R. Sancibriaif, E. Oilier, A. Fernandez · 2014. 5. 14. · Theoretical and experimental results of the mechanical behaviour for a new optical accelerometer F. Viadero, P. Mottier\

$Page 1: R. Sancibriaif, E. Oilier*, A. Fernandez · 2014. 5. 14. · Theoretical and experimental results of the mechanical behaviour for a new optical accelerometer F. Viadero*, P. Mottier\$
Theoretical and experimental results of the

mechanical behaviour for a new optical

accelerometer

F. Viadero*, P. Mottier\ R. Sancibriaif, E. Oilier*, A. Fernandez"

and F. Enemas*

"Department of Structural Design, E.T.S. de Ingenieros Industrials

y de Telecomunicacion. University ofCantabria, Avda.. de los

Castros, sin, 39005 Santander, Cantabria.

LETIICEA, Departement Microtechnologies CEA-Grenoble, 38054GRENOBLE Cedex 9, FRANCE.

b

AbstractIn this paper a correlation between the theoretical (FEM Analysis) and experimentalmechanical behaviour of a new accelerometer optical head is presented. The dynamic responsein the frequency range of interest has been studied. The development of accelerometers basedon optical technology could have an interesting application because this kind of accelerometeris capable of working in environments which have high magnetic fields. The accelerometer isa device based on the theory of the seismic mass transducer (SMT). The design of this opticalaccelerometer is based on a cantilever beam; measuring the movement of the end of this beam,it is possible to determine the movement of the fixed point of the mounting. This theory (SMT)establishes that this device measures displacements when it works beyond its first resonancefrequency and accelerations when it works below. Owing to this, it is very interesting to knowabout the behaviour, especially to know the first resonance frequency and its correspondingmode and the effects of the rest of the modes on this one. In this paper an analysis will bepresented of a new optical accelerometer, using the Finite Elements Method, in order todetermine its modes and resonance frequencies. The FE model and the results obtained fordifferent excitation loads will be described. The aim of this kind of analysis is to allow themodification of the design in order to improve its capabilities. The experimental results havebeen measured on several new optical vibration sensors that have been developed by CEA-LETI (France), employing a calibration system to determine their sensitivity curves. Theresulting curves will be shown in order to compare them with the theoretical and experimentalresults. Both theoretical and experimental results are similar and demonstrate the adequateselection of the FE model, and the good capabilities of the optical head.

Transactions on Modelling and Simulation vol 16, © 1997 WIT Press, www.witpress.com, ISSN 1743-355X

266 Computer Methods and Experimental Measurements

1. Introduction.

The development of optical technology has made it possible to build sensorsbased on optical properties. These devices have an interesting feature; they areable to work in environments which have high magnetic fields as are usual in theindustrial environments. This feature is very interesting in the particular field ofvibration measurement, specifically accelerations, on industrial machinery.

The principle of operation of an accelerometer is based on the behaviourof a mechanical system made up of a mass, a rigid element and a dampingelement. In this case and given that the optical devices typically have smalldimensions, we are confronted by a mechanical microsystem with the inherentdifficulties this entails. Therefore, it is necessary to model its behaviour preciselywith the aim of correlating the theoretical knowledge with the experimentalresults thus permitting the introduction of improvements in its behaviour as asensor.

The seismic mass transducer principle can be used to measuredisplacement, velocity and acceleration depending on the dimensions,characteristics of the material used in the device manufacture and the frequencyrange of operation.

Initially it is necessary to determine the first resonance frequency of thesystem since this will establish the limit between displacement or accelerationmeasurement.

In practice a real system does not behave as a system of one degree offreedom (as is established in SMT) but as a continuous system and so, it has aninfinite number of natural frequencies and associated modes. This factcomplicates the analysis since it is possible that the movement of the system isstrongly influenced by modes greater than the first and in this case thedisplacement of the seismic mass will not be proportional to the acceleration ofthe support. It is therefore necessary to cany out a detailed analysis of thedesign, in order to predetermine its possible frequency range (generally 1/5 or1/3 of the first natural frequency depending on the manufacturer [1]) and toensure that the superior modes do not interfere with the system behaviour.

Given that the operation principle of the sensor is based on the luminousintensity captured by two receptors which are situated in the plane of movementcorresponding to the first mode, it is very interesting to study the possibleinfluence that the modes (developed in transverse planes) can have on the systembehaviour. A great influence of these modes can condition the transversesensitivity of the design so this must be taken into account.

