Read Section 11.1 to Section 11.5 in the textbook. Read instructions on how to install strain gages.

Transcription

1 FABRICATION OF A FORCE TRANSDUCER PREPARATION: Red Section. to Section.5 the textook. Red structions on how to stll str gges. OBJECTIVE: To mke force trnsducer sed upon the endg of cntilever em nd two str gges. The trnsducer must e sensitive only to endg str, nd not xil str. The uncertty the mesurement of force will lso e determed through detiled nlysis. A dt cquisition (DAQ) system will e used to mesure the dt. INTRODUCTION: All experimentl work volves dt collection nd nlysis. To this end, it hs ecome common prctice to cquire dt usg PC tht hs een fitted with dt cquisition ord. A gret dvntge to this pproch is tht the experimentl dt will lredy e the computer where further nlysis cn e redily performed. BACKGROUND INFORMATION: A PC hs een fitted with dt cquisition (DAQ) ord mde y Ntionl Instruments. It is cple of redg severl seprte nlog voltges the rnge of either ±5 or ±0 volts (dependg upon the specific DAQ ord). A softwre pckge clled Lview llows the user to configure the wy dt is cquired s well s to configure the computer screen to disply vrious mesurements oth numericl nd grphicl formts. Most quntities mechnicl engeers wish to mesure (pressure, temperture, position) re nlog nture. The PC, however, is digitl device. The fundmentl purpose of the DAQ ord is to convert these nlog signls to digitl form the PC cn understnd; thus this process is often referred to s Anlog to Digitl conversion, or simply A/D. The followg steps re required to perform dt cquisition. The quntity eg mesured must e converted or trnsduced to voltge ( trnsducer must e used). The voltge from the trnsducer put must fll with the voltge rnge of the DAQ ord with cceptle resolution. Otherwise, signl conditiong must e performed. The voltge signl is wired to the DAQ crd. The softwre, Lview this cse, must e configured to llow for proper dt cquisition. The dt is cquired. Dt is then nlyzed either with Lview or exported for lter nlysis.

2 SHORT THEORY: A rudimentry knowledge of DAQ ord nd PC is essentil. It is complicted ensemle of devices which rgs together mny dividul components, ech of which is often delt with seprte course. The DAQ hs severl chnnels which re multiplexed (rpidly switched) to sgle nlog to digitl (A/D) converter. The digitized voltge cn then e displyed on the monitor, written to memory, to file, etc. The A/D converter used for this lortory is Ntionl Instruments PCI-604E model, which does its A/D conversion. The full scle voltge of the nlog signl is divided to 4096 ( ) units, givg the ord.444 mv resolution (0 volts/ its) for ±5 volts full rnge nd mv resolution (0 volts/ its) for ±0 volts full rnge. BACKGROUND VS. FOREGROUND: The computer s microprocessor performs mny tsks tht hve een termed either ckground or foreground ctivities. Bckground ctivities volve processg, dt cquisition, dt processg nd svg dt to file. Foreground cludes updtg the screen nd monitorg the keyord. Under norml opertion the microprocessor flips etween the ckground nd foreground ctivities through the use of computer terrupts. In this wy dt is contuously eg digitized nd updted on the screen. However, if one requires dt to e smpled very quickly (i.e. fst time-vryg signl), Lview will shut down foreground ctivity durg smplg, nd screen updtes nd keyord monitorg stops. Figure : Whetstone Bridge Str Gges nd Whetstone Bride Str gges re used to trnsduce chnge str to chnge electricl resistnce. The reltionship etween the str,, mesured y the str gge (N.B. the suscript refers to sg

