ENGR 512 Experimental Methods in Engineering

1. ENGR 512Experimental Methods in Engineering Spring 2009 Dr. Mustafa Arafa Mechanical Engineering Department mharafa@aucegypt.edu

2. Outline • PART 1: Principles of measurement • Instrument types & characteristics • PART 2: Sensors and instruments • Measurement of common engineering parameters, such as temperature, pressure, flow, force, displacement, strain • Selection of appropriate instruments • PART 3: Lab session & case studies • References: • Measurement and Instrumentation Principles, Alan S. Morris, Butterworth-Heinemann, 2001. • The measurement, instrumentation, and sensors handbook, edited by J.G.Webster, CRC Press, 1999.

3. Sensors in closed-loop control systems

4. Types of measurement • Manufacturing measurements • Discretely monitor product quality • Performance measurements • Provide performance evaluation as needed • Operational measurements • Continuously monitor operation process • Control measurements • Continuously provide feedback signals • Others • Research-related

5. Examples Cairo metro, line 1

6. Essential elements of measurement Measured variable Physical behavior Signal conditioner Output display Transducer Sensor (measurand) Variable conversion element Data acquisition system • Sensor: responds to physical quantity to be measured • Transducer: converts quantity to be measured to an analog signal • Signal conditioner: amplify, filter, integrate, differentiate, etc. • Data acquisition: records, displays, processes data (hardware & software)

7. Instrument systems Humidity sensor

8. Instrument types Active and passive instruments potentiometer Active: externally powered Passive: self powered

9. Instrument types Null-type & deflection-type instruments

10. Instrument types Analog & digital instruments Analog: signal is continuous Digital: signal can take discrete levels

11. Static characteristics of instruments

12. Static characteristics of instruments Measure of Precision • Accuracy: closeness to correct value • Precision: indication of spread of readings • Repeatability/reproducibility: variation of a set of measurements made in a short/long period of time Measure of Accuracy Need to average Bias: need to calibrate Accuracy is often quoted as a % of full-scale (f.s.) reading. Example: pressure gauge, range 0-10 bar with accuracy ±1% f.s. This means ± 0.1 bar, or if you are reading 1 bar, the possible error is 10%. High accuracy, high precision Low accuracy, high precision Low accuracy, low precision

13. Averaging

14. Static characteristics of instruments • Linearity: is the output reading linearly proportional measured quantity? • Sensitivity: change in output per unit change in input (slope) • Resolution: smallest increment that can be detected D i Resolution

15. Static characteristics of instruments • Sensitivity to disturbance: all calibrations/specifications of an instrument are only valid under controlled conditions of temperature, pressure, etc. Variation to such environmental changes can lead to • Zero drift (bias) • Sensitivity drift

16. Static characteristics of instruments Example: A spring balance is calibrated in an environment at a temperature of 20°C and has the following deflection-load characteristic. It is then used in an environment at a temperature of 30°C and the following deflection-load characteristic is measured. Determine the zero drift and sensitivity drift per °C change in ambient temperature.

17. Static characteristics of instruments • Hysteresis effects: output reading depends on whether input quantity is steadily increased or decreased • Dead space: range of input values over which there is no change in output

18. Static characteristics of instruments • Saturation: no further output, even if input is increased saturation

19. Dynamic characteristics of instruments

20. Dynamic characteristics of instruments Static characteristics: steady-state readings Dynamic characteristics: behavior of instrument between the time a measured quantity changes and the time when the instrument oupt attains a steady value in response Measured quantity Output reading x(t) X(s) y(t) Y(s) G(s) Instrument dynamics governed by the differential equation:

21. Dynamic characteristics of instruments Zero order instrument: For a step change in measured quantity, the output moves immediately to a new value. Example: potentiometer

22. Dynamic characteristics of instruments First order instrument: Example: liquid-in-glass thermometer

23. Dynamic characteristics of instruments Second order instrument: Response can be oscillatory, or damped according to damping ratio.