In this paper a F.E. model of the head produced by CEA-LETI has beendeveloped. The different natural frequencies have been determined theoreticallyalong with the associated modes. Furthermore, it is possible to predict theeffects of the rest of the modes on the first mode and other characteristics whichcan allow the improvement of the original design.


Computer Methods and Experimental Measurements 267

2. Operation Principle.

In optical sensors the physical magnitude to be measured alters some propertiesof the light, normally supported by an optic fibre. The altered property can be:

• Intensity (intensity modulation sensors)• Polarisation (polarimetric sensors)• Phase (interferometric sensors)

The accelerometer analysed in this paper is the intensity modulator type.The design is based on the fibre fixed at one end with the free end moving inrelation to two other fixed fibres which act as receptors [2]. The moving fibre isconnected to a light source. This configuration produces a variation of the lightcoupling between the free end and each one of the fixed receptors depending onthe displacement among the ends. In figure 1, the variation of the luminousintensity is shown as a function of the displacement among the fibre ends.

Input Guide

Output Guide

Figure 1: Variation of luminous intensity with displacement

In this way knowing the difference between the output intensities of thereceptor fibres it is possible to determine the displacement of the moving fibre. Ifthe displacement is known, by applying the SMT, it is possible to determine theacceleration of the fixed point in which the fibre is embedded.

In this case the fibre acts as the seismic mass while the stiffness anddamping of the set depends on the material properties and specific dimensions ofthe fibre. The basic scheme can be seen in figure 2. If the moving guide 0, as aconsequence of an acceleration, is moved up, it gets closer to guide 1 and thecoupling of light between the guides increases, and so the signal SI will increase.On the other hand, if the moving guide 0 is displaced down, it gets closer toguide 2 in such a way that the coupling between 0 and 2 and the signal S2 willbe greater.

Input Guide 0

Output Guide 1 SI

DisplacementOutput Guide 2

Figure 2: Operation Function

3. Description of the optic fibre cantilever.

Given that in this case, the sensor is based on the movement of the end of anembedded beam, the stiffness of the system depends on the characteristics of the



material (fibre optic) and the geometry (length and section of the cantilever).The real model can be seen in figure 3. This model is made up of a centralcantilever of width 13.2 (im and length 663 (im and a set of cells composed of atotal of 14 empty hexagons whose greatest dimension is 92 jim and least is 37|im. At the junction of the hexagons a hole has been drilled 40 jam diameter. Thethickness of the model is uniform and has a value 15 |Jm

500

Figure 3: Dimensions

The reason for this geometry is that in order to increase the value of thefirst natural frequency, it is necessary to situate a mass at the free end. This iswhy the hexagonal cells have been introduced [3].

Finally, it should be highlighted that the material employed for theconstruction of this optical sensor is optical fibre, which possesses the followingmechanical characteristics:

- Young's Modulus: 7x10" N/nf- Density: 2200 Kg/nf

4. The Finite Element Model.

In order to gradually approximating the theoretical model to the real systembehaviour a series of models of increasing complexity were developed. TheANSYS 5.3 © code was used

Initially a simple model composed of an embedded beam with a pointmass at the end substituting the hexagonal cells was used. Then, another modelwith the mass divided into six distributed point masses was developed. In thesetwo analyses beam-type elements were used.

Finally, a model as similar as possible to the real one was developed. Theprocess of generation of the model is described below. In the first place theshape of the model was defined and an extrusion of it was done to achieve therequired thickness. The typB of element selected was tetragonal with ten nodessince a brick element could not be used (because or the problems ofintermeshing with irregular geometry)[4]. An adaptative mesh was used,defining the number of divisions necessary in each time.


Computer Methods and Experimental Measurements

Figure 4: F.E, Model

In figure 4 the model and mesh can be seen. The mesh was considered tobe correct even though in the central cantilever there was only one element whenat least two are necessary. However this can be considered to be valid with thistype of element [4].

5. Results obtained with the F.E. model.

5.1 Modal Analysis.

The modal analysis of the design was carried out. The results obtained areshown below and they correspond to the most complex model. Table I showsthe corresponding modes and frequencies.

