Modal analysis of ultrasonic block horns by ESPI

Ultrasonics 37 (1999) 149–157

Modal analysis of ultrasonic block horns by ESPI

G. Graham a, J.N. Petzing b,*, M. Lucas ca Department of Mechanical Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK

b Department of Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UKc Department of Mechanical Engineering, University of Glasgow, Glasgow, G12 8QQ, UK

Received 4 July 1997; received in revised form 4 August 1998

Abstract

Slotted block horns are used in many high power ultrasonic tools, to achieve a uniform vibration amplitude across a wideoutput face. Finite element (FE) analysis is an established method for designing tuned block horns and for the prediction anddesign of horns with a well isolated tuned operating mode. Validation of FE models has relied on pointwise, non-contact, normal-to-surface vibration measurements, which have proved far from ideal in the analysis of horns tuned to deliver predominantlyin-plane surface vibration responses in the longitudinal mode.

This paper presents the results of a modal analysis of an ultrasonic block horn using electronic speckle pattern interferometry(ESPI ) to measure three mutually orthogonal components of surface vibration response. By monitoring an electrical input signalfrom the ultrasonic transducer, frequency response function data is obtained by fringe processing of the raw, wholefield ESPIdata, such that subsequent extraction of the modal parameters is achieved by utilising the facilities of commercial modal analysissoftware. Measurement of the surface in-plane and out-of-plane response of the block horn allows all modes to be identifiedsuccessfully and enables correlation with FE models. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Analysis; ESPI; Interferometry; Machining; Optics; Ultrasound

1. Introduction changes over the data recording period often occur dueto external influences, such as thermal effects and adjust-

Modal testing using point-wise measurement tech- ments in the excitation injection point, and the require-niques is commonly used, in conjunction with spectrum ment for a predetermined mesh of the test piece alsoanalysers and modal analysis software, to characterise introduces alignment and sensitivity errors.the dynamic behaviour of structures. Frequency Examination of high power ultrasonic machiningresponse function (FRF ) measurements, recorded by components designed to operate at 20 kHz or aboveaccelerometers or laser Doppler vibrometers (LDV ), compounds the analysis procedure. The operationalprovide data which are used to derive the modal charac- mode of many such components is predominantly longi-teristics from normal to surface measurements. Although tudinal in-plane, yet most accelerometers and LDVs areLDV instruments that can measure the in-plane response only responsive to normal-to-surface displacements (out-are now commercially available, a prerequisite for point- of-plane). Moreover, the high surface accelerations ofwise modal analysis is a grid of data points to allow the high power ultrasonic components tend to eject acceler-interpolation of a wholefield response for the object and ometers and, until recently, the frequency response cut-this generally requires repetitive experimentation with off for many of the LDV models was 20 kHz, therebythe transducer being relocated on the mesh between making reliable measurement problematic.experiments. Disadvantages of this methodology arise Recently completed research [1] has demonstrated abecause of the need to estimate an appropriate mesh technique for obtaining wholefield modal data usingbefore the modes are known, which can result in missing electronic speckle pattern interferometry (ESPI), withessential data points from the grid. Further, response the initial work being completed on a clamped mem-

brane. This method relies upon wholefield laser illumina-tion and the generation of correlation fringe patterns* Corresponding author. Fax: +44 1509 223934;

e-mail: [email protected] describing surface displacement vectors. A dense mesh

0041-624X/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.PII: S0041-624X ( 98 ) 00050-X

150 G. Graham et al. / Ultrasonics 37 (1999) 149–157

of data points (up to 512×512) grabbed simultaneously, This unit is specifically designed to resonate in the firstorder longitudinal mode at 20 kHz. For this mode, thesubstantially reduces the time required to record modal

test data, and provides the basis for displacement and longitudinal displacements will occur along the X-axisin Fig. 1, whilst Poisson motion will be observed on thevibration phase information. The application of ESPI

has been extended from the simple out-of-plane (one- main face of the horn as having mainly an in-planecomponent in the Y-direction and an out-of-plane com-dimensional ) analysis of a clamped plate, to the three-

