E-02 - 2 Basic principles of metal forming 2.1 Methods of...

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Unformatted text preview: 2 Basic principles of metal forming 2.1 Methods of forming and cutting technology 2.1.1 Summary As described in DIN 8580, manufacturing processes are classified into six main groups: primary shaping, material forming, dividing, joining, modifying material property and coating (Fig. 2.1.1). Primary shaping is the creation of an initial shape from the molten, gaseous or formless solid state. Dividing is the local separation of material. Joining is the assembly of individual workpieces to create subassemblies and also the filling and saturation of porous workpieces. Coating means the application of thin layers on components, for example by galvanization, painting and foil wrapping. The purpose of modifying material property is to alter material characteristics of a workpiece dividing primary shaping forming coating joining modifying material property Fig. 2.1.1 Overview of production processes Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 6 Basic principles of metal forming to achieve certain useful properties. Such processes include heat treatment processes such as hardening or recrystallization annealing. Forming – as the technology forming the central subject matter of this book – is defined by DIN 8580 as manufacturing through the threedimensional or plastic modification of a shape while retaining its mass and material cohesion. In contrast to deformation, forming is the modification of a shape with controlled geometry. Forming processes are categorized as chipless or non-material removal processes. In practice, the field of “forming technology” includes not only the main category of forming but also subtopics, the most important of which are dividing and joining through forming (Fig. 2.1.2). Combinations with other manufacturing processes such as laser machining or casting are also used. 2.1.2 Forming Forming techniques are classified in accordance with DIN 8582 depending on the main direction of applied stress (Fig. 2.1.3): – – – – – forming under compressive conditions, forming under combined tensile and compressive conditions, forming under tensile conditions, forming by bending, forming under shear conditions. forming parting joining forming under tensile conditions forming under shear conditions forming under compressive conditions forming under compressive and tensile conditions Fig. 2.1.2 Production processes used in the field of forming technology Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 joining through forming forming by bending dividing Methods of forming and cutting technology 7 forming forming under compressive conditions DIN 8583 forming under compressive and tensile conditions DIN 8584 forming under tensile conditions DIN 8585 forming by bending DIN 8586 forming under shearing conditions DIN 8587 extending by stretching forming by forcing through an orifice closed die forming open die forming bending with rotary die movement bending with linear die movement stretch forming wrinkle bulging deep drawing displacement expanding stripping spinning flanging Fig. 2.1.3 Classification of production processes used in forming in accordance with DIN 8582 The DIN standard differentiates between 17 distinct forming processes according to the relative movement between die and workpiece, die geometry and workpiece geometry (Fig. 2.1.3). Forming under compressive conditions Cast slabs, rods and billets are further processed to semi-finished products by rolling. In order to keep the required rolling forces to a minimum, forming is performed initially at hot forming temperature. At these temperatures, the material has a malleable, paste-like and easily formable consistency which permits a high degree of deformation without permanent work hardening of the material. Hot forming can be used to produce flat material of the type required for the production of sheet or plate, but also for the production of pipe, wire or profiles. If the thickness of rolled material is below a certain minimum value, and where particularly stringent demands are imposed on dimensional accuracy and surface quality, processing is performed at room temperature by cold rolling. In addition to rolling semi-finished products, such as sheet and plate, gears and threads on discrete parts are also rolled under compressive stress conditions. Open die forming is the term used for compressive forming using tools which move towards each other and which conform either not at all or only partially to the shape of the workpiece. The shape of the workpiece is created