows [1].Fundamentally, LDV measures the velocity of a light-scattering particle which is seeded

into the flow of interest, and it is assumed that the particle follows the flow faithfully.Under normal operating conditions the velocity of a group of seeding particles in the

measurement region is detected. Clearly, the number density of scattering particlesis important since they essentially sample the flow, and much of the early work inLDV was concerned with the validity or otherwise of statistical conclusions drawn froma particular measurement. An obvious practical problem to be overcome was the

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intermittence of seeding particles. An analysis system which claimed time-resolvedmeasurement had to be able to cope with periods of signal drop-out in which,instantaneously, either no particles were present in the measurement area or the vectoraddition of the light signals from particles combined to produce a very low signal

amplitude.For solid surface velocity measurement, light-scattering particles can be considered to

be replaced by light-scattering surface elements. Then, theoretically, there is never any lossof signal due to absence of scatterers, and it was probably this single reason which meant

that this form of measurement was considered to be relatively straightforward comparedwith its fluid counterpart. However, when coherent light is scattered by a diffuselyreflecting surface, a laser speckle pattern is formed in space in front of the target [2], andthe signal is produced by detecting the intensity of one or more speckles. It is this factwhich distinguishes a solid surface velocity measurement and, indeed, it is the specklepattern dynamics which limit the performance of the LDV system (see section 4.1).

The physical principle of all LDVs relies upon the detection of the Doppler frequencyshift in coherent light which occurs when it is scattered from a moving object. In Figure 1is shown a schematic diagram of the effect when a particle moving with velocity U scatterslight of wavelength l in a direction K2 from a laser beam of essentially single frequencytravelling in a direction K1 (K1 and K2 are unit vectors). The change in light frequency Dfproduced by the moving particle is given by

Df=U (K2K1)/l=U K/l, (1)

where K=K2K1. A formal proof of this equation can be found in the text byWatrasiewicz [3]. It has been assumed that the refractive index of the medium in whichscattering occurs is unity.

In Figure 2 is shown an optical geometry which is appropriate for a solid surfacemeasurement where the laser beam is directed normal to the surface. In this geometry K1and K2 are parallel, i.e., K1=K2, so that the Doppler frequency shift fD measuredcorresponds to the surface velocity component in the direction of the incident beam andis given by

fD=2U/l, (2)

where U==U=. In this way, by measuring and tracking the change in fD , which is of theorder of MHz, a time resolved measurement of the solid surface velocity U can be made.

Figure 1. The Doppler effect. Df=U (K2K1)/l.

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Figure 2. The optical geometry for solid surface velocity measurement.

The scattered light shown in Figures 1 and 2 has a frequency which is of the orderof 1015 Hz, and a frequency modulation of the order of MHz cannot be demodulateddirectly. The Doppler shift fD is measured electronically by mixing the scattered lightwith a reference beam derived from the same coherent source, onto the surface of aphotodetector. The latter responds to the intensity from the total light collected and thisnon-linear detection produces a heterodyne or beat in the current output, the frequency

of which is equal to the difference in frequency between the two collected beams. This isshown schematically in Figure 3, where a beam splitter has been used to mix the twobeams.

Unfortunately, the system as depicted in Figure 3 is ambiguous in the measurement ofthe direction of motion. In Figure 4 is shown the frequency spectrum of the photodetectoroutput. The Doppler signal assumes a zero frequency value twice per vibration periodwhen the solid surface velocity is zero. When the Doppler signal has a non-zero frequencyvalue it is not possible to distinguish whether the target surface is moving away from ortowards the detector. Vibration engineers require amplitude and phase of the target surfacemotion and this is usually provided by frequency pre-shifting the reference beam.

In Figure 5 is shown an equivalent optical geometry in which the reference beam hasbeen frequency pre-shifted by an amount fR . When considering the frequency spectrum

of the photodetector output, it is now clear that the frequency pre-shift provides a carrier

frequency which the target surface velocity can frequency modulate. The frequency shiftedsignal is often referred to as the Doppler signal, and when this is demodulated it is possible

Figure 3. Reference beam heterodyning.

