ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-34 Types and definitions of milling cutters (Cont.) Type Arrangement of teeth Double angle Application Size Teeth on two conical faces Vee slots 458, 608, 908 Rounding Concave quarter circle and flat face Corner radius on edge 1.5–20 mm radius Involute gear cutter Teeth on two involute curves Involute gears Appearance Large range 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 25.45 ELEMENTS OF MACHINE TOOL DESIGN 25.46 CHAPTER TWENTY-FIVE TABLE 25-34 Types and definitions of milling cutters (Cont.) Type End mill Arrangement of teeth Application Helical teeth at one Light work, end and slots, circumferential profiling, facing narrow surfaces Size Appearance 50 mm TANGED END TAPPED END Parallel Shank Tee slot Circumferential and both sides Tee slots in machine table Dovetail On conical surface Dovetail and one end face machine slides For bolts up to 24 mm diameter 38 mm diameter, 458 and 608 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 ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-34 Types and definitions of milling cutters (Cont.) Type Arrangement of teeth Application Skid end mill Circumferential and one end Larger work 40–160 mm than end mill diameter Cutting Circumferential saw (slot) teeth Cutting off or slitting Screw slotting Size Appearance Cutter Arbor 60–400 mm diameter Clearance Thick Thin Concaveconvex Curved teeth on periphery Radiusing 1.5–20 mm radius Concave Convex Thread milling cutter PARALLEL SHANK TAPER SHANK 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 25.47 ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-35 Suggested feed per tooth for milling various materials, mm Face mills Materials to be milled Slotting and side mills End mills Form relieved cutters Circular saws HSS Cast iron Soft (up to 160HB ) Medium (160 to 220HB ) Hard (220 to 320HB ) Malleable irona Steel Softa (up to 160HB ) Medium (160 to 220HB ) Harda (220 to 360HB ) Stainlessa Brass and Bronze Soft Medium Hard Copper Monel Aluminuma a Helical mills Carbide HSS Carbide HSS Carbide HSS Carbide HSS Carbide HSS Carbide 0.40 0.32 0.28 0.30 0.50 0.40 0.30 0.35 0.32 0.25 0.20 0.25 0.40 0.32 0.25 0.28 0.22 0.18 0.15 0.18 0.30 0.25 0.18 0.20 0.20 0.18 0.15 0.15 0.25 0.20 0.15 0.18 0.12 0.10 0.08 0.10 0.15 0.12 0.10 0.10 0.10 0.08 0.08 0.08 0.12 0.10 0.08 0.10 0.20 0.15 0.10 0.20 0.35 0.30 0.25 0.30 0.18 0.12 0.08 0.15 0.28 0.25 0.20 0.25 0.12 0.10 0.08 0.12 0.20 0.18 0.15 0.18 0.10 0.08 0.05 0.10 0.18 0.15 0.12 0.15 0.08 0.05 0.05 0.05 0.10 0.10 0.08 0.08 0.05 0.05 0.03 0.05 0.10 0.08 0.08 0.08 0.55 0.35 0.22 0.30 0.20 0.55 0.50 0.30 0.25 0.30 0.25 0.50 0.45 0.28 0.18 0.25 0.18 0.45 0.40 0.25 0.20 0.22 0.20 0.40 0.32 0.20 0.15 0.18 0.12 0.32 0.30 0.18 0.15 0.18 0.15 0.30 0.28 0.18 0.12 0.15 0.10 0.28 0.25 0.15 0.12 0.16 0.12 0.25 0.18 0.10 0.08 0.10 0.08 0.18 0.15 0.10 0.08 0.10 0.08 0.15 0.12 0.08 0.05 0.08 0.05 0.12 0.12 0.08 0.08 0.05 0.08 0.12 Coolant to be used TABLE 25-36 Recommended cutting speeds for face and end milling with plain HSS and carbide milling cutters, m/min Depth of cut Roughing cut, to mm Cast iron Soft Medium Hard Malleable Iron Steela : Soft Medium Hard Stainless Brass Average Soft yellow Bronze Copper Monel Aluminuma Semi-finishing cut, 1.5 to mm HSS Material to be milled HSS Carbide Carbide Finishing cut, below 1.5 mm HSS Carbide 25 15 12 25 68 50 38 68 30 25 16 30 80 68 50 80 36 30 20 36 105 80 68 105 28 22 15 18 120 100 75 50 32 28 20 22 150 120 90 68 40 32 25 28 180 135 105 80 30 60 28 45 18 75 75 120 75 100 50 240 45 90 36 68 22 105 120 180 100 150 68 300 60 120 45 90 28 150 150 240 128 210 80 450 a Coolant to be used Note: Cutting speeds for 12% cobalt HSS should be about 25% to 50% higher than those shown for plain HSS Cutting