handbook of die design 2nd edition phần 6 docx

As can be expected, not all materials can handle such a rough treatment the reversed bending presents. This operation introduces a massive amount of strain into the formed sec- tion (i.e., mainly the corners). This may not only weaken these areas; it will also cause a greater than ordinary work hardening of the same. Tearing of the metal, wrinkling, and other defects may result. 8-9 FORMING Metal forming is a process totally dependent on the influence of outside tensile forces against the structure of the material. The resulting permanent deformation is called forming. The force-exerting instrument is the punch, which by pulling the sheet-metal material along, makes it enter the die, where it is compelled to take upon itself the impression of the assembly. The decision if the part is to be formed or drawn is usually based on the evaluation of its shape and dimensional requirements. Drawing is utilized for those parts made of thicker materials or for those with vertical (or slightly inclined) walls and sharp corners at the bottom. Since a forming die may often be instrumental in the formation of wrinkles or cause development of excessive tensile strains in the material, which away tear the part in the process, drawing is often resorted to in such cases. 8-9-1 Forming of Singular Recesses Singular recesses in the flat metal sheet are usually formed by stretching or drawing. Stretching is reserved for parts with smooth connection of contours, without excessively sharp edges. Several samples of stretched parts are shown in Fig. 8-47. The maximum amount of stretch for a given material depends on its distribution over the area of stretch. Naturally, the larger such an area is, the greater the maximum amount of stretch that can be obtained. To evaluate the strain with respect to the amount of stretch, Eq. (8-15) may be used: (8-15) where s = stretch All other values are in Fig. 8-48. s LL L s o o = − BENDING AND FORMING OPERATIONS 359 FIGURE 8-47 Shapes of stretched parts. Suchy_CH08.qxd 11/08/05 10:57 AM Page 359 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS The linear distance of the drawn-in portion of the radius R in can be calculated: (8-16) All calculations or measurements should be taken between mold lines, ignoring the radii of the edges. The mold line, as shown in Fig. 8-48, is an extension of the curved or linear portion, connecting with another line sharply, with no radius applied (see detail “P”). Round recesses can be assessed from Table 8-9. Their stretch values are based on the ratio of the depth h to the length of the recess in flat L s . 8-9-2 Stretch Flange Forming Stretch flanges, when viewed from the top, form a concave curvature. These are flanges which on forming must be lengthened or stretched (Fig. 8-49). They may be compared to flanges surrounding a hole in sheet metal. Processes such as extruding, dimpling, and coun- tersinking are all basically stretch flange forming. RDD osin =− 1 2 () 360 CHAPTER EIGHT FIGURE 8-48 Dimensional values of a stretched recess. TABLE 8-9 Stretch Values of Circular Recesses Ratio L s /L o Ratio h/L o Stretch % 1.05 0.157 5 1.10 0.218 10 1.15 0.264 15 1.20 0.302 20 1.25 0.334 25 1.30 0.361 30 1.35 0.386 35 1.40 0.408 40 1.45 0.429 45 1.50 0.447 50 Suchy_CH08.qxd 11/08/05 10:57 AM Page 360 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS The evaluation of the flange type should be pursued by observing the flat layout of a part, which clearly shows where the material for each flange may be taken from. Owing to their stretching, the material thickness of stretch flanges decreases. This places a lateral strain on the material, with a resulting circumferential tension. The strain S e can be calculated from the ratio of the wall thickness ∆t and the amount of wall thickness change t as follows: (8-17) A minus sign attached to Eq. (8-17) depicts the variation in wall thickness, which in stretch flanges diminishes (−) and in shrink flanges increases (+). From this relationship, other values may be assessed with the use of the formula (8-18) where all values are as shown in Fig. 8-50. However, with the bend radius being too small, the value a of flange movement may be approximated. In such a case, the