XIX IMEKO World Cogress Fudametal ad Applied Metrology September 6, 9, Lisbo, Portugal INCREASE OF STRAIN GAGE OUTPUT VOLTAGE SIGNALS ACCURACY USING VIRTUAL INSTRUMENT WITH HARMONIC EXCITATION Dalibor Kuhiek, Igor Zorić, Josip Butorac Uiversity of Zagreb, Faculty of Miig, Geology ad Petroleum Egieerig, Zagreb; Croatia, dalibor.kuhiek@rg.hr, igor.zoric@rg.hr Uiversity of Zagreb, Faculty of Electrical Egieerig ad Computig, Zagreb; Croatia, josip.butorac@fer.hr Abstract This paper describes the priciple of harmoic excitatio of strai gages i bridge cofiguratio. This system s properties are mathematically determied ad measuremets are coducted with commutated excitatio, AC ad harmoic excitatio - with ad without filterig. The possibility of icreasig the accuracy of output bridge voltage measuremet by usig harmoic excitatio is show. Keywords: harmoic excitatio, resistive bridge, virtual istrumet.. INTRODUCTION I measuremet of sample deformatio strai gages covert sample deformatio ito the resistace chage. This resistace chage is usually small (permitted strai gage deformatio is, %), therefore the resistace chage is measured i bridge cofiguratio where measured sigals are small ad oisy. If bridge cofiguratio is excited with higher voltages, the output voltage will be higher for the same measured deformatio. The bridge ca be excited with direct or alteratig voltage source with certai advatages ad disadvatages []. The properties of direct voltage excitatio ca be improved usig voltage commutatio which ca elimiate thermocouple voltages ad DC errors. Errors due to oise, power lie frequecy, its harmoics, offset ad offset drifts are more difficult to elimiate i DC excitatio systems. The use of AC excitatio is a better solutio because of lower sesitivity (better immuity) to oise ad DC errors (offset) ad power lie frequecy harmoics but it requires the use of more expesive equipmet ad maipulatio with measured sigal (filterig ad demodulatio) []. Whe a higher rate of measuremet system data acquisitio is required, it is ecessary to perform commutatio fast eough ad if cotacts switchig time is ot shorter tha required sample rate this becomes a sigificat problem. A importat property is also the expected accuracy of measuremet system which is greater if the measured sigal amplitude is higher. It will be greater if the bridge excitatio amplitude is higher, but it is limited by dissipatio - heatig of strai gages. By usig the harmoic excitatio it is possible to achieve higher excitatio amplitudes with uchaged heatig, similar to the use of impulse excitatio. Aother advatage of harmoic excitatio is i lower required badwidth ad therefore lower cotributio of oise to total expected error.. PROPOSED APPROACH Whe strai gages are excited usig voltage source, strai gages are heated (Joule s law) ad resistace chage achieves statioary state after trasiet respose to chage i heatig. Maximum voltage of strai gages excitatio is defied as the maximum effective voltage which ca be applied to the bridge cotaiig strai gage. Heatig of strai gages limits the excitatio voltage ad therefore also the output voltage obtaied by cotiuous bridge excitatio. The secod optio is to use impulse excitatio of strai gages. The excitatio ad measuremet are coducted i time τ which i relatio to the period T fulfils the coditio τ < T. Similar to the impulse excitatio is the applicatio of harmoic excitatio. The basic groud of this excitatio procedure is the multiplicatio of AC excitatio priciple which uses sigle frequecy voltage ad is called frequecy carrier techique []. If more tha oe frequecy carrier is used (two or more) it is possible to achieve a higher amplitude sigal while maitaiig the same effective value. The total sigal is modulated ad basically the procedure is similar as to sigle frequecy carrier techique but multiplied. The umber of processig segmets of bad pass filters ad demodulatio used is equal to the umber of frequecy carriers. Subsequetly, liearly added sigals give higher output (measured) sigal i compariso to the use of just sigle frequecy carrier. Advatages of harmoic excitatio ca be achieved eve without the described sigal processig (filterig ad demodulatio), but i this case frequecy carriers must have such a phase shift that the amplitudes of all sigle frequecy carriers coicide with amplitude of basic frequecy. I that way, the maximum possible amplitude of complex excitatio is achieved. Sice white oise depeds o badwidth, such solutio will have the same oise as i DC system.
