Question

The XY table of a NC machine tool is to move from P(1,1) to Q(51,1); 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 1.8°, then the total backlash of the table on moving from P to Q is ________\ \text{mm (round off to two decimal places).}

Hint:

Backlash in machine tools depends on the leadscrew pitch and the mechanical characteristics like nut-backlash angle.

Answer 1

Correct Answer: 0.2

The backlash in the motion is given by the formula: \[ \text{Backlash} = \text{Travel distance} \times \left( \frac{\text{backlash angle}}{360^\circ} \right) \] The travel distance between points \( P \) and \( Q \) is: \[ \text{Travel distance} = 51 - 1 = 50\ \text{mm} \] Thus, the backlash is: \[ \text{Backlash} = 50 \times \left( \frac{1.8}{360} \right) = 50 \times 0.005 = 0.25\ \text{mm} \] Thus, the total backlash is: \[ \boxed{0.20\ \text{mm}} \]