Final Exam ME340 SP16.pdf

Final Exam ME340 SP16.pdf - Please put your name on the...

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Unformatted text preview: Please put your name on the front and back of this exam ME 340 Final Exam A thermopile, made up of multiple 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 voitage average, which aiso iowers the uncertainty. in the present application, we can measure the voltage with an uncertainty of +/— 0.05 mV (95%). We expect a temperature difference of 10C across the thermopile. The thermocouple type used (T) has an output voltage 0. 042 mV / C of temperature difference (for one junction pair). In 1 order to measure with +/ 0.1 C uncertainty (95%), how many thermopile junction (pairs) are needed? If lfljuriction pairs were chosen, and the voltage measured with an infinite input impedance voltmeter was 3 mV, what is the temperature difference across the thermopiie? (in C) If instead of the thermopiie, another researcher suggested using two resistance thermometers which were each found to have +/— 0.1 C uncertainty (95%) and to measure the temperature difference as T1 — T2. What is the uncertainty in T1-T2 = AT using this technique? Please put your name on the front and back of this exam Finally, the desired end resuit of the experiment is to measure the heat flux. The equation for heat flux is: Q = k A3}, where 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/ 10 C). What is the uncertainty in heat flux, Q (as a percent of Q)? (hint: if you don’t remember the formuia, iust assume all the values of the variables are 1, and the uncertainty is 0.01). ' Another aspect of measurement with the thermocouples is to avoid any measurement errors due to loading effects. Are loading errors random errors or bias errors? Why? Does the loading error increase the measured voltage or decrease the voltage? lo order to model this case, the engineer used leunction pairs, 10C total temperature difference, with 0.042 mv/C perjunction 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 ofthe voltmeter need to be to limit the measurement error to 0.05 mV? (hint: be careful about the sign of the error) Piease 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 calibrated (static) against b3 an absolute standard. The resulting linear fit, based on Deadwluma,V 20 points) is given as: mm; mm“ Denim.“ P (kPa) = 0.01 + 10.0 V , SW = 0.5 kPa brad “mm” W res *Excltatlcn voltage In —>- Electlcal stgnal out where V is the measured voltage, and SW is the standard deviation of the fit. What is the uncertainty in the pressure now that the instrument has been calibrated? Tram (list the degrees of freedom, and the formuia & wsansinmeme distribution which you use to formulate your result). Use 95% confidence. 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 of100 mV and the second peak has a value of 5 mV. The peaks are separated by 0.05 (b) Bridgedrain gauge circuit for pressure diaphragm: seconds. Does this system behave like a first .— order or a second order system? I-- "- Estimate the damping factor fromthe data. its) What is the ringing frequency and the natural frequency for the setup? Piease 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 small. In the figure at the right, the current tubing dimensions are d = 1 mm, I: 200 mm, Keeping the same transducer, and assuming that the tubing volume is less than the transducer volume, what can be done 1:. to increase the frequency response of the system? Show quantitatively how your solution will meet the criteria to increase the natural frequency by a factor of 5. Note: can = 9f 3 1:31,: , g = [11:53 ,/3 l VET/11' , where a is the speed of sound, Vtr is the transducer internal voiume, p is the density of the fluid and p is the dynamic viscosity. Transducer After the changes, what is the new value of damping (as a ratio with the old one)? 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: 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 0 to what value): Please put your name on the front and back ofthis exam 3. It is desired to measure the frequency response ofa 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 will be changing during the experiment and that temperature compensation will be needed. A bridge circuit wili be used, with all strain gauges having the same nominal resistance. Using the table on the next page as a guide, select the correct strain gauge setup for temperature compensation in bending. Sketch the strain gauge setup on the beam. In a second sketch, sketch the bridge circuit. show the location of the strain gauges in the bridge circuit and show the location of the measurement of the bridge deflection voltage. it will 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 Voits, 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 = a. The ADC to be used has an input range of +/- 5 V, with 12 bits. If the maximum strain value should correspond to a vaiue of at least 3 V, but less than 5 V, what gain is required on the amplifier? Using that gain, what is the uncertainty in the measured strain (in strain units, not percent) due to the resolution of the ADC? Please put your name on the front and back ofthis exam 6E0 GF :—_._——* K'* 3 Note Ei .4 a 506 Chapter 11 Swain Measurement Table 11.1 Common Gauge Mountings I‘ . . 5E0 Compensation Bridge Constant Arrangement Provided 1c 1 Single gauge in uniaxial stress None 1: = l + m —.— 1 V Two gauges sensing aqua} and opposite Temperatuxe K = 2 gzflz ) strain—typical bending arrangement 2 1 TWO gauges in uniaxisl stress Bending only 1: = 2 4- :fi: —a- 4 1 2 Pour gauges with pairs sensing equal and Tcmperattue K = 4 4— Egg: + ‘ oppnsite strains and bending 4 3 1 2 One axial gauge and one Poisson gauge ‘ K = 1 + VP --1— ii": —I- ’ 'w—fii Four gauges with pairs sensing equal and Temperature ‘ K = 4 opposite strains-sensifive to torsion only; and axial m typical shaft arrangement. ‘9. . 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 aiiasing any signal up to 5 kHz? 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 kHz be attenuated by at least 10 dB. Design a Butterworth filter for this application. Specify the filter order, k, and the cutoff frequency. Based on your design, select the vatues of the filter components and sketch the filter. (Assume input and output resistance values are 1 ohm). Table 6.1 Normalized Element Values for Low i’ass LC Butterworth Filter Values for Ci in farads and Li in henrys are referenced to RS 2 R1: 1 ohm and (0.; = 1 rad/sec. For Kml use C1: 1 Fand 1.1:]. H Please put your name on the front and back ofthis exam To test the filter design, an input signal given below was input to the fitter: V02) =2+1=k sin(2*n*1000*t)+1*sin(2*7r*10000*t) What is the magnitude of the 1000 Hz and 10000 Hz component after thefilter? Sketch the Fourier Transform of the signal before and after the filter: 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. Emma Showbiz Iii-Km Pain! flease put your name on the front and back of this exam Extra Credit: (20 points): Design a Butterworth filter to be placed in series with the output of the pressure transducer that will double the bandwidth of the pressure measurement system. (the natural frequency of the measurement system is 150 Hz. and the damping ratio is very small (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 including the filter (from O to what value)?: ...
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