.. Frequecy carrier amplitude ad effective value Whe usig two frequecy carriers with frequecy f ad 3 f, without phase shift, total excitatio voltage u(t) is: () πt 3 πt u t = Asi + Asi () T T i.e. its effective value ca be calculated usig (). A + A U = () For frequecy carriers effective value is equal to: A + A +... + A A U = = (3) i.e. for certai effective value U ad frequecy carriers of the same amplitude A, where amplitude of each of frequecy carriers is calculated usig (4). A= U (4) Fig.. shows amplitude A of frequecy carriers ad for equal effective value of excitatio voltage. Amplitude of frequecy carrier sigals A (V),,8,6,4, 3 4 5 6 7 8 9 Number of frequecy carriers Fig.. Amplitude of frequecy carrier sigals A i depedece to the umber of frequecy carriers. Accordig to calculatios, effective value does ot deped o frequecy or phase shift betwee frequecy carriers so ay other combiatio of frequecies ad/or phase shifts gives equal effective value... Total amplitude of excitatio voltage Although effective value does ot deped o phase shift betwee frequecy carriers, the total waveform chages for differet phase shifts. This chages maximum of the total amplitude of excitatio voltage ad for certai phase shift is equal to the sum of sigle amplitudes ad is equal to: Am = U = U (5) So for example, for three frequecy carriers with frequecy of f, 3f ad 5f, maximum amplitude is achieved with phase shift of φ=, φ 3 = 8, φ 5 =. I this case, amplitudes of sigle siusoids are at the same positio of 9 to ull value of basic sigal, i.e. shift of T/4, givig the total amplitude of,73 times larger tha the amplitude of oe frequecy carrier with equal effective value. By icreasig the umber of frequecy carriers, the total maximum amplitude is also icreased at a certai poit of time at the expese of the remaiig part of the period. The impulse excitatio effect is achieved, eve though cotiuous harmoic excitatio is used. Maximal amplitude A m withi periode (V) 3,5 3,5,5,5 3 4 5 6 7 8 9 Number of frequecy carriers Fig.. Depedece of maximum obtaied excitatio amplitude A m o the umber of frequecy carriers used..3. Total output voltage whe usig multiple frequecy carriers Whe bridge is excited with frequecy carriers, the total output voltage u o will be equal to the sum of sigle resposes to each frequecy carrier which depeds o deformatio ε: o () ( ) u t = U ε πt πt πt si + si +... + si T T T Accordig to equatio (6), it ca be cocluded that by usig multiple frequecy carriers, the amplitude of the output sigal will be times higher whe compared with oe frequecy carrier for the same effective voltage. Output voltage (V),6,4, -, -,4 -,6 DC excitatio AC excitatio Harmoic excitatio,,4,6,8,,,4 Time (s) Fig. 3. Output voltage for same effective voltage excitatio. (6)
The more frequecy carriers are used, the lower sigle frequecy carrier amplitudes will be, to maitai equal effective value of excitatio voltage Fig. 3 shows output voltages for a bridge that is excited with DC, AC ad harmoic voltage with equal effective value. AC voltage frequecy ad base harmoic frequecy is equal to 5 Hz. Harmoic excitatio cosists of frequecy carriers of f, 3f ad 5 f, with phase shift of φ=, φ 3 = 8, φ 5 =..4. Sigal to oise ratio If equal sigal processig is applied to output sigal as for AC excitatio, filterig ad demodulatio is used. ig passes equal badwidth for each frequecy carrier, filtered sigals are demodulated ad the liearly added. Total effective value of oise equals to [3]: A = A + A +... + A (7) oise oise oise oise Total sigal to oise ratio equals to: S / N = log U A oise Equatio (8) shows that sigal to oise ratio does ot deped o the umber of frequecy carriers. This calculatio applies to white oise which occurs i strai gages ad with assumptio that measuremet system has egligible cotributio to the overall oise..5. Absolute accuracy The accuracy of measured voltage usig virtual istrumet is calculated accordig to data give by the maufacturer for the used measuremet card ad it depeds o gai ad offset errors ad their temperature drifts, differetial oliearity ad oise [4]. Error limits are determied by calculatig absolute accuracy (AA) accordig to maufacturer s directios, i.e. absolute accuracy cosists of gai error cotributio GE, offset error OE ad oise cotributio accordig to (9). Noise cotributio depeds o effective oise value σ ad umber of samples N which are collected. 