AME 20213: Measurements and Data Analysis Technical Memo Date Submitted: 24 September 2014 Dates Performed: 10 September 2014 and 17 September 2014 To: Professor John Ott From: Evan Hicks Subject: Lab Exercise 1 – Sensors/Measurement Systems/Calibration Summary: During this lab, three experiments were conducted with each having individual characteristics of sensor calibration and approximations calculated from the calibrations. The first experiment included the calibration of a cantilever strain gage apparatus connected to a full Wheatstone bridge configuration, which output the voltage as a function of the induced strain. The output voltage was then amplified before displayed by the voltmeter. The use of the strain gage and voltage was to signify if a player had made a shot into the cup at the end of the strain gage with a ping-­‐pong ball. The gage was calibrated using standard masses. The calibration showed a high linear relationship with a high coefficient of determination (𝑟 ! = .998), but with an error of ±.04 𝑉. It was found that the error increased as a result of the voltage amplifier. It was determined that if a player made a ping-­‐pong ball in the cup, a voltage would be output, signaling the completion of the shot. The second experiment comprised of the calibration of an accelerometer to determine the relationship between output voltage and acceleration, which then was used to create a 1 calibration curve relating the faucet angle and the flow rate of a faucet. The calibration of the accelerometer and the output voltage exhibited a strong linear relationship with a high coefficient of determination (𝑟 ! = .999). The calibration of the faucet angle against the flow rate was not very linear. The curve had a coefficient of determination (𝑟 ! = .707). The lack of linearity was attributed to the valve of the faucet, which controls how much water comes out at a given faucet angle. The faucet handle has some give and did not exactly translate into how water was coming out. It was determined that when using water correctly, water for up to 11 people could be saved. The third experiment included the recording of two sensors, an RTD and a thermistor, as well as the calculation of fan speed from a FFT. The two sensors used resistance to measure the temperature inside the PS3 around the heat sink and just outside of the fans. The last sensor was a photocell that measured the fan speed when calculated correctly. It was determined that the fan responds appropriately to the internal temperature and attempts to cool the CPU and power supply off the ventilation of hot air. Findings: Beerless Pong: In the first experiment a cantilever strain gage was connected to a full Wheatstone bridge. A calibration curve was created and used to determine the output voltage that corresponds with the mass of a ping-­‐pong ball. The calibration was constructed by a linear regression analysis and quantitative data was drawn from the conclusions. The strain gage determined the output voltage based on how much resistance was created by the strain. When more mass was added, the output voltage increased. It was determined that because the data showed a high correlation of linearity 𝑟 = .999 , the linear regression analysis would be appropriate. The linear regression analysis takes on the form of : 2 𝑉 = 𝑎𝑚 + 𝑏 where V is in volts and m is mass. The actual calibration curve takes form of: 𝑉 = .0577𝑚 + .066 Plotted in figure 1 is the approximation of the mass of a ping-­‐pong ball based off the calibration curve against the number of ping-­‐pong balls, as well as the published mass versus the number of ping-­‐pong balls. 20
Mass in grams (g)
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Exact Mass of Ping Pong Balls Versus Number of Balls
Approximate Mass of Ping Pong Balls Based on Calibration Curve
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Figure 1: Plot of Exact Mass and Approximate Mass Against the Number of Ping Pong Balls Several remarks can be made about the approximate error of this curve, the sensitivity of this curve, and whether the calibration is sufficient. The approximate error of the measurement was ±.04 𝑉, which translates into a maximum error in the mass calculation of 1.3832 grams, which is 51% of the published mass of a ping pong ball. The sensitivity of the curve is simply the slope, which is 𝐾 = .0577 𝑔. The slope suggests a very low sensitivity to changes in mass. The curve also is not suited for mass larger than 50 g because the max voltage output of the setup was limited to 3 V. With that being said, the