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Page 1: Sheet Metal Forming Process

Sheet-Metal Forming Processes

Haipan Salam

Page 2: Sheet Metal Forming Process

Sheet-Metal Forming Processes

• TABLE 7.1 General characteristics of sheet-metal forming proceses.

Process CharacteristicsRoll Forming Long parts with constant complex cross-sections; good surface finish; high

production rates; high tooling costs.Stretch forming Large parts with shallow contours; suitable for low-quantity production; high

labor costs; tooling and equipment costs depend on part size.Drawing Shallow or deep parts with relatively simple shapes; high production rates;

high tooling and equipment costs.Stamping Includes a variety of operations, such as punching, blanking, embossing,

bending, flanging, and coining; simple or complex shapes formed at highproduction rates; tooling and equipment costs can be high, but labor cost islow.

Rubber forming Drawing and embossing of simple or complex shapes; sheet surfaceprotected by rubber membranes; flexibility of operation; low tooling costs.

Spinning Small or large axisymmetric parts; good surface finish; low tooling costs, butlabor costs can be high unless operations are automated.

Superplasticforming

Complex shapes, fine detail and close tolerances; forming times are long,hence production rates are low; parts not suitable for high-temperature use.

Peen forming Shallow contours on large sheets; flexibility of operation; equipment costscan be high; process is also used for straightening parts.

Explosive forming Very large sheets with relatively complex shapes, although usuallyaxisymmetric; low tooling costs, but high labor costs; suitable for low-quantity production; long cycle times.

Magnetic-pulseforming

Shallow forming, bulging, and embossing operations on relatively low-strength sheets; most suitable for tubular shapes; high production rates;requires special tooling.

Page 3: Sheet Metal Forming Process

Localized Necking in Sheet Metal• FIGURE 7.1 (a) Localized

necking in a sheet specimen under tension. (b) Determination of the angle of neck from the Mohr’s circle for strain. (c) Schematic illustration for diffuse and localized necking. (d) Localized necking in an aluminum strip stretched in tension. Note the double neck.

Page 4: Sheet Metal Forming Process

Yield Point Elongation

• FIGURE 7.2 (a) Yield point elongation and Lueder’s bands in tension testing. (b) Lueder’s bands in annealed low-carbon steel sheet. (c) Stretcher strains at the bottom of a steel can for household products. Source: (b) Reprinted with permission from Caterpillar, Inc.

Page 5: Sheet Metal Forming Process

Stress-Corrosion Cracking

• FIGURE 7.3 Stress-corrosion cracking in a deep-drawn brass part for a light-fixture. The cracks developed over a period of time. Brass and austenitic (300 series) stainless steels are among metals that are susceptible to stress-corrosion cracking.

Page 6: Sheet Metal Forming Process

Shearing

• FIGURE 7.4 Schematic illustration of the shearing process with a punch and die. This process with a punch and die. This process is a common method of producing various openings in sheet metals.

Page 7: Sheet Metal Forming Process

Characteristics of Hole and Slug

• FIGURE 7.5 Characteristic features of (a) a punched hole and (b) the punched slug. Note that the slug has been sealed down as compared with the hole.

Page 8: Sheet Metal Forming Process

Shearing

• FIGURE 7.6 (a) Effect of clearance c between the punch and die on the deformation zone in shearing. As clearance increases, the material tends to be pulled into the die, rather than being sheared. In practice, clearances usually range between 2% and 10% of the thickness of the sheet. (b) Microhardness (HV) contours for a 6.4-mm-thick (0.25-in.-thick) AISI 1020 hot-rolled steel in the sheared region. Source: After H. P. Weaver and K. J. Weinmann.

FIGURE 7.7 Typical punch-penetration curve in shearing. The area under the curve is the work done in shearing. The shape of the curve depends on process parameters and material properties.

Page 9: Sheet Metal Forming Process

Punching, Blanking and Shearing Operations

• FIGURE 7.8 (a) Punching (piercing) and blanking. (b) Examples of various shearing operations on sheet metal.

Page 10: Sheet Metal Forming Process

Fine Blanking

• FIGURE 7.9 (a) Comparison of sheared edges by conventional (left) and fine-blanking (right) techniques. (b) Schematic illustration of the setup for fine blanking. Source: Feintool U.S. Operations.

