also clear that such an understanding is a prerequisite for controlling. and optimizing existing processes and the sustainable development. of new technology, Mechanics of Wiredrawing, Deformation in wiredrawing is influenced by a number of factors. wire chemistry approach angle lubrication drawing speed and. reduction are the most significant The primary emphasis in wire. drawing mechanics is on understanding and defining the relation. ships that exist between these process conditions and the resulting. thermo mechanical response of the wire Many of the technological. developments that have taken place in wiredrawing over the past 20. years have been the result of an increased understanding of these. relationships, Constancy of Volume, Although the fact that volume is not lost during deformation may. seem obvious it is in fact a highly useful concept that forms the. basis for analyzing a number of wiredrawing problems One of the. most common applications involves the determination of wire speed. at different stands and the necessary capstan speeds that should be. used Simply stated constancy of volume states that the volumetric. rate of wire entering a die must be the same as that exiting Because. the cross sectional area is reduced during drawing it is necessary that. a wire must increase in speed for the same volumetric rate of materi. al to enter and exit the die Volumetric rate is defined as the cross. sectional area of the wire multiplied by the wire velocity This can be. expressed mathematically as, where Vi and Vf represent the wire velocities feet or meters per. minute and di and df are the wire diameters inches or millimeters. entering and exiting the die respectively For circular wire Equation. 1 can be simplified and reduced to, In multi pass drawing wire speed exiting each die must increase. so that the volumetric rate of metal flow is equal at all dies. Therefore capstans having an angular velocity equal to the exiting. wire speed are used to pull the wire through the die after each reduc. tion If this is not done the wire will break due to unequal wire ten. sion between dies Because the volumetric rate must be the same at. all points wire velocity can be calculated at any intermediate stand. once the incoming wire speed at the first stand is known As an. example consider a 0 100 in 2 5 mm wire paid off from a spool at. 1 200 feet per minute and reduced to 0 090 in 2 286 mm by using. two passes The velocity of the wire as it exits the last die can then be. calculated by using Equation 2a as follows, Wire diameter increases as drawing dies wear in actual produc. tion therefore based on constancy of volume wire speed will. decrease as the dies increase in size If the linear speed of the pulling. capstan is matched to the wire size of a new die capstan speed will. be faster than the wire speed as the wire diameter increases This. increased capstan speed will apply high tensile stress on the wire. often breaking the wire Therefore capstans in multi pass drawing. machines are designed so that the wire slips on the capstan as the dies. wear and the wire speed decreases see Chapter 13 Slip is facilitat. ed by limiting the number of wraps around the pulling capstan and. wetting the wire and capstan surfaces with drawing lubricant. Forces and Energy in Wiredrawing, Although it may seem that the forces and power in wiredrawing. could be analyzed by using simple tension deformation conditions. in wire are in fact far more complex due to compressive and drag. forces generated by the die surface A free body diagram of the forces. acting on a wire is shown in Figure 1 Draw force F represents the. total force that must be applied at the die block to overcome friction. at the die surface and resistance of the deforming material Because. the draw force is being transmitted by unsupported material the. draw force must be limited to prevent any plastic deformation from. occurring outside of the die Thus yield stress of the drawn wire rep. resents an upper limit to the allowable draw stress Accepted draw. ing practice normally limits draw stress to 60 of the yield strength. of the drawn wire Draw stress is found by dividing the draw force by. the cross sectional area of the drawn wire, Fig 1 Free body diagram showing the primary. forces operating in wiredrawing, While it would appear that the work or energy consumed at a. given draw stand is dictated by the material and reduction taken the. actual amount needed is considerably higher in practice This is the. result of inefficiencies that exist during deformation which are pri. marily governed by the approach angle Such inefficiencies do not. make any useful contributions in reducing the cross sectional area. and generally serve only to increase energy requirements and. adversely influence wire quality The total work consumed at a draw. stand can be partitioned into three components see Fig 2 These. are a useful homogeneous work required to reduce the cross sec. tion b work required to overcome frictional resistance and c. redundant inhomogeneous work required to change the flow direc. tion see Fig 3 Homogeneous work is determined by drafting. reduction and is essentially independent of the approach angle. Friction and redundant work on the other hand are closely coupled. to die geometry and have an opposite effect as the approach angle is. changed Under normal drawing conditions typical losses are on the. order of 20 for frictional work and 12 for redundant work 1. Fig 2 Components of work that operate during, wiredrawing. Fig 3 Illustration of a homogeneous b frictional, and c redundant work in wiredrawing. Redundant work and frictional work have adverse effects on wire. properties in addition to increasing the energy needed for drawing. One consequence is that mechanical properties will not be homoge. neous across the wire cross section Because redundant and friction. al deformations are concentrated near the wire surface higher levels. of strain hardening will result in the surface and near surface layers. analogous to temper rolling and will be greater than the strain that. results from cross section reduction This strain gradient can be ver. ified easily by performing a hardness survey on a transverse section. of cold drawn wire Also redundant deformation has an adverse. effect on ductility and this is clearly shown by Caddell and Atkins 2. Their results showed that equal yield strengths were obtained at far. lower strains for drawn stainless steel rod than for rod deformed in. uniaxial tension For example to achieve yield strength of approxi. mately 90 ksi 620 MPa a rod only needed to be drawn to a true. strain of 0 090 whereas the same material stretched in uniaxial ten. sion required a true strain of 0 185, Ductility is inversely related to strain therefore redundant