程序代写 (a) Describe “Non-destructive Evaluation” (NDE), explaining its importance

(a) Describe “Non-destructive Evaluation” (NDE), explaining its importance and giving examples of where it is used. Give one example of an NDE measurement technique. [5]
Non-destructive testing is the process of inspecting, testing or evaluating materials, components or assemblies for discontinuities, or differences in characteristics without destroying the serviceability of the part or system
It is vital for many industries particularly to those that are safety critical: i.e. Aerospace NDE is used to monitor the materials, processes and final parts that go into many different products. Also during their life cycle so we test component integrity so that we know when things are beginning to fail so they can be replaced.
Examples: aging power stations, planes, trains, rails, etc.

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[1 mark] [2 marks]
Many different techniques are employed using a variety of different sensing mechanisms.
(Magnetic Particle Testing (MT), Liquid Penetrant Testing (PT), Radiographic Testing (RT) Ultrasonic Testing (UT), Electromagnetic Testing (ET), Visual Testing (VT), Acoustic Emission Testing (AE), Guided Wave Testing (GW), Laser Testing Methods (LM), Leak Testing (LT), Magnetic Flux Leakage (MFL), Neutron Radiographic Testing (NR), Thermal/Infrared Testing (IR), Vibration Analysis (VA))
[1 mark for example]
(b) Explain what measurands are, giving three examples. For each measurand give examples of the properties that could be measured. [5]
A measurand is the physical quantity or property that is to be measured
Mechanical
Force, Pressure, Stress, Strain, Mass, Density, Moment, Torque, Viscosity, Stiffness Roughness, Velocity, Acceleration, Position.
Wave, Amplitude, Phase, Polarisation, Spectrum
Electrical
Charge, Current, Potential, Potential Difference, Electric Field, Conductivity, Permittivity
Wave Amplitude, Wave Velocity, Frequency
Temperature, Heat Flux, Specific Heat, Thermal Conductivity
Components, Concentration
Type, Energy, Intensity
Biological
Biomas, Concentration, States,
Magnetic Field, Magnetic Flux, Permeability
1 Mark for 3 measurands and up to 2 marks for example properties at 0.5 marks each [5 marks]

(c) Using diagrams explain how the term accuracy differs in meaning from the term precision in the context of sensor performance. [5]
The accuracy of a measurement quantifies the degree of correctness of a measurement. It is a measure of by how much the measurement is expected to be in error.
For high accuracy a small error is expected whilst for low accuracy a large error is expected.
The precision is often confused with accuracy, but in fact has a different meaning. Precision refers to the similarity of successive measurements; hence a precise instrument, if used repeatedly, will produce results with small differences between them, expressed as a small standard deviation.
On the other hand an accurate instrument will give results where the mean of the results is close to the actual value.
Good diagram and basic explanations, or basic diagram and in depth explanations will get [5 marks]
(d)Show by derivation why averaging is a useful signal processing tool – How does it improve the SNR of the resultant signal and what are the requirements for its use?
From lecture notes: derive m
𝑚1 =𝑠+𝑛1 𝑚2 =𝑠+𝑛2
𝑚 = 𝑁 ∑ 𝑠𝑖 + 𝑛𝑖
1𝑁 1𝑁 𝑚=𝑁∑𝑠𝑖 +𝑁∑𝑛𝑖
𝑚 = 𝑁 𝑁𝑠 + 𝑁 ∑ 𝑛𝑖

𝑚 = 1 𝑁𝑠 + 1 √𝑁𝜎𝑛 𝑁𝑁
𝑚 = 𝑠 + 𝜎𝑛 √𝑁
Hence the signal to noise ratio for average voltage is:
𝑆𝑁𝑅 = 𝑠/ 𝜎𝑛 √𝑁
𝑆𝑁𝑅 = 𝑠√𝑁 𝜎𝑛
The SNR has improved by factor square root of M.
This is a very important result. The idea is used the world over in signal processing. We need to line up an ensemble of time domain records, synchronised in time and average them to improve SNR.
The signal of interest has to be repeating in time for this to be employed
(e) Using a diagram and equations, briefly describe the operation and limitations of a resistive displacement sensor [5]
Simple displacement sensor uses a resistive area and a contact on the moving object Source voltage (Vs) applied across full resistive bar.
Voltage at the object depends on the position on the bar.
Limitations include:
• Limited resolution depending on form,
• contacts wear out due to friction during use,
• non linear response from loading.

Figure 1 below shows the circuit of a quarter bridge circuit in which R3 represents the strain gauge element, R2 is set to a value R0, equal to the unstrained value of R3, and R1=R4.
Figure 1 – Bridge Circuit
(a) Explain the operation of a resistance strain gauge and derive an expression for the gauge factor, which expresses the sensitivity of the device in terms of the relative change in the gauge resistance per unit of strain.
[12 marks]
This is formed from a resistive elastic material whose change in resistance is a function of applied strain.
The change in resistance depends on the change in length, area and resistivity.
If the strain gauge is bonded to the test piece, then changes in the dimensions of the piece due to strain will affect the strain gauge in the same way.

Derrivation of the equations:
[3 marks] The longitudinal strain is 𝜀𝑙,However the cross-sectional area will also change
due to the poissons ratio (𝜈) of the material. So we can work out how the change in length effects the area.
Finally we get:
𝑑𝑅 =(1+2𝜈)𝜀𝑙 +𝑑𝜌 𝑅𝜌
Per unit strain this is:
𝑅 =(1+2𝜈)+𝑑𝜌
[1mark] [1mark]
Show that the output voltage of the bridge in response to a strain applied to R3 is:
Where S is the gauge factor, 𝑉 is source voltage and 𝜀 is the longitudinal strain.
[10 marks]

If 𝑉 = 10 V, S = 2, and the maximum strain to be measured is 5×10-2 𝑠
calculate the gain A (c.f. Figure 1) required of the differential amplifier
to give an output signal of 5 V at the maximum strain.
𝜕𝑉 ≈ 𝑉 𝑆𝜀 = 10×2×5×10−2 = 0.25𝑉 𝑠
Gain A is 5V/0.25 = 20
A in dB = 20*log10(20) = 26dB
[2 marks] [2 mark]
(d) Under the same conditions as in question 2(c) what will be the power dissipated in the gauge resistance if its value is 120 Ω?
V drop over R3 is 0.5*Vs = 5v. [1 mark]

Because R1=R3 Power = V^2/R 5*5/120 = 208mW
[1 mark] [1 mark] [1 mark]

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