Application of Omega Deformer for Stress Measuring in Dynamic Loading of the Structure

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1 Mlade M. Regodić Teachig Assistat Gora B. Šiiković Emil A. Veg Zoraa V. Jeli Nead Gubeljak Full Professor Uiversity of Maribor Sloveia Applicatio of Omega Deformer for Stress Measurig i Dyamic Loadig of the Structure Strai gauge is a basic tool used to measure the stress of the material. I idustry, it has bee i use for more tha sevety years. The area of applicatio of the strai gauges is very wide. They are used to measure the stress of mechaical ad buildig costructios, idividual machie parts, devices ad aids i medicie, etc. Straig gauges are made of differet materials, i differet shapes ad dimesios. I spite of the wide presece, the aplicatio of the straig gauges ca be difficult i certai weather coditios. Low temperature ad high humidity sigificatly egativly affect the materials used for placig the gagues o the surface of the part to be tested. I order to overcome these problems, deformeters are used. This study examies the possibility of usig a specially desiged deformeters i the form of a letter omega (Ω). Tests were carried out i laboratory coditios, o a freebeam, uder the actio of dyamic loads. The mai objective of the test was to determie the degree of correlatio betwee the results obtaied by direct readig from the strai gauge ad the results read by the deformeter. The aalysis of the results of comparative tests showed a high degree of correlatio, which cofirmed the possibility of usig "Omega" deformeter o the structures that are exposed to dyamic load. Keyword:Strai gauge, Stress, Omega Trasducer, Dyamic Load 1. INTRODUCTION The strai gauges are ofte used i idustry. A large umber of sesors uses the strai gauges as a core sesig elemet [1-6].There is a wide variety of shapes ad dimesios of the strai gauges i the market, ad the possibility of applicatio is very diverse [7-8]. Sometimes, i difficult weather coditios, strai gauges applicatio ca be difficult. I such a eviro met, there is a eed for the use of a deformer with strai gauges. Strai gauge type trasducers electrically measure physical quatities such as load ad displacemet. They operate by covertig the physical quatities ito mechaical stress, ad the detectig that stress with a strai gauge. The deformeter is most ofte made of a metal part that is flexible eough to detect the imposed stresses. Deformers cotai oe or more strai gauges. The history of the applicatio of strai gauges ca be divided ito two phases. Charles Charles Wheatstoe gave his first theoretical assumptios about the workig priciples of the strai gauges i his publicatios i 1843 [9]. This effect is the chage of resistace i a coductor due to the effects of mechaical stress. William Thomso ( , Lord Kelvi after 1892) wet further with some work published i 1856 [10]. However, the use of strai gauges bega oly i the 1930s (i the 1930s). The basic idea of this paper was to examie the liearity ad degree of correlatio of the specially desiged "Omega" deformeter i the case of dyamic stress of the costructio[11-15]. 2. STRAIN GAUGE PRINCIPLES Ay electrical coductor chages its resistace with mechaical stress, e.g. through tesioor compressio forces. The resistace chage is partially due to the coductor's deformatio ad partially due to the chage i the resistivity Q of the coductor material as a result of microstructural chages. This process is described by the relatioship (1): dr dq = ε( 1+ 2ν) + (1) R0 Q where R is the electrical resistace, ε is the strai, v is the Poisso s ratio ad Q is the resistivity. Exteral force applied to a elastic material gee rates stress, which subsequetly geerates deformatio of the material. At this time, the legth L of the material exteds to L+ΔL if applied force is a tesile force. The ratio of ΔL to L, that is ΔL/L, is called strai (Precisely, this is called ormal strai or logitudial strai). O the other had, if compressive force is applied, the legth L is reduced to L- ΔL. Strai at this time is (- ΔL)/L. Strai is usually represeted as ε. Received: Jauary 2018, Accepted: March 2018 Correspodece to: Dr Emil Veg,,, Kraljice Marije 16, Belgrade 35, Serbia eveg@mas.bg.ac.rs doi: /fmet r,, Belgrade. Allrights reserved FME Trasactios (2018) 46,

Supposig the cross sectioal area of the material to be A ad the applied force to be P, stress σ will be P/A, sice a stress is a force workig o a defiite cross sectioal area.