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Figure 4. Doppler signal ambiguity.

to produce a time-resolved analogue measurement of the solid surface velocity in both

amplitude and phase, as shown schematically in the figure.A complete description of the various means of demodulating a Doppler signal is beyond

the scope of this paper, and readers are again referred to the text by Durst et al. [1]. Thechoice of method is dictated by the characteristics of the Doppler signal itself, which aredirectly related to the particular measurement problem. All demodulation techniquesproduce a time-resolved voltage analogue of the Doppler frequency with an associatedfrequency response limit.

Figure 5. Frequency shifting and time-resolved measurement.

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In the case of solid surface vibration measurement Doppler signals are continuous, butthey can be subject to periods of low amplitude due to speckle dynamic effects. Periodsof low signal amplitude are analogous to drop-outs in the fluid flow case.

Where it can be reasonably assured that a target surface is moving parallel to the incident

laser beam, the Doppler signal takes the form of a frequency modulated carrier ofessentially constant amplitude. This form of signal can be demodulated with extremeaccuracy and sensitivity and measurement of vibration velocity as low as nanometres persecond are possible. If the target motion induces spatial or temporal changes in the speckle

pattern formed on the detector, then performance is degraded. This is the case whentorsional vibration measurements are attempted on rotating targets, and this issue isaddressed in section 4.1.

Laser Doppler velocimeters for solid surface target use are often referred to as laserDoppler vibrometers, or simply laser vibrometers. They all work on the physical principledescribed in this section and differ only in the choice of optical geometry and the type offrequency shifting device used. Just as frequency shifting is paramount for solid surfacevibration measurement, it is also included as a standard item in all commercially availableLDV systems which are used for flow measurement. It is obviously necessary formeasurements in highly oscillatory flows, and in practice it is extremely useful to have acarrier frequency corresponding to zero motion for alignment and calibration purposes.For a discussion of frequency shifting devices, readers are referred to the text by Durst

et al. [1].Fortunately, for the purpose of torsional vibration measurements, the unidirectional

motion of a surface scattering element on a rotating target means that use of frequencyshifting is not necessary.

2.2. -

The cross-beam, or dual beam, laser Doppler velocimeter [1] provided a means ofmeasuring tangential surface velocities and hence torsional vibration velocity withoutsurface contact, and this is shown schematically in Figure 6. With this optical geometry

Figure 6. The cross-beam velocimeter instrument.

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the backscattered light produces a Doppler beat frequency fD in the photodetector outputwhich is given by

fD=(2U/l) sin (u/2), (3)

where U is the tangential surface velocity at the point of intersection of the beams, l isthe wavelength of the laser light and u is the included angle between the incident laserbeams. Demodulating the Doppler signal produces a time-resolved voltage analogue ofU,the fluctuating part of which is proportional to the torsional vibration velocity. This design

was used to measure torsional oscillations of the crankshaft of a six cylinder in-line dieselengine [4]. A comparison of the results obtained with those given by using a slotted discsystem mentioned in the Introduction is shown in Figure 7. A further laser measurementtaken with the engine operating under no load conditions confirms the expected overallreduction in vibration level. Broad agreement with the slotted disc system is achievedexcept at very low levels, which can be attributed to the limited sensitivity of the discsystem used. With reference to Figure 6, the cross-beam laser velocimeter suffers twomajor disadvantages in practice. Firstly, the intersection region of the laser beams (wherethe target surface must remain at all times) is typically less than 1 mm in length andconsequently the target must have a circular cross-section and the instrument must betripod-mounted at a fixed distance. Clearly, gross solid body movement of the target orinstrument will prevent a measurement being taken. Secondly, because the target has a

solid body oscillation in practice, the component of oscillation in the direction of thetangential surface velocity contaminates the data, so that with this cross-beam geometrytorsional oscillations cannot be distinguished from solid body movement. A final practicalpoint is that the mean Doppler frequency is dictated by the angle of the beam intersectionu, which is fixed. If the instrument is to be used over a wide speed range (10010 000 rpm),then the associated electronic processing must have a very wide bandwidth which addsexpense and complexity to the final design.

