In orthogonal cutting, the tool approaches the workpiece with its cutting edge parallel to the uncut surface and at right angles to the direction of cutting. Thus tool approach angle and cutting edge inclination are zero.
The study of forces acting on a tool during the process of metal cutting is necessary for making the analysis of the process on a qualitative basis. The relationship among the various forces had been found out by Merchant with a large number of assumptions.
These assumptions are listed below:
(i) The tool is perfectly sharp and there is no contact along the clearance face.
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(ii) The shear surface is a plane extending upward from the cutting edge.
(iii) The cutting edge is a straight line, extending perpendicular to the direction of motion and generates a plane surface as the work moves past it.
(iv) The chip does not flow to either side.
(v) The depth of cut is constant.
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(vi) Width of the tool is greater than that of workpiece.
(vii) The work moves relative to the tool with uniform velocity.
(viii) A continuous chip is produced with no built-up edge.
(ix) Plane strain conditions exist, i.e. the width of the chip remains equal to the width of the workpiece.
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(x) Chip is assumed to shear continuously across plane AB on which the shear stress reaches the value of shear flow stress.
For studying the forces acting on chip, let us isolate it as a free body as shown in Fig. 22.15. Obviously only two forces are acting on it. The force between the tool face and chip (R) and the force between the work-piece and the chip along the shear plane (R’) must be equal for equilibrium, i.e. R = R’.
In Fig. 22.15, α is the rake angle of tool, β depends on coefficient of friction between surface and chip and f is the shear angle. The forces R and R’ can be conveniently resolved into three sets of components along the directions of interest to us as shown in Fig. 22.15.
The directions along which the forces R and R’ are resolved are as follows:
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1. Along the horizontal and vertical direction FH and Fv.
2. Along and perpendicular to the shear plane, Fs and Ns.
3. Along and perpendicular to the tool face, F and N. F is the actual friction force which resists sliding of the chip over the face of the tool.
If the forces R and R’ (being equal) are plotted at the tool point instead of at their actual points of application along the shear plane and tool face, we obtain a convenient and compact diagram as shown in Fig. 22.16.
Here R and R’ (which are equal and parallel) are coincident, and are made the diameter of the dotted reference circle shown. Then, by virtue of the geometrical fact that lines that terminate at the ends of diameter R and intersect at any point on the circle will interest at right angles, we can conveniently resolve R into orthogonal components in any direction.
Analytical relationship may be obtained for the shear and friction components in terms of the horizontal and vertical components (FH and Fv), which are the components normally determined experimentally by means of a dynamometer.
From the Fig. 22.17 (a), it is evident that:
The tool face components are of importance, since they enable the coefficient to friction for the tool face (µ = tan β) to be determined, where β = mean angle of friction at the rake surface.
µ, the coefficient of friction between chip and the tool is a measure of the resistance to sliding encountered by the chip as it passes over the face of the tool.
µ can also be related to the cutting ratio r by the equation:
It may be appreciated that chip gets deformed plastically and as such concept of coefficient of friction in ordinary cases can’t be applied for chips. In the case of metal cutting, µ is dependent upon the normal force, whereas in ordinary cases µ is independent of N.
It has been found that µ increases from 0.58 to 1.19 with increase in rake angle from – 20° to + 20°. Further, contrary to the concepts of classified friction, the area of contact and the sliding force required is independent of normal force.
Other important mechanical quantities are:
Mean shear strength (Ss). It is the mean shear stress on the plane of the shear.
It can be determined from the formula:
(b = chip width and t = chip thickness before removal from workpiece).
Work done in shear (W) (portion of the work done in removing a chip consumed in shearing of the metal on the plane of the shear) can be calculated from the formula WS = SS [cos f + tan (f – α)]
Work done in overcoming friction between chip and tool (Wf) can be calculated from the formula:
Merchant also developed a relationship between the shear angle f, the friction angle α and cutting rake angle a as follows.
2f + β – α = C, where C = machining constant for the work material dependent on the area and change of the shear strength of the metal with applied compressive stress, besides taking the internal coefficient of friction into account. Machining constant is essentially a property of the metal being cut and its value is closely related to the plastic properties of the metal.
Since it has a direct control on the size of the shear angle, it determines to a large degree how easily a material can be machined. It is not greatly affected by cutting conditions. Value of C varies from 70° to 80° for various types of steel.
Power consumed at cutter in removing a unit volume of metal in unit time is proportional to:
Forces in Orthogonal Cutting:
The cutting force F in orthogonal cutting can be expressed by the formula:
where F = cutting force in kg.
t = uncut chip thickness in mm/rev. or feed (f) in turning operation.
b = width of cut in mm or depth (d) in turning operation.
x = constant for the material machined. Its value may be taken as 0.85 for all steels over the usual ranges of rake angles,
and C = a material constant at a given cutting speed and rake angle.
It varies from 98 for free machining carbon steel with hardness of 120 HB to 224 for carbon steel with hardness of 225 HB for positive rake angles. For negative rakes at high cutting speed, value of C is about 10% higher.