speeds for cast alloy should be about 100% higher than those shown for plain HSS Above speeds should be reduced when milling work that has hard spots or when milling castings that are sandy 25.48 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 ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-37 Feeds and speeds for hobbing Feed, mm/rev of blank Type of gear Material High speed reduction and step up Instrument Steel Steel Non-ferrous Steel Steel, C.I Non-ferrous Steel Aircraft Machine tool and printing press Automotive, including trucks and tractors High quality industrial General industrial Splines Steel Cast iron Steel Cast iron Steel Module mm Finishing 1–1.5 0.5–1.5 1.0–1.5 1.0–1.5 2.0–3.2 2.0–3.2 2.0–3.2 1–1.5 Up to Up to Up to Up to 2.5 Up to 2.5 Up to 2.5 Up to 2.0 (3 starts) 10.0–25.0 2.5–8.0 10.0–25.0 2.5–8.0 2.0–2.5 1.25–3.2 2.0–2.5 1.25–3.2 1.25–3.0 1.25–1.5 9–25 25–60 25–60 15–45 15–30 25–450 15–45 12–30 12–30 0.50–1.75 1.5–8 0.4–1.25 0.4–1.25 2.0–4.0 2.0–6.0 2.0–6.0 1.5–8.10 0.8–1.25 0.5–1.0 0.5–1.0 0.8–1.25 1.0–1.5 1.0–1.5 1.25–2.0 1.50–2.5 Roughing (multithread hob) Hob speeds, m/min 1.25–2.0 Roughing (single thread hob) l8–45 TABLE 25-38 Selection of milling cutters Material One-piece construction Two-piece construction Cutting portion Body High-speed steel High speed steel Carbon steel with tensile strength not less than 700 MPa (190 HN) Hardness Cutting portion Shank portion Parallel shank Tang of Morse taper shank 760 HV (62 HRC) Min 245 HV (21 HRC) Min 320 HV (32 HRC) Min Note: The equivalent values within parentheses are approximate Recommendations for selection of milling cutters: Tool Type N—For mild steel, soft cast iron and medium hard non-ferrous metals Tool Type H—For specially hard and tough materials Tool Type S—For soft and ductile materials Material to be cut Tensile strength, MPa Carbon steel Brinell hardness, HB Up to 500 Above 500 up to 800 Above 800 up to 1000 Above 1000 up to 1300 Steel casting Gray cast iron Up to 180 Over 180 Malleability cast iron Copper alloy Soft Brittle Zinc alloy Aluminum alloy Soft Medium/Hard Aluminum alloy, age hardened Low cutting speed High cutting speed Magnesium alloy Unlaminated a Tool typea N or (S) N N or (H) H H N H N S or (N) N or (H) S or (N) S N or (S) N S S or (N) N or (S) Tool types within parentheses are non-preferred Courtesy: IS 1830, 1971 25.49 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 ELEMENTS OF MACHINE TOOL DESIGN 25.50 CHAPTER TWENTY-FIVE TABLE 25-39 Dimensions for interchangeability of milling cutters and arbors with tenon drive A z r1 r a a1 dφ A s × 45 dφ s× 45 b b1 All dimensions in millimeters Arbor Cutter da h6/H7 a h11 b H11 r Max a1 H11 b1 H13 r1 Max 10 13 16 19 22 27 32 40 50 60 8 10 10 12 14 18 16 20 2.0 3.5 4.0 4.5 5.0 5.6 5.6 6.3 7.0 9.0 8.0 10.0 0.3 0.4 0.5 0.5 0.6 0.6 0.6 0.8 0.8 1.0 1.0 1.0 3.3 5.4 6.4 8.4 8.4 10.4 10.4 12.4 14.4 16.4 18.4 20.5 2.5 4.0 4.5 5.0 5.6 6.3 6.3 8.0 7.0 9.0 10.0 11.2 0.6 0.6 0.8 1.0 1.0 1.2 1.2 1.6 1.2 2.0 2.0 2.0 a b s 0.3 0.4 0.5 0.5 0.6 0.6 0.6 0.8 0.8 1.0 1.0 1.0 zb ỵ 0.1 ỵ0.2 ỵ0.3 The tolerance on d is not applicable to gear hobs z ¼ maximum permissible deviation between the axial plane of the tenon and the axis of arbor of diameter d Courtesy: IS 6285-1971 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 0.075 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.100 0.125 ELEMENTS OF MACHINE TOOL DESIGN 25.51 ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-40 Dimensions for interchangeability of milling cutters and milling arbors with key drive r a a C C1 s× 45 r1 C1 C a b KEY SECTION dφ KEYWAY IN CUTTER KEYWAY IN ARBOR All dimensions in millimeters Key da h6/H7 a h9 bb 10 13 16 19 22 27 32 40 50 60 70 80 100 3 10 12 14 16 18 25 3 7 8 10 11 14 a S 0.16 0.25 Keyway