Figure 7. A comparison of cross-beam velocimeter and slotted disc torsiograph results; eighth order of rotation.w, Slotted disc, full load; q, laser, full load; W, laser, no load.

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These points prevent the cross-beam geometry providing a reliable and user friendlyinstrument, and laser technology for torsional vibration measurement did not develop forover a decade, until the invention of a new geometry which will be described in the nextsection.

2.3.

The optical geometry for the laser torsional vibrometer is shown schematically inFigure 8. With reference to this figure, the theory will be developed for the system

operating on the side of a shaft of arbitrary cross-sectional area which is rotating aboutan axis defined by the unit vector z which is assumed to be perpendicular to the plane ofthe latter. The shaft itself is allowed to oscillate as a rigid body with an instantaneousvelocity vector V.

The laser beam is divided into two equal intensity parallel beams of separation d, whichimpinge on the shaft surface at points A and B in a direction defined by the unit vectori. The instantaneous shaft surface velocities, with respect to the axis of rotation, at thesepoints are V1 and V2, respectively. Under normal circumstances the laser used would bea low powered (22 mW) heliumneon which produces red light at a wavelengthl=63281010 m. The essentially single frequency light from this laser undergoes aDoppler shift fD when scattered by the moving surface and light collected in directbackscatter is shifted by an amount given by equation (2) of

fD=2U:l, (4)

where U is the instantaneous velocity in the direction of the incident laser beam and l isthe laser wavelength. Accordingly light backscattered from the points A and B undergoesDoppler shifts fA and fB given by

fA=(2/l)i (V+V1), fB=(2/l)i (V+V2), (5, 6)

respectively. When this backscattered light is mixed onto the surface of a photodetector,heterodyning takes place and the output current from the detector is modulated at the

difference or beat frequency, fD , given byfD=fAfB=(2/l)i (V1V2), (7)

where now the sensitivity to solid body motion V has been removed.

Figure 8. The laser torsional vibrometer optical geometry.

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Considering the vector V1V2, one can write

V1=2pN(R1z), V2=2pN(R2z), (8, 9)

where N is the shaft revolutions per second. Thus

V1V2=2pN(R1R2)z=2pNBAz,

where BA represents the vector R1R2.Equivalently,

fD=(4pN/l)z (iBA). (10)

Examining the vector product term

(iBA)==i= =BA(sin d)t, (11)

where t is a unit vector perpendicular to i and BA, and d is their included angle, suggestsa simplification, in that =BA=(sin d) is equal to the beam separation, d, and hence

fD=(4pN/l) d z t. (12)

The scalar product term z t can be expanded to give the final general result,

fD=(4pd/l)(cos u)N, (13)

where u is the angle between the normal to the plane of the incident beams and therotational axis of the shaft. If the instrument is held so that the plane of the incident laserbeams is parallel to the shaft cross-section, then u=0 and hence

fD=(4pd/l)N. (14)

Doppler frequency demodulation of the photodetector output now provides atime-resolved voltage analgoue of the speed of rotation of the target component, thefluctuating part of which is the torsional vibration. The frequency response of theinstrument is dictated by that of the demodulation system used and the usual bandwidth

of practical interest is up to 1 kHz.The optical geometry used makes the instrument insensitive to solid body oscillation ofthe target or operator. The incident laser beams are parallel and therefore any solid bodymotion produces an identical Doppler frequency shift in the light scattered from the points

A and B. The subsequent heterodyning of this light at the photodetector, which producesa current output proportional to any frequency difference, is therefore insensitive to thisform of motion.

With reference to Figure 8, the frequency shift in the backscattered light from A or Bis not dependent on their radial distance from the rotational axis and is thereforeindependent of the cross-sectional shape of the component. This fact allows the instrumentto work successfully on targets of arbitrary cross-section, such as gear wheels, and thereis no restriction to components of circular cross-section as with the cross-beam geometrydiscussed in the last section. When the light is heterodyned, the beat frequency is

dependent only upon the beam separation d.With reference to equation (14), if this position is considered as a reference a lateral tilt

or rotation of the laser beam plane will result in a value ofu other than zero. For endof shaft use, it is necessary to note that careful choice ofu is needed which, together with

suitable adjustment of the beam separation, d, can provide immediate control of the meanvalue of the beat frequency. This aids electronic design for the frequency to voltageconverter required to demodulate the output signal from the photodetector.