dimensional analysis of a high power ultrasonic machin- ponent in the Z-direction.ing block horn, with specific interferometers measuringthree mutually orthogonal components of surface vibra- 2.2. Modal analysistion response (out-of-plane, horizontal in-plane andvertical in-plane data). The primary reason for generating modal analysis

data is to allow the validation of finite element analysis(FEA) models of the component in question. The limita-tions of boundary modelling approximations in all FEA2. Theorysoftware packages means that predicted componentbehaviour can have a poor correlation with actual2.1. Ultrasonic componentscomponent behaviour. In order to improve model con-fidence, it is necessary to generate experimental resultsUltrasonic machining systems of all types have

common design foundations. Components are generally which will allow a comparison of not only modalfrequencies but also mode shapes. Once these have beenhalf-wavelength units or multiples thereof, usually based

around the axial longitudinal velocity of sound [2] obtained, then the FEA model can be improved. Furtherreasons for mode shape comparison are to determinewithin the respective component material (usually an

aluminium or titanium alloy), although certain systems whether two adjacent modes are significantly differentand to compare different sets of test data from the sameare noted for employing radial modes of vibration for

operation [3]. Fig. 1 shows a three dimensional represen- structure having undergone some form of designalteration.tation of a typical HE15 aluminium alloy ultrasonic

block horn (136 mm×122 mm×70 mm). The ‘half- A common technique for mode shape comparison isthe modal assurance criterion (MAC), which provideswavelength’ length of the unit is immutably dependent

on the speed of sound within the aluminium alloy. a measure of the least square deviation from a straightline correlation, and is analogous to the scalar productLateral dimensions and features such as slots and flanges

can be altered to suit the application in question and between two unit vectors. If the two vectors comparewell, then the product is close to unity and if they areoptimise the performance of the ultrasonic component.

Fig. 1. Block horn schematic.

151G. Graham et al. / Ultrasonics 37 (1999) 149–157

perpendicular, then the product is zero. When perform- previous optical design, the speckle pattern observed onthe block horn is recorded at the image plane of theing a MAC operation with two or more mode shapes,

two identical modes will result in a MAC value of 1.0 CCD-TV camera and is then post-processed in order togenerate the correlation fringes describing in-plane dis-and if they are strongly dissimilar, the MAC value will

be close to zero. A MAC value of less than 1.0 can placement. The in-plane interferometer may be usedwith the object beams horizontally orientated to recordoccur when expecting a strong correlation for a number

of reasons, such as non-linearities in the test structure, horizontal in-plane displacement components (X-axis)and with the object beams vertically orientated to recordnoise contamination of the measurement or comparing

mismatched data sets. vertical in-plane displacement components (Y-axis).For both forms of interferometer, the total light

received at the image plane from the two illuminating2.3. Electronic speckle pattern interferometrywavefronts is U1+U2=UT. More importantly, the inten-sity of the light (I ) for any point at the image plane isElectronic speckle pattern interferometry (ESPI), or

less commonly TV-holography, is the name given to proportional to the square of the total light field, i.e.13UTUT*, which, via mathematical manipulation, canseveral laser speckle-based techniques which are used

for measuring discrete displacement components. Two be reduced to a term synonymous with speckle met-rology:different optical designs are available; one to produce

out-of-plane (OOP) displacement data and the other toIA=I

1+I

2+2EI

1I2

cos y. (1)produce horizontal and vertical in-plane (HIP and VIP,respectively) displacement data, all of which rely on

In this instance, the descriptor IA is used as a means ofCCD-TV cameras at the image plane for the recording

identifying the intensity distribution of the object in itsof data [4,5]. A schematic of the out-of-plane ESPI

initial state.system used for the modal analysis is shown in Fig. 2,

If the object receives a dynamic displacement (but ashowing the illuminating object wavefront, the camera

pulsed laser is used to strobe the surface with the correctaxis and the reference wavefront. The speckle pattern

synchronisation), an optical phase change, D(x, y) isobserved on the block horn is recorded at the image

introduced into the object wavefront due to the displace-plane of the CCD-TV camera and is then post-processed

ment. Using the same arguments as for the initial objectin order to generate the correlation fringes describing

state, the new intensity distribution at any given pointout-of-plane displacement (Z-axis).

