XX IMEKO World Congress Metrology or Green Growth September 9 14, 01, Busan, Republic o Korea APPLICATION OF A SCANNING VIBROMETER FOR THE PERIODIC CALIBRATION OF FORCE TRANSDUCERS Christian Schlegel, G. Kieckenap, and R. Kumme Physikalisch-Technische Bundesanstalt, D-38116 Braunschweig, Bundesallee 100, Germany, Christian.Schlegel@ptb.de Abstract: This paper describes a procedure or the dynamic calibration o orce transducers using sinusoidal excitations. Thereby, the main output o such a calibration is the dynamic sensitivity: the ratio between the electrical output signal o the transducer and the acting dynamic orce. The orce is traced back to the mass time s acceleration. With the aid o a scanning vibrometer, the acceleration distribution can be measured and a more realistic uncertainty or the acceleration can be given. In addition, parameter identiication rom the resonance behaviour can be applied. Keywords: dynamic calibration, orce transducer, acceleration measurement, parameter identiication 1. INTRODUCTION In the past, very precise procedures or static orce measurements were developed and are now routinely used by calibration services and in national metrology institutes [1]. Thereby, relative measurement uncertainties down to 10-5 are obtained using deadweight machines, which are the best standard to realize a traceable orce. Besides the precise realization o a orce in a standard machine, there must be selected orce transducers available which can be used as a transer standard to give the primary calibration to the secondary calibration laboratories and industry. The crucial act now is that oten these statically calibrated orce transducers are used in dynamic applications. That is the reason why more and more NMIs have established procedures or a dynamic calibration o orce transducers and also other sensors. Currently in the European Metrology Research Programme (EMRP) one promoted research topic is the Traceable Dynamic Measurement o Mechanical Quantities, which includes, apart rom a work package on dynamic orce, also work packages on dynamic pressure, dynamic torque, the electrical characterization o measuring ampliiers and mathematical and statistical methods and modelling []. Similar to the static calibration philosophy, primary calibrations have to be provided which guarantee traceability to the SI base units and also transer transducers (reerence standards) to transer these calibrations, e.g. to an industrial application. This transer turned out to be the most complicated task because o the crucial inluence o environmental conditions present in certain applications. Mostly, the transducers are clamped rom both sides which leads to sensitivity losses due to the dynamics o these connections, which are more or less not ininitely sti. On the other hand, the resonant requency oten shits down to lower requencies which can also drastically change the sensitivity. The problem can be solved to a certain extent by modelling the whole construction, including all relevant parameters. For that reason it is also important to determine the orce transducer parameters, like stiness and damping, which can also be obtained during a dynamic calibration. This article describes one possibility or a primary dynamic orce calibration using sinusoidal excitations. The whole procedure as well as most o the setups were developed over two decades and are extensively described in [3-5]. Other methods as well as analysis procedures or dynamic orce calibration are described in [5-7]. S = ( m t. THE MEASURAND The main output o a dynamic calibration is the requencydependent sensitivity, S. Thereby, the sensitivity is the ratio o the electrical output signal o the transducer, U, to the acting dynamic orce. To initiate a orce on the transducer, an additional mass is mounted on top o the transducer. This mass, m t, in combination with the transducer s own head mass, m i, contributes to the inertial orce generated by the sinusoidal movement. The acceleration, & x& t, is measured on top o the loading mass using a scanning vibrometer. Finally, the sensitivity is given by U + m ) && x K i t corr S 0 (1 pω ) The parameter, K corr, takes into account the vertical acceleration gradient over the mass body. Finite element simulations have shown that the individual mass points o the mass body have slightly dierent accelerations in the vertical direction [3]. This correction actor can be neglected i quite small masses are used (only a ew centimetres in height). From the theory it can be shown that the sensitivity can be approximated by a second-order (1)
polynomial. This is very useul to average and interpolate sensitivities measured, e.g. with dierent orces. Thereby, the actor, S 0, is the static sensitivity obtained or the limiting case ω=0, whereby p is a parameter which is determined by the ratio o the damping to the stiness o the transducer. As one can see rom the equation, the sensitivity is reduced quadratically with increasing requency ω. The periodic excitation o the orce transducer can be used also to determine the parameter s resonance requency, stiness and damping actor o the transducer. This can be obtained by analyzing the resonance line obtained by the ratio o the acceleration measured on the top mass and the acceleration measured on the shaker table or the ratio o the orce transducer signal to the acceleration on the shaker table. The resonance line can be itted by the unction o the mechanical resonator, whereby the amplitude, A, is given as a unction o the requency,, by: A( ) = ( a a 0 1 ) + 4a The parameter a 1 is the resonance requency 0 according to: 1 k 0 = a1 = (3) π m From the resonance requency the stiness, k, o the orce transducer can be obtained rom equation 3. The parameter a is connected with the damping actor according to: b = πma The mass, m, is the top mass o the orce transducer including the internal head mass o the transducer. Sometimes it is useul also to know the bandwidth,, o the peak which is given by the width o the resonance at 1 / o the amplitude. This can be calculated by the dierence o the two requencies, 1 and which correspond to this: 1, = a1 a m a a 1 a (5) With the bandwidth, a quality actor, Q, can be calculated which is the ratio o the resonance requency and the bandwidth: Q = 0 It should be noted that the resonance peak can also be itted by other peak unctions like the Lorentz unction. These unctions characterize a peak oten with the ull width at hal maximum, (FWHM). The FWHM can also be used to calculate the Q-Value, however in this case the square o the transer unction must be itted. From the Q-Value also the damping actor can be calculated according to: b = km Q 1 () (4) (6) (7) 3. TECHNICAL DETAILS The measurement arrangement can be seen in Figure 1. For the sinusoidal excitation three electromagnetic shaker systems can be used; a small one or orces up to 100 N and 10 Hz until khz, a medium one up to 800 N or 10 Hz -3 khz, and a large shaker up to orces o 10 kn and requencies o 10 Hz to khz. The shakers consist o two parts, the vibration exciter itsel and a power ampliier. The sinusoidal signal is ed rom an arbitrary signal generator directly into the power ampliier and modulates the current signal, which drives the coil o the shaker armature. The beam o the laser vibrometer is guided via a 45 mirror down to the surace o the loading mass, mounted on top o the orce transducer. The vibrometer is on a special rame, which is equipped with a passive and an active damping table. The active damping table is mounted directly below the vibrometer. Inside the table six accelerometers continuously measure the vibration. This measurement inormation is used in a closed loop control to steer 4 servo motors, which keep the position o the table always exactly in the horizontal position. Experience has shown that the table is able to suppress vibrational inluences originating rom the shaker very well. In addition, a irst damping is perormed via the passive damping table, which is placed directly on the platorm o the mounting rame, see Figure 1. Figure 1. Calibration setup consisting o the electrodynamic shaker with the mounted orce transducer and a scanning vibrometer or the acceleration measurement. The transducer is equipped with an additional loading mass. The scanning vibrometer, PSV-400 M, is an instrument rom Polytec. This device consists o the laser head, a controller (OFV-5000), a junction box and a PC system equipped with a 4 channel 5 MHz sampling card rom National Instruments. The laser beam can be scanned in an angle region o ±0º in the horizontal and vertical directions. Thereby, the angle resolution is <0.00º. The controller includes several parts, two velocity encoders with analogue and digital outputs, an analogue displacement output and a digital decoder or the output o a down-converted IQ signal. The velocity decoder, reerred to as VD-07, or the low requency range up to 350 khz, can measure velocities up to 500 mm/s and a second decoder, reerred to as VD-09, or requencies in the range rom 10 Hz -.5 MHz, can measure
velocities up to 10 m/s. In addition to the velocity proportional analogue output signals, the VD-07 decoder has a digital S/P-DIF output with a ixed sampling rate o 4 khz with 4 bit resolution. The digital IQ converter, reerred to as DD-600, provides the baseband Doppler signal in a bandwidth o 0-5 MHz with an IQ phase tolerance o ±.5º. without and with a special mechanical adapter to mount the top mass, one can see the inluence o such a coupling. 4. CALIBRATION EXAMPLE In the ollowing example a piezoelectric orce transducer, Type Kistler 9175 B, with a nominal orce o 8 kn or tension and 30 kn or compression, was measured. The charge o this transducer was measured with a B&K Nexus charge ampliier. Figure shows the dynamic sensitivity o the transducer measured with ive top masses. Figure 3. Averaged sensitivity o the data points displayed in Figure according to equation 1. Figure. Dynamic sensitivity o a piezoelectric orce transducer measured up to khz using 5 loading masses. Compared with the strain gauge transducer, the correspondence between data sets o dierent loading masses is not so good. Especially beyond 1 khz the curves drit apart quite widely. One reason or that is perhaps the special construction o this kind o orce transducer. The transducer is a kind o ring which is clamped rom both sides with special screws, so that a certain prestress is created. Both screws can be seen in a mathematical model also as additionally damped spring mass systems, as shown in section 1. The complex vibration between all these coupled spring systems can lead to a more sophisticated behaviour o the orce transducer, as in the previously discussed case o the strain gauge transducer. Especially the bump in the sensitivity around 1 khz might originate rom a cross resonance, due to the special construction o the orce transducer. The obtained sensitivities o the piezoelectric orce transducer can be averaged according to equation 1. The result o this is shown in Figure 3. Thereby, the more straight