Page 11: Sheet Metal Forming Process

Sitting and Shaving Operations

• FIGURE 7.10 Sitting with rotary knives. This process is similar to opening cans.

FIGURE 7.11 Schematic illustrations of shaving on a sheared edge. (a) Shaving a sheared edge. (b) Shearing and shaving, combined in one stroke.

Page 12: Sheet Metal Forming Process

Shear Angles For Punches and Dies

• FIGURE 7.12 Examples of the use of shear angles on punches and dies.

Page 13: Sheet Metal Forming Process

Progressive Dies

• FIGURE 7.13 (a) Schematic illustration of the making of a washer in a progressive die. (b) Forming of the top piece of an aerosol spray can in a progressive die. Note that the part is attached to the strip until the last operation is completed.

Page 14: Sheet Metal Forming Process

Tailor-Welded Blanks

• FIGURE 7.14 (a) Production of an outer side panel of a car body by laser welding and stamping. (b) Examples of laser welded and stamped automotive body components. Source: After M. Geiger and T. Nakagawa.

Page 15: Sheet Metal Forming Process

Bending

• FIGURE 7.15 (a) Bending terminology. The bend radius is measured to the inner surface of the bend. Note that the length of the bend is the width of the sheet. Also note that the bend angle and the bend radius (sharpness of the bend) are two different variables. (b) Relationship between the ratio of bend radius to sheet thickness and tensile reduction of area for various materials. Note that sheet metal with a reduction of area of about 50% can be bent and flattened over itself without crackling. Source: After J. Datsko and C. T. Yang.

Page 16: Sheet Metal Forming Process

Minimum Bend Radii

• TABLE 7.2 Minimum bend radii for various materials at room temperature.

MATERIAL MATERIAL CONDITION SOFT HARD

Aluminum alloys Beryllium copper Brass, low-leaded Magnesium Steels austenitic stainless low-carbon, low-alloy, and HSLA Titanium Titanium alloys

0 0 0

5T

0.5T 0.5T 0.7T 2.6T

6T 4T 2T

13T

6T 4T 3T 4T

Page 17: Sheet Metal Forming Process

Length of Bend And Edge

Condition/Ratio of Bend Radius

• FIGURE 7.16 The effect of length of bend and edge condition on the ratio of bend radius to thickness of 7075-T aluminum. Source: After G. Sachs and G. Espey.

Page 18: Sheet Metal Forming Process

The Effect of Elongated Inclusions• FIGURE 7.17 (a) and (b) The

effect of elongated inclusions (stringers) on cracking as a function of the direction of bending with respect to the original rolling direction of the sheet. This example shows the importance of the direction of cutting from large sheets in workpieces that are subsequently bent to make a product. (c) Cracks on the outer radius of an aluminum strip bent to an angle of 90˚.

Page 19: Sheet Metal Forming Process

Springback in Bending• FIGURE 7.18 Terminology for springback

in bending. Springback is caused by the elastic recovery of the material upon unloading. In this example, the material tends to recover toward its originally flat shape. However, there are situations where the material bends farther upon unloading (negative springback), as shown in Fig. 7.20.

FIGURE 7.19 Springback factor K, for various materials: (a) 2024-0 and 7075-0 aluminum; (b) austenitic stainless steels; (c) 2024-T aluminum; (d) 1/4- hard austenitic stainless steels; (e) 1/2-hard to full-hard austenitic stainless steels. Source: After G. Sachs.

Page 20: Sheet Metal Forming Process

Negative Springback

• FIGURE 7.20 Schematic illustration of the stages in bending round wire in a V-die. This type of bending can lead to negative springback, which does not occur in air bending (shown in Fig. 7.26a). Source: After K. S. Turke and S. Kalpakjian.

Page 21: Sheet Metal Forming Process

Methods of Reducing or Eliminating Springback

• FIGURE 7.21 Methods of reducing or eliminating springback in bending operations. Source: V. Cupka, T. Nakagawa, and H. Tyamoto.

Page 22: Sheet Metal Forming Process

Common Die-Bending Operations

• FIGURE 7.22 Common die-bending operations, showing the die-opening dimension W used in calculating bending forces. [See Eq,(7.11).]

Page 23: Sheet Metal Forming Process

Bending Operations In a Press Brake

• FIGURE 7.23 Schematic illustration of various bending operations in a press brake.

