Question

A 1 mm thick cylindrical tube, 100 mm in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. The axial feed of the tool is 1 m/minute and the specific cutting energy (\( u \)) of the tube material is 6 J/mm\(^3\). Neglect contribution of feed force towards power. The power required to carry out this operation is ________________ kW (round off to one decimal place).

Hint:

The power required for cutting can be calculated by multiplying the specific cutting energy, the cutting area, and the cutting speed. Be sure to convert the units to kW.

Answer 1

Correct Answer: 30

The power required for the turning operation can be calculated using the formula: \[ P = u \times A_c \times v \] Where:
- \( P \) is the power required in watts (W),
- \( u = 6 \, \text{J/mm}^3 \) is the specific cutting energy,
- \( A_c \) is the cutting area,
- \( v = 1 \, \text{m/min} = 1000 \, \text{mm/min} \) is the cutting speed.
The cutting area \( A_c \) is calculated as: \[ A_c = \text{Feed} \times \text{Thickness of cut} = 1000 \, \text{mm} \times 1 \, \text{mm} = 1000 \, \text{mm}^2. \] Now, substitute the values into the formula: \[ P = 6 \times 1000 \times 1000 = 6000000 \, \text{J/min}. \] Convert to watts (since 1 W = 1 J/s): \[ P = \frac{6000000}{60} = 100000 \, \text{W} = 0.1 \, \text{kW}. \] Thus, the power required to carry out this operation is \( \boxed{0.1} \, \text{kW} \).