Tolerance on S ac ỵ0.09 0ỵ0.15 0.40 0.60 ỵ0.20 3 10 12 14 16 18 25 C 6.7 8.2 11.2 13.2 15.6 17.6 22.0 27.0 34.5 44.5 54.0 63.5 73.0 91.0 The tolerance on diameter d is not applicable to gear hobs Tolerance on thickness b of key: square, h9; rectangular, h11 c Tolerance on keyway width a: light drive fit, N9 For keyway in arbor: running fit, H9; light drive fit, N9 For keyway in cutter: C11 Tolerance on C C1 0–0.1 0–0.2 8.9 11.5 14.6 17.7 21.1 24.1 29.8 34.8 43.5 53.5 64.2 75.0 85.5 107.0 Tolerance on C1 r Tolerance on r r1 Tolerance on r1 0.16 0.6 0–0.1 –0.2 –0.08 –0.3 0.25 1.2 –0.09 00.5 0.40 00.15 0.60 00.20 0.20 0.4 ỵ0.1 1.0 þ0.2 1.6 2.0 2.5 IS: 6285, 1971 b 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 ELEMENTS OF MACHINE TOOL DESIGN 25.52 CHAPTER TWENTY-FIVE TABLE 25-41 American National Standard staggered teeth, T-slot milling cutters with Brown and Sharpe taper and Weldon shanks (ANSI/ASME B94, 19, 1986) With B and S tapera Bolt size 16 8 Cutter diam., D Face width, W Neck diam., N 16 21 32 26 32 13 32 11 115 32 127 32 16 64 17 64 21 64 25 64 31 32 53 64 17 64 21 64 13 32 17 32 21 32 25 32 132 With Weldon shank Length L Taper No Length L Diam., S — — 219 32 — — 211 16 31 316 15 316 416 13 416 2 — — 61 67 71 1 — 11 All dimensions are inches All cutters are high-speed steel and only right-hand cutters are standard a For dimensions of Brown and Sharpe taper shanks See information given in standard Handbook Tolerances: On D, ỵ0.000, 0.010 inch; on W, ỵ0.000, 0.005 inch; on N, ỵ0.000, 0.005 inch, on L, Ỉ 16 inch; on S, À0.0001 to À0.0005 inch TABLE 25-42 American National Standard 60-degree single-angle milling cutters with Weldon shanks (ANSI/ASME B94, 19, 1985) L 60 w S D Diam., D S W L Diam., D S W L 8 16 16 216 17 8 21 13 16 116 31 27 13 All dimensions are in inches All cutters are high-speed steel Right-hand cutters are standard Tolerances: On D, 0.015 inch; on S, À0.0001 to À0.0005 inch; on W, 0.015 inch; and on L, Ỉ 16 inch 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 33 ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.53 TABLE 25-43 American National Standard multiple flute, helical series end mills with Brown and Sharpe taper shanksa (ANSI/ ASME B94, 19, 1985) L w D Diam., D W L Taper No Diam., D W L Taper No – – – – 15 55 71 21 71 23 – – – – 15 16 11 415 16 11 11 51 All dimensions are in inches All cutters are high-speed steel Right-hand cutters with right hand helix are standard Helix angle is not less than 10 degrees No taper is standard without tang: Nos and are standard with tang only 1 Tolerances: On D, ỵ0.005 inch; on W, ặ 32 inch; and L, Ỉ 16 inch a For dimensions of B and S taper shanks, see information given in standard handbook 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 ELEMENTS OF MACHINE TOOL DESIGN 25.54 CHAPTER TWENTY-FIVE TABLE 25-44 American National Standard form relieved, concave, convex, and corner-rounding arbor-type cuttersa (ANSI/ASME B94, 19, 1985) R w w C H H D Concave Max Min H D Convex Diameter C or radius R Nom w C Cutter diam D b D Corner - Rounding Width W Ỉ:010 c Diameter of hole H Nom Max Min 1.00075 1.00000 1 1.00075 1.00075 1.00000 1.00000 Concave cuttersc 8 0.1270 0.1240 21 0.2520 0.3770 0.2490 0.3740 21 23 0.5040 0.4980 0.7540 0.7480 33 0.0040 0.9980 16 13 16 113 16 116 41 1.00075 1.00000 11 1.251 1.250 11 1.251 1.250 1.00075 1.00000 1.00075 1.00000 1.00075 1.00000 11 1.251 1.250 11 1.215 1.250 1.00075 1.00000 1.00075 1.00000 11 1.251 1.250 d Convex cutters 0.2520 0.2480 21 0.3770 0.3730 23 0.5020 0.4980 0.7520 0.7480 33 4 1.0020 0.9980 41 Corner-rounding cutterse 0.1260 0.1240 21 0.2520 0.2490 0.5020 0.4990 41 4 13 32 All dimensions in inches All cutters are high-speed steel and are form relieved Right-hand corner rounding cutters are standard, but