by the execution of a free or defined relative movement Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 twisting coining rolling 8 Basic principles of metal forming die workpiece Fig. 2.1.4 Open die forming between the workpiece and tool similar to that used in the hammer forging process (Fig. 2.1.4). Closed die forming is a compressive forming process, where shaped tools (dies) move towards each other, whereby the die contains the workpiece either completely or to a considerable extent to create the final shape (Fig. 2.1.5). Coining is compressive forming using a die which locally penetrates a workpiece. A major application where the coining process is used is in manufacturing of coins and medallions (Fig. 2.1.6). Forming by forcing through an orifice is a forming technique which involves the complete or partial pressing of a material through a forming die orifice to obtain a reduced cross-section or diameter. This technique includes the subcategories free extrusion, extrusion of semi-finished products and extrusion of components (cf. Sect. 6.1). upper die workpiece lower die Fig. 2.1.5 Closed die forming Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 9 embossing punch workpiece Fig. 2.1.6 Coining During free extrusion, a billet is partially reduced without upsetting or bulging of the non-formed portion of the workpiece (Fig. 2.1.7 and cf. Sect. 6.5.4). Free extrusion of hollow bodies or tapering by free extrusion involves partial reduction of the diameter of a hollow body, for example a cup, a can or pipe, whereby an extrusion container may be required depending on the wall thickness. In extrusion of semi-finished products a heated billet is placed in a container and pushed through a die opening to produce solid or hollow extrusions of desired cross-section. Cold extrusion of discrete parts involves forming a workpiece located between sections of a die, for example a billet or sheet blank (cf. Sects. 6.5.1 to 6.5.3 and 6.5.7). In contrast to free extrusion, larger deformations are possible using the extrusion method. punch workpiece press bush Fig. 2.1.7 Free extrusion of shafts Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 10 punch workpiece press bush blank Basic principles of metal forming ejector Fig. 2.1.8 Backward can extrusion Extrusion is used for the manufacture of semi-finished items such as long profiles with constant cross sections. Cold extrusion is used to produce individual components, e. g. gears or shafts. In both methods, forming takes place using either rigid dies or active media. In addition, a difference is drawn depending on the direction of material flow relative to the punch movement – i.e. forwards, backwards or lateral – and the manufacture of solid or hollow shapes (cf. Fig. 6.1.1). Based on the combination of these differentiating features, in accordance with DIN 8583/6 a total of 17 processes exist for extrusion. An example of a manufacturing method for cans or cups made from a solid billet is backward cup extrusion (Fig. 2.1.8). Forming under combination of tensile and compressive conditions Drawing is carried out under tensile and compressive conditions and involves drawing a long workpiece through a reduced die opening. The most significant subcategory of drawing is strip drawing. This involves drawing the workpiece through a closed drawing tool (drawing die, lower die) which is fixed in drawing direction. This allows the manufacture of both solid and hollow shapes. In addition to the manufacture of semi-finished products such as wires and pipes, this method also permits the production of discrete components. This process involves reducing the wall thickness of deep-drawn or extruded hollow cups by ironing, and has the effect of minimizing the material input, particularly for pressure containers, without altering the dimensions of the can bottom (Fig. 2.1.9 and cf. Sect. 6.5.5). Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 11 punch sinking die workpiece Fig. 2.1.9 Can ironing Deep drawing is a method of forming under compressive and tensile conditions whereby a sheet metal blank is transformed into a hollow cup, or a hollow cup is transformed into a similar part of smaller dimensions without any intention of altering the sheet thickness (cf. Sect. 4.2.1). Using the single-draw deep drawing technique it is possible to produce a drawn part from a blank with a single working stroke of the press (Fig. 2.1.10). In case of large deformations, the forming process is performed by means of redrawing, generally using a number of drawing operations. This can be performed in the same direction by means of a telescopic punch (Fig. 