material thickness is to be considered zero and the flange width constant. The formula to be used is then a = b(1− cosa) (8-19) Stretch flanges are limited by the amount of material from which they can draw for their development. Beyond such a limit, the flanges will crack around the edges and tear. Too small a radius of curvature also adds to the problems, and it should be made as generous as possible, with a definite preference for straight forming lines. The limits on the 90° flange are as given by the equation (8-20) e Rb B limit =− − 1 1 cos / α e a Rb B = − ∆t t e =− 2 BENDING AND FORMING OPERATIONS 361 FIGURE 8-49 Stretch flange. Suchy_CH08.qxd 11/08/05 10:57 AM Page 361 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS 8-9-3 Shrink Flange Forming Shrink flanges are those which are reduced in length on forming, or shrunk. The shrunk flange, when viewed from the top, usually forms a convex line. The wall thickness of these flanges increases, which is caused by a circumferential compression during the forming process. The lateral strain, acting within the flange material, can be calculated by using Eq. (8-17). Similarly as with the stretch flanges, other pertinent values may be assessed: (8-21) where the values are as shown in Figs. 8-50 and 8-51. e a Rb B =− + 362 CHAPTER EIGHT FIGURE 8-50 Stretch flange geometry. FIGURE 8-51 Shrink flange and its geometry. Suchy_CH08.qxd 11/08/05 10:57 AM Page 362 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS And again, the value a of flange movement may be approximated, using Eq. (8-19). Shrink flanges are actually quite difficult to form from a flat blank. The material is often reluctant to succumb to such compressive stresses and has a tendency to wrinkle or buckle. With wider flanges, the tendency to wrinkling is increased. Buckling is found controllable where the ratio of the flange width to the material thick- ness remains within a range of 3 to 4. 8-10 BENDING AND FORMING PRESSURE CALCULATIONS Several formulas are utilized for calculation of bending and forming pressures. They may vary with the type of bending utilized. 1. Bending in a V-die, with rectangular cross-section: (8-22) where k V = die opening factor, 0.75 to 2.5 (larger values are for smaller R/t ratios and vice versa). A 1.33 value is used for a die opening of 8 times metal thickness. W = width of the bent-up portion L = distance between material supports (see Fig. 8-52) S = ultimate tensile strength (Table 8-10) 2. Bending in a U-die, equipped with a spring-loaded pressure pad: (8-23) where k U = die opening factor, 0.4 to 10 R E = radius, die edge (see Fig. 8-53) R D = radius, bottom of U channel P pad = pressure of spring-loaded support P k SWt RRt P U U ED = ++ + 2 pad P k SWt L V V = 2 BENDING AND FORMING OPERATIONS 363 TABLE 8-10 Ultimate Tensile Strength of Materials Tons/In. 2 MPa [N/mm 2 ] Steel, low carbon, 1025 30–51.5 410–710 Steel, medium carbon, 1045 40–91 550–1,250 Steel, high carbon, 1095 45–106.5 620–1,470 Steel, stainless, 303 42.5–62.5 585–860 Aluminum alloy, cold worked 6.0–31.5 80–435 Aluminum alloy, heat treated 11.0–41.5 150–570 Copper 16–28.5 220–390 Phosphor bronze 20–64 275–880 Zinc 9.75–15.5 135–215 Suchy_CH08.qxd 11/08/05 10:57 AM Page 363 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS FIGURE 8-53 U-die bending geometry. FIGURE 8-52 V-die bending geometry. 3. Bending with bottoming (coining): P bottom = (2 to 4)P = Ap (8-24) where P = bending pressure of the particular process A = area of part, subjected to coining p = bending pressure (see Table 8-11) 364 CHAPTER EIGHT Suchy_CH08.qxd 11/08/05 10:57 AM Page 364 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS FIGURE 8-54 Wipe bending geometry. TABLE 8-11 Approximate Bending Pressures Tons/in. 2 kPa Material thickness, in. Material thickness, mm Under 0.125 0.125–0.375 Under 3 3–10 Steel, annealed 29–36 36–43 0.4–0.5 0.5–0.6 Steel, hard 36–43 43–58 0.5–0.6 0.6–0.8 Aluminum 7–15 15–22 0.1–0.2 0.2–0.3 Brass 22–36 36–43 0.3–0.4 0.4–0.5 Source: Svatopluk ˇ Cernoch, Strojn ˇ e technická p ˇ ríru ˇ cka, 1977. Reprinted with permission from SNTL Publishers, Prague, CZ. 4. Wipe bending dies’ pressure calculation: (8-25) where L = distance between supports of the material (see Fig. 8-54) W = width of