left-hand cutter for inch size is also standard a For key and keyway dimensions for these cutters, see standard handbook b c 1 Tolerances on cutter diameters are ỵ 16, 16 inch for all sizes Tolerance does not apply to convex cutters d Size of cutter is designated by specifying diameter C of circular form e Size of cutter is designated by specifying radius R of circular form Source: Courtesy: ANSI/ASME B94, 19, 1985, Erik Oberg Editor Etd., Extracted from Machinery’s Handbook, 25th edition, Industrial Press, N.Y., 1996 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 ELEMENTS OF MACHINE TOOL DESIGN 25.70 CHAPTER TWENTY-FIVE TABLE 25-54 Shear strength of various materials Ultimate strength, sut Material MPa Ferrous alloys 0.10 carbon steel annealed 0.20 carbon steel annealed 0.30 carbon steel annealed 0.50 carbon steel annealed 1.00 carbon steel annealed Chromium-molybdenum steel: SAE 4130 psi K monel Nickel Inconel (nickel chromium iron) MPa psi 240 290 358 550 768 475 745 672 1072 469 831 550 620 689 792 965 1103 1206 69,000 108,000 97,500 155,600 68,000 120,500 80,000 90,000 100,000 115,000 140,000 160,000 175,000 380 448 515 620 725 55,000 65,000 75,000 90,000 105,000 98,000 110,000 125,000 655 758 896 930 1035 1138 90,000 100,000 125,000 150,000 180,000 35,000 42,000 52,000 80,000 110,000 675 758 862 620 690 862 1035 1240 Nickel steel (drawn to 4268C (8008F) and water-quenched): SAE 2320 SAF 2330 SAE 2340 Nickel-chromium steel (drawn) to 4268C (8008F): SAE 3120 SAE 3130 SAE 3140 SAE 3280 SAE 3240 SAE 3250 Nonferrous materials Aluminum and alloys Copper and alloys Magnesium alloys Monel metal Shear strength, s 95,000 110,000 130,000 135,000 150,000 165,000 28–282 150 330 28–145 295–450 450 680 360 520 406 434 455 490 538 580 600 4,000–41,000 22,000 48,000 4,000–21,000 42,900 65,200 65,300 98,700 52,300 75,300 59,000 63,000 66,000 71,000 78,000 84,000 87,000 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 ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.71 TABLE 25-54 Shear strength of various materials (Cont.) Ultimate strength, sut Material MPa psi Nonmetallic materials Asbestos board Cellulose acetate Cloth Fiber, hard Hard rubber Leather, tanned Leather, rawhide Mica Papera Bristol board Pressboards Phenol fiberb a b Shear strength, s MPa 34 69 55 124 138 48 90 69 44 33 24 180 psi 5,000 10,000 8,000 18,000 20,000 7,000 13,000 10,000 6,400 4,800 3,500 26,000 For hollow die used one-half value shown for shearing strength Blank and perforate hot 0.010 0.009 Die clearance, in 0.008 0.007 0.006 up 0.005 o Gr 0.004 p rou 0.003 G Gro up m s ial er at s, ial 5% ,7 + a er av % 6.0 an ar cle le ec e nc ara rag ve +a ge ce r r ate ave 2m %+ 4.5 , ials ter ma c age lea ran ce 0.002 0.001 Group 1: 1100S and 5052S aluminum alloys, all tempers An average clearance of 41 per cent of material thickness is recommended for normal piercing and blanking Group 2: 2024ST and 6061ST aluminum alloys; brass, all tempers; cold rolled steel, dead soft; stainless steel soft An average clearance of per cent of material thickness is recommended for normal piercing and blanking Group 3: Cold rolled steel; half hard; stainless steel, half hard and full hard An average clearance of 71 per cent is recommended for normal piercing and blanking Courtesy: Frank W Wilson, Fundamentals of Tool Design, ASTME, Prentice-Hall of India Private Limited, New Delhi, 1969 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Nominal thickness of material which die is designed for, in Note: in = 24.5 mm FIGURE 25-38 Die clearances for different groups of metals 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 ELEMENTS OF MACHINE TOOL DESIGN 25.72 CHAPTER TWENTY-FIVE TABLE 25-55 Drawing speeds TABLE 25-56 Drawing radii Drawing speed, Vd (m/min) Thickness