Page 24: Sheet Metal Forming Process

Various Bending Operations

• FIGURE 7.24 Examples of various bending operations.

Page 25: Sheet Metal Forming Process

Bead Forming

• FIGURE 7.25 (a) Bead forming with a single die. (b) Bead forming with two dies in a press brake.

Page 26: Sheet Metal Forming Process

Flanging Operations• FIGURE 7.26 Various

flanging operations. (a) Flanges on flat sheet. (b) Dimpling. (c) Piercing sheet metal to form a flange. in this operation, a hole does not have to be prepunched before the punch descends. Note, however, the rough edges along the circumference of the flange. (d) Flanging of a tube. Note the thinning of the edges of the flange.

Page 27: Sheet Metal Forming Process

Roll-Forming Process

• FIGURE 7.27 The roll-forming process.

FIGURE 7.28 Stages in roll forming of a sheet-metal door frame. In Stage 6, the rolls may be shaped as in A or B. Source: G. Oehler.

Page 28: Sheet Metal Forming Process

Bending of Tubes

• FIGURE 7.29 Methods of bending tubes. Using internal mandrels, or filling tubes with particulate materials such as sand, is often necessary to prevent collapsing of the tubes during bending. Solid rods and structural shapes are also bent by these techniques.

Page 29: Sheet Metal Forming Process

Tube Forming

• FIGURE 7.30 A method of forming a tube with sharp angles, using axial compressive forces. Compressive stresses are beneficial in forming operations because they delay fracture. Note that the tube is supported internally with rubber or fluid to avoid collapsing during forming. Source: After J. L. Remmerswaal and A. Verkaik.

Page 30: Sheet Metal Forming Process

Stretch-Forming Process

• FIGURE 7.31 Schematic illustration of a stretch-forming process. Aluminum skins for aircraft can be made by this process. Source: Cyril Bath Co.

Page 31: Sheet Metal Forming Process

Bulging Of A Tubular Part

• FIGURE 7.32 (a) Bulging of a tubular part with a flexible plug. Water pitchers can be made by this method. (b) Production of fittings for plumbing by expanding tubular blanks with internal pressure. The bottom of the piece is then punched out to produce a “T.” Source: J. A. Schey, Introduction to Manufacturing Processes, 2d. ed., New York: McGraw-Hill Publishing Company, 1987. Reproduced by permission of the McGraw-Hill Companies. (c) Manufacturing of Bellows.

Page 32: Sheet Metal Forming Process

Forming with a Flexible Pad

• FIGURE 7.33 Examples of bending and embossing sheet metal with a metal punch and a flexible pad serving as the female die. Source: Polyurethane Products Corporation.

Page 33: Sheet Metal Forming Process

Hydroform Process

• FIGURE 7.34 The hydroform, or fluid-forming, process. Note that, unlike in the ordinary deep-drawing process, the dome pressure forces the cup walls against the punch. The cup travels with the punch, and thus deep drawability is improved.

Page 34: Sheet Metal Forming Process

Tube-Hydroforming Process

• FIGURE 7.35 (a) Schematic illustration of the tube-hydroforming process. (b) Example of tube-hydroformed parts. Automotive exhaust and structural components, bicycle frames, and hydraulic and pneumatic fittings are produced through tube hydroforming. Source: Schuler GmBH.

Page 35: Sheet Metal Forming Process

Spinning Processes

• FIGURE 7.36 Schematic illustration of spinning processes: (a) conventional spinning and (b) shear spinning. Note that in shear spinning, the diameter of the spun part, unlike in conventional spinning, is the same as that of the blank. The quantity f is the feed (in mm/rev or in./rev).

Page 36: Sheet Metal Forming Process

Shapes in Spinning Processes

• FIGURE 7.37 Typical shapes produced by the conventional-spinning process. Circular marks on the external surfaces of components usually indicate that the parts have been made by spinning. Examples include aluminum kitchen utensils and light reflectors.

Page 37: Sheet Metal Forming Process

Spinnability• FIGURE 7.38 Schematic illustration

of a shear-spinnability test. As the roller advances, the part thickness is reduced. The reduction in thickness at fracture is called the maximum spinning reduction per pass. Source: After R. L. Kegg.

FIGURE 7.39 Experimental data showing the relationship between maximum spinning reduction per pass and the tensile reduction of area of the original material. Note that once a material has about 50% reduction of area in a tension test, any further increase in the ductility of the original material does not improve the material’s spinnability. Source: S. Kalpakjian.

