A cutting tool operates at a depth of 2 mm and a feed of 1,3 mm per revolution

Question

of the spindle on a 45 mm diameter work piece in a lathe rotating at 1300 r/min. The cutting pressure on the cutting tool is 1,3 kN/mm².

Calculate the power supplied to a cutting tool if 25% is to be allowed for frictional losses.

Answer 1

First, we need to calculate the cutting speed of the tool:

Cutting speed (V) = π * diameter * rotational speed
V = π * 45 mm * 1300 r/min
V = 56700 * π mm/min
V ≈ 178000 mm/min

Next, we calculate the material removal rate (MRR):

MRR = depth of cut * feed * cutting speed
MRR = 2 mm * 1.3 mm * 178000 mm/min
MRR = 462200 mm^3/min

Then, we calculate the cutting power:

Cutting power = cutting pressure * MRR
Cutting power = 1.3 kN/mm² * 462200 mm^3/min
Cutting power = 600,860 W

Now, we allocate 25% of the cutting power for frictional losses:

Power for cutting = Cutting power / (1 - 0.25)
Power for cutting = 600,860 W / 0.75
Power for cutting ≈ 801,147 W

Therefore, the power supplied to the cutting tool is approximately 801,147 Watts.