solid line corresponds to the averaged sensitivity o the masses o 1kg and kg, which were measured without a special adapter. The other curve was obtained rom the data measured with a 6kg and a 10kg top mass, which were mounted with a special adapter. The corresponding dashed lines are the error bands obtained rom the error o the it parameters. In this case, where measurements were done In one case, where the top mass was screwed directly onto the orce transducer, the coupling is very sti and has no inluence on the dynamics; in the other case, the adapter brings an additional sotness to the mounting, which results in a sensitivity loss. The coupling can be modelled according to equation 1 with a damped spring. I a dynamic orce acts now via the top mass on the transducer, energy also goes into the compression o the adapter spring, which will be missed or the compression o the transducer spring. This behaviour can generally be observed; more springs are mounted in between the source o orce and the sensing transducer, as more sensitivity is lost. 15 10 5 0 180 5 10 15 mm 150 10 10 40 90 70 Figure 4. Acceleration distribution measured on the surace o the top mass. The illed circles are the measuring points, the shaded area in between was calculated through interpolation o neighbouring measuring points. The big advantage in using a scanning vibrometer is the more detailed measurement o the acceleration. In Figure 4 the acceleration distribution measured on top o a loading mass is illustrated. As one can see, in this special case, there is no uniorm distribution. Due to rocking modes o the top 60 300 30 330 0 5.36 5.70 6.04 6.38 6.7 7.05 7.39 7.73 8.07 acceleration in m/s
mass which might originate rom the kind o coupling to the orce transducer, the acceleration can vary over the surace. Most o the calibrations which were perormed, were normally measured in the middle o the top mass, which do not account or this eect. By averaging all the measured points o the acceleration distribution, one can take into account mechanical inluences, like rocking modes in the calibration result. are shown or three kinds o data sample. The individual uncertainties according to Figure 5 are averaged or each top mass in Figure 6. Thereby, dierent sets o data were chosen: irst, all data o a certain top mass, second, all data up to a requency o 1 khz and, third, all data up to the beginning o the resonance. From this igure, one can conclude that the uncertainty o the acceleration is below 0.5% i the resonance region is avoided. On the other hand, one can see, e.g. on the data obtained with a kg top mass (dashed ellipses), that special inluences, which are initiated, e.g. by an imperect mechanical adaption, can be rapidly detected. In this special case, it might be that the mounting screw thread was not perectly aligned with the middle axis o the mass cylinder. Figure 5. Relative uncertainty o the acceleration obtained rom the averaging o the acceleration distribution measured on the surace o the top mass. Furthermore, the standard deviation resulting rom this can be used or a more realistic uncertainty evaluation o the acceleration measurement. To illustrate the actual situation, in Figure 5, the relative uncertainty o the acceleration is shown as a unction o the requency or our dierent top masses. Thereby, the data points were obtained by the averaging o 50-60 acceleration scan points. According to Figure 5, the acceleration uncertainty is mainly below 1%, apart rom the data points obtained with the kg loading mass. On the other hand, the inluence o the resonance region leads to higher uncertainties and especially beyond a resonance one will be aced with higher measurement uncertainties. Figure 6. Averaged relative uncertainties or each top mass amplitude normalized 1.0 0.8 0.6 0.4 0. 0.0 data it mech. resonator 0 500 1000 1500 000 Frequency in Hz Value rel. dev. % a0 878.41 1.45337 a1 880.8150 0.067 a 13.7091 1.87137 1 866.783 0.04083 894.073 0.03314 k in N/m 1.89806E 0.0456 b in kg/s 1068.364 1.8761 Q 3.10937 1.878 Figure 7. Example o a resonance peak measured with a chirp excitation o the orce transducer, together with a it unction (solid line), which was chosen according to equation. The inset table shows the it parameters and their relative deviations. The amplitude was normalized o the peak maximum. As mentioned in section 1, the dynamic measurement can be used to determine the parameter stiness and damping o the orce transducer. According to equation, this parameter can be determined by measuring a resonance peak, as shown in Figure 7. There are several possible ways to obtain such resonance data. In the shown case, the transducer was excited via the shaker system with a chirped excitation. Ater that, the ratio between the signal o the acceleration measured on the top mass to the acceleration measured on the shaker table was calculated, which can be seen in Figure 7. The data can then be itted with the unction o the mechanical resonator according to equation. Each top mass results in a resonance by a dierent requency. From the data pairs, resonance requency and top mass, one can perorm a it according to equation 3, with the stiness as a it parameter. With the knowledge o the stiness, one can calculate the damping actor rom the band width o the peak o the mechanical resonator unction. As shown in Figure 7, the resonance requency and the stiness connected with it, are well determined with quite low uncertainties. In contrast, the damping actor has a slightly higher uncertainty.