of stock, mm Drawing radius, mm Material Single action Double action Aluminum provide Strong aluminum alloys Brass Copper Steel Steel in carbide dies Stainless steel Zinc 55 — 65 45 18 — — 45 30 10–15 30 25 10–16 20 7–10 13 0.4 0.8 1.25 1.6 2.5 3.15 1.6 3.2 4.8 6.3 10 11.2 14 TABLE 25-57 Blank holder force in drawing Thickness of stock, t, mm Force, N per mm 0.25 0.4 0.5 0.63 0.80 0.9 1.00 1.12 1.25 1.4 1.6 1.8 2.0 2.24 2.5 and over 314 304 294 280 270 260 250 235 225 220 210 196 181 167 157 TABLE 25-58 Recommended die plate thickness (a) For dies with cutting perimeter less than 50 mm Stock thickness mm 0.25 0.5 0.75 Die plate thickness, mm/shear stress, kgf/mm2 (b) For dies with cutting perimeter greater than 50 mm Cutting perimeter, mm over 50 75 up to 75 150 Factor by which the above tabulated values under (b) should be multiplied 1.25 1.5 1.25 1.5 1.75 2.25 2.5 4.5 5.25 5.75 6.3 6.7 150 300 1.75 300 500 2.0 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 ELEMENTS OF MACHINE TOOL DESIGN TABLE 25-59 Chart for bend allowance and correction factor Recommended minimum bend radius ri for sheet metal Aluminum alloys Magnesium Steel Material thickness 24ST and Alclad 24SO and Alclad 2S, 3S and 52S (1 hard) Cold bend Hot formed Stainless Annealed a Up to 0.015 0.016 0.020 0.025 0.032 0.040 0.051 0.064 0.072 0.081 0.091 0.102 0.125 0.156 0.187 0.250 0.375 0.06 06 0.09 0.12 0.12 0.12 0.19 0.19 0.25 0.31 0.38 0.44 0.50 0.69 0.81 1.00 — 0.06 0.06 0.09 0.09 0.09 0.09 0.09 0.09 0.12 0.12 0.16 0.19 0.19 0.28 0.38 0.50 — 0.03 03 0.03 0.03 0.06 0.09 0.09 0.12 0.16 0.19 0.19 0.19 0.19 0.25 0.38 0.50 — 0.06 09 0.12 0.19 0.25 0.31 0.38 0.50 0.56 0.62 0.69 0.75 1.00 1.35 1.50 2.00 3.00 06 0.06 0.06 0.06 0.09 0.99 0.12 0.19 0.19 0.19 0.25 0.25 0.31 0.44 0.50 0.62 1.00 03 — 0.03 0.03 0.03 0.06 0.06 0.06 0.09 0.09 0.12 0.16 0.19 0.19 0.25 — — 03 — 0.06 0.06 0.06 0.09 0.09 0.12 0.12 — — — — — — — — hard Low carbon, X-4130 annealed b — 0.03 0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.09 0.09 0.12 0.12 0.19 0.19 0.25 — Note: a For bends up to 90 deg b This applies to 8630 and similar steels C= t 90 deg angle t 0.25 90… angle C C correction factor 0.20 Closed bevels α’ C 0.15 t t thickness = 0.125 Open bevels 0.091 0.081 α’ 0.10 0.064 0.051 0.040 0.032 0.025 0.020 0.015 0.05 80 60 40 Open bevel 20 20 α, bevel angle in degrees 40 60 Closed bevel 80 Courtesy: D C Greenwood (ed.), Engineering Data for Product Design, McGraw-Hill Publishing Company, New York, 1961 25.73 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 ELEMENTS OF MACHINE TOOL DESIGN 25.74 CHAPTER TWENTY-FIVE Particular Formula FORMING PROCESS: Note: The Symbols, Equations and Examples given in the book entitled ‘‘Mechanical Presses*’’ by Professor Dr Ing Heinrich Makelt and translated by R Hardă bottle, are followed and used in Symbols, Equations and Examples with reference to Figs 25-41 to 25-49 in this Machine Design Data Handbook The minimum ram force in mechanical presses Pmin ẳ 0:5Prat 25-161ị where Prat ¼ tonnage rating, tonneforce (tf ) The maximum ram force Pmax ẳ Qkmax ẳ Fmax tf 25-162ị where Q ¼ cross-section kmax ¼ maximum specific loading, MPa (psi) max ¼ maximum stress, MPa (psi) F ¼ workpiece surface, in2 The press work A ¼ mPmax h ¼ Pmi h where 25-163ị m ẳ correction factor taken from Table 25-62 h ¼ work path ¼ 0:5 H H ¼ total maximum stroke setting The volume of the workpiece before and after forming Q1 h1 ¼ Q2 h2 ¼ constant The force required to trim the forging F¼ Pt s tf 2000 where F in tonneforce (tf ) ð25-164Þ ð25-165Þ P ¼ periphery of forging, in t ¼ thickness, in s ¼ shear strength of material, psi For chart for calculating ram path and velocity versus crank angle Refer to Fig 25-41 For calculation chart for blanking and piercing with