1 ENGR 512 Experimental Methods in Engineering Spring 2011 Dr. Mustafa Arafa Mechanical Engineering Department

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, – 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 Physical behavior Sensor Transducer Signal conditioner 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) Measured variable Variable conversion element Output display (measurand)

7 Instrument systems Membrane Pressure Strain gauge Electrical bridge Calibration Output voltage Environment being sensed for pressure

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

9 Null-type & deflection-type instruments Instrument types

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

11 Static characteristics of instruments

12 Static characteristics of instruments  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 Measure of Precision 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 precisionLow accuracy, high precisionLow accuracy, low precision Bias: need to calibrate Need to average

13 Averaging

14 Static characteristics of instruments  i Resolution  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

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. Load (kg)0123 Deflection (mm) It is then used in an environment at a temperature of 30°C and the following deflection-load characteristic is measured. Load (kg)0123 Deflection (mm) 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 saturation Static characteristics of instruments  Saturation: no further output, even if input is increased

19 Dynamic characteristics of instruments

20 Instrument dynamics governed by the differential equation: G(s) x(t) X(s) y(t) Y(s) 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

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

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

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

24 Errors in measurement Errors in measurement systems: 1.Arise during the measurement process a)Systematic errors b)Random errors 2.Arise due to later corruption of the signal by induced noise Systematic error Random error Systematic errors: consistently on 1 side of the correct reading Sources: 1.System disturbance (ex: cold thermometer in hot fluid) 2.Environmental changes 3.Bent meter needles 4.Uncalibrated instruments 5.Drift Random errors: perturbations on either side of true value Sources: 1.Human observation of analog meters 2.Electrical noise (spurious signals picked up by lead wires)

25 Errors in measurement Other sources of error: 1.Improper sensing position 2.Improper data acquisition 3.Improper sampling rate Usually we record a continuous signal y(t) by a set of samples y s (t) at discrete intervals of time  t. y(t) t y S (t) t tt The no. of samples recorded each second is defined as the sampling frequency, f S

26 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. Original signalSampled data Errors in measurement Under sampling of test data

27 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. High frequency signal, sampled with low sampling rate Errors in measurement Aliasing

28 Errors in measurement

29 Strain Measurement

30 Strain gauges Strain gauges are devices that experience a change in resistance when they are stretched or strained Typical displacements: 0-50  m 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 120 

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

32 Mechanical strain FF Base length Strain: change in length over some specified base length Extension

33 L Conductor Resistance of a conductor :Resistance :Resistivity :Length :Area 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.

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

35 Change in resistance due to strain 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 ofallows measurement of the strain. This is the principle of the resistance strain gauge In the absence of a direct resistivity change, For commonly used strain gauges, GF is close to 2. GF = slope Change in Resistance with Strain for Various Strain Gage Element Materials

36 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.

37 Wheatstone bridge R1R V R2R2 R4R4 R3R3 VoVo To convert small changes in resistance to an output voltage, strain gauges are commonly used in bridge circuits. Circuit requires DC input or excitation. V: Bridge excitation

38 R1R V R2R2 R4R4 R3R3 VoVo If R 1 R 3 =R 2 R 4 V o =0 Bridge is balanced Assume you start with a balanced bridge with R 1 =R 2 =R 3 =R 4 =R. Then V o =0. Now assume one (or more) of the resistances change by dR 1, dR 2, dR 3 and dR 4. The output voltage would then change. Wheatstone bridge

39 Electrical resistance strain gauge R1R V R2R2 R4R4 R3R3 VoVo  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

40 Other bridge configurations R1R V R2R2 R4R4 R3R3 VoVo Half bridge configuration (two active gauges) Useful for measuring bending strain in a thin beam or plate. 1 2

41 Other strain gauge configurations