Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)
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1 Lesson 8 Thermomechnicl Mesurements for Energy Systems (MEN) Mesurements for Mechnicl Systems nd Production (MME) A.Y Zccri (ino ) Del Prete
2 Mesurement of Mechnicl STAIN Strin mesurements re perhps the most widespred mesurements done in engineering (tension, force, pressure, ): We mesure here the lengthening nd shortening of mechnicl structures. If we know the Young s Modulus E of the mteril, fter mesuring the strin ε we cn obtin the vlue of mechnicl tension σ = E ε! Trnsverse strin is mesured by considering the rdil contrction D2 D / D nd involves the knowledge of the Poisson Coefficient: t Which for metllic mterils rnges from 2 up to Conventionlly ν = 0,3 L 2 L L L L
3 Ductile nd brittle mterils: A first type of instruments used to mesure the strin or the displcement between two djcent points re the Mechnicl Extensometers
4 Mechnicl Extensometers : The displcement is mesured between two points, initilly t distnce l 0 When the specimen elongtes Δl, the indictor rottes of n ngle θ nd we reed the output λ l b The rtio is : l b And the grdution curve is then: l l 0 l b 0
5 Electricl STAIN GAGES : (historicl reliztion) However, wht we relly need is punctul strin mesurement, so to effectively monitor the zones of the surfce where the strin concentrtes. Electricl strin gges re bsed on resistnce vrition with elongtion! l S irst we hve to elborte bit the bsic physicl reltion of resistivity (modern reliztion) ln l ln S ln ln l ln S
6 then we derivte the reltion nd we trnsform the infinitesiml terms into finite differences d d dl ds dt dt l dt S dt l l S S Becuse it is S 2 D ds dd S D nd 2D D S DD dt dt t 2 t 2 D D S 2 D 2 2t S 2 D D l D it remins 2 ( ε t sign is the opposite of ε ) 2 t 2 l D 2 with 0. 3 we would hve.5. 7 l l however, vrition of Δρ/ρ is not zero! l l
7 Becuse the contribution of the resistivity vrition Δρ is difficult to clculte, strin gge producer proceed experimentlly nd «mesure» the fctor for certin number of gges. The resulting number is then ssigned to the sme lot of trnsducer tht is the gge fctor 2 Strin gge «grdution curve» Note tht Δρ/ρ is lmost constnt for strins up to 5-6 %!! Commercil strin gges :
8 Therml effects : Unfortuntely, becuse n electric current is flowing through every strin gge, there is n dditionl therml ' contribution on resistnce vrition: T Due to heting, the strin gge wire undergoes lso therml elongtion generlly NOT equl to the therml elongtion of the underlying mteril. resistnce vrition due to mechnicl strin: 2. resistnce vrition due only to therml effects: T There is lwys n pprent strin which, in fct, is NOT rel : l' l l'' l ' '' T pp ' T '' T T which, moreover, is We hve therefore: ' '' T Becuse the coefficients α nd β depend on the gge wire mteril while the coefficient β depends on the underlying mteril, if we cn mke ' '' 0 then we re nulling the pprent therml contribution ε pp Temperture self-compensted strin gges pproximtely relize: '' '
9 Temperture self-compenstion is not perfect, nor constnt with temperture, nd it works ONLY if the strin gge is pplied on the correct underlying mteril If how much is ctully the resistnce vrition if we mesure strin of 00μm/m with 20Ω gge? m It s vrition of only the 0,02% of the bse resistnce! These smll vritions re optiml to be mesured with the Whetstone Bridge
10 We hve now combined mesurement chin: Strin Gge + Whetstone Bridge The two grdution curves work then together e E Which combined give us: e E e E the combined grdution curve! Strin gge (2) does not mesure ny strin but, it undergoes the sme therml effects of strin gge () ' '' T T T 2
11 If the two strin gges () nd (2) re pplied on contiguous rms of the Whetstone Bridge, the therml effects re utomticlly eliminted : e E T T T 2 0 This is perhps the most importnt service the WB does during strin mesurement! Mesurement of tensile strin: The second gge (2) cn be pplied more efficiently on the specimen to increse the mesurement sensitivity, but it must be rotted 90 in XY configurtion to give useful signl. It will then mesure the trnsversl strin t producing the grdution curve: e E t where the fctor ( + ν) =,3 is n extr mplifiction due only to the bridge configurtion, clled «bridge fctor»
12 Mesurement of bending strin: the upper gge mesures the stretched fiber strin while the bottom gge mesures the compressed fiber strin : becuse it is Ad the bridge fctor is equl to 2! e f f 2 E e f f E 2 f f f 2 f Note tht the bridge fctor cn be incresed up to if we employ four strin gges connected s shown on the left nd mke the full bridge ctive! 2 3 2
13 Strins, of course, cn be composed in more complicted wys, s shown in the figures...
14 Mesurement of torsion strin: undmentl ppliction for the crnkshfts, where we wont to mesure the drive torque to get the power output of n engine: W mecc C Strin gges re plced s in the figure, ligned with the mximum strin 5 lines on the shft surfce. The strins will be 3 2 nd the grdution curve results: e E with full bridge fctor equl to!
15 Exmples of complete strin gge mesurement chins : Note tht strin gge chnnels need to be clibrted before use, this is done by connecting internlly shunt resistors s tht simulte specific strin vlues: g elettric with e g s g nd elettric g E s g
16 Exmple of strin gge ppliction in Lod Cell to mesure force Physicl bsic eqution: k x where (for tension nd compression) k AE l Grdution curve is liner : x AE And sensitivity is constnt : S x AE
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