**In this article we will discuss about the metal forming processes: 1. Types of metal forming processes 2. Classification of metal forming processes 3. Techniques of metal forming processes. And also the below mentioned article provides a lecture note on metal forming processes.**

In doing so, we shall show how-

(i) The work load can be estimated from the knowledge of the material properties and the working conditions, and

(ii) Certain other aspects of the processes can be better understood.

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**When studying the mechanics of forming processes, the acceleration, and consequently the inertia forces, of the flowing materials are negligible. Hence, the equations for static equilibrium can be applied in all cases. **

#### Type # **1. Rolling: **

**The basic objectives of the analysis we give here are to determine: **

(i) The roll separating forces,

(ii) The torque and power required to drive the rolls, and

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(iii) The power loss in bearings.

**An analysis considering all the factors in a real situation is beyond the scope of this text, and therefore the following simplifying assumptions will be made: **

(i) The rolls are straight and rigid cylinders.

(ii) The width of the strip is much larger than its thickness and no significant widening takes place, i.e., the problem is of plane strain type.

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(iii) The coefficient of friction μ is low and constant over the entire roll-job interface.

(iv) The yield stress of the material remains constant for the entire operation, its value being the average of the values at the start and at the end of rolling.

**Determination of Rolling Pressure: **

Figure 3.8a shows a typical rolling operation for a strip with an initial thickness t_{i} which is being rolled down to a final thickness t_{f}. Both the rolls are of equal radius R and rotate with the same circumferential velocity V. The origin of the coordinate system xy is taken at the midpoint of the line joining the centres O_{1} and O_{2}. (The operation is two-dimensional, and so the position of O along the axis mutually perpendicular to O_{x }and O_{y} is of no significance. In our analysis, we shall assume that the width of the strip is unity.)

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The entry and exit velocities of the strip are V_{i} and V_{f}, respectively. In actual practice, V_{f}> V> V_{i}. Therefore, at a particular point in the working zone, the velocity of the strip will be equal to V, and this point will hereafter be referred to as the neutral point.

Considering a general case, we assume that the stresses σ_{xi} and σ_{xf} are acting on the entry and the exit sides (Fig. 3.8a). However, depending on the situation, either one or both of these stresses may be absent.

**Determination of Roll Separating Force: **

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Assuming that the width of the strip is unity, the total force F trying to separate the rolls can be obtained by integrating the vertical component of the force acting at the roll-strip interface. Since the angle θ_{i} is normally very small, the contribution of the roll-strip interface friction force is negligible in the vertical direction. Thus,

**Driving Torque and Power: **

The driving torque is required to overcome the torque exerted on the roll by the interfacial friction force. So, the driving torque corresponding to unit width can be expressed as

It should be noted that friction resists the rotation of the roll before the neutral point, whereas it helps the rotation afterwards. By this method, the result comes out as the difference of two, nearly equal, large numbers, causing the numerical error to be significant. This limits the use of equation (3.21) in practice.

An alternative approach to determine t is to consider the horizontal equilibrium of the deformation zone of the strip. Figure 3.10 shows the deformation zone along with the forces acting on it, including an equivalent horizontal force F^{e} which represents the net frictional interaction between each roll and the strip (the reaction – F^{e} of F^{e }has to be overcome by the roll driving torque T). F^{e} can be determined by considering the horizontal equilibrium of the system.

Thus,

**Power Loss in Bearings: **

The friction in the bearings, supporting the rolls, obviously causes some power loss. An exact analysis of the power loss in bearings is too complicated. However, to estimate the approximate power requirement of the rolling mill, it is sufficient to assume that the power loss in each bearing is given by

#### Type # **2. Forging: **

In this article, our analysis is mainly devoted to determining the maximum force required for forging a strip and a disc between two parallel dies. Obviously, it is a case of open die forging.

**Forging of Strip: **

Figure 3.11a shows a typical open die forging of a flat strip.

**To simplify our analysis, we shall make the following assumptions: **

(i) The forging force F attains its maximum value at the end of the operation.

(ii) The coefficient of friction μ between the work piece and the dies (platens) is constant.

(iii) The thickness of the work piece is small as compared with its other dimensions, and the variation of the stress field along the y-direction is negligible.

(iv) The length of the strip is much more than the width and the problem is one of plane strain type.

(v) The entire work piece is in the plastic state during the process.

