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final exam solution ME340 sp16.pdf

final exam solution ME340 sp16.pdf - Please put your name...

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Unformatted text preview: Please put your name on the front and back of this exam flEfl i :7 ME 340 Final Exam A thermopile, made up of multipie thermocouples (see figure on the right) can be used to measure temperature differences across an object directly creating a voltage proportional to the temperature difference. The more junctions used, the voltage is magnified to create an effective voltage average, which also lowers the uncertainty. in the present application, we can measure the voEtage with an uncertainty of +/— 0.05 mV (95%). We expect a temperature difference of 10C across the thermopiie. The thermocouple type used (T) has an output voltage O. 042 mV / C of temperature difference {for one junction pair) In order to measure with +/— 9 1 C uncertainty (95%), how many thermopiie junction (pairs) are needed? 903 ml/ 2:. :h/ C eeA/e_g)94:gm/@ fvfl/[fi‘ “t fw’gm/Z fifih m fox/{fféflg‘g If 10 junction pairs were chosen, and the voltage measured with a high‘input impedance voitmeter was 3 mV what is the temperature difference across the thermopiie? ot/le/ ,/&fie'pxeT3 EMV 6 m 2a M ac If instead of the thermopiie, another researcher suggested using two resistance thermometers which were each found to have ~i—I- 0.1 C uncertainty (95%) and to measure the temperature difference as T1 — T2. What is the uncertainty in Tl—TZ = AT using this atechnique?£fi (1L. ac) Please put your name on the front and back of this exam Finaiiy, the dAesired end resuit of the experiment is to measure the heat fiux. The equation for heat flux is: Q: It A—— L, Twhere the uncertainty in each of k, A, and L' Is 1% of their value and the uncertainty In AT is also 1% of its value {.1 C I 10 C). What is the uncertainty In heat flux, (1 [as a percent of Q}? (hint: if you don’t remember the formula, just assume alt the values of the variables are 1, and the uncertainty is w) (A) a, it) {<22 m eifif @fl fifégz Another aspect of measurement with the thermocoupies is to avoid any measurement errors due to loading effects. Are loading errors random errors or bias errors? Why? Efaxb @aW &/026~M33 aficrfififlég fife/51%? 6:" Does the loading error increase the measured vottage or decrease the voltage? (agameerr r //e Wage; In order to model this case, the engineer used 10 junction pairs, 10C total temperature difference, with 0.042 mv/C per junction pair, giving a total expected’voltage of 4.2 mV'(no current flow). The engineer computed the expected resistance of the thermocouple wires to be 60 ohms. What does the input impedance of the voltmeter need to be to limitg1 the measurement error to 0.05 mV? (la; Qt: @2, FL ..... Cdfia ”got feQe-cefr “The; ‘5‘? ”"3 ”H Eéfii‘m 6"” C” j a: ,f_ y fl, . é,[email protected] fl/L a: Ere :95 ,z-r Irr’ér-Iwr? .: ffflg a are; Please put your name on the front and back of this exam 2. A pressure transducer to be used to measure air pressure differences has been caiibrated (static) against LP an absolute standard. The resulting Einear fit, based on .E mummy 20 points) is given 35: 5mm 0::an Slgnal auditioning P lkPa) = 0.01 + 10.0 v, s,“ = 0.5 kPa iii: Em“ “ft“fiflfliaflnn velhaga in —>- Electrica! signal out where V is the measured voltage, and SW is the standard mifiridge—shahyupacflwit for uredi mums. deviation of the fit. What is the uncertainty in the m a: pressure now that the instrument has been calibrated? 1pm (list the degrees of freedom, and the formula 8: (nJSenslngschema distribution which you use to formuiate your result). Use 95% confidence. N325) erlg ”35f“ 25:3”.5) rent? (2% 55333:: EE: _ :_ 5: :2 :E as: We at $37”? P l stanepressmemeneitperrment For dynamic calibration, a pop test is performed. The results of the pop test are shown on the right. The first peak has a vaiue of 100 mV and the second peak has a value of 5 mV. The peaks are separated by 0.05 seconds. Does this system behave like a first order or a second ordersysteggfiméi 6&6?” Estimate the damping factor from the data. (3( 33) EE WWZWW EEE : EWQEl \ll PM Me- f”) What is the ringing frequency and the natural frequency for the setup? T; 3? W3 g: /W f1: :ClOZQ £33 :2? l ::::. 2a (”14922 ”“5 {Km/rig 5,: 3:; EEE’E my 230(2/[5 Pieese put your name on the front and back of this exam After the pop test, it was determined that the frequency . response is a factor of 5 too smali. In the figure at the right, the current tubing dimensions are d = 1 mm, i2 200 mm. Keeping the same transducer, and assuming that the tubing _ ~ . Transducer .: volume IS less than the transducer volume,what can be done 10. ‘ to increase the frequency response of the system? Show ' qua ntitativeiy how your solution will meet the criteria to increase the natural frequency by a factor of 5. Note: con = 9rd 3 1:11;; , c = :3; 1/3 thr/rr , where a is the speed of sound, Vtr is the transducer internal volume, p isge density of the fluid and p. is the dynamic viscosity. cw n27 ' 'Wm > S’— iif dz ‘>°§”&§.3 (er mm} M 7 e rs e ester rrmi. she“ see c: e mewsfiew After the changes, what is the new value of damping (as a ratio with the old one)? . _ 's h -. § of tiff/£93 e». Spa/g; Tel—£2: s it) 633— fil‘fiifimg Suppose the natural frequency of the measurement system is