Metrology and Inspection

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Question 1

A 76.2 mm gauge block is used under one end of a 254 mm sine bar with roll diameter of 25.4 mm. The height of gauge blocks required at the other end of the sine bar to measure an angle of

30^{\circ}

is __________mm (round off to two decimal places).

A	203.2
B	145.6
C	214.3
D	542.6

GATE ME 2021 SET-2 Manufacturing Engineering

Question 1 Explanation:

\begin{aligned} \sin 30^{\circ} &=\frac{h_{1}}{254} \\ \text{or}\qquad h_{1} &=254 \sin 30^{\circ}=127 \mathrm{~mm} \\ H_{2} &=76.2+127=203.2 \mathrm{~mm} \end{aligned}

\\ Case II:

\begin{aligned} \sin 30^{\circ} &=\frac{76.2-h_{1}}{254} \\ \text{or}\qquad h_{1} &=76.2-254 \sin 30^{\circ}\\ &=-50.8 \mathrm{~mm} \end{aligned}

Which is not feasible
Therefore final answer 203.2 mm.

Question 2

The allowance provided in between a hole and a shaft is calculated from the difference between

A	lower limit of the shaft and the upper limit of the hole
B	upper limit of the shaft and the upper limit of the hole
C	upper limit of the shaft and the lower limit of the hole
D	lower limit of the shaft and the lower limit of the hole

GATE ME 2021 SET-2 Manufacturing Engineering

Question 2 Explanation:

It is minimum clearance or maximum interference. It is the intentional difference between the basic dimensions of the mating parts. The allowance may be positive or negative.

Question 3

Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.

The reaction at the point of contact between two spheres is _______N (round off to one decimal place).

A	110
B	125
C	258
D	324

GATE ME 2021 SET-1 Manufacturing Engineering

Question 3 Explanation:

\begin{aligned} B C &=250^{2}-150^{2} \\ \cos \theta &=\frac{200}{250} \\ \theta &=36.869^{\circ} \end{aligned}

\begin{aligned} R_{2} \cos \theta &=100 \\ R_{2} &=\frac{100 \times 250}{200}=125 \mathrm{~N} \end{aligned}

Question 4

Consider the surface roughness profile as shown in the figure.

The center line average roughness (

R_a \text{ in }\mu m

) of the measured length (L) is

A	0
B	1
C	2
D	4

GATE ME 2021 SET-1 Manufacturing Engineering

Question 4 Explanation:

R_{G}=\frac{\sum_{i=1}^{n} y}{n}=\frac{4}{4}=1

Question 5

Two rollers of diameters

D_1

(in mm) and

D_2

(in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights

H_1

(in mm) and

H_2

(in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.

Which one of the following is the correct relationship to evaluate the angle

\alpha

as shown in the figure?

A	$\sin \alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-(D_1-D_2)}$
B	$\cos \alpha =\frac{(D_1-D_2)}{2(H_1-H_2)-2(D_1-D_2)}$
C	$cosec\; \alpha =\frac{(H_1-H_2)-(D_1-D_2)}{2(D_1-D_2)}$
D	$\sin \alpha =\frac{(H_1-H_2)}{(D_1-D_2)}$

GATE ME 2020 SET-2 Manufacturing Engineering

Question 5 Explanation:

\begin{aligned} O B &=\left(H_{1}-\frac{D_{1}}{2}\right)-\left(H_{2}-\frac{D_{2}}{2}\right)\\ &=\left(H_{1}-H_{2}\right)-\left(\frac{D_{1}-D_{2}}{2}\right) \\ O A &=\frac{D_{1}-D_{2}}{2} \\ \sin \alpha &=\frac{\frac{\left(D_{1}-D_{2}\right)}{2}}{\left(H_{1}-H_{2}\right)-\frac{\left(D_{1}-D_{2}\right)}{2}} \\ \sin \alpha &=\frac{\left(D_{1}-D_{2}\right)}{2\left(H_{1}-H_{2}\right)-\left(D_{1}-D_{2}\right)} \end{aligned}

Question 6

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various specifications whose definitions are listed below.

P: Maximum Waviness Height (mm);
Q: Maximum Roughness Height (mm);
R: Minimum Roughness Height (mm);
S: Maximum Waviness Width (mm);
T: Maximum Roughness Width (mm);
U: Roughness Width (mm);