Although the laser torsional vibrometer is insensitive to solid body movement of the

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operator or shaft, hand holding the instrument can produce a tilt of the laser beam plane.A tilting motion of the operator or shaft rotational axis will modulate the Dopplerfrequency fD as a result of changes in u as defined by equation (13). For a discussion ofthese effects, readers are referred to the paper by Halliwell and Eastwood [5] and the recent

work of Miles et al. [6].Tilt effects have been shown to be negligible in practice if the instrument is used such

that the plane of the incident beams is parallel with the shaft cross-section (u=0). Theymust be considered, however, if use is envisaged at a non-zero value of u (end of shaft

use).

3. LASER TORSIONAL VIBROMETER MEASUREMENTS

3.1.

A photograph of the first prototype laser torsional vibrometer built at ISVR is shownin Figure 9. This instrument was used to measure the rotational speed variations of a discdriven by a brushless d.c. motor, the drive voltage of which was modulated by a sinusoidalvoltage. For comparison, the speed variations were also measured with a cross-beam

torsional vibrometer as described in section 2.2. In Figure 10 are shown the angulardisplacements measured by the two instruments against variations in the frequency of thevoltage supply. Agreement to within 05 dB is demonstrated over the range 30130 Hzachieved in this test. In Figure 11 two torsional vibration spectra with a fundamental

frequency of 100 Hz which were obtained in this way are compared and excellentagreement is observed.

A photograph of the commercial version of the laser torsional vibrometer produced byBruel and Kjaer Ltd of Denmark is shown in Figure 12. This is the Type 2523 TorsionalDisplacement Meter. This instrument was used to measure the torsional vibrations inducedin a rotating shaft by a Hookes joint [7] which provides a means of checking the levelsof torsional vibration velocity. With reference to Figure 13, speed fluctuations aregenerated in the driven shaft due to the time-variant torque transmission characteristicsof the Hookes joint. The amplitude of the fluctuations depends upon the angle f shownin the figure and the amplitude of the second order fluctuation is readily calculated [7].When the driven shaft is measured by the Type 2523 comparison between experiment andtheory is straightforward. The results of this comparison are shown in Figure 14 where

Figure 9. The prototype laser torsional vibrometer.

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Figure 10. A comparison of results from the cross-beam velocimeter (W) and laser torsional vibrometer (w).

the abscissae represents negative and positive inclination angles f and the ordinaterepresents angular displacement in degrees peak. Experimental results are shown formeasured values of the second order of torsional vibration at three different speedsof rotation. These results demonstrate the accuracy and consistency of the TorsionalVibration Meter Type 2523. The theoretical curve is independent of the rotational speedand consequently the arbitrarily chosen rotational speeds all provide the samemeasurement results to close agreement. This demonstrates the capability of the TorsionalVibration Meter Type 2523 precisely to measure the torsional vibration experienced by anyrotating component.

3.2. :

The majority of diesel engines require some form of damping or detuning device to befitted in order to prevent the build-up of large vibration amplitudes and stresses at torsional

resonance. Two basic designs are in common use, these being the viscous shear damperand the elastomeric (rubber) equivalent. The former is the usual choice for higher poweroutput engines because of its superior heat dissipation capability, while the latter is acomparatively cheap unit and is very popular for automotive type engines. The lasertorsional vibrometer has provided a means of assessing the performance of a torsionalvibration damper in situ, and readers are referred to the papers by Halliwell and Eastwood[8, 9] for a full description of this application.

With reference to Figure 15, elastomeric dampers consist of a heavy seismic mass(the inertia ring) and a relatively lighter hub which is attached to the free end of the

engine crankshaft. The two members are coupled by an elastomer element which providesstiffness and damping. A vibration damper of this design, therefore, adds another massand elasticity to the basic equivalent dynamic system of the engine and introduces anadditional torsional natural frequency. It therefore has a tuning capability.