Page 38: Sheet Metal Forming Process

Internal And External Tube Spinning

• FIGURE 7.40 Examples of external and internal tube spinning and the variables involved.

Page 39: Sheet Metal Forming Process

Tube And Shear Spinning of Compressor Shaft

• FIGURE 7.41 Stages in tube and shear spinning of a compressor shaft for the jet engine of a supersonic Concorde aircraft. Economic analysis indicated that the best method of manufacturing this part was to spin a preformed (forged and machined) tubular blank.

Page 40: Sheet Metal Forming Process

Explosive Forming Process

• FIGURE 7.42 Schematic illustration of the explosive-forming process. Although explosives are generally used for destructive purposes, their energy can be controlled and employed in forming large parts that would otherwise be difficult or expensive to produce by other methods.

FIGURE 7.43 Influence of the standoff distance and type of energy-transmitting medium on the peak pressure obtained using 1.8 kg (4 lb) of TNT. To be effective, the pressure-transmitting medium should have high density and low compressibility. In practice, water is a commonly used medium.

Page 41: Sheet Metal Forming Process

Explosive Tube Bulging and Electrohydraulic Forming

• FIGURE 7.44 Schematic illustration of the confined method of explosive bulging of tubes. Thin-walled tubes of nonferrous metals can be formed to close tolerances by this process.

FIGURE 7.45 Schematic illustration of the electrohydraulic-forming process.

Page 42: Sheet Metal Forming Process

Magnetic-Pulse-Forming Process

• FIGURE 7.46 (a) Schematic illustration of the magnetic-pulse-forming process. The part is formed without physical contact without physical contact with any object

Page 43: Sheet Metal Forming Process

Diffusion Bonding and Superplastic Forming

• FIGURE 7.47 Two types of structures made by diffusion bonding and superplastic forming of sheet metal. Such structures have a high stiffness-to-weight ratio. Source: Rock-well International Corp.

Page 44: Sheet Metal Forming Process

Peen-Forming

• FIGURE 7.48 Peen-forming machine to form a large sheet-metal part, such as an aircraft-skin panel. The sheet is stationary, and the machine traverses it. Source: Metal Improvement Company.

Page 45: Sheet Metal Forming Process

Methods of Making Honeycomb Materials

• FIGURE 7.49 Methods of making honeycomb materials: (a) expansion process and (b) corrugation process. Source: Materials Engineering. Reprinted with permission. (c) Making a honeycomb sandwich.

Page 46: Sheet Metal Forming Process

Introduction Basic Principles of Drawing

Drawing is a sheet metal forming operation used to make cup-shaped, box-shaped, or other complex-curved, hollow-shaped parts. It is performed by placing a piece of sheet metal over a die cavity and then pushing the sheet into the opening with a punch. The blank is held down flat against the die by a blankholder.

46

Page 47: Sheet Metal Forming Process

A blank of diameter Db is drawn into the die by means of a punch of diameter Dp. The punch and die have corner radii Rp and Rd, respectively. The sides of the die and punch are separated by a clearance, c, which is about 10% greater than the sheet thickness. The punch applies a downward force, F, to deform the metal while the downward holding force, Fh, is applied by the blankholder.

47

Mechanics of Drawing

Page 48: Sheet Metal Forming Process

Mechanics of DrawingAs the punch proceeds towards its final position, the workpiece experiences a complex sequence of stresses and strains as it is formed into its final shape.

In step 1, the blankholder force, Fh, is applied and the punch begins to move towards the sheet material.

In step 2, the sheet material is subjected to a bending operation. The sheet is bent over the corner of the punch and the corner of the die.

In step 2, as the punch continues moving down, a straightening action occurs in the metal that was previously bent over the die radius. 48

Page 49: Sheet Metal Forming Process

Mechanics of DrawingIn step 3, as the punch continues moving down, a straightening action occurs in the metal that was previously bent over the die radius. Metal from the outside edge of the blank is drawn into the die opening to form the cylinder wall.

