Shaping Operation

Shaping is a machining process used to produce flat surfaces or surfaces of revolution by cutting the workpiece with a single-point cutting tool. In a shaping operation, the cutting tool reciprocates over the workpiece, removing material in each stroke.

Average Cutting Speed Formula

The average cutting speed (V) in a shaping operation can be calculated using the formula:

V = S × N × (1 - R) / 2

where:

S = Stroke length
N = Number of strokes per minute
R = Quick return ratio

Explanation of Formula

- Stroke Length (S): It is the distance that the cutting tool travels in one stroke. It is measured in millimeters (mm).
- Number of Strokes per Minute (N): It is the number of times the cutting tool reciprocates over the workpiece in one minute. It is measured in strokes per minute (spm).
- Quick Return Ratio (R): It is the ratio of the time taken by the cutting tool to travel forward to the time taken by it to return back. It is a dimensionless quantity.
- (1 - R): It is the time taken by the cutting tool to travel back to its initial position after completing one stroke.
- (1 - R) / 2: It is the time taken by the cutting tool to complete one cycle (forward and return stroke).

Hence, the average cutting speed is the product of stroke length, number of strokes per minute, and the time taken by the cutting tool to complete one cycle.

Conclusion

Option D is the correct answer as it is the formula for calculating the average cutting speed in a shaping operation. The other options do not consider the quick return ratio, which is an important factor in determining the cutting speed.