3 σ AA = GE+ OE+ (9) N 3. MEASUREMENT SYSTEM 3.. Implemetatio of measuremet systems To compare the properties of differet excitatios to measuremet systems, virtual istrumets accordig to Table. are implemeted. Measuremet system is realised with measuremet card NI PCI 68 ad fixed resistace divider accordig to Fig. 4. This reduces the ifluece of the amplifier, used for bridge excitatio, o measuremet results. Fixed resistace divider eables measuremet without iflueces of differet heatig of sigle strai gages mouted o a trasducer. Therefore, istead of a bridge with some disballace, fixed resistor of fixed disballace was used. (8) Table. Descriptio of realized measuremet systems. Implemetatio Descriptio Commutated (rectagular) voltage Oe frequecy carrier f=5 Hz, A=,5 V, without bad pass filter Oe frequecy carrier f=5 Hz, A=,5 V, with bad pass filter 3 Three frequecy carriers f, 3f (φ=8 ), 5f, f=5 Hz, A =A =A 3 =,5 V 3, without bad pass filter 4 Three frequecy carriers f, 3f (φ=8 ), 5f, f=5 Hz, A =A =A 3 =,5 V 3, with bad pass filter Maximum output curret of D/A coverter is 5 ma ad therefore it is ot possible to coect output of a D/A coverter directly to strai gage bridge with resistaces of 35 Ω. Used divider has resistace of R = kω ad R = Ω, i.e. divider ratio is approximately : ad with voltage source of,5 V, curret through divider is approximately 5 µa. With DC excitatio of,5 V bridge imbalace is proportioally smaller accordig to divider ratio ad is approximately,5 mv. Measured voltage ratio (output voltage divided to excitatio voltage) is approximately, mv/v. Software geerates voltage at the output of the measuremet card D/A coverter which is coected to divider ad the divided voltage is coected to the iput of A/D coverter. The lowest measuremet rage of measuremet card of ± mv is used. D/A R R Fig. 4. Measuremet cofiguratio. A/D After data acquisitio, filterig (measuremet implemetatio ad 4) ad rectificatio of measured sigals are coducted. Rectificatio is implemeted by software usig fuctio absolute value. Subsequetly, mea or maximum value is determied from certai amout of gathered samples. Fig. 5. shows block diagrams of sigal processig of all implemetatios. filters are implemeted usig labview filter fuctio as Bessels IIR 8 th order filters. Bessels filter has the best step respose; o overshoot or udershoot, oly a rise time iversely proportioal to the filters corer frequecy. Bessels filter are suited for applicatios requirig miimal distortio of fast chagig sigals [5]
Implemetatio Implemetatio Implemetatio Implemetatio 3 Implemetatio 4 Mea () + Fig. 5. Block diagram of implemetatio sigal processig. Some AC measuremet systems use frequecy carrier of 5 Hz [], therefore this value is chose to be the basic frequecy of these implemetatios. Samples are geerated with sample rate of 9 khz ad data are acquired usig the same sample rate. As samplig is coheret with geerated sigal the bias is equal to zero [6]. Usig this sample rate of geeratig ad acquirig data, 4 samples are acquired withi the duratio of oe period of base frequecy carrier. I commutated excitatio, mea value from positive ad the egative samples is calculated, ad subsequetly mea value of the positive ad egative part of period is calculated. For other excitatios, maximum value from samples of positive ad egative part of period is determied, ad the mea value is calculated. From every 4 collected samples, oe sample cotaiig iformatio of measured disballace is obtaied. The described procedure of sample acquisitio ad data processig gives samples that represet evelope plotted by harmoic excitatio frequecy carriers. 3.. Accuracy of measured voltage usig virtual istrumet Cotributio of oise to error depeds o the umber of samples ad o/off state of the 4 khz low pass filter withi measuremet card. The filter was o for all measuremets to reduce the effective value of measuremet card oise from 9 to µv. For steady DC sigals, measuremet card absolute accuracy is withi the rage of 3,6 to 8,3 µv for measured voltages from to mv ad for samples averagig. Gai error is equal to 47 ppm of measured value i.e. up to 4,7 µv for mv. Offset error is equal to 3 ppm of measuremet rage i.e. 3, µv. Noise cotributio is equal to 6 µv for sigle sample ad decreases with square root from sample umber. Calculatig absolute accuracy for each measured voltage, measuremet ucertaity ca be determied as B type where absolute accuracy is divided with 3 (rectagular distributio). Sice all implemetatios periodically chage voltage excitatio polarity ad durig sigal