Calibration Report Final

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Clemson University *

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2220

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Mechanical Engineering

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Feb 20, 2024

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Rony Ramirez Jr Calibration Lab Report ME 2220 Section 009 Siqi Zheng “I certify that all the writing presented here is my own and not acquired from external sources (including the student lab manual). I have cited sources appropriately and paraphrased correctly. I have not shared my writing with other students, nor have I acquired any written portion of this document from past or present students.” ______Rony Ramirez Jr________

1 Introduction: In engineering applications, the main focus in the calibration lab is to find the value of uncertainty. The concept of uncertainty is commonly used in Engineering as a form for measurements. Uncertainty is used when a scientist or someone calculating or measuring to collect some data, and they want to assume an exact value from the data they are calculating. Also, when finding the value of the uncertainty, it is used to find the actual measurement of the range of data that is collected. This lab aims to find the value of the uncertainty by using different items to calculate the value. For example, using a Potentiometric Displacement transducer is one way to find the value. Also, using an ultrasonic distance sensor is another way to find the value of uncertainty. Using these two devices gives the user multiple input and output parameters to then calculate multiple numbers to come to an end to see the uncertainty. Experimental Methods: The lab had different days of experiments. On one day of the lab experiment, a PDT (Potentiometric Displacement transducer) was used to grab input parameters. On the second day, a UDS (ultrasonic distance sensor) was used to do the same thing. In the first experiment, the PDT was attached to a mount that had a micrometer head on it to measure. The PDT was attached to a power source set to five volts that had a multimeter attached to find the output volts. The micrometer head is used by turning it every 0.005 going in upscale first and then going downscale. In the second portion of the experiment, a UDS (ultrasonic distance sensor) was used instead of the PDT. The necessary tools required to do the experiment are an HC-SR04 which is the UDS,

2 breadboards, LEDs, resistors, and an Arduino microcontroller. Using everything after connecting everything together, the UDS is used to grab time values for every inch. Experimental Results: The first experiment was performed with a PDT (Potentiometric Displacement transducer) to get measurements of input and output values. 0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 4.5 4.55 4.6 4.65 4.7 4.75 4.8 4.85 4.9 4.95 f(x) = − 2.55 x + 4.9 f(x) = − 2.54 x + 4.91 Day 1 Calibration Lab Upscale Linear (Upscale) Downscale Linear (Downscale) Displacement (in) Vo (V) Table 1 : Calibration Day 1 Results

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3 Max Linear Error 0.000989 in Range 0.0995 in %FSE 1 % Sensitivity - 2.54 Total Uncertainty 0.00565 in The second experiment had a UDS (ultrasonic distance sensor) to measure distances as input and output to get the uncertainty value. 0 2 4 6 8 10 12 14 0 200 400 600 800 1000 1200 1400 1600 1800 2000 f(x) = 147.59 x + 24.68 UDS Bounce Time at Distance Length (in) Time (micro seconds)[sec x 10^-6] Table 2 : Calibration Day 2 Results Max Linear Error 0.309 in Range 0.267 in %FSE 0.785 % Standard Deviation. 0.811 in Total Uncertainty 1.65 in Sensitivity 148 Analytical Methods: The calibration process has a procedure of finding the sensitivity, which is the slope of the best fit line using your input and output measurements, which is seen by using the regression analysis of the PDT (Potentiometric Displacement transducer).

4 m = y 2 − y 1 x 2 − x 1 The hysteresis is used when having a set of points and going in the opposite direction with different values. e hys. = | y upscale − y downscale | Finding the Instrument Range will be defined by finding the maximum value a set a value can measure. Range =( V max − V min )/ | S | Also, the purpose of the linear error is to find the deviation of the data from the best fit line. e i = | y i − y ci | The percent full-scale error is the see how much there is an error in the PDT calibration. %FSE = e max Range ∗ 100% To calculate the uncertainty requires a series of calculations to find the correct value. The first value is the zero-order uncertainty. u 0 , PDT = ± 1 2 [ Resolution of Voltmeter ] Next is the uncertainty of the reference measurement, which is used as a reference's length measurement. u 0 , Micrometer = ± 1 2 [ Resolution of Micrometer ] Also, other known errors are the hysteresis error and the linear errors. u hys. = ±max ( e hys ) u lin. = ±max ( e i ) Finally,

5 u PDT = ± √ u 0 , PDT 2 + u 0 , Micrometer 2 + u hys. 2 + u lin . 2 For the second experiment, when a UDS (ultrasonic distance sensor) is used, the method to calculate the uncertainty is a bit different than before. In a UDS, the standard deviation must be calculated in order to find the first-order uncertainty. u 1 = ± 2 ∗ S x Once finding the first order of uncertainty, the uncertainty of reference measurement is next. u 0 , ruler = ± 1 2 [ Resolution of Ruler ] Next is finding the linear error: u lin. = ±max ( e i ) Then finally, in order to calculate the total uncertainty, the total uncertainty is then calculated using the first order, references measurement, and the linear error uncertainty. u UDS = ± √ u 1 2 + u 0 , ruler 2 + u lin 2 Discussion of Findings: The calibration of the process is needed to perform the total uncertainty value; the calibration is used to provide values of input values and output values of the instruments. Without the calibration process, the value cannot be exact. Using sensitivity in the calibration experiment is used to find the best fit line of data points by grabbing a "y" value coordinate and subtracting it, but they value before it and then dividing it by an "x" value coordinate and subtracting it but the "x" value before it. The sensitivities of the PDT (Potentiometric Displacement transducer) is - 2.54 inches, and in the UDS (ultrasonic distance sensor) is 147 inches. The two numbers are completely different because the way the values are measured is completely different. The ranges between the two numbers are also different because it has different values for maximum and minimum values.

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6 The maximum linear error value is important to find the deviation of the best fit line. While the percent error is used to see how much of an error there is between the actual calculated number the experimental value. Using the two instruments are both great ways to use the calibration process, but the UDS (ultrasonic distance sensor) is a better sensor for applications because it gives way more values to find the lowest percent error when finding the correct answer. Conclusion: In this lab, two experiments were performed to determine a series of calculations to find the total uncertainty. Also, the other purpose of the lab was to understand what is the calibration method. In the first experiment, a PDT (Potentiometric Displacement transducer) was used to grab a known set of input values and observing the output values, to calculate the total uncertainty. In the second lab, a UDS (ultrasonic distance sensor) was used instead of the PDT to do another form of calibration. Throughout both labs the necessary tools were needed such as grabbing forms of known input values to get the output values in order to fully calculate the correct value (total uncertainty).