Laser torsional vibrometry was used to assess the performance of an elastomeric(bonded rubber) damper which was fixed to the end of the crankshaft of a six-cylinderturbocharged diesel. A simple, two-mass model [8] of the crankshaft system predicted twotorsional resonances excited by the ninth order harmonic at engine speeds of 1050 rpm and

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Figure 11. A comparison of torsional vibration spectra. (a) Laser torsional vibrometer; (b) cross-beamvelocimeter.

1850 rpm respectively. This theoretical result is shown in Figure 16. For comparison, inFigure 17 is shown an experimentally determined ninth order plot obtained by using a lasertorsional vibrometer, which verifies the use of the model for resonance prediction to within5% error.

Loss of elastomeric damper performance can be attributed to changes in the materialproperties of the elastomer element over time. In particular, changes in the stiffnessprovided by the damper under optimal conditions will rapidly produce a decline inperformance through de-tuning. It is well known that stiffness of the element changes withtemperature and, consequently, monitoring the performance of a damper from cold start

of the engine to normal operating conditions would represent that which might beanticipated from a damper progressively degrading with age and/or wear. It should benoted, however, that in the former case the behaviourial trend will occur in reverse andat a greatly accelerated rate.

Two laser torsional vibrometers simultaneously measured the response of the hub (u)and the inertia ring (ud). Data was recorded immediately following engine start-up andsubsequently after intervals of ten minutes. The results are presented in Table 1. For theengine under test, the sixth order was monitored at an engine speed of 1895 rpm.

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Figure 12. The Bruel & Kjaer type 2523 Laser Torsional Displacement Meter.

Figure 13. The Hookes joint checking method.

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Figure 14. A measurement comparison with Hookes joint predictions. , Theoretical; , 700 rpm;W , 100 rpm; q , 1300 rpm.

Figure 15. The elastomeric damper.

Measurements obtained after a period of 30 minutes are omitted since after this time theratio (ud/u) remained constant.

For the two-mass model [8] these results show that a change in stiffness of thedamper element of approximately 62% has occurred between cold and stable operatingconditions. Such a difference is not uncommon; manufacturers report differences of over100% in some circumstances.

4. PRACTICAL CONSIDERATIONS

4.1.

It is the dynamics and characteristics of the laser speckle pattern [2] collected by thephotodetector which dictate the sensitivity of the laser torsional vibrometer. This isbest understood by considering the geometry of a standard laser vibrometer as shown inFigure 5 and analyzing the sensitivity of this device.

When engineering target surfaces which are rough on the scale of the optical wavelengthscatter coherent light, a speckle pattern forms in space in front of the target. This can be

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Figure 16. The theoretical prediction of ninth order torsional vibration [8, 9].

observed on a screen as a continuous random array of dark and bright spots which havea grainy speckly appearance and hence the name laser speckle pattern. The phenomenonoccurs because each scattering surface element within the laser spot acts like a pointsource of coherent light. At a point in space, individual scattered wavelets from thesesources interefere constructively or destructively to produce the bright or dark speckle,respectively, which is observed on the screen. The speckle pattern is a continuous randomdistribution of light amplitude and phase although in practice we simply observe the

corresponding intensity distribution.An average speckle size can be calculated and attributed to the distribution observed

on the screen [10]. Within this correlation region the amplitude and phase of the light maybe assumed to be constant. In laser vibrometry, the photodetector active area in the

instrument is sampling a speckle pattern. One or more speckles may be sampled, dependingupon the optical geometry used in a given measurement situation and also the collectingoptics used (if any) for the scattered light. If the detector area collects several speckles,the current output is proportional to the instantaneous sum of the intensity distributionwhich has been sampled.

Figure 17. As Figure 16, but experimental measurement.

