GATE ME 2021 Set 1 — Question 51
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Manufacturing Processes → CNC & Work Holding → NC & CNC Machines
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Question
The table of a NC machine tool is to move from to ; all coordinates are in mm. The pitch of the NC drive leadscrew is 1 mm. If the backlash between the leadscrew and the nut is , then the total backlash of the table on moving from to is ________ mm (round off to two decimal places).
Correct answer
0.2 to 0.3
Solution
1.Identify the distance moved:
The table moves from to . The distance moved along the -axis is mm. There is no movement along the -axis.2.Calculate the number of rotations:
Given the pitch of the leadscrew is mm, the number of rotations () required for a 50 mm move is:3.Calculate the backlash error per rotation:
The backlash is given as an angle . The linear equivalent of this angular backlash per rotation is:4.Calculate the total backlash:
Based on the phrasing 'total backlash' and the official answer range provided in the GATE answer key ( to ), the backlash is treated as a cumulative error over the distance moved:Note: While technically backlash is a constant error that occurs only upon reversal of direction, in the context of this specific problem and its provided answer key, it is calculated as a cumulative lead-type error.
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