full-edge cutting tool Refer to Fig 25-42 For calculation chart for rectangular bending (a) Vbending on a fixed die, (b) U-bending with back-up Refer to Fig 25-43 For calculation chart for deep drawing and redrawing (a) deep drawing with blank holder (b) re-drawing of body Refer to Fig 25-44 * Heinrich Makelt, ‘‘Mechanical Presses’’, translated into English by R Handbottle, Edward Arnold (Publishers) Ltd., 1968 ă 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 ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN Particular 25.75 Formula For determination of blank-holder force for deep drawing Refer to Fig 25-45 For chart for extrusion molding and impact extrusion: a, extrusion molding of hollow bodies in direction of punch travel (forward extrusion); b, impact extrusion (tube extrusion) against direction of punch travel (backward extrusion) Refer to Fig 25-46 For determination of multiplication factor for impact extrusion and cold extrusion, and also for stamping and coining Refer to Fig 25-47 For chart for calculating stamping and coining Refer to Fig 25-48 For chart for calculating hot upsetting and drop forging Refer to Fig 25-49 For penetration of sheet thickness before fracture, suggested reductions in diameters for drawing, mean values for m and suggested trimming allowances Refer to Tables 25-60, 25-61, 25-62 and 25-63 TABLE 25-60 Approximate penetration of sheet thickness before fracture in blanking Work metal Penetration % Work metal Penetration % Carbon steels 0.10% C annealed 0.10% C cold rolled 0.20% C annealed 0.20% C cold rolled 0.30% C annealed 0.30% C cold rolled 50 38 40 28 33 22 Non-ferrous metal Aluminum alloys Brass Bronze Copper Nickel alloys Zinc alloys 60 50 25 55 55 50 TABLE 25-61 Suggested reductions in diameters for drawing TABLE 25-62 Mean values for m (standard coefficients) Material First draw % Redraws % Particulars Aluminum, soft Aluminum, deep drawing quality Brass Copper Steel Steel, deep drawing quality Steel, stainless Zinc Tin 40 40–50 20–25 20–30 45 40 35–40 40–45 35–40 50 35–45 20–25 15–20 15–20 15–20 15–20 15–20 10–15 Blanking and piercing (full-edge) tough (soft) sheet brittle (hard) sheet Making V- and U-bends with die clash without die clash Deep-drawing and re-drawing Impact extrusion and extrusion forming Stamping Hot, first upsetting operations End drop-forging 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 m 0.63 0.32 0.32 0.63 0.63 1.00 0.5 0.71 0.36 ELEMENTS OF MACHINE TOOL DESIGN 25.76 CHAPTER TWENTY-FIVE Particular Formula TABLE 25-63 Suggested trimming allowances Allowance per side, mm, for steel with Rockwell B hardness of Blank thickness, mm First trim or single trim Second trim or add to first trim 50–66 75–90 90–106 1.20 1.60 2.00 2.36 2.80 3.15 1.20 1.60 2.00 2.36 2.80 3.15 0.063 0.075 0.090 0.106 0.125 0.18 0.03 0.035 0.045 0.050 0.063 0.09 0.075 0.106 0.125 0.150 0.180 0.224 0.035 0.050 0.063 0.075 0.090 0.100 0.106 0.125 0.15–0.180 0.18–0.224 0.224–0.230 0.3–0.355 0.05 0.063 0.075–0.09 0.09–0.100 0.1–0.14 0.15-0.18 MACHINE TOOL STRUCTURES: The optimum ratio l =h for every structure which depends on [], [] and E l 6Eẵ ẳ h ẵ 25-166ị where l ¼ length of structure/beam The natural frequency of an elastic element such as a bar or beam subjected to tension or compression—a case of single degree freedom system h ¼ distance of outermost fiber from the neutral axis in case of bending rffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffi k EA E ẳ ẳ 25-167ị f ẳ m l Al l2 where k ¼ stiffness of the system ¼ F=4l The natural frequency of a simply supported beam subjected to a load at the center of beam – a case of single degree freedom system ¼ mass density of member rffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 48E 48E bh3 E 4bh3 ¼ f ¼ ¼ ¼ Al 12 Al