the bent-up portion S = ultimate tensile strength (Table 8-10) Subsequently, each of the three forces acting upon the appropriate point in the assembly is one-third of the total force. These forces are: (1) force of blank holder; (2) bending force of the punch; (3) final bottoming force of the punch (see Fig. 8-54). (8-26) P SWt L 1 2 0 333 or 2 or 3 = . P SWt L total-wipe = 2 BENDING AND FORMING OPERATIONS 365 Suchy_CH08.qxd 11/08/05 10:57 AM Page 365 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS 5. Calculation of the pressure involved in rotary bending is as follows: (8-27) where S T = Tensile strength of the formed material L = PR + PT + B all other values per Fig. 8-55. PS PL PT L total = 225 2 . ()() T 366 CHAPTER EIGHT FIGURE 8-55 Rotary bending geometry. (Reprinted with permission from Ready Technology, Inc., Dayton, OH. Patent Number 5,404,742.) Suchy_CH08.qxd 11/08/05 10:57 AM Page 366 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. BENDING AND FORMING OPERATIONS DRAWN PARTS 9-1 DRAWING OF SHEET METAL Drawing is a technological process during which a flat piece of sheet-metal material (i.e., blank) is transformed into a hollow, three-dimensional object. Such transformation can be produced either in a single step, or in a sequence of operations, each of them changing the shape but partially. During the process of drawing, the material is forced to follow the movement of a punch, which pulls it along, on its way through the die. There the shape of the part and sometimes even the thickness of it are altered. At first, the drawn material has to overcome its own elastic limit, succumbing to plastic deformation right afterwards. Various forces are acting upon the drawn cup (as shown in Fig. 9-1), be it the blankholder’s pressure, or the friction between the drawn shell and other components of tooling. The blank is sometimes restricted from unreservedly following the punch, by having its edges confined between the surface of the die and those of a blankholder. The main area of concern on the drawn part is located between the heel of the verti- cal wall and the bottom of the shell, where, due to the change in flow direction, the ver- tical tension acting upon the material is transformed into a triple-axial tension. In this section, the material is being bent, while moving around the edge of the drawing punch, only to be straightened right afterwards, so that another successive segment can be bent- and-straightened. This is where the wall thickness can often become diminished on account of the length of the shell, which is being increased by the drawing process. Because of such drastic changes within material, this is where much cracking and tear- ing can be observed. In drawing, the metal taken from the flange of the shell is used up to produce increase in height of the part. A rather crude demonstration of this shift is depicted in Fig. 9-2. Here the segments of material are being displaced, flowing away from the flange toward the body of the shell, pulled by the action of the drawing punch and drawing die. The basic shape in drawing operation, the “blank,” is but a flat piece of sheet-metal material of uniform thickness, most often round. From this shape, a shell can be drawn. Even though during the process of drawing the blank’s shape changes, often along with its thickness, its volumnar value remains the same, should it be drawn into a short, thick- walled cylinder, or a tall, thin-walled shell (Fig. 9-3). With regard to the thinning of the drawn shells’ wall, the final products can be divided into two basic categories: • Those having the wall of the same thickness as the blank (Fig. 9-4a) • Those having the wall thickness diminished (Fig. 9-4b) CHAPTER 9 367 Suchy_CH09.qxd 11/08/05 11:08 AM Page 367 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Source: HANDBOOK OF DIE DESIGN 368 CHAPTER NINE FIGURE 9-1 Forces involved in cup-drawing process. FIGURE 9-2 Displacement of metal in drawing. Suchy_CH09.qxd 11/08/05 11:08 AM Page 368 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. DRAWN PARTS [...]... to the Terms of Use as given at the website Suchy_CH09.qxd 11/08/05 11:08 AM Page 380 DRAWN PARTS 380 CHAPTER NINE TABLE 9-2 Factors B1 and B2 Stock thickness in mm First-operation die, B1 value Any redrawing die, B2 value 0.015–0.018 0.021 0.022–0.024 0.027 0.031 0. 