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## Q. 1.3

Discuss the cutting speed, feed and depth of cut in shaping, planning and slotting operations.

## Verified Solution

The cutting speed, V, in planing, shaping and slotting operations is the speed of the tool (or the work) in the direction of the primary cutting motion during the working stroke when the metal is being cut. The cutting speed may be either constant or variable depending upon the design of the machine tool.

Shapers with crank and slotted arm mechanisms have a variable cutting speed and a variable return speed (Fig. 1.70) of the tool. The speed is minimum at the beginning and end of the stroke and maximum in the middle of the stroke. The cutting speed can be determined by the formula:

$V=\frac{L N(1+K)}{1000} m / min .$

where                                 L = Length of ram stroke, mm
N = number of full strokes/min,

that is, a full stroke comprises working and return strokes.

K = Ratio of return time to cuttingtime.

Planers with a rack and pinion drive for the table have a constant cutting speed, which can be determined from the formula :

$V=\frac{2 N L}{1000}, m / min$

The feed, f, in planing, shaping or slotting (Fig. 1.70) is the relative movement of the tool or work in a direction perpendicular to the primary cutting motion per full stroke and is expressed in mm/stroke.

The depth of cut, d, is the thickness of layer of metal removed in one cut or pass. It is measured in a direction perpendicular to the machined surface.

The cross-sectional area of the undeformed chip is the product of the thickness, t, and the width, b, of the undeformed chip :

Area of undeformed chip = t × b = f × d mm².

Cutting speeds in these kinds of machining operations are not usually very high, since difficulties are encountered in designing machine tools with high speed of reciprocating motion due to high inertia forces developed in the motion of the units and components of machine. Thus in planing cast iron, the recommended cutting speed is 15 to 20 m/min for roughing and 4 to 12 m/min for finishing. The corresponding depths of cut are 0.5 to 0.8 mm, and 0.08 mm respectively, with feed ranging from 1.50 to 2.00 mm/stroke.