Figure 5.- Mode 1, Bending XY Figure 6.- Mode 2, Bending YZ

Figure 7.-Torsion Mode



Mode123456110

Frequency (Hz)57366938139862796146826219653299622469003

Mode TypeBending XYBending XZTorsion

Second bending mode XYSecond bending mode XZSecond torsion mode

Third bending mode XZAxial

Table L- Modes and natural frequency

5.2 Response to Harmonic Excitation.

Once the modes and frequencies of vibration are known, a forced responseanalysis is carried out, using harmonic-type excitation in order to study thelinearity between the displacement of the end and the acceleration of the body.One of the simplest models was used for this study given the problems inapplying an acceleration in the bedding using ten-node tetragonal elements. Themodel used in this study is made up of 3D beam-type elements and point masses.The amplitude of the excitation introduced is 10 times the acceleration due togravity and the frequency was varied from 0 Hz to 8000 Hz. In fact, a total of800 different frequencies were analysed with increments of 10 Hz.

Freq

Figure 8: Displacements Figure 9: Error

Figure 8 shows the amplitudes of the nodes corresponding to the end andthe fixed point. The first resonance frequency can be seen clearly, where thedifference between amplitudes of the end node and base node are greatest. Thefact that a low frequencies, near zero, the graph has this form is due to themodes of the free solid. In practice these modes do not appear since the sensor issupposed to be perfectly embedded.

Figure 9 shows the magnitude of the difference between the displacementof the end node and the base node for different frequencies. For thisrepresentation, the reference value chosen corresponds to 100 Hz, showing the


Computer Methods and Experimental Measurements 271

rest of the values as a percentage deviation with respect to it. The specificexpression used is as follows.

[(End Amp-Base Amp.)-(End Amp.Ref.-Base Amp.Ref.)]%error = xi 00

(End Amp.Ref.-Base Amp.Ref.)

This graph is similar to that shown in the calibration chart of anyconventional accelerometer, although in this case the value represented on theY-axis is that of the sensor sensitivity. The sensitivity of any sensor is therelationship between magnitude generated by the sensor (in general an electricmagnitude) and the magnitude to be measured. In this case the magnitude to bemeasured is the acceleration which according to the SMT is proportional to therelative displacement between the seismic mass and the body. For this design thiscorresponds precisely to the relative displacement between the cantilever endand the fixed point. Thus the sensitivity and the relative end-base displacementare directly related.

In practice, as a general rule, an accelerometer is utilised between 0 Hzand 1/5 or 1/3 (according to the manufacturer) of its first natural frequency. Thisapproximately corresponds to the range of frequencies where its sensitivity doesnot vary more than 5 %. Given that the frequency range to be covered using thisaccelerometer is between 30 and 450 Hz, it can be considered that the design iscorrect and that it will fulfil the demands made, at least from a mechanicalbehaviour point of view.

5.3 Response to 45° Harmonic Excitation.

Using this analysis the influence of the modes in the XZ plane on the responsedue to the XY plane modes is determined. That is, if the excitation of the XZplane modes influences the total response of the system. An excessive influenceof these modes could affect the transverse sensitivity of the accelerometer andtherefore its practical use.

To analyse this influence, a force has been introduced on the beddingwhich forms an angle of 45-. Therefore, the excitation force is the sum of twoperpendicular forces.

Specifically, for the end node and for the frequency of 1000 Hz, in thecase of normal harmonic excitation the displacement is of 2.57734 (im, while forthe case of 45- harmonic excitation it is 2.57730 jim. Since the differencebetween the values is practically negligible (0.00004 |im), it is possible toconclude that the excitation of the modes on the XZ plane has no influence onthe sensor response.

6. Experimental Test.

With the aim of checking the results obtained by the F.E. analysis and given thatthe LETI prototype was available, diverse experimental tests were carried out.



The experimental tests were carried out using the sensor along with itsconditioning unit, analysing its global response. That is, the electric signalobtained at the end of the chain. This response should correspond to themechanical behaviour obtained in the F.E. analysis.

6.1 Frequency Calibration.

Firstly, the prototype was frequency calibrated. This type of calibration consistsof determining the sensitivity of the accelerometer in function of the frequency.For this, an automatic calibration system was used, based on a back-to-backcomparison method [5], This system uses a piezoelectric accelerometerconstructed internally in the armature of the shaker as a reference accelerometerand has NIST tractability.

In the case of the accelerometer prototype under study, the electronicconditioning unit has a high-pass and a low-pass filter in order to limit thesignals to the range of interest (from 30 to 450 Hz) and avoid possible readingerrors. It was therefore necessary to eliminate these filters to obtain the responseto frequencies greater than 450 Hz and so compare with the theoretical results.Once the filters were eliminated, frequency sweeps were carried out between 20Hz and 10 kHz. Figure 10 shows the sensitivity curve obtained. It should benoted that the curve represents variations in % between 20 and 1000 Hz whilebetween 1000 and 10000 Hz the deviations are shown in dB.