2.1.11) or by means of reverse drawing, which involves the second punch acting in opposite direction to the punch motion of the previous deep-drawing operation (Fig. 2.1.12). punch blank holder blank drawn part die Fig. 2.1.10 Single-draw deep drawing with blank holder Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 12 punch for 2nd draw punch for 1st draw as blank holder for redraw initial hollow body 2nd drawn part die Basic principles of metal forming Fig. 2.1.11 Multiple-draw deep drawing with telescopic punch The most significant variation of deep drawing is done with a rigid tool (Fig. 2.1.10). This comprises a punch, a bottom die and a blank holder, which is intended to prevent the formation of wrinkles as the metal is drawn into the die. In special cases, the punch or die can also be from a soft material. There are deep drawing methods which make use of active media and active energy. Deep drawing using active media is the drawing of a blank or hollow body into a rigid die through the action of a medium. Active media include formless solid substances such as sand or steel balls, fluids (oil, water) and gases, whereby the forming work is performed by a press using a method similar to that employed with the rigid tools. The greatest field of application of this technique is hydromechanical drawing, for example for the manufacture of components from stainless steel (Fig. 2.1.13, cf. Sects. 4.2.4 and 4.2.5). blank holder for 1st draw die for 1st draw punch for1 st draw as die for reverse draw blank holder for reverse draw punch for reverse draw Fig. 2.1.12 Reverse drawing Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 13 punch blank holder workpiece seal pressure medium pressure medium container Fig. 2.1.13 Hydromechanical deep drawing Flanging is a method of forming under combined compressive and tensile conditions using a punch and die to raise closed rims (flanges or collars) on pierced holes (Fig. 2.1.14). The holes can be on flat or on curved surfaces. Flanges are often provided with female threads for the purpose of assembly. Spinning is a combined compressive and tensile forming method used to transform a sheet metal blank into a hollow body or to change the periphery of a hollow body. One tool component (spinning mandrel, spinning bush) contains the shape of the workpiece and turns with the workpiece, while the mating tool (roll head) engages only locally (Fig. 2.1.15). In contrast to shear forming, the intention of this process is not to alter the sheet metal thickness. Wrinkle bulging or upset bulging is a method of combined tensile and compressive forming for the local expansion or reduction of a generally tubular shaped part. The pressure forces exerted in the longitudinal direction result in bulging of the workpiece towards outside, inside or in lateral direction (Fig. 2.1.16). punch blank holder workpiece die Fig. 2.1.14 Flanging with blank holder on a flat sheet Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 14 Basic principles of metal forming spinning mandrel circular blank workpiece spinning roller Fig. 2.1.15 Spinning a hollow body Forming under tensile conditions Extending by stretching is a method of tensile forming by means of a tensile force applied along the longitudinal axis of the workpiece. Stretch forming is used to increase the workpiece dimension in the direction of force application, for example to adjust to a prescribed length. Tensile test is also a pure stretching process. Straightening by stretching is the process of extending for straightening rods and pipes, as well as eliminating dents in sheet metal parts. pressure ring workpiece punch container ejector Fig. 2.1.16 Wrinkle bulging to the outside Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 15 mandrel workpiece Fig. 2.1.17 Expanding by stretching Expanding is tensile forming to enlarge the periphery of a hollow body. As in case of deep drawing, rigid (Fig. 2.1.17) as well as soft tools, active media and active energies are also used. Stretch forming is a method of tensile forming used to impart impressions or cavities in a flat or convex sheet metal part, whereby surface enlargement – in contrast to deep drawing – is achieved by reducing the thickness of the metal. The most important application for stretch forming makes use of a rigid die. This type of process includes also stretch drawing and embossing. Stretch drawing is the creation of an impression in a blank using a rigid punch while the workpiece is clamped firmly around the rim (Fig. 2.1.18). Embossing is the process of creating an impression using a punch in a mating tool, whereby the impression or cavity