squared normalized amplitude 1.0 data it Lorentz 0.8 0.6 0.4 0. 0.0 Value rel. dev. % 0 879.99 0.01 FWHM 5.9 0.88 k 1.90E+0 0.0 b 985.13 0.88 Q 34.80 0.89 600 800 1000 100 1400 Frequency in Hz Figure 8. The square o the amplitude (ratio o the measured accelerations) itted by a Lorentz-Peak. The table shows the it parameter, resonance requency, 0, and the ull width at hal maximum, FWHM=w, according to equation 8. The parameters, stiness, k, in N/m, the damping, b, in kg/s and Q are calculated rom the it parameter. As mentioned above the resonance can also be itted with other peak itting unctions. A good candidate is thereby the Lorentz unction: y = y 0 A w + π 4( x xc) + w From a it o the Lorentz unction one can obtain the oset, y0, the peak area, A, the FWHM, w and the resonance requency, xc. The FWHM can be used to calculate the Q- Value and rom this one can obtain the damping actor according to equation 7. A comparison between the it using the model o the mechanical resonator and the Lorentz peak shows only small dierences in the resonance requency and an approximately 6% deviation in the Q- Value. (8) As seen in Figure 8 the resonance peak has a small tail on the right-hand side. This tail is an indication o a second small underlying peak. To unold this peak rom the main resonance a second Lorentz peak was included in the it procedure. The result shows a very good agreement between the data points and the combined it curve. According to the table with the parameters o the it inside Figure 8, one can see that the width o this second small peak is approximately twice as wide as the main resonance. The origin o this disturbance might come rom the mechanical coupler which connects the top mass to the transducer. Another possibility to obtain the resonance peak is to analyze the ratio o the orce signal to the acceleration measured on the shaker table. In this case the requency response o the conditioning ampliier has to be unolded irst rom the data. It should be noted that or the determination o the damping actor, the described procedure might not be the best choice. Other methods using a step or impulse response might be more suited. 5. CONCLUSION The dynamic calibration o orce transducers using sinusoidal excitations initiated by electromagnetic shaker systems was shown. A main part o such a calibration is the acceleration measurement. By using a scanning vibrometer, it is possible to measure the whole acceleration distribution on the surace o the top mass. From this distribution a more precise uncertainty o the acceleration can be given than in the case o a point measurement. In addition, mechanical inluences like alignment problems or rocking modes can be seen, e.g. rom an asymmetrical distribution. The resonance behaviour o the orce transducer can be used to make a parameter identiication o the orce transducer to obtain the resonance requency, the stiness and the damping value. From the physical point o view the model o the mechanical resonator is the best choice. On the other hand also other peak itting unctions like the Lorentz unction give reasonable results or the parameters. Thereby only very small dierences in the resonance requency and the stiness are obtained, the deviation or the damping actor is only at a low percent level. Acknowledgement The research within the project has received unding rom the European Union on the basis o Decision No 91/009/EC. 6. REFERENCES Figure 9. The resonance peak itted by the combination o two Lorentz peaks. The inset table shows the it parameters o both peaks according to equation 8. The irst parameters correspond to the main resonance. Reerences: [1] F. Tegtmeier, R. Kumme, M. Seidel, Improvement o the realization o orces between MN and 5 MN at PTB the new 5 MN orce standard machine, XIX IMEKO World Congress, pp. 186-191, Lisbon, 009.
[] European Metrology Research Programme (EMRP), http://www.emrponline.eu. [3] R. Kumme, Investigation o a primary method or a dynamic calibration o orce measuring instruments: a contribution to reduce the measuring uncertainty, doctoral thesis (in German), PTB, 1996. [4] Ch. Schlegel, G. Kieckenap, B. Glöckner, A. Buß and R. Kumme, Traceable periodic orce Measurement, 01, Metrologia, 49, 4-35. [5] Ch. Schlegel, G. Kieckenap, B. Glöckner and R. Kumme, Sinusoidal Calibration o Force Transducers Using Electrodynamic Shaker Systems, 01, Sensors & Transducers, Vol. 14-1, 95-111. [6] M. Kobusch, The 50 kn primary shock orce calibration device at PTB, IMEKO 010, Thailand, Pattaya, November 010. [7] S. Eichstädt, C. Elster, T. J. Esward and J. P. Hessling, Deconvolution ilters or the analysis o dynamic measurement processes: a tutorial, 010, Metrologia, 47, 5-533. [8] C. Elster and A. Link, Uncertainty evaluation or dynamic measurements modelled by a linear time-invariant system, 008, Metrologia, 45, 464-473.