In step 4, friction between the sheet material and surfaces of the blankholder and die must be overcome in order for the material to be drawn. Compression is also occurring at the outer edge of the blank. As the metal is being drawn in toward the center, the outer perimeter becomes smaller. The volume of metal remains constant, however, and thus the metal is squeezed and becomes thicker in the flange area. 49

Page 50: Sheet Metal Forming Process

Mechanics of DrawingThe downward motion of the punch results in a continuation of the metal flow caused by drawing and compression. Some thinning at the cylinder walls occurs as well. Step 5 shows the completed drawing process.

50

Page 51: Sheet Metal Forming Process

Mechanics of DrawingThe next slide illustrates the deep drawing process. However, in this situation the punch (gray in color) is stationary and the blank being deformed is not shown.

The animation clearly shows how the top die (blue) lowers towards the binder plate (red). The sheet rests on the plate and once the top die makes contact with the sheet, a cup is formed around the stationary punch. The cushion pins (green rods) transmit the blankholder force acting on the binder plate to the hydraulic piston (cushion) which is located below the press table.

51

Page 52: Sheet Metal Forming Process

Mechanics of Drawing

Click figure for animation

52

Binder plate

Upper Die

Punch

Cushion Pins

Page 53: Sheet Metal Forming Process

Engineering Analysis of Drawing

The drawing ratio, DR, gives an indication of the severity of the drawing operation: the higher the ratio, the greater the severity. The drawing ratio is defined as:

Where, Db = blank diameter and Dp = punch diameter. This value is dependant upon punch and die corner radii, friction conditions, draw depth, and material properties of the sheet metal.

53

p

b

D

DDR

Page 54: Sheet Metal Forming Process

Engineering Analysis of DrawingThe drawing force required to perform a drawing operation can be roughly estimated by the following formula:

WhereF = Drawing forcet = Original blank thicknessTS = Tensile strengthDb = Blank diameter

Dp = Punch diameter54

7.0

p

bp D

DTStDF

Page 55: Sheet Metal Forming Process

Engineering Analysis of DrawingThe blankholder force required for a drawing operation to prevent defects is approximated by the following formula:

WhereFh = Blankholder force

Y = Yield strengthDb = Blank diameter

Dp = Punch diameter

Rd = Die corner radius55

22 22.2015.0 dpbh RtDDYF

Page 56: Sheet Metal Forming Process

Defects in Drawing

A number of defects in drawing can occur, which include:

(a) Wrinkling in the flange occurs due to compressive buckling because of a small blank holder force.(b) Wrinkling in the wall takes place when a wrinkled flange is drawn into the cup.(c) Tearing occurs because of high tensile stresses that cause thinning and failure of the metal in the cup wall. Tearing can also occur in a drawing process if the die has a sharp corner radius.(d) Earring occurs when the material is anisotropic, i.e. has varying properties in different directions.(e) Surface scratches can be seen on the drawn part if the punch and die are not smooth or if the lubrication of the process is poor.

56

Page 57: Sheet Metal Forming Process

Objectives

This lab has the following objectives:• Become familiarized with the basic processes

used in sheet metal forming.• Analyze a cup drawing operation and attempt

to select the best process parameters.

57

Page 58: Sheet Metal Forming Process

Sheet Metal Forming – Cup Drawing

• Test Materials and Equipment– Robinson (Open Back Inclinable- OBI) press

• Model A3• 25-ton capacity

• Safety Equipment and Instructions– Wear safety glasses.– Conduct the test as directed by the instructor.– Do not use hands to put or remove specimens on

the die – use the supplied tongs.– Turn off the OBI press whenever you need to adjust

its setting.58

Page 59: Sheet Metal Forming Process

Sheet Metal Forming – Cup Drawing

Procedure:• Obtain specimens to be

tested and record the material data onto your data sheet.

• Choose one sample and place it in the tooling using the tongs.

• For the first specimen, set the air pressure for the blankholder cylinders to approximately 30 psi.

• Step on the foot pedal to cycle the press one time.

59

Page 60: Sheet Metal Forming Process

Sheet Metal Forming – Cup Drawing

Procedure (continued):• If the part does not fall out of the bottom on its own, remove it

using the tongs or power down the press and blankholder before attempting to remove the part. Be sure the flywheel has completely stopped before attempting to retrieve the part!

• Inspect the formed part and record any observed defects. If the part is not ideal, decide what process parameters you might adjust to improve the part quality. You may adjust the blankholder force or use a lubricant.

• Select another specimen of the same material and try your new process parameters. Again, record any defects and speculate appropriate adjustments to the process parameters.