3 str gge ) nd the normlized chnge resistnce R R is where G is the gge fctor of the str gge. R sg = () G R A Whetstone ridge is used to trnsduce the chnge electricl resistnce to chnge electricl potentil (i.e. voltge), s seen the Figure. The put voltge, v, of the Whetstone ridge is function of the put voltge, v, nd the resistnces of the dividul legs of the ridge, given y R, R, R 3, nd R, respectively, s 4 RR4 RR3 v = v. () ( R + R )( R3 + R4 ) Str gges cn e wired up to the Whetstone ridge ny or ll of the legs. Sce the str gges chnge resistnce slightly s function of str, it is of terest to see how smll chnges of resistnce, R = R,0 + R, etc., lters the vlue of v, where R, 0 dictes the noml unstred vlue of R, nd R dictes smll chnge the vlue of R. By tkg the totl differentil of v, nd ssocitg the R with dr nd v with dv, etc., we cn see how the put voltge vries s function of the slight chnges of the R, R, R3, R. The 4 result is R,0 R4,0 R,0R3,0 v = v + ( R,0 + R,0 )( R3,0 + R4,0 ). (3) R,0 R,0 R 3,0 4,0 R R R R + 3 R4 v ( R,0 + R,0 ) R,0 R,0 ( R3,0 + R4,0 ) R3,0 R4,0 For the specil cse where the unstred noml resistnces of the str gges re equl, we cn write R,0 = R,0 = R3,0 = R4, 0. Under this condition, the first term on the right side of Eqution is zero, nd the Whetstone ridge is sid to e lnced. Thus, the expression for v reduces to v R R R3 R4 v = +. (4) 4 R,0 R,0 R3,0 R4,0 Further, if ech of the str gges hs n identicl gge fctor, G = G = G3 = G4 = G, then y sustitutg Eqution to Eqution 4, the reltionship etween put voltge nd the strs pplied to the str gges is v v G 4 [ + ] = 4 3 (5)

4 where the suscript on the strs dicte dividul legs of the Whetstone Bridge Figure. The vlue of v is typiclly very smll vlue, on the order of few millivolts. Therefore, it is common to use wht is known s str gge signl conditioner tht mplifies v y g of A, so tht the ctul signl mesured y the DAQ system is v = Av. Quick Review of Cntilever Bems A cntilever em is illustrted schemticlly Figure. In generl, ny force exerted t the end of the em cn e decomposed to component, F tht duces endg nd n xil component, F, tht duces pure tension. Considerg now only non-zero F exerted on the end, it is cler tht the em ends the direction of F. A str gge is mounted on one surfce of the cntilever em position # nd nother is mounted position # on the opposite surfce of the em. The distnce from the lod pot of F to the center of the str gges is L. The thickness of the cntilever em is given y, h, nd the width is given y. DAQ Figure : Cntilever em with two str gges nd mss t end. For now we will consider the cse of pure endg, so tht we ssume F = 0. Sce the crosssection of the em is symmetric, the tensile stress, on the surfce of the em t position # is the sme mgnitude s the compressive stress, t position #. The mgnitude of the stress t position # is give y Mh = (6) I 3 where M = F L is the moment on the em t the position of the str gges, nd I = h is the moment of erti of the em. The str, sg, mesured y str gge is relted to the stress y Hooke s lw for unixil deformtion, = E, where E is Young s modulus. On the other hnd, if only n xil force, F, is pplied to the em with F = 0, the stress t

5 oth pots # nd # is = = F / h. Therefore, sce Hooke s lw pplies t oth plces, the strs t pots # nd # re the sme mgnitude nd sme sign. APPARATUS: PC with DAQ. Lview progrm written y l group. Cntilever em Supplies to stll str gge COMPUTER PROGRAMMING Write computer progrm usg Lview to mesure the rw voltge from the put of the Whetstone Bridge. The progrm should then process the dt to ot the force. Before strtg to write the Lview progrm, you should wtch the on-le video tht cn e found from lk on the course wiki. Crete folder for your group with the folder entitled MECE L 0-0 on the computer t the l sttion. Strt the Lview progrm on the computer t the experimentl sttion go to the screen tht sys Block Digrm. Right-click on the mouse nd then go through the menus: Express-Input nd fd the icon nmed DAQ Assistnt. Drg the DAQ Assistnt icon with the Block Digrm of Lview. This will itite the set up the dt cquisition. Choose Anlog Input, then Voltge. You will then see the words Dev (PCI-604E) which dictes the nme nd type of the Ntionl Instruments dt cquisition crd the computer. Select the specific chnnels i0. This structs Lview to mesure voltge from chnnels 0. Then click Fish. Set the Mx nd M s t 5 nd -5 volts, respectively. Further, set the terml configurtion to e Differentil mode tht directly mesures the voltge difference etween the two put wires from the Whetstone Bridge. Flly set the option to cquire N smples. Then click OK to fish the set-up process. You should then see n icon on the Block Digrm tht hs numer of different rrowheds on its left nd right edges. Plce the cursor over the rrowheds to see their functions. Then right click on the rrowhed tht sys rte nd then go to the Crete menu choose Control. This will plce second icon on the Block Digrm s well s n icon on the Front Pnel. Use the mouse to chnge the text t the top of the new icon to red DAQ rte (Hz). Then do the sme for the rrowhed for numer of smples. Then you should hve two controls on the Front Pnel so tht you cn specify the DAQ rte nd the numer of dt pots to mesure. The next step is to process the rw dt so tht our put is for force Newtons. Right click on the Block Digrm nd go to the Express menu nd then to the Arithmetic & Comprison menu nd drg the Formul icon to the Block Digrm. This will open wizrd tht llows you to specify vrile nmes nd then to enter formul. One vrile nme (lel) you enter should e Vm which could stnd for mesured voltge. You ll lso need to hve vrile lels for ll the other vriles you need for the processg. Then enter the right side of the eqution tht effects the processg. Then you cn click OK.

