GATE ME 2020 Set 2 — Question 42
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Metrology, CIM & Additive Mfg → Metrology & Inspection → Linear & Angular Measurement
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Question
Two rollers of diameters (in mm) and (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights (in mm) and (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 as shown in the figure?
Correct answer
(A) sin α = ((D₁ - D₂))/(2(H₁ - H₂) - (D₁ - D₂))
Solution
From the geometry of the V-groove measurement:
The distance from the vertex of the V-groove to the center of a roller of diameter is .
The height measured from the base to the top of the roller is:where is the constant distance from the vertex to the base.For two rollers of diameters and :Subtracting the two equations:This matches option (A).
The distance from the vertex of the V-groove to the center of a roller of diameter is .
The height measured from the base to the top of the roller is:where is the constant distance from the vertex to the base.For two rollers of diameters and :Subtracting the two equations:This matches option (A).
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