GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

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A point ‘P’ on a CNC controlled XY-stage is moved to another point ‘Q’ using the coordinate system shown in the figure below and rapid positioning command (G00).

A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of 0.5 mm. The time needed to position the point ‘P’ to the point ‘Q’ is ___________ minutes (round off to 2 decimal places).

Your Answer:

Validate

Solution:

Since pair of steeping motors with controlling both the x and y motion so time needed in x-direction:

{t}_{ {x}}=\;{( {x}_{2}- {x}_{1})}/{ {f}_{ {m}}}=\;{(800-200)}/{0.5 × 800}

{t}_{ {x}}=\;{600}/{400}=1.5 {min}

Time needed in

y

-direction

{t}_{ {y}}=\;{( {y}_{2}- {y}_{1})}/{ {f}_{ {m}}}=(\;{600-300}/{400})

\;\; =0.75 {min} .

Since both are working simultaneously so the maximum time of both direction will be the machining time.

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