now 150 Hz. and the damping ratio is very small (assume 0}. Sketch the frequency response of the measurement system for this case: W‘x E‘s-“(g he? if it is desired to have the dynamic error be less than 1% (either high or low), what is the bandwidth of the measurement system (from D to what vaiue): {WMW M; {Afr/€072 Y 7* /w 2W1?) . i gefij We *3 Metre. Wigmé/fl Piease put your name on the front and back of this exam 3. It is desired to measure the frequency response of a beam subject to bending stress, similar to that performed in your laboratory experiment. However, in this case, it is expected that the temperature of the beam wili be changing during the experiment and that temperature compensation wiil be needed. A bridge circuit will be used, with aii strain gauges having the same nominal resistance. Using the table on the next page as a guide, seiect the correct strain gauge setup for temperature compensation in bending. Sketch the setup and show the location of the strain gauges. Show the location of the measurement of the bridge deflection voltage. It wili be assumed that any resistors used in place of strain gauges have nominal resistances equal to that of the strain gauge nominal resistance. Assume a GP = 2, an input voltage of 10 Volts, and the , bridge constant k from your set—up above, what is the expected output voltage of the bridge circuit if our maximum strain value is expected to be 1.0 e—4 m/m = s. ng M éifi ” M" a. 1.636%“? “QQE it its if ‘“ w w W i get M Q % e t. i \‘N Eey’ The ADC to be used has an input range of +g— S V, with 12 bits. lf the maximum strain vaiue should correspond to a value of at least 3 V, but less than 5 V, what gain is required on the ampiifier? 6 "fl 3 V 2:» §®@@ genie (as 2:: SE at: fee? if . teatime” e age Mféfiflm Using that gain, what iS the uncertainty“ In the measured strain (in strain units, not percent) due to the resolution ems of the ADC? a. V ’ (J i use. M f I flmm '2‘ “PR63 MFLi‘é’iQmTQ [6.9/2 :2. m 2 (gig/f my I ' a. £6 tit/V... #2 222 M L/ (5" e2 ”1 £23m We“? éJEM 5r we Kfsgm Please put your name on the front and back of this exam 6E0 GF :.___ _-— __ * K * 8 Note Er: 4 a 506 Chapterll Strain Measurement Table 11.1 Common Gauge Mountings I‘ ,. ‘l __._.....«——__e._..__.___,_4 .____..- Compensation Bridge Constant Arrangement Provided K 1 Single gauge in uniaxial stress None K = l «a- :fi: ~12- 1 _ Two gauges sensing equal and opposite Temperature K = 2 (2%: ) airflow—typical bending arrangement 2 1 Two gauges in uniaxiai stress Bending only K = 2 -e- 22%: —:.. 4 i 2 Four gauges with pairs semen g equal and Temperature 1: z: 4 fig _3'" opposite strains and bending 4 3 i 2 One axial gauge and one Poisson gauge ' tr; = 1 + up «w»- 2%: —r— 2 Shaft ~—-——¢_ Four gauges with pairs sensing equal and Temperature ' K = 4 opposite strains—sensitive to torsion only; and axial typioal shaft arrangement. ,Piease put your name on the front and back of this exam In the experiment, it is desired to capture all frequencies up to 5 kHz. What is the minimum sample frequency needed to avoid aliasing any signal up to 5 kHz? 9% 2 to me» A sample frequency of 20 kHz has been chosen. It is desired that the frequency response up to 5 kHz be attenuated by less than 1 dB, frequencies at 10 ki-iz be attenuated by at least 10 dB, whfle'STgn-ais-aelflm (We: .. 'u'..---- and the cumff fr\‘3Ctuencv. l&B£/@ fig) K/fiKSYflj‘K) WEE/Q’Q‘X/wgérfigfrs) , QK g: ml! mi 53‘“ {$ng 9:00. 9/) .4. L’D/Q) * #5“ e E I; :22 g... V ass-3W3“ l; ! meflm Design a Butterworth filter for this application. Specify the filter order, it, Based on your design, select the values of the filter components and sketch the filter. (Assume input and output resistance vaiues are 1 ohm). Table 6.1 Normaiized £lement Values for Low Pass LC Butterworth Filter Values for Ci in farads and Li in henrys are referenced to RS = R: = 1 ohm and we a 1 rad/sec. For K=1 use C1=1 Fand i421 H n... ., \., s2. QM Axle? C fie ., m C’s; mutt,“ F Aetmfle cgfilcgcttefi $3” Please put your name on the front and back of this exam To test the filter design, an input signal given below was input to 1the fitter: V(t) m 2 + 1* sin(2 *7t* 1000 *t) + 1 *sin(2*1t*10000 #15) What is the magnitude of the 1000 Hz and 10000 Hz component after the fiiter? g “a" g ( 2 2/4; . W 77777777777773: M ‘9 (/{%:34) MM? EU 'bésvjf i M a i a ‘7 we 33/ Q, l {5%}; wife I 73 [WW One portion of the output spectrum of the strain gauge for a beam impact response test is shown in the figure on the right. Based on the figure what is the ringing frequency, the damping ratio and the natural frequency of this lowest mode for the beam/ gm {LL}: M” AL} - . E” m #33:?” Please put your name on the front and back of this exam b! c} 0 w tau extra-’63! “i $69.: 3/” Extra Credit: (20 points): Design utterwarth filter to be placed in series with the output fithe pressure transducer that wiil m the bandwidth of the pressure measurement system. (the naturai frequency of the measurement system is 150 Hz. and the damping ratio is very smaii (assume 0). If it is desired to have the dynamic error be less than 1% (either high or low), what is the bandwidth of the measurement system (from O to what vatue): a, I (I " UK M( : - 2 96 It if; m ("5) / — (7%) [/7‘ (”99] é”: "m (39$ 63% A Wigsmmflg Wf'éfifiw fittest mm: M3 ['0 M (/séeEDe K96 ...
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