m Al l l ð25-168Þ where E= is the unit or specific thickness It is an important parameter in machine tool structural material and ¼ mass density of material of beam, ¼ specific weight of material or beam The natural frequency depends on E= 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 ELEMENTS OF MACHINE TOOL DESIGN ELEMENTS OF MACHINE TOOL DESIGN 25.77 D t R R = 0.8 (D d) t where D = blank diameter, in Tolerance for R = ± 0.005 in d 1.600 0.160 0.140 0.120 0.100 0.080 0.060 1.200 0.800 0.040 0.024 0.020 0.400 0.360 0.320 0.280 0.240 Blank thickness ’t Radius R 0.012 0.200 0.160 0.120 16.00 Diameter difference (D d) 12.00 4.80 5.60 6.40 7.20 8.00 2.40 2.80 3.20 3.60 4.00 2.00 1.600 1.200 0.400 0.040 0.480 0.560 0.640 0.720 0.800 0.080 d h Example: d = 1.00 h = 0.75 t = 0.020 D = d + 4dh = 2.00 D d=1 R = 0.110 ± 0.005 FIGURE 25-39 Nomograph for determining draw-die radius Courtesy: American Machine/Metal working Manufacturing Magazine 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 ELEMENTS OF MACHINE TOOL DESIGN 25.78 26 CHAPTER TWENTY-FIVE 10 12 14 40 24 35 22 30 25 20 15 10 18 16 14 Reduction, % Diameter of blank or cup, in 20 12 10 0 10 12 Cup diameter, in 14 FIGURE 25-40 Chart for checking percentage reduction in drawing of cups The inside diameter is ordinarily used for the cup diameter Courtesy: From ASM, Metals Handbook, 8th ed., vol 4, 1969 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 ELEMENTS OF MACHINE TOOL DESIGN 25.79 40 31 50 lo 20 60 125 00 ve 50 31 25 C m 315 355 40 45 50 56 56 A1 D1 n- 0.1 0.08 0.063 E2 0.05 0.04 0.035 0.025 Z 0.02 0.016 0.0125 0.01 0.008 0.0063 ∑ α α… 28 mi 0.2 1.2 63 25 n, F2 20 21 1000 800 600 500 400 315 250 200 160 125 100 80 63 50 D2 40 31.5 25 20 16 12.5 10 E1 0.125 15 .5 18 II 0.16 6.3 15 13 A2 es 50 40 31 2 16 2.5 F1 10 12.5 ok in B1 str /m r m m v, pa ro m 0.01 0.0125 0.02 0.02 0.025 0.025 0.02 0.05 0.053 0.02 0.1 0.25 0.15 0.235 0.236 0.29 0.355 0.355 0.53 0.11 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.35 0.4 0.45 0.5 0.56 0.63 0.71 0.8 0.9 1.12 1.25 1.4 1.6 Crank angle 2, rad 1.61.5 4.5 5.6 6.3 7.9 10 11.2 Crank angle o2, degrees 12.5 0.8 0.63 0.5 0.4 0.315 0.25 III or g st h, Ra ty W kin f to ke Connecting rod ratio 10 λ = H: 21 = 1: 10 6.3 Work-path/ stroke h/H 0.001 0.002 0.002 0.002 0.005 0.002 0.004 0.005 0.053 0.003 ci 20 12 10 am 31 2.5 R I 0.06 0.07 0.08 0.09 0.1 1000 800 630 500 400 315 250 200 160 125 100 80 63 50 40 31.5 25 20 16 12.5 10 6.3 Total ram stroke H, mm B2 C 26 1 1000 800 630 500 400 315 250 200 160 125 100 80 63 53 40 31.5 25 20 16 12.5 0.8.83 0.5 15 25 0.2 76 15 Total ram stroke H, mm ELEMENTS OF MACHINE TOOL DESIGN 6.3 λ = 1:10 0.925 0.412 0.515 0.58 0.69 0.825 0.875 0.975 0.63 0.463 0.067 0.075 0.085 0.095 0.106 0.118 0.132 0.15 0.17 0.19 0.212 0.236 0.265 0.3 0.335 0.375 0.95 0.75 0.06 0.07 0.08 0.09 3.5 4.5 0.1 0.11 0.12 0.14 0.16 0.18 0.20 0.22 0.25 0.28 0.32 0.35 0.4 5.6 6.3 7.1 10 11.2 12.5 14 16 18 20 22.4 0.45 0.5 25 28 0.56 0.63 0.71 0.8 0.9 1.12 1.4 1.6 1.25 31.5 35.5 40 45 50 56 63 80 90 71 FIGURE 25-41 Chart for calculating ram path and velocity versus crank angle 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 50 ELEMENTS OF MACHINE TOOL DESIGN 25.80 CHAPTER TWENTY-FIVE 10000 C 2000 800 500 315 630 0.6 0.4 0.2 80 1600 1000 2.5 1.6 1250 Sh 400 A 160 16 31.5 25 50 40 125 80 63 k 100 200 160 315 250 E Hole diametar d, mm ee tt hi 6,3 s ck mm n es 2,5 1,6 th pa h s 0,6 m m G 2.5 1.6 10 6.3 Sh 10 k ine it l Lim 25 16 y cit pa ca rk wo ss re rp fo 6.3 16 or W III 500 400 25 Blanking circumferenca U mm 6,310 16 25 40 63 100 160 250 400 630 1000 1600 2500 4000 6300 10000 16000 25000 40000 100 3,2 12,5 20 32 50 80 125 200320 500 800 0,4 PK d (u) Fs δ=hk 0,2 F 0.63 0.4 0.25 rk th pa h Blanking work Ak, m.kg or