2 where e is the voltage output, E is the excitig voltage, R 1 is the gauge resistace, R 2 ~ R 4 is the fixed resistace Figure 1. Dilatatio of elastic material [3] ε = ΔL (2) L where ε is the strai, L is the origial legth, ΔL is the chage of legth. Supposig the cross sectioal area of the material to be A ad the applied force to be P, stress σ will be P/A, sice a stress is a force workig o a defiite cross sectioal area. I a simple uiaxial stress field as illustrated below, strai ε is proportioal to stress σ, thus a equatio σ = E ε (3) is satisfied, provided that the stress σ does ot exceed the elastic limit of the material. "E" i the equatio is the elastic modulus (Youg's modulus) of the material. Exteral force applied to a ferritic material geerates physical deformatio ad electrical resistace chage of the material. I case that such material is sticked oto test specime via electrical isulatio, the material produces a chage of electrical resistace correspodig to the deformatio. Strai gauges cosist of electrical resistace material ad measure proportioal strais to the resistace chages. ΔR ΔL ε = = R L K (4) which ε is the strai measured, R is the Gauge resistace, ΔR is the resistace chage due to strai ad K is the gauge factor. Figure 2. Strai gauge costructio [3] Figure 3. Strai gauge cofiguratio Normally, this resistace chage is very small ad requires a Wheatstoe bridge circuit to covert it to voltage output. e= FME Trasactios RR R R ( R + R )( R + R ) E (5) Figure 4. Wheatstoe bridge circuit 3. DEFORMETER The tested deformeter has a form of a letter "Omega". The figure 4 shows the shape ad dimesio of the deformeter. Figure4. Dimesios ad shape of Omega deformeter The deformeter is made of steel ti sheet i the shape of a letter the "Omega ad two steel footigs used to bod it to the substrate. The material of the steel ti sheet is sprig steel. O the cetral part of the deformeter, there are two strai gauges fixed, as show i Fig. 4. For such a cofiguratio of the strai gauges, Bridge factor" has a value of 2 (B = 2) [5]. The followig formula is used to calculate the stress i the deformeter: U ε = B k U 4 A EA (6) where ε is the Strai, B is the bridge factor, k is the gauge factor, UE is the bridge iput voltage ad UA is the bridge output voltage. Due to the deformatio costructio itself, the voltage that occurs i it does ot correspod to the actual voltage o the structure we measure, but these voltages are i direct correlatio. I order for the measured voltage to fit the real oe, it is ecessary to itroduce the correctio coefficiet RRQ. Based o the calculatio ad experimets, it is determeed that for the tested deformeter this coefficiet is RRQ = VOL. 46, No 4,

Based o the experimets carried out uder static stresses, a high degree of Correlatio [σsg; σω x RRQ] is determied ad it is 0.99, which is described i [12]. 4.

I the cetre of the beam there are 2 fixed strai gauges of which the first oe is active while the other is passive ad is used for temperature compesatio.

At the begiig of the test, the beam was i a state of rest.

At the very ed of the test, the beam osci llatios were compulsively dimmed. The crude sigals are filtered usig the "Movig Average" fuctio.

Figure5 Set of a beam ad Omega Deformeter The dyamic load was itroduced by a device made up of a electric motor with a rotor cotrolled by a frequecy regulator.

3 Based o the experimets carried out uder static stresses, a high degree of Correlatio [σsg; σω x RRQ] is determied ad it is 0.99, which is described i [12]. 4. TESTING IN LABORATORY CONDITIONS The deformeter test was carried out o a steel shaft o a square cross-sectio of 30x30 mm, wall thickess of 2 mm ad a legth of 4 m. Figure 5 shows the experimet settig. I the cetre of the beam there are 2 fixed strai gauges of which the first oe is active while the other is passive ad is used for temperature compesatio. Strai gauges are placed i a half bridge cofiguratio. The spot where the strai gauges is fixed is take as the referece measurig poit. "Omega" deformeter is placed above the active strai gauge. At the begiig of the test, the beam was i a state of rest. After three secods of the experimet, a dya mic load was iitiated by startig a electric motor that lasted util the 22 d secod whe the egie was switc hed off. At the very ed of the test, the beam osci llatios were compulsively dimmed. The crude sigals are filtered usig the "Movig Average" fuctio. After filterig ad zeroig the sigal,their comparative disp lay is show i Figure 8. Figure5 Set of a beam ad Omega Deformeter The dyamic load was itroduced by a device made up of a electric motor with a rotor cotrolled by a frequecy regulator. A cocetrated mass was placed o the rotor by meas of which we itroduced the ubalace. Whe rotatig a ubalaced rotor, a dyamic force is geerated whose frequecy is proportioal to the umber of rotor rotatios. The device is rigidly liked to the steel beam, which istatly trasmits the iitiative to it. The costat value of the agular speed of the rotor provides a dyamic drive of costat frequecy. The frequecy regulator ca achieve full cotrol ad fie tuig of the dyamic drive frequecy. DyaLog (RoTech, Serbia) device was used for sigal acquisitio. The device has a 16-bit AD coverter with a samplig rate of up to 2000 Hz. Figures 6 ad 7 give graphical represetatios of test results. Figure7. Omega deformeter RAW sigal Figure 8. Strai gauge ad Omega deformeter visual comparatio Figure 6. Strai gauge RAW sigal Figure9. Strai gauge ad corrected Omega deformeter visual comparatio 522 VOL. 46, No 4, 2018 FME Trasactios