processig positive ad egative part of measured amplitude is averaged, it ca be cocluded that offset error is cacelled out. Remaiig cotributio is gai error, which depeds o measured amplitude ad oise cotributio which is costat. For each measuremet with oise cotributio larger tha gai error cotributio, the domiat part will be oise cotributio. This is the case whe small voltages are measured. Calculated absolute accuracy is show i Fig. 6. ad Fig. 7. as vertical bouded lies. I Fig. 6, absolute accuracy is calculated for two samples per base carrier frequecy periode. I Fig. 7, absolute accuracy for commutated excitatio is calculated for 4 samples, which lowers oise cotributio. For frequecy carriers, times larger amplitude is measured. Measured value is also time larger, therefore both measured value ad error limits should be divided with. Sice the icrease of error limits is lower tha icrease of measured value, measuremet error limits ad cosequetly measuremet ucertaity are decreased. Accordig to Fig. 6., the absolute accuracy is decreasig whe the umber of frequecy carriers icreases. Measured bridge voltage,,,,99,98,97,96 Commutated fc fc 3 fc 4 fc Implemetatio Fig. 6. Absolute accuracy i depedece o the umber of frequecy carriers 4. RESULTS It is ot possible to coduct measuremets simultaeously. Therefore they were coducted sequetially withi the shortest possible time period. This reduces the possible ifluece of system compoets chage due to drift ad ifluece of temperature chage o results. Measuremet results ad the correspodig error of output voltage usig differet systems are preseted i Table. Implemetatio Number of measuremet samples Table. Measuremet results. Measured output voltage (µv) Absolute accuracy (µv) Measured voltage ratio Ratio absolute accuracy (µv/v) 4 5,3,99,9,4 357, 4,9,, 356, 4,9,8, 3 67,9 4,33,9,7 4 64,8 4,33,4,7
Voltage o measuremet card iput is times larger for excitatio with oe frequecy carrier ad 6 times larger for measuremet with three frequecy carriers i compariso with rectagular DC excitatio. Whe output to excitatio voltage ratio is calculated, it is ecessary to divide the result with, or with 6. Absolute accuracy is also divided with a appropriate factor. Implemetatio 3 has absolute accuracy, almost times lower tha excitatio with oe frequecy. Accuracy improvemet is accordig to previously metio. Implemetatio ad 4 has a lower result which is preseted i Fig 7. Lower value is measured due to the ifluece of digital filterig to measured sigals. Whe usig bad pass filters, the ifluece of filterig o sigal amplitude reductio should be take ito accout, i.e. correctio factor should be applied. Measured bridge voltage,3,5,,5,,5,,995,99 3 4 Implemetatio Fig. 7. Measured voltage ratio ad absolute accuracy i depedece to implemetatio. Whe output bridge voltage is small, the the icrease of sigal for ad almost uchaged absolute accuracy result i maximum possible reductio of absolute accuracy of ratio. For example, for sigal of mv ad the use of harmoic excitatio with three frequecy carriers would result i voltage which is 3 times larger. Absolute accuracy would be 4,39 µv ad 4,49 µv respectively. Measuremet result should be divided with 3, so absolute accuracy for the secod measuremet are 4,49 µv/ 3 or,6 µv. 5. CONCLUSIONS The use of excitatio with multiple frequecy carriers icreases the accuracy of measured output bridge voltage. This is achieved by icreasig voltage i oe part of the period at the expese of the remaiig part. Measured sigal is i the evelope of frequecy carriers ad measuremet of peak values achieved by frequecy carriers provides iformatio o true output to excitatio voltage ratio. This procedure is particularly appropriate for small sigals where sigal icrease is more sigificat ad absolute accuracy is slightly icreased. I these cases, the improvemet accordig to law is achieved. REFERENCES [] R.P. Arey, J.G. Webster, Sesors ad sigal coditioig, Secod Editio, Joh Willey ad Sos, New York, 999. [] M. Kreuzer, High-precisio measurig techique for strai gage trasducers, Hottiger Baldwi Messtechik, Datadt [3] B. Zovko-Cihlar, Noise i Radiocommuicatios, Školska kjiga, Zagreb, 987. (i Croatia) [4] Natioal Istrumets NI PCI 68 datasheet [5] R.P. Arey, J.G. Webster, Aalog sigal processig, Joh Willey ad Sos, New York, 999. [6] S. Nuccio, C. Spataro, Approaches to Evaluate the Virtual Istrumetatio Measuremet Ucertaities, Trasactios o istrumetatio ad measuremet, vol. 5, º. 6, pp. 347-35, December.