defor. mation also acts to limit the number of passes and maximum reduc. tion that can be taken prior to annealing 3 Even if this does not lead. to problems in drawing the resultant loss in ductility can lead to frac. turing in subsequent forming processes such as bending and cold. Effect of Friction, Layers at the wire surface will not only undergo a change in cross. section but they will also deform in shear because of drag presented. by the die surface see Fig 3b Even for highly polished die surfaces. and hydrodynamic lubrication a certain amount of frictional work. will be present Frictional work dominates at low die angles where. surface drag is increased as a result of higher contact length in the. approach zone for a given reduction Frictional work can be. decreased by using a larger approach angle and to a lesser extent by. improving lubrication or die surface condition Although friction. forces are also related to die load normally little effort is made to con. trol friction by limiting reduction since this would require additional. stands Instead normal practice is to optimize approach angle and. lubrication effectiveness, The effect of friction is most conveniently quantified by using the. Coulomb coefficient of friction usually represented by the Greek. symbol mu The actual value of depends on the surface condi. tion of the die and lubrication used Its exact value can be obtained. experimentally by using the split die technique proposed by. McClellan 4 In practice normally ranges from 0 01 to 0 07 for dry. drawing and 0 08 to 0 15 for wet drawing 5 In addition to surface. condition and lubrication coefficient of friction is inversely related to. drawing speed An experimental investigation of single hole drawing. by Ranger 6 and later by Fowler 7 showed that coefficient of friction. dropped significantly as drawing speed increased, Redundant Deformation. As wire enters the approach zone of a drawing die material lay. ers near the surface will undergo deformation due to the reduction in. area and change direction of flow i e bending to conform to the. direction change going from the approach zone into the bearing zone. of the die represented by using flow lines in Figure 3c Redundant. deformation like frictional deformation will not be evenly distrib. uted over the wire and will be at maximum at the surface with a cor. responding increase in hardness Redundant deformation is promot. ed by larger die angles since material further away from the center. line will undergo a sharper change in direction than the material near. the centerline and will experience higher levels of distortion. Based on split wire and X ray diffraction studies redundant. deformation influences the level of residual stress in drawn wire As. the approach angle is increased the deformation gradient between. the surface and centerline also increases This leads to progressively. higher tensile stresses at the surface and compression stresses at the. core The reverse effect occurs during drawing and center bursts can. develop due to the high levels of tensile stresses generated in the core. of the wire, Optimum Die Angle, Selection of the proper die angle is crucial for the success of any. wiredrawing operation Based on the fact that frictional work increas. es with decreasing die angle and redundant work increases with increas. ing die angle an optimum approach angle should exist one which. minimizes both frictional and redundant work and as a consequence. the drawing force A number of investigators have confirmed that a. balance between frictional and redundant work can be achieved. through proper selection of the die angle This effect is illustrated in. Figure 4 In addition to minimizing force requirements the optimum. die angle will also provide improved surface quality and finish 8. Fig 4 Optimum die angle which minimizes, frictional and redundant work as a die angle. function for various reductions 5, Delta Factor, The geometry of the working part approach zone of a die is a. key factor in wiredrawing This geometry can be defined by the delta. factor which is the ratio of the circular arc spanning the mid. points of the die face to the length of contact between wire and die 5. For conical dies the factor is, where 2 is the included approach angle is the approach semi. angle D1 is the initial wire diameter and D2 is the final wire diam. eter For small approach semi angles sin in radians and by. multiplying the right side of Equation 3a by D1 D2 D1 D2. and substituting reduction in area r 1 D2 D1 2 in place of the ini. tial and final wire diameters can be written as 9, Low values small semi angle or higher reduction in area indi. cate larger friction effects and surface heating due to longer wire contact. in the approach zone Higher values of large semi angle or lower. reduction in area are indicative of increased levels of redundant. deformation and surface hardening due to excessive direction change. during flow through the die Large often results in a greater tenden. cy toward void formation and center bursting Representative values. of for a range of die semi angles and reductions are given in Table 1. Delta values of 1 50 perform well in many commercial drawing oper. ations delta factors in excess of 3 0 should be avoided in general. Table 1 Delta parameter values for various approach semi. angles and reductions in wiredrawing, Percent Reduction in Area. 5 10 15 20 25 30 35 40, Semi Angle, 2 2 72 1 33 0 86 0 63 0 49 0 39 0 33 0 27. 4 5 44 2 65 1 72 1 25 0 97 0 78 0 65 0 55, 6 8 17 3 98 2 58 1 88 1 46 1 18 0 98 0 82. 8 10 89 5 30 3 44 2 51 1 94 1 57 1 30 1 10, 10 13 61 6 63 4 30 3 13 2 43 1 96 1 63 1 37. 12 16 33 7 95 5 16 3 76 2 92 2 35 1 95 1 65, 14 19 06 9 28 6 02 4 38 3 40 2 75 2 28 1 92. 16 21 78 10 60 6 88 5 01 3 89 3 14 2 60 2 20, 18 24 50 11 93 7 74 5 64 4 38 3 53 2 93 2 47. 20 27 22 13 26 8 60 6 26 4 86 3 92 3 25 2 75, Drawing Force Calculation. Numerous equations have been proposed to predict drawing. force though many of these calculations involve the use of empirical. constants and or lengthy calculations Quite often there is a simpler. equation to estimate the force that is needed However it should be. noted that equations based only on homogeneous deformation. should not be used as frictional work and redundant deformation. have a significant effect and will seriously underestimate drawing. force if not included Frictional work and redundant work are nor. In multi pass drawing wire speed exiting each die must increase so that the volumetric rate of metal flow is equal at all dies Therefore capstans having an angular velocity equal to the exiting wire speed are used to pull the wire through the die after each reduc tion If this is not done the wire will break due to unequal wire ten

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