Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Textbook Question
Chapter 1, Problem 1.54P
For the calibration data of Table 1.5, determine the static sensitivity of the system at (a) X = 5, (b) X = 10, and (c) X = 20. For which input values is the system more sensitive? Explain what this might mean in terms of a measurement and in terms of measurement errors.
Table 1.5 Calibration Data
| X [cm] | r[V] | X [cm] | r[v) |
| 0.5 | 0.4 | 10.0 | 15.8 |
| 1.0 | 1.0 | 20.0 | 36.4 |
| 2.0 | 2.3 | 50.0 | 110.1 |
| 5.0 | 6.9 | 100.0 | 253.2 |
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Consider the voltmeter calibration data in the following table. Plot the data using a suitable scale.
Specify the percent maximum hysteresis based on full-scale range.
Increasing Input [mV]
Decreasing Input [mV]
Y
Y
0.0
0.1
5.0
5.0
1.0
1.1
4.0
4.2
2.0
2.1
3.0
3.2
3.0
3.0
2.0
2.2
4.0
4.1
1.0
1.2
5.0
5.0
0.0
0.2
2. Consider the voltmeter calibration data in Table 1. Plot the data using a suitable scale.
a) Specify the percent maximum hysteresis based on full-scale range.
b) Referring to increasing input calibration, determined the sensitivity and linearity errors.
Increasing input (mV)
Decreasing input (mV)
X
Y
Y
0.0
1.0
0.1
5.0
5.0
1.1
4.0
4.2
2.0
2.1
3.0
3.2
3.0
3.0
2.0
2.2
4.0
4.1
1.0
1.2
5.0
5.0
Table 1: Calibration results
0.0
0.2
b) Figure 1 shows the calibration data of a sensor. Determine the static sensitivity at the
input of X= 0, X= 5 and X= 10. For which input values is the system more sensitive?
Calibration Data
300
250
y = 0.875x1.055
200
150
100
50
20
40
60
80
100
120
Input value, cm
Figure 1
c) Suppose you found a dial thermometer in a stockroom. Discuss several methods by
which you might estimate random and systematic error in the thermometer? How
would you estimate its uncertainty?
Output value, V
Chapter 1 Solutions
Theory and Design for Mechanical Measurements
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