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T 1

The simulation of elastomeric torsional damper failure

Amplitude of sixth order

torsional harmonic(degrees)ZXXXXXCXXXXXV Amplitude

Elapsed time from Damper Inertia ratio,cold start (mins) hub, u ring, ud ud/u

0 increasing 0497 1179 23710 stiffness 0251 0923 36820 3 0226 0899 39830 0179 0774 433

When a frequency-shifted reference beam is superposed onto the photodetector, aheterodyne beat occurs as described in section 2.1. For simplicity, consider what happenswhen the reference beam has a constant spatial phase distribution across the dector areaand the target is stationary. It is useful to think of each speckle region as an interferometerwhich has a distinct value of intensity and phase. In practice, the detector output is theresultant vector addition of the outputs from all these separate interferometerscorresponding to each speckle collected. In this way, for a stationary target the output fromthe detector is at the beat frequency with a constant amplitude and phase.

When the target moves normal to surface and parallel to the incident laser beam, theDoppler effect produces a uniform rate of change of phase across the detector area anda pure frequency modulation of the detector output occurs with negligible amplitude

modulation. A word of caution is necessary here. Speckles form small, continuouscigar-shaped volumes in space and the detector plane effectively moves along the major

Figure 18. The torsional vibration spectrum: speckle pattern periodicity.

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In practice, the photodetector takes the sum ofIp (t) over its active area A, and one musttherefore consider the spatial distributions ofIR and IT and their respective phases fR andfT. For convenience, one can assume that reference beam intensity and phase is uniformin space and one need consider only the speckle pattern distribution. Accordingly, one can

write the detector output current i(t) as

i(t)=gA [IR+IT(a)+2zIRIT(a) cos $vRtgvT dt+fRfT(a)% dA, (16)where A is the photodetector area, IT(a) is the speckle intensity distribution and fT(a) isthe speckle phase distribution. Examination of equation (16) confirms the earlier discussionthat if the spatial distribution of the speckle pattern changes during a measurement period(i.e., ifIT(a) and fT(a) are functions of time) then spurious information will be contributedwhen i(t) is frequency demodulated. Unfortunately, in practice, this noise is usually linkedto the vibration frequency of interest, introducing uncertainty into the measurement.

When a laser vibrometer is pointed at a rotating target, the spatial and temporalcharacteristics of the speckle pattern sampled by the photodetector change with time.With reference to equation (16), the terms IT(a) and fT(a) describing the speckle patternintensity and phase distribution across the detector surface become periodic at the rotationfrequency and are demodulated as pseudo-vibration. Consequently, when the target

surface is not vibrating but simply rotating, the laser vibrometer will produce a noise floorwhich has a spectrum typical of a pseudo-random signal. This consists of a fundamentalat the rotation frequency and higher order harmonics of similar magnitude. It is producedbecause the changing speckle pattern produces random phase and amplitude noise whichrepeats exactly in sympathy with the rotating target. For a further discussion of this effect,the reader is referred to the papers by Rothberg et al. [1113].

Unfortunately, in practice, the vibration frequencies of interest are usually direct integermultiples of the rotation frequency and consequently the distribution of this speckle noiseis a worst possible case. It is at this stage that a degree of engineering judgement is required

before deciding whether the vibration levels measured in a given bandwidth are not thoseassociated with the pseudo-vibration of speckle noise. Users need to be wary of the verylow noise floors and sensitivities quoted by instrument manufacturers in the literature.These have usually been measured on a stationary target and, in practice, as discussed in

the last section, the true noise floor is peculiar to the speckle pattern behaviour caused bytarget surface dynamics during the actual measurement.

For the laser torsional vibrometer, and with reference to Figure 8, the photodetectorcollects two speckle patterns from points A and B which then heterodyne on its active area.If the target component has no torsional vibration whatsoever, the frequency spectrum ofthe instrument output due to the steady rotation will take the form of a periodogram atthe fundamental rotation frequency. An example of this is shown in Figure 18, where theinstrument was used to measure the speed fluctuation of a d.c. motor from a tape recorderdrive. The displacement spectrum shown clearly exhibits the periodic nature of the speckle

noise which completely masks the intended measurement.Fortunately, the insensitivity of the instrument to solid body oscillation means that the

speckle periodicity can be destroyed by moving the laser beam plane during the course ofthe measurement. Hand holding the instrument and moving the beams from side to side

means that the speckle pattern incident on the photodetector does not exactly repeat. InFigure 19 is shown the equivalent measurement taken on the d.c. motor when the incidentlaser beam plane was moved from side to side at very low frequency of about 1 Hz. Thefigure shows the effect of removing the speckle pattern periodic noise, in this way, and

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the wow of the motor can now be distinguished. For most mechanical engineeringapplications, a level of 60 dB re 1 peak means that torsional vibrations have ceased tobe a problem and therefore speckle periodicity is not troublesome.