At the instant shown in Fig. 3.11a, the thickness of the work piece is h and the width is 2l. Let us consider an element of width dx at a distance x from the origin. [In our analysis, we take the length of the work piece as unity (in the z-direction).] Figure 3.11b shows the same element with all the stresses acting on it.

Considering the equilibrium of the element in the x-direction, we get

Near the free ends, i.e., when x is small (and also at x ≈ 2l; the problem being symmetric about the mid plane, we are considering only one-half in our analysis, i.e., 0 ≤ x ≤ l), a sliding between the work piece and the dies must take place to allow for the required expansion of the work piece. However, beyond a certain value of x (in the region 0 ≤ x ≤ l) say, x_{s} there is no sliding between the work piece and the dies. This is due to the increasing frictional stress which reaches the maximum value, equal to the shear yield stress, at x = x_{s} and remains so in the rest of the zone, x_{s} ≤ x ≤ l. Hence, for 0 ≤ x ≤ x_{s,}

**Forging of Disc****:**

Figure 3.12 shows a typical open die forging of a circular disc at the end of the operation (i.e., when F is maximum) when the disc has a thickness h and a radius R. The origin of the cylindrical coordinate system r, θ, y is taken at the centre of the disc. An element of the disc, subtending an angle dθ at the centre, between the radii r and r + dr is shown in Fig. 3.13 along with the stresses acting on it. In our analysis here, we make the same assumptions as in the forging of a strip, except (iv). Considering the cylindrical symmetry, it can be shown^{ }that

#### Type # **3. Drawing: **

In a drawing operation, in addition to the work load and power required, the maximum possible reduction without any tearing failure of the work piece is an important parameter. In the analysis that we give here, we shall determine these quantities. Since the drawing operation is mostly performed with rods and wires, we shall assume the work piece to be cylindrical, as shown in Fig. 3.14.

A typical drawing die consists of four regions, viz., – (i) a bell-shaped entrance zone for proper guidance of the work piece, (ii) a conical working zone, (iii) a straight and short cylindrical zone for adding stability to the operation, and (iv) a bell-shaped exit zone. The final size of the product is determined by the diameter of the stabilizing zone (d_{f}), the other important die dimension being the half-cone angle (α).

Sometimes, a back tension F_{b} is provided to keep the input work piece straight. The work load, i.e., the drawing force F, is applied on the exit side, as shown in Fig. 3.14. A die can handle jobs having a different initial diameter (d_{i}) which, in turn, determines the length of the job-die interface. The degree of a drawing operation (D) is normally expressed in terms of the reduction factor in the cross-sectional area. Thus,

**Determination of Drawing Force and Power: **

The case being an axisymmetric one, a cylindrical coordinate system r, x (θ being of no importance) is chosen with its origin O at the vertex of the die cone, as shown in Fig. 3.14. An element of length dx at a. distance x, along with the stresses acting on it, is shown in Fig. 3.15a.

**To simplify our analysis, we make the following assumptions: **

(i) The coefficient of friction μ, and the half-cone angle α are small.

(ii) The yield stress σ_{Y} is constant and given by the average of the initial and the final values.

(iii) -p and σ_{x} are the principal stresses.

(iv) σ_{x} does not vary in the radial direction.

It should be noted that both p and μp act on the whole conical surface of the element. Now, from Fig. 3.15a,

where σ_{x} and p are related through the yield criterion. A segment of an annular element of thickness δr at the surface is shown in Fig. 3.15b. The resultant radial stress at the surface is composed of the radial components of both p and μp. Now, considering the radial equilibrium of the segment, we get –

Using the von Misses yield criterion given by equation (3.3), along with equations (3.4) and (3.54), we get –

Where σ_{Xf} is obtained from equation (3.56). If the drawing speed, i.e., the exit velocity, is V, the power required for the drawing operation is –

**Determination of Maximum Allowable Reduction****: **

The maximum allowable reduction or the maximum degree of a drawing operation (D) is determined from the constraint that the pulling stress σ_{Xf} cannot be more than the tensile yield stress of the work material. So, at this limiting condition,

#### Type # **4. Deep Drawing:**

From the point of view of analysis, the process of deep drawing is very complex. In this process, various types of forces operate simultaneously. The annular portion of the sheet metal work piece between the blank holder and the die is subjected to a pure radial drawing, whereas the portions of the work piece around the corners of the punch and the die are subjected to a bending operation.