can be described as:A different optical design is required for the measure-

ment of the in-plane displacement components and is IB=I1+I

2+2EI

1I2

cos(y+D ). (2)shown in Fig. 3. In this system, two illuminating wave-fronts are used for the block horn at equal but opposite The interferometer data are displayed on a TV moni-

tor as correlation fringes, which may be formed via aangles to the surface normal camera axis. As in the

Fig. 2. Out-of-plane ESPI system schematic.


Fig. 3. In-plane ESPI system schematic.

subtraction process using software or hardware based Quantitative wholefield data is generated by applyingphase-stepping techniques to the subtraction ESPI corre-frame stores. For subtraction fringes, the change of

intensity between the initial object state and the dis- lation fringes [6 ]. Initially grey scale maps (0–255) ofoptical phase are produced, which are then calibratedplaced state (dI=IA−IB) is produced by storing the

initial undisplaced intensity distribution as a reference with respect to the interferometer used [Eqs. (4) and(5)], resulting in wholefield-calibrated displacement andimage and subtracting all subsequent displaced intensity

distributions from this reference. This process is vibration phase data sets and plots.described mathematically as:

dI=4EI1I2

sin(y+D ) sinD

2. (3) 3. Experimentation

This brief summary of laser speckle physics describes The object analysed using the wholefield optical tech-the formation of the correlation fringes. Knowing the nique was a 136 mm aluminium alloy block horninterferometer sensitivity function, the optical phase attached to a Branson Ultrasonics 2 kW piezo-ceramicchange (and fringe order) for the out-of-plane interfer- transducer. Electrical energy and input control wasometer can now be directly related to out-of-plane provided by a Hewlett Packard HP3330A frequencydisplacement (w), such that: synthesiser via an FFR Autotuner, acting as a power

amplifier. The frequency synthesiser also provided anw=

nl

2(4) input reference signal for monitoring and for laser

synchronisation.The wholefield analysis of the block horn used anwhere n is the fringe order number and l is the laser

out-of-plane (OOP) ESPI interferometer and an in-planewavelength.(IP) ESPI interferometer with a pulsed Nd:YAG laserSimilarly, for the in-plane interferometer, the opticalas the illumination source (l=532 nm at 25 Hz). Aphase change (and fringe order) can be related to theschematic of the experimental apparatus is shown inhorizontal and vertical in-plane displacements (u and v,Fig. 4. The pulsed laser was used in order to avoid therespectively), such that:generation of time-averaged interferograms typical of acontinuous wave (CW ) laser-based analysis, althoughu=

nl

2 sin h, v=

nl

2 sin h, (5)

synchronization of the pulsed laser with the TV camera


Fig. 4. Schematic of experimental apparatus.

Fig. 5. Out-of-plane block horn resonant mode fringe pattern.


Fig. 6. Horizontal in-plane block horn resonant mode fringe pattern.

and the block horn resonant frequency was necessary, 4. Experimental resultsin order to obtain consistent stationary fringe pattems.

4.1. Wholefield optical analysisThe phase-stepping operations were controlled from aPC-based ITI 15040 image processing system, which

An example of the out-of-plane ESPI analysis iscalculated the optical phase distribution and producedprovided in Fig. 5, which shows a subtraction correlationthe calibrated 512×512 data files. The software usedfringe pattern, each fringe delineating constant out-of-for the modal analysis was Star Modal, which wasplane displacement. Similar data was produced from thelimited to a total of 200 input data points. Therefore,in-plane ESPI interferometers and examples of thesethe wholefield optical results required sub-sampling tofringe patterns are shown in Figs. 6 and 7. Processingproduce a 14×13 mesh of data, via conversion routinesthis correlation speckle information via the image pro-completed in Matlab. The grid of data points is thereforecessing equipment leads to calibrated displacement andlimited in this case by the modal analysis software butvibration phase data. It should be noted that the vibra-

