# hw1soln - ME 365 Homework Set 1 Out August 25, 2011 Due...

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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 ( μ inches ) 0 5. 10. 15. 20. 25. 30. 35. 40. 45. 50. 55. Output ( mVolts ) 0 0 0 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100 105 (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? Solution: Start by making plot of calibration data:

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ME 3 The e Outp (b) (c) The i resol Output (mVolts) 365 equation of put (mVolt) i. in th ii. ou th iii. se iv. bi v. re (s vi. m 1 0 instrument lution is 0.4 -40 -20 0 20 40 60 80 100 120 0 p( ) Cali the “straigh = -25 +2.5*D put range is hese two val utput range hese two val ensitivity is as is the “y” esolution of ensitivity) = aximum no 00*25/100 does not m 4 micro inch 10 2 Di ibration
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## This note was uploaded on 12/26/2011 for the course ME 365 taught by Professor Merkle during the Fall '07 term at Purdue University-West Lafayette.

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hw1soln - ME 365 Homework Set 1 Out August 25, 2011 Due...

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