Further, the portion of the job between the punch and the die walls undergoes a longitudinal drawing. Though in this operation varying amount of thickening and thinning of the work piece is unavoidable, we shall not take this into consideration in our analysis.

The major objectives of our analysis are – (i) to correlate the initial and final dimensions of the job, and (ii) to estimate the drawing force F. Figure 3.16 shows the drawing operation with the important dimensions. The radii of the punch, the job, and the die are r_{p}, r_{j}, and r_{d}, respectively.

Obviously, without taking the thickening and thinning into account, the clearance between the die and the punch (r_{d} – r_{p}) is equal to the job thickness t. The corners of the punch and the die are provided with radii r_{Cp} and r_{Cd}, respectively. A clearance (c) is maintained between the punch and the blank holder.

To start with, let us consider the portion of the job between the blank holder and the die. Figure 3.17a shows the stresses acting on an element in this region. It should be noted that the maximum thickening (due to the decreasing circumference of the job causing a compressive hoop stress) takes place at the outer periphery, generating a line contact between the holder and the job. As a result, the entire blank holder force F_{h} is assumed to act along the circumference (Fig. 3.17b). Thus, the radial stress due to friction can also be represented by an equivalent radial stress 2μF_{h }/ (2πr_{j}t) at the outer periphery.

There is a further increase in the stress level around the punch corner due to bending. As a result, the drawn cup normally tears around this region. However, to avoid this, an estimate of the maximum permissible value of (r_{j }/ r_{d}) can be obtained by using equations (3.64) and (3.63) with σ_{z} equal to the; maximum allowable stress of the material.

Since r_{d} is the final outside diameter of the product, it is easy to arrive at such an estimate. This estimate is based on the consideration of fracture of the material. However, to avoid buckling (due to the compressive hoop stress in the flange region), (r_{j} – r_{p}) should not, for most materials, exceed 4_{t}.

**Normally, the blank holder force is given as: **

#### Type # **5. Bending:**

In a bending operation, apart from the determination of work load, an estimate of the amount of elastic recovery (spring back) is essential. When the final shape is prescribed, a suitable amount of over bending is required to take care of this spring back.

Figure 3.19 shows a bending operation with characteristic dimensions. A radius r_{p} is provided at the nose of the punch and, accordingly, the die centre has a radius (r_{p} + t), where t is the job thickness.

The portions of the die, in contact with the job during the operation, are also provided with some radius, say, r_{d}. The angle between the two faces of the punch and the die is α. At the instant shown, the angle between the two bent surfaces of the job is (π – 2θ). As we shall subsequently show, the bending force F is maximum at some intermediate stage, depending on the frictional characteristics. The degree of a bending operation is normally specified in terms of the strain in the outer fibre.

The width of the job w (in the direction perpendicular to the plane of the paper) is much larger as compared with t, and hence a plane strain condition can be assumed. It is obvious that the stock length should be calculated on the basis of the length of the neutral plane of the job. Since the radius of curvature involved in a bending operation is normally small, the neutral plane shifts towards the centre of curvature.

Usually, a shift of 5-10% of the thickness is assumed for the calculation of strain and stock length. Thus, the strain in the outer fibre of the bend is given as assuming a 5% shift of the neutral plane.

Depending on the ductility of the job material, ԑ_{max} has a limiting value beyond which a fracture takes place. So, from equation (3.67) and the limiting value of ԑ_{max} (=ԑ_{fracture}), we can determine the smallest punch radius for a given job thickness.

Since the job undergoes plastic bending, the stress distribution at the cross-section along the centre line (XX) is as shown in Fig. 3.20a. This distribution is obtained by neglecting all other effects of curvature except the shift of neutral line.

It is obvious that in the zone on either side of the neutral plane the strain level is within the elastic range. When the strain (both in the tensile and the compressive zones) reaches the yield limit, plastic deformation starts. Assuming the yield stress to be σ_{Y0} (same in both tension and compression) and linear strain hardening, the stress distribution will be as shown in the figure. The magnitude of σ_{Y1} and σ_{Y2} is different due to the shift of the neutral plane. For the sake of simplicity, the stress distribution for large plastic bending is idealized as shown in Fig. 3.20b.