is small in comparison to the overall dimension of the workpiece (Fig. 2.1.19). s1 s0 collet workpiece punch s1< s 0 Fig. 2.1.18 Stretch forming Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 16 Basic principles of metal forming punch workpiece die Fig. 2.1.19 Embossing Forming by bending In bending with a linear die movement the die components move in a straight line (cf. Sect. 4.8.1). The most important process in this subcategory is die bending, in which the shape of the part is impacted by the die geometry and the elastic recovery (Fig. 2.1.20). Die bending can be combined with die coining in a single stroke. Die coining is the restriking of bent workpieces to relieve stresses, for example in order to reduce the magnitude of springback. Bending with rotary die movement includes roll bending, swivel bending and circular bending. During roll bending, the bending moment is applied by means of rolling. Using the roll bending process, it is possible to manufacture cylindrical or tapered workpieces (Fig. 2.1.21). The roll bending process also includes roll straightening to eliminate undesirable deformations in sheet metal, wire, rods or pipes (Fig. 2.1.22 and cf. Sect. 4.8.3) as well as corrugating and roll forming (Fig. 2.1.23 and cf. Sect. 4.8.2). punch workpiece bending die U die V die Fig. 2.1.20 Die bending Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 17 workpiece rollers Fig. 2.1.21 Roll bending Swivel bending is bending using a tool which forms the part around the bending edge (Fig. 2.1.24). Circular bending is a continuous process of bending which progresses in the direction of the shank using strip, profile, rod, wire or tubes (Fig. 2.1.25). Circular bending at an angle greater than 360°, for example is used in the production of springs and is called coiling. Forming under shear conditions Displacement is a method of forming whereby adjacent cross-sections of the workpiece are displaced parallel to each other in the forming zone by a linear die movement (Fig. 2.1.26). Displacement along a closed die edge can be used for example for the manufacture of welding bosses and centering indentations in sheet metal components. straightening rollers workpiece Fig. 2.1.22 Roll straightening Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 18 Basic principles of metal forming Twisting is a method of forming under shearing conditions in which adjacent cross-sectional surfaces of the workpieces are displaced relative to each other by a rotary movement (Fig. 2.1.27). Fig. 2.1.23 Roll forming clamping jaws workpiece cheek Fig. 2.1.24 Swivel bending workpiece support workpiece bending mandrel clamping fixture Fig. 2.1.25 Circular bending Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 19 blank holder punch workpiece Fig. 2.1.26 Displacement ϕ MT workpiece MT Fig. 2.1.27 Twisting 2.1.3 Dividing Dividing is the first subgroup under the heading of parting, but is generally categorized as a “forming technique” since it is often used with other complementary production processes (cf. Fig. 2.1.2). According to the definition of the term, dividing is taken to mean the mechanical separation of workpieces without the creation of chips (non-cutting). According to DIN 8588, the dividing category includes the subcategories shear cutting, wedge-action cutting, tearing and breaking (Fig. 2.1.28). Of these, the shear cutting is the most important in industrial application. Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 20 Basic principles of metal forming parting dividing shear cutting wedge-action cutting tearing breaking Fig. 2.1.28 Parting techniques classified under forming Shear cutting – known in practice as shearing for short – is the separation of workpieces between two cutting edges moving past each other (Fig. 2.1.29 and cf. Sect. 4.5). During single-stroke shearing, the material separation is performed along the shearing line in a single stroke, in much the same way as using a compound cutting tool. Nibbling, in contrast, is a progressive, multiple-stroke cutting process using a cutting punch during which small waste pieces are separated from the workpiece along the cutting line. Fine blanking is a single-stroke shearing method that uses an annular serrated blank holder and a counterpressure pad. Thus the generated blanked surface is free of any incipient burrs or flaws, which is frequently used as a functional surface (Fig. 2.1.30 and cf. Sect. 4.7). punch die open shearing blanking contour Fig. 2.1.29 Shearing Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 21 punch annular serrated blank holder serrated ring die counterpunch Fig. 2.1.30 Fine blanking