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ME 322: Instrumentation Lecture 40

ME 322: Instrumentation Lecture 40. April 30, 2014 Professor Miles Greiner. Announcements/Reminders. This week: Lab 12 Feedback Control HW 14 d ue now (Last HW assignment) Review Labs 9, 10, 11, and 12; Today and Friday Supervised Open-Lab Periods

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ME 322: Instrumentation Lecture 40

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  1. ME 322: InstrumentationLecture 40 April 30, 2014 Professor Miles Greiner

  2. Announcements/Reminders • This week: Lab 12 Feedback Control • HW 14 due now (Last HW assignment) • Review Labs 9, 10, 11, and 12; Today and Friday • Supervised Open-Lab Periods • May 2-4, 2014, 11-2 Friday through Sunday (will those times work?) • Extra Credit Lab 12.1 (due in class Monday, 5/5/2014) • See Lab 12 instructions (study effect of DT, DTi, TSP, heater and TC locations) • Check out Lab-in-a-Box for DeLaMare Library • Only 0.5% of grade • Lab Practicum Finals (May 6-14) • Guidelines, New Schedule • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Tests/Index.htm • How many of you will graduate this year (2014) or next year (2015). • If it will be later than 2015, was there something the ME Department did that delayed your graduation?

  3. Lab 9 Transient TC Response in Water and Air • Start with TC in room-temperature air • Measure its time-dependent temperature when it is plunged into boiling water, then room-temperature air, then room-temperature water • Determine the heat transfer coefficients in the three environments, hBoiling, hAir, and hRTWater • Compare each h to the thermal conductivity of those environments (kAir or kWater) • Also calculate Biot number (dimensionless thermal size) and delay time for center to respond

  4. LabVIEW VI

  5. Dimensionless Temperature Error T Environment Temperature TF Initial Error EI = TF – TI Error = E = TF – T ≠ 0 TI TI t t = t0 • At time t = t0 a thermocouple at temperature TI is put into a fluid at temperature TF. • Theory for a uniform-temperature TC predicts: • Dimensionless Error: • Time Constant for a spherical thermocouple TF T(t)

  6. Measured Thermocouple Temperature versus Time • From this chart, find • Times when TC is placed in Boiling Water, Air and RT Air (tB,tA,tR) • Temperatures of Boiling water (maximum) and Room (minimum) (TB, TR) • Thermocouple temperature responds more quickly in water than in air • Slope does not exhibit a step change in each environment • Temperature of TC center does not response immediately • Transient time for TC center: tT ~ D2rc/kTC

  7. Type J Thermocouple Properties • State estimated diameter uncertainty, 10% or 20% of D • Thermocouple material properties (next slide) • Citation: A.J. Wheeler and A.R. Gangi, Introduction to Engineering Experimentation, 2nd Ed., Pearson Education Inc., 2004, page 431. • Best estimate: • Uncertainty: • tT ~ D2rc/kTC; = ?

  8. TC Wire Properties (App. B)

  9. Dimensionless Temperature Error, • For boiling water environment, TF = TBoil, TI = TRoom • For room-temperature air and water, TF = TRoom, TI = TBoil • How can we find the time range t1 < t < t2 when decays exponentially with time?

  10. Data Transformation (trick) • Where , and b = -1/t are constants • Take natural log of both sides • Instead of plotting versus t, plot ln() versus t • Or, use log-scale on y-axis • During the time period when decays exponentially, this transformed data will look like a straight line

  11. Find decay constant b using Excel • Use curser to find beginning and end times for straight-line period • q exhibits random variation when it is less than q < 0.05 • Add a new data set using those data • Use Excel to fit a y = Aebx to the selected data • For this data b = -13.65 1/s • Since b = -1/t, and t, • Calculate (power product?), ? • Assume uncertainty in b is small compared to other components

  12. Dimensionless Temperature Error versus Time for Room-Temperature Air and Water • Decays exponentially during two time periods: • In air: • t = 3.83 to 5.74 sec, b = -0.3697 1/s • In water: • t = 5.86 to 6.00 sec, b = -7.856 1/s.