24. Errors in measurement • Errors in measurement systems: • Arise during the measurement process • Systematic errors • Random errors • Arise due to later corruption of the signal by induced noise Systematic error • Systematic errors: consistently on 1 side of the correct reading • Sources: • System disturbance (ex: cold thermometer in hot fluid) • Environmental changes • Bent meter needles • Uncalibrated instruments • Drift Random error • Random errors: perturbations on either side of true value • Sources: • Human observation of analog meters • Electrical noise (spurious signals picked up by lead wires)

25. y(t) yS(t) t t Errors in measurement • Other sources of error: • Improper sensing position • Improper data acquisition • Improper sampling rate Usually we record a continuous signal y(t) by a set of samples ys(t) at discrete intervals of time t. t The no. of samples recorded each second is defined as the sampling frequency, fS

26. Errors in measurement Under sampling of test data Original signal Sampled data • If we sampled too slowly, a recorded data will present a distortion from the original signal. • Over sampling, on the other hand, raises storage issues.

27. Errors in measurement Aliasing High frequency signal, sampled with low sampling rate High frequency signal when sampled with a low sampling rate may cause the sampled data to appear to have a lower frequency. This behavior is known as aliasing, and the lower frequency (false) signal is often said to be the alias. To avoid aliasing, the sampling rate must be at least twice the highest frequency in the analog signal.

28. Strain Measurement

29. Strain gauges • Strain gauges are devices that experience a change in resistance when they are stretched or strained • Typical displacements: 0-50 mm • Can be used as parts in other transducers (ex: pressure sensors) • Accuracies within ±0.15% of full-scale are achievable • Manufactured to nominal resistances (most commonly 120W)

30. Strain gauges Sensitive to axial strain Less sensitive to transverse strain Gauge element Solder Jumper wire Solder Gauge element tab Lead wires Gauge tab

31. Mechanical strain Strain: change in length over some specified base length F F Extension Base length

32. Resistance of a conductor Conductor :Resistance :Resistivity :Length :Area L • Now assume the conductor stretched or compressed. • Resistance will change due to dimensional changes (L,A) AND due to a fundamental property of materials called piezoeresistance. • Piezoresistance: dependence of on the mechanical strain.

33. Change in resistance due to strain For a small change in R, use Taylor series expansion: Change in resistance Gives: D Longitudinal strain: Transverse strain: dL L For linearly elastic behavior:

34. Change in resistance due to strain GF = slope In the absence of a direct resistivity change, For commonly used strain gauges, GF is close to 2. Change in Resistance with Strain for Various Strain Gage Element Materials • Gauge Factor (GF) is a measure of the sensitivity of the material, i.e. the resistance change per unit applied strain. • If you know GF, then measurement of allows measurement of the strain . • This is the principle of the resistance strain gauge

35. Example Measurement of strain in a steel beam. For a stress level of 20 MPa and elastic modulus of 200 GPa: In engineering materials, typical strain levels range from 2 to 10,000 micro strain.

36. Wheatstone bridge • To convert small changes in resistance to an output voltage, strain gauges are commonly used in bridge circuits. • Circuit requires DC input or excitation. R1 R2 + - V Vo V: Bridge excitation R4 R3

37. Wheatstone bridge R2 R1 + - V Vo R4 R3 If R1R3=R2R4 Vo=0 Bridge is balanced • Assume you start with a balanced bridge withR1=R2=R3=R4=R. Then Vo=0. • Now assume one (or more) of the resistances change bydR1, dR2, dR3and dR4. The output voltage would then change.

38. R2 R1 + - V Vo R4 R3 Electrical resistance strain gauge • If we replace only one resistance with an active strain gauge, any changes in resistance will unbalance the bridge and produce a non-zero output voltage. • Quarter bridge configuration (one active gauge) Output is proportional to excitation voltage Quarter bridge

39. R2 R1 + - V Vo R4 R3 Other bridge configurations • Half bridge configuration (two active gauges) • Useful for measuring bending strain in a thin beam or plate. 1 2

40. Other strain gauge configurations