Question Paper: Mechanical Measurement and Control : Question Paper Dec 2014 - Mechanical Engineering (Semester 5) | Mumbai University (MU)

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## Mechanical Measurement and Control - Dec 2014

### Mechanical Engineering (Semester 5)

TOTAL MARKS: 80

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Assume data if required.

(4) Figures to the right indicate full marks.
**1 (a)** Following table list the measuring instruments (left hand side column of the table) for measuring mechanical properties (right band side column of the table) of the system. Student shall match the measuring instrument with the corresponding mechanical property.

Measuring Instruments |
Properties |

Optical pyrometer | Temperature |

McLeod Gauge | Speed |

Rotameter | Pressure |

Stroboscope | Flow rate |

Further student shall explain only the working principle of the measurement instrument listed on left hand side column of the table.(4 marks)

**1 (b)**Construct the block diagram that combines the following set of equations expressed in the 's' notation (Laplace notation).

1) W=X-Y,

2) V=W-Z

3) Z(S+6)=V(S+2)

4) Y(S

^{2}+6S+8)=Z

Given X is the input to the system and Y is the output from the block diagram. Find the transfer function.(6 marks)

**2 (a)**Explain the following terms with respect to the measurement system:

i) Threshold and Resolution

ii) Sensitivity and Drift

iii) Hysteresis(5 marks)

**2 (b)**With a neat sketch explain the working of LVDT.(5 marks)

**2 (c)**Consider the following state representation of single input single output system $$ \begin{Bmatrix} \cdot \\ x_1\\ \cdot \\ x_2 \\ \cdot \\ x_3 \end{Bmatrix} = \begin{bmatrix} 0 &1 &0 \\0 &0 &1 \\-1 &-3 &-2 \end{bmatrix} \begin{Bmatrix} x_1 \\x_2 \\ x_3 \end{Bmatrix} + \begin{Bmatrix} 0\\0 \\1 \end{Bmatrix} u (t), \\ and \ y(t) = \begin{bmatrix} 1 &0 &0 \end{bmatrix} \begin{Bmatrix} x_1\\x_2 \\x_3 \end{Bmatrix} $$ Here x

_{1}, x

_{2}and x

_{3}are state-variables, u(t) is a force vector and y(t) being the system response. Obtain transfer function of the system.(10 marks)

**3 (a)**With a neat sketch explain the constructional feature and working of (i) piezoelectric accelerometer, (ii) Ionization gauge for pressure measurement.(10 marks)

**3 (b)**Figure 1 shows the unit step response of a second order system.

Determine the following from the plot

i) Gain

ii) Damping ratio

iii) Natural Frequency

iv) Transfer function (10 marks)

**4 (a)**Consider a single strain gauge of resistance 120Ω mounted along the axial direction of an axially loaded specimen of steel (E=200 GPa). If the percentage change in length of the rod due to loading is 3% and the corresponding change in resistivity of the strain gauge material is 0.3%, estimate the percentage change in the resistance of the strain gauge and its gauge factor; Poisson ratio=0.3. If the strain gauge is connected to a measurement device capable of determine change in resistance with an accurate of ± 0.02 Ω, what is the uncertainty in stress that would result in using this resistance measurement device? (10 marks)

**4 (b)**For a control system open loop transfer function consist of $$ G(s) H(s) = \dfrac {K}{S^2 (s+2)(S+3)} . $$ Find the value of K" to limit steady state error to 10(10 marks)

**5 (a)**For a particular unity feed-back system $$ G(S) = \dfrac {242 (S+5)} {S(S+1)(S^2+5S+121} $$ Sketch a Bode plot. Further comment on stability of the system.(10 marks)

**5 (b)**With a neat sketch explain working of an Operational Amplifier (Op-Amp). Enumerate limitations of the same.(10 marks)

**6 (a)**Draw the root-locus of the feedback system whose open-loop transfer function is given by $$ G(S) H(S) = \dfrac {K}{S^2(S+1)} $$(10 marks)

**6 (b)**Explain generalized measurement system elements with block diagram. Describe its functions with suitable example.(10 marks)