When the strain hardening rate is n, then neutral plane which is very small, it can be neglected in comparison with the other forces. The normal and frictional forces exerted by the die and the punch at their contact lines (since r_{p} is small as compared with the other dimensions, the finite contact between the job and the punch can be idealized as a line) are N and μN, respectively. As t is small, the moment due to μN is negligible. Hence, M = Nl / cos θ. One-half of the bending force per unit width is given as

**Estimation of Spring Back****: **

Figure 3.22a shows the stress-strain characteristics of a linearly strain hardened material. When the material is unloaded from the point A, the path of unloading is given by the line AB, as shown. The amount of recovered strain obviously is

So, the amount of bending strain recovered is given by the elastic bending strain resulting from a bending moment M which is removed when the operation is over. The elastic strain of a beam due to a bending moment M results in an included angle ɸ (as shown in Fig. 3.22b) such that (when the curvature effect is neglected).

Where I and R are the second moment of area of the beam cross section and the radius of curvature, respectively, and L is the length of the neutral plane.

#### Type # **6. Extrusion: **

The basic nature of the deformation in extrusion is, to some extent, similar to that in drawing. Here instead of applying a tensile load at the exit end, a compressive load is applied at the other end. However, a number of complexities arise as the die is commonly flat-face (i.e., the equivalent half-cone angle is very large unlike in the drawing die). Consequently, with the same assumptions as in drawing, the results become highly inaccurate.

In our analysis here, we shall determine the work load and the frictional power loss for a simple forward extrusion with a flat-face die. For doing this, we shall use two approaches; of these, one is in line with that used for drawing, whereas the other is based on the energy consideration. Since both involve rather drastic assumptions, we shall compare the results obtained from the two approaches.

**Determination of Work Load from Stress Analysis****: **

With a flat-face die and high friction between the material and the container wall, a dead zone, shown in Fig. 3.24a, develops where no flow of material takes place. We assume that the dead zone can be approximated by a half-cone angle of 45°.

The material undergoing deformation can be divided into two regions, namely – (i) section AA to BB, where the flow of material is considered as a rigid body motion, and (ii) section BB to CC, where the flow is analogous to that in a drawing operation (of course, with a compressive load). Figure 3.24b shows an element in the region BB-CC along with the stresses acting on it.

Comparing Fig. 3.24b with Fig. 3.15a, the similarity between extrusion and drawing is easily discernible. The only change here is that σ_{x} is compressive. Therefore, following the same analysis as in drawing, equation (3.56) can be rewritten as –

**Determination of Work Load from Energy Consideration: **

The mode of material deformation here is assumed to be the same as that in the foregoing analysis, the only exception being that the frictional stress between the dead zone and the conical work surface is taken as the shear yield stress K. Assume the axial velocity at the section BB as V_{B}, which is the same as the ram velocity. Hence, the rate of energy input to the conical working zone across the section BB is –

**Determination of Frictional Power Loss: **

The total frictional power loss can be found out by summing up the frictional power losses in the conical and the cylindrical regions of the work material. The contribution from the second region can be expressed as –

#### Type # **7. Punching and Blanking: **

The punching and blanking processes cannot, strictly speaking, be grouped under the forming operations. In these processes, a finite volume from a sheet metal is removed en bloc by using a die and a punch. The shape and size of the portion removed are determined by the geometry of the die and the punch. If the final product happens to be the removed portion, then the operation is termed as blanking.

On the other hand, if the pierced sheet metal is the final product, then the operation is called punching. Since the basic mechanics of material removal is the same in both the operations, we shall discuss these under a single heading, namely, punching.

Figure 3.26 shows a simple punching operation. As in deep drawing, so too here the job is held by job holders to prevent any distortion and to provide a support. It should be noted that the punch and die corners are not provided with any radius (unlike in the deep drawing operation) as the objective in this process is to cause a rupture of the material. A clearance c is provided between the punch and the die. Hence, the die diameter d_{d} = d_{p} + 2c, where d_{p} is the diameter of the punch.

**Mode of Metal Deformation and Failure: **

To develop a mathematical model for the punching and blanking operations, it is necessary to study the nature of metal deformation with the progress of the punch, and the mechanism of ultimate failure of the material. Figure 3.27 shows the nature of metal deformation as the punch penetrates the work piece.

It is clear** **that the work piece bends and is pulled down by the punch movement and the grains elongate near the punch corner B. A similar type of deformation takes place near the die corner D. When the grain elongation or the local natural strain in the surface fibre AB (of the work piece) reaches a limiting value, the fibre ruptures. Since the local strain is maximum at the corner, a crack opens up just ahead of the punch comer. After this, with a slight movement of the punch, the inner fibres also get ruptured.