  13. Lab 9 Results • Water environments have orders of magnitude higher h (and b) than air • Similar to kFluid • Nusselt numbers (power product) are more dependent on flow conditions (steady versus moving) than environment composition • Biot number (dimensionless size)

  14. Air and Water Properties (bookmark)

  15. Lab 9 Sample Data • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2009%20TransientTCResponse/LabIndex.htm • Plot T vs t • Find TB, TR, tB,tA, andtR • Calculate q and plot vs time on log scale • In Boiling Water, TI = TR, TF = TB • In Room Temperature air and water, TI = TB, TF = TR • Select regions that exhibit exponential decay • Find decay constant for those regions • Calculate and wh for each environment • For each environment calculate • NuD • BiD

  16. Lab 10 Vibration of a Weighted Cantilever Beam LE LB • Accelerometer Calibration Data • i.e. C = 616.7 mV/g • Use calibration constant for the issued accelerometer • Inverted Transfer function: a = V/C • During Final you will be given values and uncertainties of E, W, T • Measure (3s uncertainty) • MT, MW: Analytical balance, = 0.1 g • LB, LE, LT: Tape measure, = 1/16 in Clamp MW W T E (given) Accelerometer LT MT

  17. Table 1 Measured and Calculated Beam Properties LE LB Clamp MW W T E (given) Accelerometer LT MT • Intermediate mass (later)

  18. Figure 2 VI Block Diagram

  19. Figure 1 VI Front Panel

  20. Disturb Beam and Measure a(t) Steel Aluminum • Use a sufficiently high sampling rate to capture the peaks • fS > 2fM • When plotting a versus t, use time increment Dt = 1/fS • Looks like • Is b constant? • Measure f from spectral analysis ( fM) • Find b from exponential fit to acceleration peaks

  21. Figure 4 Acceleration Oscillatory Amplitude Versus Frequency • The sampling period and frequency were T1= 10 sec and fS = 200 Hz. • As a result the system is capable of detecting frequencies between 0.1 and 100 Hz, with a resolution of 0.1 Hz. • To plot aRMS vs t, use frequency increment Df= 1/T1 • The frequency with the peak oscillatory amplitude is fM = 8.70 ± 0.05 Hz. This frequency is easily detected from this plot.

  22. Fig. 5 Peak Acceleration versus Time Aluminum Steel • For aluminum, exponential decay changed at t = 2.46 s • During the first and second periods the decay rates are • b1 = -0.292 1/s • b2 = -0.196 1/s • Decay “constant” b was not constant

  23. Equivalent Endpoint Mass LE LB Clamp MW • Beam is not massless, • Its mass affects its motion and natural frequency • (linear sum) • mass of weight, accelerometer, pin, nut • (contribution form beam mass) LT MT ME Beam Mass MB

  24. Beam Equivalent Spring Constant, KEQ F LB • Power product? d

  25. Predicted Frequencies • Undamped • Power Product? • Damped • Power product? • If , then , and • Measured Damping Coefficient

  26. Table 2 Calculated Values and Uncertainties • The equivalent mass is not strongly affected by the intermediate mass • The predicted undamped and damped frequencies, fOP and fP, are essentially the same (frequency is unaffected by damping). • The confidence interval for the predicted damped frequency fP = 9.0 ± 0.2 Hz does not include the measure value fM= 8.70 ± 0.05 Hz.

  27. Time and Frequency Dependent Data • http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/Labs/Lab%2010%20Vibrating%20Beam/Lab%20Index.htm • Plot aversus t • Time increment Dt = 1/fS • Plot aRMSversus f • Frequency increment Df= 1/T1 • Measured Damped (natural) Frequency, fM • Frequency with peak aRMS • Uncertainty • Exponential Decay Constant b (Is it constant?) • Show how to find acceleration peaks versus time • Use AND statements to find accelerations that are larger than the ones before and after it • Use If statements to select those accelerations and times • Sort the results by time • Plot and create new data sets before and after 2.46 sec • Fit data to y = Aebx to find b

  28. Thermal Boundary Layer for Warm Sphere in Cool Fluid Thermal Boundary Layer • h increases as k increase and object sized decreases • = Dimensionless Nusselt Number (power product?) TF T r D Conduction in Fluid

  29. Lab 9 Transient TC Response in Air & Water Wire yourself TC → Conditioner (+)TC → White Wire (-)TC → Red Stripe Conditioner to → MyDAQ Com → (-) Vout → (+) Write VI Easy Fig 1 & 2 will not be given

  30. Acquire Data Fs = 1000 Hz T­i = 8 sec At least 2 seconds in each environment. • Room temp water • Boiling water • Room temp air • Room temp water Fig 3 Plot T Vs. t ID time tB , tA , tR ID Temp TRoom = Tmin TBoil = Tmax

  31. Fig 4 For boiling water vs. t Identify: Start & end times of exponential decay period (looks linear) • Select exp decay data y • Add data to plot • Fit to that data • Show results on the plot • Find b • Units s-1 Fig 5 Room Temp Air & Water vs. t Find Find Table 2

  32. Lab 10: Vibrating Beam You will be given beam and its E and WE VI fig 1 &2

  33. Table 2

  34. Undamped Predicted Frequency if b = 0, λ = 0 Measured Damping Coeff If Then Wfp≈ Wfop Is

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