# Metrology and Inspection

 Question 1
An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavelength 0.5 $\mu m$, 12 fringes were observed over a length of 15 mm of gauge B. If the gauges are placed 45 mm apart, the height difference of the gauges is ______ $\mu m$. (Answer in integer)

 A 5 B 9 C 10 D 12
GATE ME 2023   Manufacturing Engineering
Question 1 Explanation:
\begin{aligned} \lambda & =0.5 \mu \mathrm{m} \\ \mathrm{n} & =12 \text { per } 15 \mathrm{~mm} \\ \theta & =\frac{\lambda}{2 \times \frac{15}{12}}=\frac{0.5}{2 \times 15} \times 12 \\ \mathrm{~h} & =\theta \times 45=\frac{0.5}{2 \times 15} \times 12 \times 45 \\ & =9 \mu \mathrm{m} \end{aligned}
 Question 2
A coordinate measuring machine (CMM) is used to determine the distance between Surface SP and Surface SQ of an approximately cuboidal shaped part. Surface SP is declared as the datum as per the engineering drawing used for manufacturing this part. The CMM is used to measure four points P1, P2, P3, P4 on Surface SP, and four points Q1, Q2, Q3, Q4 on Surface SQ as shown. A regression procedure is used to fit the necessary planes. The distance between the two fitted planes is _______ mm. (Answer in integer)

 A 4 B 5 C 6 D 8
GATE ME 2023   Manufacturing Engineering
Question 2 Explanation:
Since $y$-coordinate of all four points $P_{1}, P_{2}, P_{3}$ and $\mathrm{P}_{4}$ is zero. Hence the regression plane fitted by points $P_{1}, P_{2}, P_{3}$ and $P_{4}$ is $x-z$ plane.
The distance of any point (i.e. $\mathrm{Q}_{1}, \mathrm{Q}_{2}, \mathrm{Q}_{3}$ and $\mathrm{Q}_{4}$ ) from $x-z$ plane is equal to $y$ co-ordinate

Therefore,
The distance of $Q_{1}$ from $x-z$ plan $=6 \mathrm{~mm}$
The distance of $Q_{2}$ from $x-z$ plan $=6 \mathrm{~mm}$
The distance of $Q_{3}$ from $x-z$ plan $=4 \mathrm{~mm}$
The distance of $Q_{4}$ from $x-z$ plan $=4 \mathrm{~mm}$
The distance of best fitted plane by $Q_{1}, Q_{2}, Q_{3}$ and $Q_{4}$ from $x-z$ plane is equal to average of 6,6,4 and 4 , which is equal to $5 \mathrm{~mm}$.
Hence, the distance between two fitted planes is $5 \mathrm{~mm}$.

 Question 3
A part, produced in high volumes, is dimensioned as shown. The machining process making this part is known to be statistically in control based on sampling data. The sampling data shows that D1 follows a normal distribution with a mean of 20 mm and a standard deviation of 0.3 mm, while D2 follows a normal distribution with a mean of 35 mm and a standard deviation of 0.4 mm. An inspection of dimension C is carried out in a sufficiently large number of parts.
To be considered under six-sigma process control, the upper limit of dimension C should be ______ mm.
(Rounded off to one decimal place)

 A 12.4 B 16.5 C 18.6 D 24.4
GATE ME 2023   Manufacturing Engineering
Question 3 Explanation:
D1 and D2 follow normal distribution.
So,
Upper limit $=\mu +3\sigma$
Lower limit $=\mu -3\sigma$
$\bar{D1}=20mm, \bar{D2}=35mm, \sigma _{D2}=0.4mm,\sigma _{D1}=0.3mm$
Mean value of $(\bar{C}) =\bar{D2}-\bar{D1}=35-20-15$
Standard Devialtion of C
$\sigma _C^2=\sigma _{D2}^2 -\sigma _{D1}^2$
$\sigma _C=\sqrt{0.4^2-0.3^2}=0.2645$
Upper Limit of C $\bar{C}+6 \times \sigma _C=15+6 \times 0.2645=16.587$
 Question 4
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch (p) and included angle of the thread are 4 mm and $60^{\circ}$ , respectively. The diameter of the best size wire is ___________ mm (round off to 2 decimal places).

 A 1.12 B 2.31 C 4.25 D 3.36
GATE ME 2022 SET-2   Manufacturing Engineering
Question 4 Explanation:
Pitch $(p) = 4 mm$
Thread angle $2\alpha =60^{\circ}$
Semi Thread Angle $\alpha =30^{\circ}$
Diameter of best size wire
\begin{aligned} d_w&=\frac{p}{2}\sec \alpha \\ d_w&=\frac{4}{2} \sec 30^{\circ}\\ d_w&=2.039 mm=2.31mm \end{aligned}
 Question 5
A shaft of diameter $25^{^{-0.04}}_{-0.07}$mm is assembled in a hole of diameter $25^{^{+0.02}}_{0.00}$mm.
Match the allowance and limit parameter in Column I with its corresponding quantitative value in Column II for this shaft-hole assembly.

Allowance and limit parameter (Column I)
P. Allowance
Q. Maximum clearance
R. Maximum material limit for hole

Quantitative value (Column II)
1. 0.09 mm
2. 24.96 mm
3. 0.04 mm
4. 25.0 mm
 A P-3, Q-1, R-4 B P-1, Q-3, R-2 C P-1, Q-3, R-4 D P-3, Q-1, R-2
GATE ME 2022 SET-2   Manufacturing Engineering
Question 5 Explanation:

(1) Allowance = Lower limit of hole - upper limit of shaft
Allowance = 25.00 - 24.96 = 0.04 mm

(2) Maximum clearance $C_{max}$ = Upper limit of hole - lower limit of shaft
$C_{max}$ = 25.02 - 24.93 = 0.09 mm

(3) Maximum material limit for hole = minimum size of hole = 25.00

There are 5 questions to complete.

### 4 thoughts on “Metrology and Inspection”

1. Please correct the answer to Q. 29. It’s (a) outside diameter but not roundness.