As already metioed, sigal from the deformeter is weaker tha the actual sigal. It is ecessary to correct such a sigal by itroducig the correctio coefficiet RRQ.

4 As already metioed, sigal from the deformeter is weaker tha the actual sigal. It is ecessary to correct such a sigal by itroducig the correctio coefficiet RRQ. After correctio of the Omega deformeter sigal, a compariso of both sigals is give i Figure 9. Figure 10 shows the part of the sigal betwee the 15 th ad 22 d secod of the experimet. Figure10. Strai gauge ad corrected Omega deformeter visual comparatio After the filterig ad correctio of the sigal, a umerical compariso of the obtaied results was also arraged. For the compariso of give sigals, the correlatio method ad the followig formula were used: (, ) correl X Y = FME Trasactios ( x x) ( y y) ( x x) ( y y) 2 2 (7) x = σsg values of stress o the beam y = σω x RRQ values of stress o the Omega deformeter x i= 1 i x = average value of the σsg y i= 1 i y = average value of the σω x RRQ The degree of correlatio is: Correl [σsg ; σω x RRQ ] = RESULTS ANALYSIS I the previous paper, the relatioship betwee the voltage i the beam ad the voltage i the Omega deformeter is explaied, ad it has bee show that this deformeter, i static motios, ca faithfully trasmit deformatios from the desired measurig poit. Durig dyamic testig of the deformeter, the same sigal compariso method as i static testig was used. The source voltage sigals from the strai gauges ad omega deformeter are simultaeously sampled. Dilatatio is calculated usig formula (8). For Wheatstoe's halfbridge, with oe active gauge ad oe temperature compesatiggauge, the Bridge factor is B = 1. This cofiguratio is o the beam. 4 U ASG k UESG ε = (8) O the omega deformeter, a differet cofiguratio of Wheatstoe's half-bridge is set, with two active strai gauges. For such a cofiguratio, the bridge factor is B=2 [5], ad the correspodig dilatio is calculated usig the followig formula: 4 U ε AΩ Ω = (9) 2 k UEΩ Accordig to Hook's law, the voltage ad dilatatio are i direct proportios. Thaks to this fact, whe comparig the sigal from the beam ad omega deformeter we ca also use the dilatatio. The 94% correlatio rate is at a satisfactory level, bearig i mid that the equipmet used to acquire the sigal has a 16- bit ADC embedded i it. With ADC of a lesser resolutio, the sigal stregth is icreased. I Figure 9 it ca be see that i the first 5 secods of the experimet there is a very weak sigal with a lot of oise. Such a sigal multiplied by RRQ leads to greater deviatio of the result. After the itroductio of the dyamic iitiative, the sigal from the strai gauge ad the Omega deformeter have a very good match. Eve after the expiry of the dyamic iitiatio effect, i the phase of forced dampig, the sigal from the Omega deformeter is followed by a referece sigal from the strai gauge. 6. CONCLUSION The tested Omega deformeter is a type of sesor that ca replace the strai gauge if there is a difficulty i implemetig the strai gauge itself. I the previous paper [12], the applicatio of Omega deformeter with the static load of the costructio, is preseted. Studies have show that i the case of static load, the degree of correlatio is 99%. I this paper, a deformeter testig is carried out i the dyamic load of the costructio. The sigal from The Omega deformeter is corrected usig the RRQ correctio factor as well as static testig. The mai objective of the study is to perform a comparative aalysis of the voltage obtaied from the sigal from the strai gauges ad voltage that is read o the Omega deformeter. The results of the study showed a high degree of correlatio ad itwas 94%. I this way it is cofirmed that Omega deformeter applicatio was possible both for static ad for dyamic loadigs of costructios. REFERENCES [1] TML, Strai Gauges, Tokyo Sokki Kekyujo Co., Ltd, TML Pam E-1007C [2] TML, Strai Gauge-type Trasducers, Tokyo Sokki Kekyujo Co., Ltd, TML Pam E-2020B [3] Hoffma, Karl: A Itroductio to Stress Aalysis ad Trasducer Desig usig Strai Gauges, HBM, [4] TML, Strai Gauge-type Civil Egieerig Trasducers, Tokyo Sokki Kekyujo Co., Ltd, TML Pam E-720S [5] Hoffma, Karl: Applyig the Wheatstoe Bridge Circuit VOL. 46, No 4,

