GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 43 of 65

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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

α

as shown in the figure?

Solution:

Upper roller having diameter

( {D}_{1})=

Lower roller having diameter

{D}_{2}

{O}_{1} {O}_{2}=

Distance between centre of roller

=(H_{1}-\;{D_{1}}/{2})-(H_{2}-\;{D_{2}}/{2})

O_{1} O_{2}=(H_{1}-H_{2})-(\;{D_{1}}/{2}-\;{D_{2}}/{2})

Difference in radius

=(\;{D_{1}}/{2}-\;{D_{2}}/{2})

By geometry in

△ {AO}_{2} {O}_{1}

\sin α=\;{({D_{1}}/{2}-{D_{2}}/{2})}/{(H_{1}-H_{2})-(\;{D_{1}}/{2}-\;{D_{2}}/{2})}

\sin α=\;{(D_{1}-D_{2})}/{2(H_{1}-H_{2})-(D_{1}-D_{2})}

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