GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 12 of 65

Marks: +1, -0

A sheet metal with a stock hardness of 250 HRC has to be sheared using a punch and a die having a clearance of

1 {mm}

between them. If the stock hardness of the sheet metal increases to

400 {HRC}

, the clearance between the punch and the die should be

{mm} .

Solution:

Given

{C}_{1}=1 {mm} \;\;\;\; ( {\HRC})_{1}=250

{C}_{2}=? \;\;\;\; \;\;\;\;\;( {\HRC})_{2}=400

{C}=0.0032 {t} √{τ}

{C} ∝ √{ {C}} ∝ √{ {HRC}}

\;{ {C}_{2}}/{ {C}_{1}}=√{\;{( {HRC})_{2}}/{( {HRC})_{1}}}

⇒ \;{ {C}_{2}}/{1}=√{\;{400}/{250}}

{C}_{2}=1.264 {mm}

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