5 [6] SabrieSoloma: Sesor Hadbook, Secod Editio, Mc Graw Hill, 2010 [7] Petrasiovic, N., Petrasiovic, D., Rasuo, B., Milkovic, D.: Aircraft Duralumiium Wig Spar Fatique Testig, FME Trasactios Vol. 45, pp , [8] Kastratovic, G., Vidaovic, N., Grbovic, A., Rasuo, B.: Approximate determiatio of stress itesity factor for multiple surface cracks, FME Trasactios, Vo. 46, No. 1, pp , [9] Wheatstoe, Charles: A Accout of several ew Istrumets ad Processes for determiig the Costats of a Voltaic Circuit. Philosophical Trasactios of the Royal Society of Lodo, 1843 [10] Thomso, William: O the Electro-dyamic Qualities of Metals. Philosophical Trasactios of the Royal Society of Lodo, 1856 [11] Kojima, Y., Dyamic Respose of Foil Strai Gages (a Study o the Shapes of Foil Strai Gages, the 4th Report), Tras. Jp. Soc. Mech. Eg.,47A (415), (1981)). [12] Kojima, Y., O the Measuremet of Dyamic Strai Usig Foil Strai Gages (a Study o the Shapes of Foil Strai Gages, the 5th Report), Tras. Jp. Soc. Mech. Eg.,49A (437), (1983). [13] М. Regodic, G. Siikovic, Е. Veg, А. Veg, R. Adrejevic, N. Gubeljak: Developmet of Ome ga Deformeter, 14th World Cogress i Mecha ism ad Machie Sciece, Taipei, Taiwa, 2015 [14] Paciroli, R.: Assessmet of a Structural Health Moitorig techique through sythetic data geeratio, FME Trasactios, Vol. 44, No. 4, p.p , [15] Skoblar, A., Žigulić, R., Braut, S., Blažević, S.: Dyamic Respose to Harmoic Trasverse Excitatio of Catilever Euler-Beroulli Beam Carryig a Poit Mass, FME Trasactios, Vol. 45, No. 3, p.p , ПРИМЕНА ОМЕГА ДЕФОРМЕТРА ЗА МЕРЕЊЕ НАПРЕЗАЊА ПРИ ДИНАМИЧКОМ ОПТЕРЕЋЕЊУ КОНСТРУКЦИЈА М. Регодић, Г. Шиниковић, Е. Вег, З. Јели, Н. Губељак Мерне траке су основни алат који се користи за мерење напрезања материјала. У индустрији се примењују већ више од седамдесет година. Област примене мерних трака је веома широка. Користе се за мерења напрезања машинских и грађевинских конструкција, појединачних машинских делова, уређаја и помагала у медицини итд. Мерне траке се израђују од различитих материјала, у различитим облицима и димензијама. И поред широке заступљености, примана мерних трака може бити отежана у одређеним временским условима. Ниска температура и повећана влажност ваздуха веома неповољно утичу на материјале помоћу којих се мерне траке постављају на површину дела каји се испитује. Да би се превазишли наведени проблеми користе се деформетри. У раду је испитана могућност примене специјално дизајнираног деформетра у облику слова омега (Ω). Испитивања су изведена у лабораторијским условима, на простој греди, при дејству динамичких оптерећења. Главни циљ испитивања био је утврђивање степена корелације резултата добијених директним очитавањем са мерних трака и резултата очитаних са деформетра. Анализа резултата упоредних испитивања показала су висок степен корелације чиме је потврђена могућност примене Омега деформетра на конструкцијама које су изложене динамичком оптерећењу. 524 VOL. 46, No 4, 2018 FME Trasactios

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