system is still 3 sufficient because it registered a change in mass, which output a voltage. Even if the curve were not sufficiently calibrated, the system as a whole would work correctly. Water Conservation The accelerometer determined the gravitational acceleration based on the angle of the accelerometer. By creating a calibration curve using the linear regression analysis, a link between accelerometer, which displays in volts, and angle could be established. The equation takes form of: Θ = 𝑎V + 𝑏 where Θ is the angle of the faucet and V is in volts. The resulting curve takes form of: Θ = −281.16V + 446.10 Similarly, the equation for the flow rate against the faucet angle takes the form of: FR = 𝑎Θ + 𝑏 Where FR is flow rate in 𝑚𝐿 𝑠 and Θ is the faucet angle in degrees. The resulting curve takes the form of: FR = −.6891Θ + 121.44 The two curves are represented in figure 2 and 3 respectively. 100
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Figure 2: Calibration Curve for the Accelerometer Against the Faucet Angle 4 150
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Figure 3: The Calibration Curve for the Faucet Angle Against the Flow Rate It was determined that the average time a person washed their hands was 30 seconds. If a person were economic and trying to save water, they would use 5 seconds to lather up and 10 seconds to wash off, turning the water off in between, only using 15 second of water. Assuming they were the most economic and barely had the water flowing, and on average washing their hands 5 times a day, the person would use 3.408 L of water. On the other hand, the more average user would leave the water running for the whole 30 seconds and use a higher flow rate. With washing 5 times a day, they would use 24.991 L of water. If they were to cut down, they could save enough water to sustain 11 people. PS3 Hot Shot: The thermistor and RTD both have defined calibration curves designed by the companies that manufacture the sensors. The curves link temperature and resistance. The calibration of the curve for the thermistor takes the form of: 𝑇 𝑅!!!"# = ((𝐴 + 𝐵𝑙𝑛
𝑅!!!"#
𝑅!!!"#
𝑅!!!"# !!
+ 𝐶𝑙𝑛!
+ 𝐷𝑙𝑛!
) 𝑅!"#
𝑅!"#
𝑅!"#
T being temperature in degrees Kelvin and 𝑅!!!"# is the function of the resistance based on the temperature. Below is the curve given by the manufacturer: 5 𝑇 𝑅!!!"# = ((3.354016×10!! + 2.56985×10!! 𝑙𝑛
+ 2.620131×10!! 𝑙𝑛!
𝑅!!!"#
10000
𝑅!!!"#
𝑅!!!"# !!
+ 6.383091𝑥10!! 𝑙𝑛!
) 10000
10000
The equation for the calibration curve for the RTD takes form of: 𝑇 𝑅!"# = .2957 𝑅!"# − 259.92 Once again, T being the temperature and 𝑅!"# is the function of resistance based on the temperature. Both of the calibration curves are plotted in figure 4. Using the FFT method to determine the peak frequencies of the photocell data, an approximate RPM was determined as a function of time. The result is graphed in figure 4. As the core temperature went up, the fan speed increased to help cool the PS3 down. 1000
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Fanspeed in RPM
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Figure 4: Calibration Curves of Thermistor and RTD Several remarks can be made from the data in the figure. As the core temperature went up, the fan speed increased to help cool the PS3 down. Also, as the power supply began to heat up, the CPU heated up as well. The CPU required more power to function and the power supply had to work harder to supply the power. The curve relating the temperature of the CPU and the power supply was logarithmic because as the objects heat up, it takes more 6 energy to heat up. From the data, it was determined that as the internal temperature rises, the fan speed rises to accommodate for the extra heat. Conclusions: A strain gage, RTD, thermistor and accelerometer were all constructed and calibrated. The curves were linear and were limited to a small range of operation within the experimental boundaries. It was determined that the cantilever strain gage was sensitive enough to signify the mass of a ping pong ball in a cup; by reducing water consumption while washing their hands, a person can save enough water to provide for 11 people; and the PS3 fan responds appropriately to keep the internal temperature below a critical point. References: [1] Ott, John. AME 20213 Spring 2014: Lab Exercise #1 Procedure Topic:
Sensors/Measurement Systems/Calibration Calibration Curve for the Thermistor (n.d.):
n. pag.
[2] Dunn, P.F., 2009 Measurement and Data Analysis, University of Notre Dame, Notre
Dame.
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