• Adjust the parameters again and form your third specimen. Inspect the material and record any observed defects.

• Repeat steps 4-9 for the remaining materials.

60

Page 61: Sheet Metal Forming Process

Sheet Metal Forming – Cup Drawing Video

The cup drawing video on the next slide shows the following:

• Inserting and centering the sheet material into the die

• Powering up the machine• Adjusting and initializing the blank holder

force/pressure• Operating the press to create the deep-drawn

cup

61

Page 62: Sheet Metal Forming Process

Deep-drawing Process

• FIGURE 7.50 (a) Schematic illustration of the deep-drawing process. This procedure is the first step in the basic process by which aluminum beverage cans are produced today. The stripper ring facilitates the removal of the formed cup from the punch. (b) Variables in deep drawing of a cylindrical cup. Only the punch force in this illustration is a dependent variable; all others are independent variables, including the blankholder force.

Page 63: Sheet Metal Forming Process

Deformation in Flange and Wall in Deep Drawing

• FIGURE 7.51 Deformation of elements in (a) the flange and (b) the cup wall in deep drawing of a cylindrical cup.

Page 64: Sheet Metal Forming Process

Drawing Operations

• FIGURE 7.52 Examples of drawing operations: (a) pure drawing and (b) pure stretching. The bead prevents the sheet metal from flowing freely into the die cavity. (c) Possibility of wrinkling in the unsupported region of a sheet in drawing. Source: After W. F. Hosford and R. M. Caddell.

Page 65: Sheet Metal Forming Process

Draw Bead

• FIGURE 7.53 (a) Schematic illustration of a draw bead. (b) Metal flow during drawing of a box-shaped part, using beads to control the movement of the material. (c) Deformation of circular grids in drawing. (See Section 7.13.) Source: After S. Keeler.

Page 66: Sheet Metal Forming Process

Ironing Process • FIGURE 7.54 Schematic illustration of the ironing process. Note that the cup wall is thinner than its bottom. All beverage cans without seams (known as two-piece cans) are ironed, generally in three steps, after being deep drawn into a cup. (Cans with separate tops and bottoms are known as three-piece cans.)

FIGURE 7.55 Definition of the normal anisotropy ratio, R, in terms of width and thickness strains in a tensile-test specimen cut from a rolled sheet. Note that the specimen can be cut in different directions with respect to the length, or rolling direction, of the sheet.

Normal Anisotropy

Page 67: Sheet Metal Forming Process

Average Normal Anisotropy

• TABLE 7.3 Typical range of the average normal anisotropy ratio, R, for various sheet metals.

Zinc alloysHot-rolled steelCold-rolled rimmed steelCold-rolled aluminum-killed steelAluminum alloysCopper and brassTitanium alloys ()Stainless steelsHigh-strength low-alloy steels

0.4-0.60.8-1.01.0-1.41.4-1.80.6-0.80.6-0.93.0-5.00.9-1.20.9-1.2

Page 68: Sheet Metal Forming Process

Anisotropy

• FIGURE 7.56 Effect of grain size on the average normal anisotropy for various low-carbon steels. Source: After D. J. Blickwede.

FIGURE 7.57 Relationship between the average normal anisotropy, R, and the average modulus of elasticity, E, for steel sheet. Source: After P. R. Mould and T. R. Johnson, Jr.

Page 69: Sheet Metal Forming Process

Effect of Average Normal Anisotropy

• FIGURE 7.58 Effect of average normal anisotropy, R, on limiting drawing ratio (LDR) for a variety of sheet metals. Zinc has a high c/a ratio (see Figure 3.2c), whereas titanium has a low ratio. Source: After M. Arkinson.

FIGURE 7.59 Earing in a drawn steel cup, caused by the planar anisotropy of the sheet metal.

Page 70: Sheet Metal Forming Process

Deep Drawing• FIGURE 7.60 Schematic illustration of the

variation of punch force with stroke in deep drawing. Note that ironing does not begin until after the punch has traveled a certain distance and the cup is formed partially. Arrows indicate the beginning or ironing.

FIGURE 7.61 Effect of die and punch corner radii in deep drawing on fracture of a cylindrical cup. (a) Die corner radius too small. The die corner radius should generally be 5 to 10 times the sheet thickness. (b) Punch corner radius too small. Because friction between the cup and the punch aids in the drawing operation, excessive lubrication of the punch is detrimental to drawability.