for general measurement purposes, it is only limited bytion phase data is an implicit function of the correlation

the number of pixels. fringes. Uncertainties contained within these data setsThe block horn was excited at resonance, and phase- are primarily a function of fringe contrast and the

stepped subtraction correlation fringe patterns were inherent speckle noise associated with the wholefieldobtained using the out-of-plane and in-plane optical optical technique. Low pass Fourier-based filtering wasconfigurations. This data was passed into the Star Modal used before optical phase calculation in order to improvesoftware, where the mode shape of the ultrasonic unit the fringe signal-to-noise ratio (SNR) and reduce thewas derived, allowing visualisation of block dynamics influence of the speckle noise on the final result.in three dimensions. Using existing modal data obtained However, some noise is still a feature of the wholefieldfrom LDV analysis, a MAC comparison could be com- displacement data sets in terms of local variations in thepleted, allowing an assessment of the quality of the surface displacement form but these are small with

respect to the amplitude of the motion recorded.wholefield optical data.


Fig. 7. Vertical in-plane block horn resonant mode fringe pattern.

The primary benefit of the ESPI analysis is the target simultaneously, thereby reducing the analysis toone operation, and reducing the requirement of multiplewholefield generation of modal data during the course

of one experiment, which can provide a maximum of experiments. This step was not taken during the workbecause it is optically more exacting with respect to the262 000 discrete contiguous data points (if using a

512×512 processing array system) and allows analysis interferometer and the purpose of the research did notrequire such optimisation, but the development of suchup to the boundaries of the ultrasonic block horn. An

accelerometer can typically have a base contact area of an instrument is anticipated in future work.The wholefield optical analysis of the block horn20 mm2, which limits the spatial resolution of the device,

especially close to object boundaries and can introduce generates detailed spatial information describing surfacemotion and allows mode shapes to be accurately iden-approximation errors if it is assumed to be a point

source device. LDV spot area is in the order of 3 mm2, tified even if only one surface of the object is examined,because three displacement components are measuredwhich increases the spatial resolution but is still limited

with respect to the wholefield technique. The simplest for a highly dense measurement grid. Moreover, forultrasonic applications, accelerometers have proven toform of analysis of the block horn (OOP and two IP)

required three wholefield data maps, with the analysis be problematic because the high surface accelerations at20 kHz tends to dislodge the devices.performed sequentially and data obtained inside sev-

eral seconds.The second benefit of the wholefield ESPI technique 4.2. Mode identification and MAC comparison

is the ability to discretely measure in-plane displacementcomponents, as well as out-of-plane displacement com- The ESPI data was sub-sampled to reduce the mesh

density to 13×14 and transferred into the modal analysisponents. The block horn experimentation was completedsequentially, measuring out-of-plane, horizontal software (Star Modal ). The out-of-plane and in-plane

displacement components were then analysed by thein-plane and then vertical in-plane surface characteris-tics, using separate optical systems. It is feasible to software, allowing the generation of a dynamic modal

mesh depicting three-dimensional surface displacement.combine the two in-plane interferometers and the out-of-plane interferometer such that they are examining the An example of this is provided in Fig. 8, showing the


Fig. 8. Out-of-plane block horn displacement mesh plot.

undeformed mesh on the left and the deformed mesh to correlate in-plane modes using MAC to provide ameaningful assessment of model accuracy. The MACon the right of the diagram. The deformed mesh is

predominantly displaying longitudinal in-plane displace- data for the in-plane operational mode of the ultrasonicblock horn is given in Table 2.ment and out-of-plane Poisson displacement, causing a

bowing of the block horn surface. The 79% correlation shown by the modal analysissoftware provides a realistic assessment of the qualityFurther modal analysis of the ESPI data was com-

pleted by correlating with FEA and LDV data gathered of the model and also demonstrates the quality of thewholefield experimental data even at this early stage offrom the face of the block horn. These were compared

using MAC and the results are shown in Table 1. This the technique’s development. It is expected that thiscorrelation can be improved by increasing the densitymethod provides a quantitative measure of the mode

