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In design of cutting dies, the cutting pressure coming on it is very important and its magnitude is of the offer of 1.5 L x t x f_{s} .

where L = periphery of work piece,

t = thickness of work piece,

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f_{s} = ultimate shear strength of work piece.

**In addition, total cutting force depends upon: **

(i) Sharpness of cutting edge;

(ii) Clearance between die and punch;

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(iii) Angle of shear on die and punch;

(iv) Hardness of the material to be cut.

We will first of all consider the effect of angle of shear on die and punch. First the metal is subjected to the plastic deformation and after that fracture takes place instantaneously. This instantaneous fracture of metal after its plastic deformation is known as penetration and its value depends upon the ductility of the material being cut, e.g., for mild steel its value is 33.33%, i.e., for 33.33% of punch stroke, plastic deformation of metal occurs and after it instantaneous fracture occurs.

Now, if the punch be made exactly flat, i.e., no angle is given on it then suddenly the punch is subjected to maximum force as whole of the surface is coming in contact with the work-piece. This pressure remains on the punch till it has moved about one- third the thickness of sheet and after takes place and whole load drops to zero.

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This is shown in Fig. 29.7. In this way, it is observed that punch is subjected to heavy load which remains on it for short period. Thus the punch should be strong one and press should be designed for this load and motor of high capacity is needed.

Let us consider the case then angle of shear = t/3 (∠Sh = t/3), i.e. when one end of the punch is higher by t/3 from other end, where t is the thickness of work-piece. In this case, when punch has moved by t/3, the other end of the punch has not yet touched the sheet and the portion under left of punch is already sheared.

As the punch advances, the fracture of remaining portion keeps on taking place. After 2t/3 movement, the fracture is complete. Thus the force on the punch initially keeps on increasing upto t/3 movement, and it decreases to zero at 2t/3 movement.

When angle of shear is equal to t, then initially the force goes on increasing upto t/3 punch movement and one end gets fractured. After it, as the punch advances, further fracture goes on taking place from left offering no resistance, but area of punch in contact with sheet also increases.

Therefore, the total resistance after t/3 punch movement remains constant till punch movement. (The amount of force on punch will actually depend upon the shape of the punch face and the approximate magnitude of the blanking force at any instant can be found by the formula F = 1.5 L + f_{s} by substituting the appropriate value of L.

It is thus observed that as angle of shear keeps on increasing, the force acting on the punch goes on decreasing, i.e. instantaneous force is less and design of punch becomes simple. In other words, the application of ‘shear’ to the punch results, in metal failing progressively rather than almost instantaneously.

But at the same time, the travel of the punch also keeps on increasing with increase of angle of shear and the cut-out piece is distorted more and more. Considering this, a compromise is reached at depending upon the kinematics of the machine and usually the angle of shear = t is selected.

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Sometimes angle of shear is given on both sides of punch in order to balance the axial force components on either side. But in this case, the blanked portion shape will be as shown in Fig. 29.9 and thus it will go as waste.

This arrangement is adopted only in case of piercing and punching where the cut portion is waste. Considering the deformation of the work piece due to providing of angle of shear, it is better to have angle of shear on punch for piercing and punching operation; and in case of blanking operation the angle of shear should be given on the die.

**Energy Required for Cutting: **

It is already shown that P_{max}, i.e. max. force to cut any work piece

= L.t.f_{s}

Average force on the punch is encountered when the ÐSh = t

Since energy in cutting when ÐSh = 0 and ÐSh = t is same.

**Smallest Hole that can be Punched****: **

The total force required for punching has to be taken by the punch and it comes on it in the form compressive force. Thus the punch must be able to take this compressive load.

If *f*_{c} is the allowable compressive stress on the punch, then allowable compressive load on the punch = π/4 d^{2} *f*_{c} (d = diameter of hole to be punched).

**The force coming due to punching should be less than this value, i.e. **