GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 36 of 65

Marks: +1, -0

There are two identical shaping machines

S_{1}

and

{S}_{2}

. In machine

{S}_{2}

, the width of the workpiece is increased by

10 \%

and the feed is decreased by

10 \%

, with respect to that of

{S}_{1}

. If all other conditions remain the same then the ratio of total time per pass in

{S}_{1}

and

{S}_{2}

will be _________________ (round off to one decimal place).

Solution:

Two shaping machines

{S}_{1}

and

{S}_{2}

:
Machine

{S}_{1}

Machine

{S}_{2}

Width

= ω_1

width

(ω_{2})=1.1 ω_{1}

Feed

= {f}_{1} \;\;

feed

( {f}_{2})=0.1 {f}_{1}

Let quick return ratio

= {R}

(t_{m})_{1}=\;{L}/{V} × \;{ω_{1}}/{f_{1}}(1+R)

( {t}_{ {m}})_{2}=\;{ {L}}/{ {V}} × \;{ω_{2}}/{ {f}_{2}}(1+ {R})

\;{( {tm})_{1}}/{( {tm})_{2}}=\;{\;{ {LV}}/{ {V}} × {ω_{1}}/{ {f}_{1}}(1+ {R})}/{{ {L}}/{ {V}} × \;{ω_{2}}/{ {f}_{2}}(1+ {R})}

=\;{f_{2} × ω_{1}}/{f_{1} × ω_{1}}

=\;{0.9 {f}_{1} × ω_{1}}/{ {f}_{1} × 1.1 ω_{1}}

\;{( {tm})_{1}}/{( {tm})_{2}}=0.818=0.82

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