Thus, the fracture line BY propagates, following a path along which the successive inner fibres attain the fracture strain. A similar crack also propagates from the die corner D (because of the symmetry of the deformation geometry). It should be remembered that the velocity of propagation of the fracture line is very high. Now, if the amount of clearance c is optimum, then the two fracture lines meet and a clean edge is obtained after the operation (Fig. 3.28a).

If the clearance is too small, then the fracture lines miss each other and a secondary deformation takes place, resulting in an unclean edge as shown in Fig. 3.28b. Figure 3.28c shows what happens when the amount of clearance is too large. It is obvious that a significant amount of drawing action takes place and the quality of the work piece is again quite poor.

In what follows, we shall give an analysis to approximately determine the fracture line. Subsequently, we shall use this to estimate the correct amount of clearance.

**Deformation Model and Fracture Analysis: **

Figure 3.29 shows the deformation zone in detail. For the sake of simplicity, we shall assume that the problem is two-dimensional. The thickness of the sheet metal is t and the amount of clearance provided is c. At the instant shown, the original outer fibre AQ has taken the shape ASB. The portion AS is assumed to be a quadrant of a circle with centre at O and radius c. The local engineering strain e varies along the length AB, and this variation is assumed to be linear.

The criterion for fracture is taking as the maximum tensile strain rather than the stress. Thus, if the strain at B reaches the fracture limit ԑ_{f}, the outer fibre ruptures and tears open. Similarly, the inner fibre ER, originally at an infinitesimal depth δ, takes the shape ETV, Again, the portion ET is assumed to be a quadrant of a circle with centre at O’ and radius r. When the strain at V reaches the fracture limit, this inner fibre tears at V. Thus, the direction of the fracture can be considered as the line joining B and V.

The fracture operation is very quick and is completed with almost an imperceptible movement of the punch. With the optimum amount of clearance c, the fracture line BV, when extended, should pass through the die corner D.

Since the engineering strain has been assumed to be varying linearly, the elongation of the outer fibre AQ (of length c) to ASB is –

The magnitude of ԑ_{f} at which the fibres rupture depends on the material and the magnitude of the **h**ydrostatic stress, as shown in Fig. 3.30. The values of optimum clearance (c_{o}) and penetration depth (Δ + c_{o}), in terms of the thickness of the work piece (t), for various values of ԑ_{f} are calculated from equations (3.101) and (3.102), respectively.

**These values are as presented here: **

We see from these values that depending on the ductility of the material the clearance varies from 5% to 20% of the sheet thickness. A smaller clearance is required for a more ductile material. The percentage penetration is about 30% of the sheet thickness and increases very slowly with the ductility of the material being worked. It may be noted that the compressive transverse stresses σ_{2} and σ_{3} are present at the die and punch corners.

Thus, for a material which shows the value of ԑ_{f} = 1 in the tensile test (with σ_{2} = σ_{3} = 0), the effective value of ԑ_{f}, while the material is being punched, will be somewhat higher. This, in turn, means that the optimum clearance for such a material is likely to be closer to 10% of the sheet thickness.

**Determination of Working Force:**

Once the ruptures start at B and D, a slight progress of the punch causes a complete rupture of all the fibres, thus separating the blank (Fig. 3.31). Of course, in a very ductile material, some more punch travel, after the ruptures start at B and D, is needed to complete the process. So, the percentage penetration here is somewhat higher than the calculated values. The maximum force is obtained by determining the force required to cause the rupture of the area (c_{o} x L), where L is the length of the cut (equal to πD, D being the punch diameter for a cylindrical punch). Thus,

The maximum punching force can be reduced by avoiding the simultaneous failure of the total area. This can be achieved by providing an angle (commonly known as shear) to the punch edge. We now explain the effectiveness of shear assuming the availability of a punch having a straight edge. In this case, the operation is called shearing instead of punching. Figure 3.33 shows that when a shear is provided, at any instant the width of the job undergoing deformation is b which is much smaller than the total punch width L.

It should be remembered that the maximum force occurs when the punch travels up to the penetration depth p. Therefore, the average force for a width of cut b is given by the half of the maximum force for a width b, which itself is the maximum punch force with shear. The amount of shear is commonly expressed as the difference in the height of the two extreme ends of the punch. For a straight punch, we finally get –