Wedge-action cutting of workpieces is generally performed using a wedge-shaped cutting edge. The workpiece is divided between the blade and a supporting surface. Bite cutting is a method used to divide a workpiece using two wedge-shaped blades moving towards each other. This cutting method is employed by cutting nippers or bolt cutters (Fig. 2.1.31). The processes tearing and breaking subject the workpiece either to tensile stress or bending or rotary stress beyond its ultimate breaking or tensile strength. tool workpiece Fig. 2.1.31 Bite cutting Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 22 Basic principles of metal forming 2.1.4 Combinations of processes in manufacturing Various combinations of different forming processes or combinations of forming, cutting and joining processes have been found to be successful over many years. Stretch drawing and deep drawing, for example, assume an important role in the sheet metal processing industry (cf. Sect. 4.2.1). During stretch drawing, the blank is prevented from sliding into the die under the blank holder by means of a locking bead and beading rods or by applying a sufficiently high blank holder force (Fig. 2.1.32). As a result, the blank is subjected to tensile stress during penetration of the punch. So the sheet metal thickness is reduced. Deep drawing, in contrast, is a process of forming under combined tensile and compression conditions in which the sheet is formed under tangential compressive stress and radial tensile stress without any intention to alter the thickness of the sheet metal (cf. Fig. 4.2.1). For example when drawing complex body panels for a passenger car, stretch drawing and deep drawing may be conducted simultaneously. The tool comprises a punch, die and blank holder (Fig. 2.1.32). The blank holder is used during stretch drawing to act as a brake on the metal, and during deep drawing to prevent the formation of wrinkles. Modern pressing techniques today permit the desired modification of the blank holder force during the drawing stroke. The blank holder forces can be changed independently at various locations of the blank holder during the drawing stroke. The blank is inserted in the die and clamped by the blank holder. The forming process begins with penetra- drawing with blank holder punch blank holder blank die stretch forming deep drawing F St FBl FBl FBl FSt FBl s0 = s0 s1 + s0 s0 Fig. 2.1.32 Overlapping deep drawing and stretch forming in the sheet metal forming process Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Methods of forming and cutting technology 23 tion of the punch to perform a stretch drawing process in which the wall thickness of the stretched blank is reduced. The bottom of the drawn part is subsequently formed. The deep drawing process begins once the required blank holding force has been reduced to the extent that the blank material is able to flow without generating wrinkles over the rounded sections of the die. At the end of the drawing process, the blank holder force is frequently increased again in order to obtain a reproducible final geometry by respecting the stretching portion of the drawing stroke. In addition to deep drawing, body panels are additionally processed in the stamping plant by forming under bending, compressive and shearing conditions. A characteristic of the bending process is that a camber is forced on the workpiece involving angular changes and swivel motions but without any change in the sheet thickness. The springback of the material resulting from its elastic properties is compensated for by overbending (cf. Sect. 4.8.1). Another possibility for obtaining dimensionally precise workpieces is to combine compressive stresses with integrated restriking of the workpiece in the area of the bottom dead center of the slide movement. Forming is almost always combined with cutting. The blank for a sheet metal part is cut out of coil stock prior to forming. The forming process is followed by trimming, piercing or cut-out of parts (cf. Sect. 4.1.1). If neither the cutting nor the forming process dominates the processing of a sheet metal part, this combination of methods is known as blanking. Where greater piece numbers are produced, for most small and medium-sized punched parts a progressive tool is used, for example in the case of fine-edge blanking (cf. Sect. 4.7.3). However, solid forming processes often also combine a number of different techniques in a single set of dies (cf. Sect. 6.1). The call for greater cost reductions during part manufacture has brought about the integration of additional production techniques in the forming process. Stacking and assembly of punched parts, for example, combines not only the classical blanking and forming processes but also joining for the manufacture of finished stator and rotor assemblies for the electric motor industry (Fig. 2.1.33, cf. Fig. 4.6.22 and 4.6.23). Sheet metal parts can also be joined by means of forming, by the so-called hemming or flanging (Fig. 2.1.34). Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 24 Basic principles of metal forming Dividing, coating and modifying material property technologies will substantially expand the field of application covered by forming technology in the future. This will allow finish processing in only a small number of stations, where possible in a single line, and will reduce costs for handling and logistics throughout the production sequence. Fig. 2.1. 33 Joining by parting Fig. 2.1.34 Joining by forming: hemming Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 2 Basic principles of metal forming 2.2 Basic terms 2.2.1 Flow condition and flow curve Metallic materials may be shaped by applying external forces to them without reducing their structural cohesion. This property is known as the formability of metal. Deformation or flow occurs when the rows of atoms within the individual crystalline grains are able, when stressed beyond a certain limit, to slide against one another and cohesion between the rows of atoms takes place at the following atomic lattice. This sliding occurs along planes and directions determined by the crystalline structure and is only made possible by, for example, dislocations (faults in the arrangement of the atomic lattice). Other flow mechanisms such as twin crystal formation, in which a permanent deformation is caused by a rotation of the lattice from one position to another, play only a minor role in metal forming technology. Flow commences at the moment when the principle stress difference ( max – min) reaches the value of the flow stress kf, or when the shear strain caused by a purely shearing stress is equal to half the flow stress, given by: k f = σ max – σ min By neglecting the principle stress 2, this mathematical expression represents an approximate solution of the shearing stress hypothesis with the greatest principle stress 1 and the smallest principle stress 3: k f = σ1 – σ 3 Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 26 Basic principles of metal forming The value of the flow stress depends on the material, the temperature, the deformation or strain, , and the speed at which deformation or . strain rate is carried out, . Below the recrystallisation temperature, the flow stress generally rises with increasing deformation, while the temperature and deformation rate exert only a minimal influence. Exceptions to this rule are forming techniques such as rolling and forging, in which extremely high deformation rates are used. Above the recrystallisation temperature, the flow stress is generally subject to the temperature and deformation rate, while a previous deformation history has only minimal influence. The flow stress generally drops with increasing temperature and decreasing deformation rate. Accordingly, DIN 8582 differentiates between metal forming processes involving a lasting change in strength properties and those involving no appreciable change in strength properties, previously designated as cold and hot forming. In the temperature range between, deformation involves only a temporary change in the strength properties of the material. In this case, the deformation speed is higher than the recovery or recrystallisation rate. Recrystallisation starts only after completion of the forming process. The rules of metal forming with lasting change in the strength properties apply in this case. The DIN 8582 standard also breaks down the process according to forming without heating (cold forming) and forming after the application of heat (hot forming). These terms simply specify whether heating devices are necessary. Unlike their former meaning, these terms are not physically related to the material concerned. The flow stress of the individual materials is determined by experiments in function of deformation (or strain) and deformation rate (or strain rate) at the various temperature ranges, and described in flow curves. One of the uses of flow curves is to aid the calculation of possible deformation, force, energy and performance. 