6 Use the right mouse utton to mke control icons for ll the new vriles, such s, h, L, etc. Then use the mouse its spool mode to connect wire etween the dt rrowhed on the DAQ Assistnt icon to the Vm rrowhed on the Formul icon. This structs Lview to trnsfer the dt from the DAQ Assist icon to the Formul icon. When writg your eqution, recll tht the ctul mesured signl from the Whetstone ridge is v m = Av, where A is the g of the signl conditioner ( this cse it is equl to 000) nd v is the put signl from the Whetstone. The put voltge is denoted y v nd for this cse is 5 volts. The vlue of the gge fctor, G is determed from the specifiction sheet from the mnufcturer. You then need to fd the men nd stndrd devition of the processed dt. Go to the Express-Signl Anlysis menus nd choose the Sttistics icon. Wire it to the Result rrowhed of the Formul icon. Then crete numeric dictor to put the two vlues to the Front Pnel. Then right click on the Result rrowhed of the Formul icon nd crete Grph Indictor (which will pper on the Front Pnel). Chnge lels on the x- nd y-xes ccordgly (clude proper units). Then the Express-Output menus, choose the Write Mesurement File icon nd drg to Block Digrm. Wire it up to the Result rrowhed of the formul node. Red the help screen of the Write Mesurement File icon nd fd pproprite settgs. This will llow you to write your processed dt to file. EXPERIMENTAL PROCEDURE: Follow structions provided to pply two str gges to opposite sides of the cntilever em positions # nd #. Wire the two str gges to the Vishy str gge conditioner Hlf-Bridge configurtion so tht the put is sensitive only to endg force, F, nd not F. o The put voltge from the Vishy is v = 5 volts. o There is g of the Vishy is A = 000. Connect the put from the Vishy to the DAQ. Write Lview progrm to collect your dt. Use or kg mss to vlidte your force trnsducer. REPORT: Derive the eqution tht reltes the force F to the mesured voltge, v m, nd the other vriles. Mke tle tht conts the vlues of ech vrile the eqution, s well s the uncertty (one column for uncertty engeerg units nd nother column with normlized uncertty) of ech vrile. The Lview progrm you write should e used to mesure the verge vlue nd stndrd devition of F over one second time period. Do thorough uncertty nlysis, sg your nlysis upon the uncertty ll mesured vriles. Justify nd expl ech step. Sce you re only mesurg one vrile multiple

7 times, proceed s follows. Clculte the is uncertty F sed upon the uncertty vlues of ll the vriles you mesure. Cll this vlue B. Then clculte the precision uncertty, F clled P, sed upon the sttistics mesures of the repeted mesurements. From this, F determe the overll uncertty nd express oth terms of engeerg units s well s normlized uncertty. Compre the overll uncertty the force trnsducer you mke with typicl lod cells tht cn e purchsed from compnies. To fd the uncertty vlues of the dividul vriles your expression for F, you will need to do use your est judgment for some of the vriles (i.e., h nd L ). For other vriles, such s v m, A nd G, you will need to look t documenttion from the mnufcturer. The specifictions of the DAQ nd the Vishy str gge signl conditioner re on Courseworks. The uncertty G is found on the specifiction sheet tht ccompnies the str gges. You will need to lso estimte the uncertty the vlue of E. Wht two vriles troduce the most uncertty? Wht re strtegies to reduce the uncertty tht could e implemented?