# hw1 - ME 365 Homework Set 1 Out August 25,...

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Unformatted text preview: ME 365 Homework Set 1 Out August 25, 2011 Due September 1, 2011 Problem No. 1 The displacement (surface roughness) of a machined surface is measured with an optical device. In this measurement system’s design criteria, it was specified that the displacement should be measurable to within 0.2 µ in. and further the output resolution was 1 mVolt. Three years after installation of the measurement system it is being calibrated against surface displacements measured with a standard instrument. Durring this calibration the data collected are shown in the table below. Displacement 0 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. ( µ inches ) Output 0 0 0 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100 105 ( mVolts ) (a) Plot the calibration data and draw a straight line through the linear portion of the curve and determine the equation of this straight line. (b) Also calculate or determine: (i) Input range and span (ii) Output range and span (iii) Sensitivity (iv) Bias (v) Resolution of the system (vi) Maximum nonlinearity as a percentage of full scale deflection (%fsd). Mark on the plot the position of the maximum nonlinearity. (c) Does the instrument still meet the original design specification? (d) In what range of input values should this measurement system be use? Why? ME 365 Homework Set 1 Out August 25, 2011 Due September 1, 2011 Problem No. 2 The data on the following page are from manufacturers’ specifications for various gas flow meters. Determine the best flow meter that will meet the following requirements: Resolution 0.2 cubic meters / minute Operating range  ­100 to +100 cubic meters / minute Temperature operating range  ­20 °C to +40 °C Output range 0 to 10 Volts (a) Assuming that all three of the meters have negligible nonlinearity over the specified operating range, complete the data table. Input Range Meter 1  ­150 to +150 m3 / min. Output Range 1 to 7 Volts Sensitivity Bias Output Resolution 10 mV ( Input ) Resolution Operating Temp. 0 to 100 °C Cost \$50 Expected Lifetime 7 Years Of Meter Meter 2  ­200 to +200 m3 / min. 0 to 10 Volts 1 mV  ­100 to +200 °C \$2000 5 Years (b) Which air flow meter should be chosen? Why? Meter 3  ­600 to +600 m3 /min. 0 to 1.2 Volts 0.1 mV  ­50 to +50 °C \$500 6 Months ME 365 Homework Set 1 Out August 25, 2011 Due September 1, 2011 Problem No. 3 A measurement system consisting of a force transducer and an amplifier is being calibrated against a standard instrument. The calibration data are shown below. Measurements were taken by slowly increasing the force to the maximum value, then slowing decreasing the force back down to the minimum value. Plot the data on a calibration chart, and draw one straight “best estimate calibration” line through the data. Force (kN) increasing Output Voltage increasing Force (kN) decreasing Output Voltage decreasing 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 2.00 2.10 2.40 2.90 3.60 4.50 5.60 6.90 8.40 10.10 12.00 10.00 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 12.00 11.90 11.60 11.10 10.40 9.50 8.40 7.10 5.60 3.90 2.00 Determine: (a) input range and span, (b) output range and span, (c) sensitivity and bias, (d) maximum hysteresis (show on graph where this occurs and also express as a percentage of full scale, (e) resolution assuming the output maybe read to 0.25 mV, (f) maximum deviation from the straight line approximation. 10.00 ...
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