2.2.2 Deformation and material flow Actual deformation , also called logarithmic or true strain, is given by: h1 ϕ1 = h0 ∫ dh h = ln 1 h h0 Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Basic terms 27 in which 1 is deformation in one principle axis and 2 and 3 in the other two principle axes. This equation will give, for example, the amount of compression in a body with height h (Fig. 2.2.1). is calculated from the compression relative to the starting measurement e or from the relative deformation ε1 = h1 – h 0 ∆h = , h0 h0 in which h0 stands for the height of the body before compression and h1 the final height of the body after compression: ϕ1 = ln h1 = ln(1 + ε1 ) h0 In accordance with the law of volume constancy, according to which the volume is not altered by the deformation process (Fig. 2.2.1), the sum of all deformation values is always equal to zero: ϕ1 + ϕ 2 + ϕ 3 = 0 F V0 = l0 b0 h0 = V1 = l1 b1 h1 h0 h1 b1 l1 b0 l0 Fig. 2.2.1 Dimensional changes in frictionless upsetting of a cube Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 28 Basic principles of metal forming The greatest deformation, which is equal to the sum of the two other deformations, is designated the principle deformation jg: ϕ 1 = − (ϕ 2 + ϕ 3 ) = ϕ g The principle deformation must be a known quantity, as it forms the basis for every calculation, for example of deformation force. It is easy to determine, as it carries a different sign to the other two. In the compression of a cubic body, for example, the increase of width (b1 > b0) and length (l1 > l0) results in a positive sign, while the decrease of height (h1 < h0) produces a negative sign (Fig. 2.2.1). Accordingly, the absolute greatest deformation is along the vertical axis j1. . Similar to the sum of deformations, the sum of deformation rates j must always be equal to zero: ˙˙ ˙ ϕ1 + j 2 + ϕ 3 = 0 The flow law applies approximately: ϕ 1: ϕ 2: ϕ 3 = (σ 1− σ m ) : (σ 2 − σ m ) : (σ 3 − σ m ) , with the mean stress sm given by σm = σ1 + σ 2 + σ 3 3 The material flow along the direction of the stress which lies between the largest stress smax and the smallest stress smin will therefore be small and will be zero in cases of plane strain material flow, where deformation is only in one plane. 2.2.3 Force and work In calculating the forces required for forming operations, a distinction must be made between operations in which forces are applied directly and those in which they are applied indirectly. Direct application of force means that the material is induced to flow under the direct appli- Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Basic terms 29 cation of an exterior force. This requires surfaces to move directly against one another under pressure, for example when upsetting and rolling. Indirect application of force, in contrast, involves the exertion of a force some distance from the actual forming zone, as for example when the material is drawn or forced through a nozzle or a clearance. Additional stresses are generated during this process which induce the material to flow. Examples of this method include wire drawing or deep drawing. In the direct application of force, the force F is given by: F = A ⋅ kw where A is the area under compression and kw is the deformation resistance. The deformation resistance is calculated from the flow stress kf after taking into account the losses arising, usually through friction. The losses are combined in the forming efficiency factor ηF: ηF = kf kw The force applied in indirect forming operations is given by: F = A ⋅ k wm ⋅ ϕ g = A ⋅ k fm ηF ⋅ ϕg = A ⋅ w id ηF where A represents the transverse section area through which the force is transmitted to the forming zone, kwm is the mean deformation resistance and kfm the mean stability factor, both of which are given by the integral mean of the flow stress at the entry and exit of the deformation zone. The arithmetic mean can usually be used in place of the integral value. The referenced deformation work wid is the work necessary to deform a volume element of 1 mm3 by a certain volume of displacement: ϕg wid = ∫ k f ⋅ d ϕ ≅ k fm⋅ ϕ g 0 The specific forming work can be obtained by graphic or numerical integration using available flow curves, and in exactly the same way as the flow stress, specified as a function of the deformation jg. Figure 2.2.2 illustrates the flow curves and related work curves for different materials. Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 30 Basic principles of metal forming 1000 Nmm mm 3 800 700 600 500 400 300 200 100 1000 N mm 2 800 700 600 500 400 300 200 100 St 14 St 37 C 35 (normally annealed) 0,2 0,4 0,6 1,2 0,8 1,0 log. principle deformation ϕg specific deformation work wid 0 0 Fig. 2.2.2 Flow curves and curves showing the specific deformation work for different materials If there is no flow curve available for a particular material, it can be determined by experimentation. A tensile, compressive or hydraulic indentation test would be a conceivable method for this. If the specific deformation work wid and the entire volume V or the displaced volume Vd are known quantities, the total deformation work W is calculated on the following basis: flow stress k f W = V⋅ wid ηF ≅ V ⋅ ϕg ⋅ k fm k = Vd ⋅ fm ηF ηF 2.2.4 Formability The identification of formability should only be based on those cases of material failure caused as a result of displacement or cleavage fractures where no further deformation is possible without failure. If, therefore, a material breaks before reaching maximum force as a result of a cleavage Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 Basic terms 31 fracture, this characteristic may be taken as a point of reference in the determination of formability, for example during a tensile test. However, cases of failure in which the stability criterion between the outer and inner forces is indicative of the achievable deformation, cannot be used as a basis for determining formability. Such cases include for example the uniform strain of a material with marked necking. The formability of different materials differs even though other conditions are equal. Thus it is that some materials are described as malleable and others as brittle. These descriptions are usually based on the characteristics revealed in tensile testing for fractures due to shrinkage or elongation. The formability of a material is not a fixed quantity, however, it depends on the mean hydrostatic pressure pm exerted during the forming operation: pm = p1 + p 2 + p 3 3 Thus, for example, a material can have a low formability for one type of forming operation where the mean hydrostatic pressure is low. However, if a different forming process is employed in which the mean hydrostatic pressure is higher, the same material can be formed without problems. Even marble can be plastically deformed if the mean hydrostatic pressure exerted is sufficiently great. 2.2.5 Units of measurement Since the implementation of the law governing standardised units of measurement, it is only permissible to use the variables prescribed by the statutory international unit system (SI units). Table 2.2.1 provides a comparison of the units applied in the old technical system of measurement and the SI units. The given variables can be transferred to the international metric system using the factor 9.81. For approximate calculations, it is generally sufficient to use factor 10, for example: 1 kp ≈ 10 N Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 32 Basic principles of metal forming Table 2.2.1: Conversion of technical to SI units of measurement Unit system Time: t Length: l Speed: v Revolutions /no. of strokes: Acceleration: a Mass: G Density: Force: F Pressure: p Technical (m kp s) 1s 1m 1 m/s rpm 1 m/s2 9,81 kg = 1 kp s2/m 9,81 kg/m3 = 1 kp s2/m4 9,81 kg m/s2 = 1 kp 1MP = 1000 kp 9,81 N/m2 = 1 kp/m2 0,0981 bar = 1 at 1,333 mbar = 1 Torr 9,81 N/mm2 = 1 kp/mm2 9,81 N m = 1 kp m 9,81 kg m2 = 1 kp m s2 9,81 W = 1 kp m/s 0,7355 kW = 1 PS 9,81 J = 1 kp m 4,19 kJ = 1 kcal 1 dB(A) SI (MKS) 1s 1m 1 m/s rpm 1 m/s2 1 kg 1 t = 1000 kg 1 kg/m3 1 N (Newton) = 1 kg m/s2 1 kN = 1000 N 1 N/m2 = 1 Pa (Pascal) = 1 kg/m s2 105 N/m2 = 1 bar 1 N/mm2 1Nm 1 kN m = 1000 N m 1 kgm2 1 N m/s = 1 W (Watt) 1kW = 1000 W 1 J (Joule) = 1 N m = 1 W s 1kJ = 1000 J 1 kJ 1 dB(A) Tension: Torque: M Mass moment of inertia: J Performance: P Work: W Quantity of heat: Q Sound pressure level: L Bibliography DIN 8580 (Entwurf): Manufacturing Methods, Classification, Beuth Verlag, Berlin. DIN 8582: Manufacturing methods, forming, classification, subdivision, Beuth Verlag, Berlin. DIN 8583: Manufacturing methods, forming under compressive conditions, Part 1 - 6, Beuth Verlag, Berlin. DIN 8584: Manufacturing methods, forming under combination of tensile and compressive conditions, part 1 - 6, Beuth Verlag, Berlin. DIN 8585: Manufacturing methods, forming under tensile conditions, part 1 - 4, Beuth Verlag, Berlin. DIN 8586: Manufacturing methods, forming by bending, Beuth Verlag, Berlin. DIN 8587: Manufacturing methods, forming under shearing conditions, Beuth Verlag, Berlin. DIN 8588: Manufacturing methods, terms, dividing, Beuth Verlag, Berlin. Lange, K: Umformtechnik, Band 1: Grundlagen, Springer-Verlag, Heidelberg (1984). Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998 ...
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This note was uploaded on 11/04/2010 for the course ACC 411 taught by Professor Kim during the Spring '08 term at Aberystwyth University.

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