This figure shows that the response of the sensor corresponds to whatwas predicted in the theoretical analysis. However, a significant difference canbe appreciated near 100 Hz which may be due to a structural resonance of thebody or a problem of coupling between the sensor and the shaker. Anyway, theresonance around 5500 Hz can be clearly appreciated close to that obtained withthe F.E. model.

MODELO: H1 N. SERIE: 2DSensibilidad 56427mv/g a 100 Hz. iOg pk

RESPUESTA EN FRECUENCIA

Figure 10.- Frequency response


Computer Methods and Experimental Measurements

6.2 Random Excitation.

Additionally, another series of tests was carried out using a random-typeexcitation. Specifically, the response to a white-noise-type excitation werestudied, from 0 to 6400 Hz. For these tests, a dynamic signal analyser, and anelectrodynamic shaker with its corresponding amplifier were used. Since it wasnot possible to mount an additional accelerometer to determine the accelerationlevel reached by the shaker, it was only possible to cany out a qualitativeanalysis of the response obtained. Therefore the shaker signals are shown in mVwhile the prototype response is shown in g's.

6.2.1 Response to a white-noise-type excitation from 0 to 6400 Hz.Figure 11 shows the white noise signal generated by the analyser (in mV), whitefigure 12 shows the prototype's response in g's.

i

0,10,010,0010,0001

S^5 co o CM10 o o •—•— •— CM CM co

101

0.10.010.001 CM -O O

Frequency (Hz) Frequency (Hz)

Figure 11: White noise excitation Figure 12: Prototype response

In the graph of the response the attenuation of the signals can be seenabove 450 Hz which is the approximate cut-off frequency of the low-pass filter.It also clearly shows the resonance around 5500 Hz although this is attenuated.

7. Conclusions.

The development of different F.E. models, in increasing order of complexity,permitted the confirmation that the results were similar in all cases andcoincident with the behaviour of the real prototype.

In any case, the development of a model as similar to the real one aspossible was necessary in order to determine exactly, in a theoretical way, thevalue of the resonance frequency associated with the first mode and that this wasthe relevant frequency. Furthermore, by developing this model, it was provedthat there were no local vibration modes which would negatively affect thesensors behaviour.

The introduction of 45- loads does not modify the sensor response.Therefore the excitation of the modes in the XZ plane does not influence thesensor response.

From the initial theory it can be concluded that the optical sensor willbehave as expected in the range from 30 to 450 Hz. This conclusion waschecked experimentally by calibration of the prototype. Additionally, the



resonance frequency value was obtained of approximately 5500 Hz as wasindicated in the theoretical results.

The differences between the theoretical and experimental results arebecause the theoretical study using F.E. only permitted the analysis of themechanical behaviour of the moving element, while the experimental resultswere obtained from electric signals generated by the set of sensor head andsignal conditioning unit. Therefore, in the real case the light transmission by theoptical fibre and the reception of the light must be taken into account. None ofthese are considered in the theoretical model.

8. Acknowledgements.

This work has been carried out as part of BRITE-EURAM 7289 for themonitoring of T-G groups of hydroelectric power plants and the complementaryproject TAP94-1545-CE of the CICYT.

The contribution of all the partners of the project BRITE-EURAM 7289is greatly appreciated.

9. References.

1. Trampe Broch, J. Vibration measuring instrumentation, Mechanical Vibrationand Shock Measurements, Briiel & Kjaer, Denmark, 1980.2. Oilier, E., Labeye, P., Mottier, P., A new micro-optical vibration sensorintegrated on silicon, Paper submitted to "ECIO" 8th European Conference onIntegrated Optics, Stockholm - Sweden, April 2 - 4, 19973. Humar, J.L., Dynamics of Structures, Prentice Hall, 19904. Zienkiewicz, O.C. & Taylor R.L. Finite element method, Vol. 1 & 2,McGraw- Hill, 19935. Sill, R.D. Minimizing measurement uncertainty in calibration and use ofaccelerometers, TP 299 Endevco® Corporation.


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R. Sancibriaif, E. Oilier*, A. Fernandez · 2014. 5. 14. · Theoretical and experimental results of the mechanical behaviour for a new optical accelerometer F. Viadero*, P. Mottier\

R. Sancibriaif, E. Oilier, A. Fernandez · 2014. 5. 14. · Theoretical and experimental results of the mechanical behaviour for a new optical accelerometer F. Viadero, P. Mottier\