Page 71: Sheet Metal Forming Process

Redrawing Operations• FIGURE 7.62

Reducing the diameter of drawn cups by redrawing operations: (a) conventional redrawing and (b) reverse redrawing. Small-diameter deep containers undergo many drawing and redrawing operations.

Page 72: Sheet Metal Forming Process

Tractrix Die Profile

• FIGURE 7.63 Deep drawing without a blankholder, using a tractrix die profile. The tractrix is a special curve, the construction for which can be found in texts on analytical geometry or in handbooks.

Page 73: Sheet Metal Forming Process

Punch-Stretch Test

• FIGURE 7.64 (a) Schematic illustration of the punch-stretch test on sheet specimens with different widths, clamped at the edges. The narrower the specimen, the more uniaxial is the stretching. (b) A large square specimen stretches biaxially under the hemispherical punch. (See also Fig. 7.65.)

Page 74: Sheet Metal Forming Process

Bulge Test Results

• FIGURE 7.65 Bulge tests results on steel sheets of various widths. The first specimen (farthest left) stretched farther before cracking than the last specimen. From left to right, the state of stress changes from uniaxial to biaxial stretching. Source: Courtesy of R. W. Thompson, Inland Steel Research Laboratories.

Page 75: Sheet Metal Forming Process

Forming-Limit Diagram

• FIGURE 7.66 (a) Forming-limit diagram (FLD) for various sheet metals. The major strain is always positive. The region above the curves is the failure zone; hence, the state of strain in forming must be such that it falls below the curve for a particular material; R is the normal anisotropy. (b) Note the definition of positive and negative minor strains. If the area of the deformed circle is larger than the area of the original circle, the sheet is thinner than the original, because the volume remains constant during plastic deformation. Source: After S. S. Hecker and A. K. Ghosh.

Page 76: Sheet Metal Forming Process

Strains In Sheet-Metal Forming

• FIGURE 7.67 An example of the use of grid marks (circular and square) to determine the magnitude and direction of surface strains in sheet-metal forming. Note that the crack (tear) is generally perpendicular to the major (positive) strain. Source: After S. P. Keeler.

Page 77: Sheet Metal Forming Process

Major and Minor Strains In a Vehicle

• FIGURE 7.68 Major and minor strains in various regions of an automobile body.

Page 78: Sheet Metal Forming Process

Efficient Nesting of Blanks

• FIGURE 7.69 Efficient nesting of parts for optimum material utilization in blanking. Source: Society of Manufacturing Engineers.

Page 79: Sheet Metal Forming Process

Tearing and Buckling Control

• FIGURE 7.70 Control of tearing and buckling of a flange in a right-angle bend. Source: Society of Manufacturing Engineers.

Page 80: Sheet Metal Forming Process

Notches Used To Avoid Wrinkling

• FIGURE 7.71 Application of notches to avoid tearing and wrinkling in right-angle bending operations. Source: Society of Manufacturing Engineers.

Page 81: Sheet Metal Forming Process

Stress Concentrations Near Bends

• FIGURE 7.72 Stress concentrations near bends. (a) Use of a crescent or ear for a hole near a bend. (b) Reduction of the severity of a tab in a flange. Source: Society of Manufacturing Engineers.

Page 82: Sheet Metal Forming Process

Scoring For Sharper Inner Radius Bending

• FIGURE 7.73 Application of scoring of embossing to obtain a sharp inner radius in bending. Unless properly designed, these features can lead to fracture. Source: Society of Manufacturing Engineers.

Page 83: Sheet Metal Forming Process

Cost Comparison

• FIGURE 7.74 Cost comparison for manufacturing a round sheet-metal container by conventional spinning and deep drawing. Note that for small quantities, spinning is more economical.

Page 84: Sheet Metal Forming Process

Top of Aluminum Can

• FIGURE 7.75 The top of an aluminum beverage container.

Page 85: Sheet Metal Forming Process

Metal-Forming Process for Food

and Beverage Containers

• FIGURE 7.76 The metal-forming process used to manufacture two-piece beverage cans.

Page 86: Sheet Metal Forming Process

Aluminum Two-Piece Beverage Cans

• FIGURE 7.77 Aluminum two-piece beverage cans. Note the fine surface finish. Source: Courtesy of J. E. Wang, Texas A&M Univerity.