correlation between the experimental and modelling of experimental data used in the MAC, although this islimited in this case by the modal analysis software, andtechniques, but is somewhat limited in this case because

the LDV measurements are only for OOP response data. by improving boundary approximations at the excitationinjection point in the FEA model.Therefore, the comparison in the MAC table is purely

for this measured displacement component. However, itshould be emphasised that ESPI is able to measure thethree displacement components (as demonstrated in this 5. Conclusionswork), and consequently can be used to provide a morerealistic correlation with the FEA model, which also Wholefield modal analysis has been performed on an

ultrasonic block horn operating at 20 kHz, by integ-estimates the three displacement components of theobject surface dynamic behaviour. rating wholefield electronic speckle pattern interferome-

try data with a commercial modal analysis softwareInterpretation of the data in Table 1 is self evident,with an 82% correlation between FEA and ESPI and package. The spatial advantages of the wholefield tech-

nique have been demonstrated compared with the exper-an 85% correlation between LDV and ESPI. The impor-tant aspect of this data is that a correlation has been imentally intensive and potentially error prone, single

transducer approaches. The inherently fast data collec-calculated on the basis of the out-of-plane response, butthe mode is dominated by in-plane motion. It is therefore tion feature of this ESPI analysis, relying upon single

TV-camera frames of data, will allow the extension ofinadequate to use this data as an indicator of the qualityof the FEA model, even when the correlation appears the technique to the modal analysis of components in

regimes where boundary conditions can only be stabi-to be better. Using the ESPI measurements, it is possiblelised for short periods of time.

Table 1MAC comparison of block horn operational mode (OOP only) Table 2

MAC comparison of block horn operational mode (IP only)Block horn operational mode ESPI FEA LDV

Block horn operational mode ESPI FEAESPI 1.00 0.82 0.85FEA 0.82 1.00 0.92 ESPI 1.00 0.79

FEA 0.79 1.00LDV 0.85 0.92 1.00


The generation of wholefield out-of-plane and to thank Mr V. Scothern and Mr I. Tullis for theirin-plane surface displacement data allows the complete technical expertise and assistance.characterisation of ultrasonic block horn modes for eachmodal frequency from one block surface, by measuringthree components of surface vibration response at eachfrequency. The MAC results indicate that the ESPI datacorrelates well with FEA and LDV techniques, and that ReferencesESPI provides advantages of high measurement datadensity for three components of surface response. This [1] G. Graham, J. Petzing, M. Lucas, J. Tyrer, Wholefield modal

analysis using electronic speckle pattern interferometry, in: 2ndis vital for assessing the accuracy of FEA models forInternational Conference on Vibration Measurements by Laserpredicting in-plane operational characteristics of highTechniques – Advances and Applications, Ancona, Italy, 1996,power ultrasonic system resonant components. ESPISPIE 2868, pp. 352–361.can be used as an experimental technique to enhance

[2] G.M. Chapman, M. Lucas, Frequency analysis of an ultrasonicallythe model updating of FEA models which, until now, excited thick cylinder, International Journal of Mechanical Scienceshas been limited by the directionality of the experimental 32 (3) (1990) 205–214.measurements. The ability to measure the three dynamic [3] L.D. Rosenberg, V.F. Kazantsev, L.O. Marakov, D.F. Yakhimov-

ich, Ultrasonic Cutting, Consultants Bureau Enterprises, Newcomponents of displacement, and interface these withYork, 1964.existing modal analysis software, provides a powerful

[4] R. Jones, C. Wykes, Holographic and Speckle Interferometry, 2ndtool to greatly improve the reliability of FEA models.ed., Cambridge University Press, Cambridge, UK, 1989.

[5] D.C. Williams, Optical Methods in Engineering Metrology, Chap-man and Hall, London, 1993.

Acknowledgements [6 ] D.W. Robinson, G.T. Reid, Interferogram Analysis; Digital FringePattern Measurement Techniques, Institute of Physics Publishing,Bristol, UK, 1993.The authors wish to acknowledge the support of

EPSRC and Nestle Plc for this research, and would like

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Modal analysis of ultrasonic block horns by ESPI