The Type 2523 Laser Torsional Vibration Meter has a noise smearing facility. This

is intended for use at very low levels of torsional vibration and allows the speckle patternperiodicity to be destroyed by modulating the spatial position of the incident laser beamsfrom side to side in a random manner. It is not necessary to use this when measuring levelsgreater than 40 dB re 1 peak displacement, which is normally the case in practice.

4.2.

In practice, the highest levels of torsional vibration will be found in the crankshafts oflarge diesel engines of reciprocating compressors. These may be as high as a few degreesof peak displacement, but in frequency terms these levels still represent a relatively smallmodulation of the mean beat frequency resulting from the target speed. Consequently,measuring high levels does not present a problem, and it is simply necessary to ensure thatthey are within the frequency response range of the Doppler signal processor.

It is the range of possible rotational speeds which represents much more of a practicalproblem for signal processors. At a beam separation of 1 cm for beams perpendicular tothe rotational axis (u=0), speed variation of 500 rpm to 15 000 rpm produces a beatfrequency range of 15 MHz to 45 MHz! The theory for the instrument is developed on

the assumption that the incident laser beams are infinitely thin and therefore, by an orderof magnitude argument, a minimum beam separation of one cm is required. The lowerspeed range can therefore be extended by widening the beam separation in order to matchthe input bandwidth of the processor. At the higher rotational speeds, using the instrumentso that the incident laser beam plane is at an angle to the rotational axis will reduce themean beat frequency. In this situation, care should be taken to account for the effects ofoperator or component tilt [5, 6].

When a low powered heliumneon laser is used as a light source so that the outgoingbeams have about 1 mW power, the target distance for operation is up to several metres,

but retroreflective tape or paint must be used.Calibration of the laser torsional vibrometer should be carried out in situ. It is notnecessary to attempt to measure the beam separation d or angle of inclination of thenormal to the laser beam plane u with the rotational axis. In most circumstances it is

possible to rotate the target at several known speeds so that an in situ calibration of meand.c. volts per rpm is possible.

If it is not possible to rotate the target at known speeds, then a small disc can be used,which is driven at known speeds and interposed in the laser beams in place of the target.It is only necessary to monitor the d.c. voltage from the instrument at three known speedsto produce a calibration factor giving negligible error. It is usual to output the instrumentsignal straight to a real time spectrum analyzer which will integrate the output directly toproduce vibration spectra in terms of torsional vibration displacement. The alternative, ofcourse, is to tape record the analogue output on site for later analysis, but it must be

remembered that the d.c. level is important if an in situ calibration has taken place.

5. CONCLUSIONS

The problems of torsional vibration measurement have been solved by the invention ofthe laser torsional vibrometer. The use of optical, seismic and mechanical torsiographs,together with strain gauges, slip rings and slotted discs, has now been overtaken by theuse of laser technology. The laser torsional vibrometer offers in situ measurement, thus

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avoiding machinery downtime and can function on rotating components of arbitrary shapewhilst maintaining an immunity to solid body motion of the operator or component. Theinstrument is robust, user friendly and can be calibrated in situ.

Invented at ISVR in 1983 and subsequently produced commercially by Bruel and Kjaer

Ltd of Denmark as the Type 2523 Torsional Displacement Meter, the vibrometerrepresents a significant step forward in rotating machinery diagnostics. It is now used ona worldwide basis and is rapidly gaining acceptance as the standard means of measuringtorsional vibration.

ACKNOWLEDGMENTS

The author wishes to acknowledge the provision of Hookes joint results by T. J. Miles.

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6. T. J. M, M. L and S. J. R 1995 Proceedings of the ASME 15th BiennialConference on Mechanical Vibration and Noise Boston , U.S.A., September 3(C), 14511460. Thelaser torsional vibrometer: successful operation during lateral vibrations.

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