Final answer:
The cutting speed for a lathe operation with a spindle rotating at 400 rpm on a rod that is initially 75 mm in diameter is calculated using the formula V = π x D x N. The result is a cutting speed of 1.57 meters per minute.
Step-by-step explanation:
To calculate the cutting speed of a lathe operation, you need to consider the spindle rotational speed and the diameter of the workpiece. The cutting speed V is the speed at which the cutting tool moves across the face of the material being shaped and is crucial for selecting the correct cutting parameters for efficient machining.
In this case, we are concerned with a titanium alloy rod that is 75 mm in diameter and is to be turned down to 65 mm in diameter. The spindle rotates at 400 revolutions per minute (rpm). To calculate the cutting speed, we must first convert the rotational speed to cutting speed in meters per minute. The cutting speed formula is: V = π x D x N, where V is the cutting speed in meters per minute, π is Pi (approximately 3.1416), D is the diameter in meters, and N is the rotational speed in rev/min.
Calculation:
D = 75 mm = 0.075 m (initial diameter before cutting)
N = 400 rev/min
V = π x 0.075 m x 400 rev/min = π x 0.075 m x 6.6667 rev/s = 1.57 m/min
Therefore, the cutting speed is 1.57 meters per minute.