062 –0.109 0.125–0.250 0.38–0. 46 0.53 0. 56 0 .61 0 .69 0.79 1.57–2.77 3.18 6. 35 61 58 56 54 50 47 51 74 73 72 71 70–71 70 65 The reduction... 0.125–0.250 0.38–0. 46 0.53 0. 56 0 .61 0 .69 0.79 1.57–2.77 3.18 6. 35 61 58 56 54 50 47 51 68 65 63 60 56 53 51 81 80 80 79 77 75 65 77.5 76. 5 75.5 74.5 74 73.5 65 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Suchy_CH09.qxd 11/08/05 11:08... reduction of diameter 28 .6 37.5 44.4 50 55 D/d + 1 2 60 50.0 44.4 1 .60 1.50 37.5 1.40 28 .6 1.25 20.0 1.12 Percent reduction of area Strain factor of cupping, Ec DRAWN PARTS 10.7 1.00 1.0 1.12 1.25 1.40 1 .60 1.80 2.00 2.24 2.50 Ratio of blank diameter to cup diameter, D/d FIGURE 9-18 Relationship between cupping ratio D/d and the strain factor of cupping Ec (logarithmic base) (From: Frank W Wilson, Die Design. .. 0.0 36 0.042 0.0 46 0.054 0. 062 –0.124 0.125–0.250 0.25 0.38 0.53 0 .61 0.79 0.91 1.07 1.17 1.37 1.57–3.15 3.18 6. 35 27 32 35 39 42 44 46 47 47 48 47 18 20 21 22 23 26 28 28 29 30 28 17 19 20 21 22 24 25 25 26 27 26 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of. .. amount of reduction of the particular stainless-steel material may be calculated with the help of constants BSS-1 and BSS-2, listed in Table 9-4 TABLE 9-4 Factors Bss-1 and Bss-2 Material thickness First-operation die, Bss-1 value Any redrawing die, Bss-2 value in mm 18-8 SS 17Cr SS 18-8 SS 17Cr SS 0.015–0.018 0.021 0.022–0.024 0.027 0.031 0. 062 –0.109 0.125–0.250 0.38–0. 46 0.53 0. 56 0 .61 0 .69 0.79... reserved Any use is subject to the Terms of Use as given at the website Suchy_CH09.qxd 11/08/05 11:08 AM Page 3 86 DRAWN PARTS 3 86 CHAPTER NINE TABLE 9-5 Ironing-Related Deformation (F) (Percentages) First draw Second draw Material F kt F kt Steel, annealed Steel, medium hard Aluminum Brass 55 60 35–40 55 60 60 65 40–45 55 60 35–40 30–40 35–40 25–30 40–50 50 60 50–55 65 –70 50–55 40–50 where F = allowed... will be projected into a diametral size of the blank Two methods of blank calculation, both applicable only to symmetrical shells, are described further The first method is based on a theory that the area of any shape is given by the length of its profile, multiplied by the length of travel of its center of gravity 9-4-1-1 First Method of Blank Calculation Lengths of line segments L1, L2, and L3, as shown... formulas should be used For the first operation die: d1 = B1 × D 100 − 0 .63 5 D (9-12a) d2 = B2 × d1 100 − 0 .63 5d1 (9-12b) d3 = B2 × d2 100 − 0 .63 5d2 (9-12c) For all redrawing dies: where D = blank diameter d1 = mean diameter of first shell d2 = mean diameter of second shell d3 = mean diameter of third shell B1 and B2 = factors depending upon thickness of metal to be drawn, from Table 9-2 Downloaded... Severity of Draw and Number of Drawing Passes The severity of the drawing operation may be expressed by the relationship of the blank diameter to the cup diameter This ratio, often called a cupping ratio, allows for an assessment of the amount of drawing passes needed to produce a particular shell Where this ratio is exceeded, a fracture of the shell results, attributable to the exhaustion of drawing... Ec·E1·E2 ion ct –a Ec·E1 0 .63 Ec 1.0 100 63 40 n tio ac – gle Sin 25 1.4 0.40 Ec·E1·E2 Ec·E1 1 .6 1.7 1 .6 2.5 Ec 1.5 100 t/D Ratio D/t of blank diam to thickness 400 1.8 1.9 4.0 2.0 Strain factor, E FIGURE 9-14 Relationship between strain factors and blank dimensions for deep drawing with single- and double-action dies (From: Frank W Wilson, Die Design Handbook, New York, 1 965 Reprinted with permission from . 0.125–0.375 Under 3 3–10 Steel, annealed 29– 36 36 43 0.4–0.5 0.5–0 .6 Steel, hard 36 43 43–58 0.5–0 .6 0 .6 0.8 Aluminum 7–15 15–22 0.1–0.2 0.2–0.3 Brass 22– 36 36 43 0.3–0.4 0.4–0.5 Source: Svatopluk ˇ Cernoch,. 45–1 06. 5 62 0–1,470 Steel, stainless, 303 42.5 62 .5 585– 860 Aluminum alloy, cold worked 6. 0–31.5 80–435 Aluminum alloy, heat treated 11.0–41.5 150–570 Copper 16 28.5 220–390 Phosphor bronze 20 64 . subject to the Terms of Use as given at the website. Source: HANDBOOK OF DIE DESIGN 368 CHAPTER NINE FIGURE 9-1 Forces involved in cup-drawing process. FIGURE 9-2 Displacement of metal in drawing. Suchy_CH09.qxd