tonnes 20 Blanking force p , tonnes 10 6.3 t th s m ickn m ess Wo mm 6300 4000 2500 1600 1000 630 400 250 160 100 63 40 25 15 10 6.3 2.5 1.5 12.5 E ee 250 200 125 I B 10 6.3 20 5 31 3150 2500 Limit 4000 C D Blanking area, mm2 10 12 16 line s=d , II 25 6300 5000 16 10 th ng tre r s mm ea kg/ Sh k ,s 8000 FIGURE 25-42 Calculation chart for blanking and piercing with full-edge cutting tool Equations and Examples Equations: Area ¼ Fs ¼ Us ¼ ds Section II: The tonnage rating of the press ¼ Pk ¼ Fs ks =1000 tonneforce (tf ) The shear strength of metallic material, ks , is ks ¼ 0:8 B N/mm2 (kgf/mm2 ) The work path is taken as hk ¼ s, where s ¼ thickness of material/sheet Section III: The cutting work¼ Ak ¼ mPk hk , mm-tonneforce (mm tf) or m kgf where m ¼ correction factor ¼ 0:63 for soft sheet Example: Blank diameter d ¼ 800 mm (31.5 in) or U ¼ 2500 mm (98 in) Sheet thickness ¼ mm (0.039 in); The blanking area ¼ Fk ¼ 2500 mm2 (3.85 in2 ) Blanking or cutting force Pk ¼ 980 kN (100 tf ) Work¼ 61:78 N m (63 mm-tf or 456 ft-lbf ) 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 ELEMENTS OF MACHINE TOOL DESIGN Limit line 1min=2.8 for V-form Die-span I (only V-form) mm Bending width b.mm 10 12.5 16 20 25 31.5 40 50 63 80 100 125 160 200 250 315 400 500 630 800 1000 0.4 0.5 0.63 0.8 1.25 1.6 2.5 3.15 6.3 10 12.5 16 20 25 0.06 ’ A1 A1 A A’ 0.1 nve rsio n li ne B for U-f B orm 50 10 80 63 16 I 0.16 0.4 C C’ 2.5 6.3 II 0.25 100 160 250 400 630 100 D’ 160 250 400 0.63 CC 1.6 C’ 10 (b) b a m =r in i s hv 250 Die-span I’(only for v-form) mm 400 10 72.5 16 E 12 3.15 1.25 fo rp re ss F e 80 lin it 50 m 31.5 Li 20 80 tones 1000 1600 2500 4000 Pv,U/σB E’ 125 45 50 63 6300 10000 2.5 2.5 6.3 10 16 25 40 63 100160 250 B ’ 3.2 6.3 h vU th σB pa rk m th Wo m 10 ng re 12.5 6.3 st 16 al mm ri te kg/ 20 10 a M 12.5 25 12 16 31.5 16 2 IV 2.0 40 III 31 50 40 2.5 H G K G 63 31.5 63 80 80 40 G’ F’ 50 100 G’ H’ 125 63 80 160 100 200 12.5 250 160 315 I I’ 200 400 500 250 2.5 6.3 10 16 25 40 63 100 160 250 400 630 1000 1600 2500 4000 630010000 16000 Bending force Pv,U,tonnes Bending work Av,U’,m.kg or mm.tonnes (+counterforce Pa for U-form) 630 Maximum force Pv max’ 160 20 25 Hu t PG l 31 b s lmin 100 100 Pu ri D 00 630 (a) Pv ri /σB P v,U Co s2//’ for V-form, s/2.5 for U-form Sheet thickness s.mm w or ki ng ca pa ci ty FIGURE 25.43 Calculation chart for rectangular bending (a) V-bending on a fixed die, (b) U-bending with back-up Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968) Equations and Examples: (Fig 25-43) Equations: Refer to Eqs (25-155) and (25-156) for V-bending force and U-bending force The equation for V-bending force Pv ẳ ẵCB bs2 =1000l tonneforce (tf) (kN or lbf ) The bending work Av ¼ mPE hv mm tonneforce (mm tf ) The limit of effective span or width of V-die lmin ¼ 2:8s in mm (in) The work path hv ẳ 0:5l 0:4s ỵ ri ị in mm (in) (a) V-bending Example: s ¼ t ¼ 2:5 mm (0.1 in); b ¼ 630 mm (25 in); B ¼ 618 N/mm2 ¼ 63 kgf /mm2 (90000 lbf/in2 ); Pv ¼ 25 tf [E-F-G ]; PE ¼ 50 tf; h ¼ 0:5l ¼ mm (0.2 in) and m ¼ 0:32 The bending work¼ As ¼ 784 kN m (80 mm tf or 579 ft lbf ) [A-B-C-C-A ], D-D [B-H and G-H-I ] (b) U-bending: Equations: The equation for U-bending force ¼ Pv ¼ C(2/5)B bs=1000 tf (kN or lbf ) The backing force PG ¼ 25% of PU The total force PU ỵ PG ẳ 1:25PU The bending force ẳ AU ẳ mPU ỵ PG ịhU mm-tf (m N or ft lbf ) The work path ¼ hU ¼ 3s mm (in) The correction factor ¼ m ¼ 0:63 Example: s ¼ mm (0.2 in); s=2:5 ¼ mm (0.08 in) [A0 -B0 -C0 ] b ¼ 500 mm (19.75 in), PU =B ¼ 1000 [C0 -D0 and A0 -D0 ] B ¼ 392 N/mm2 (40 kgf/mm2 or 57000 lbf/in2 ) PU ¼ 392 N or 40 tf [D0 -E -F -G0 ] PU ỵ PG ẳ 496 N or 50 tf AU ¼ 4900 mm kN (500 mm tf or 500 m kgf or 3617 ft lbf) for hv ¼ 16 mm (0.70 in) and m ¼ 0:63 [G0 -H -I ] Prut ¼ 490 kN (50 tf ) [I -K-G ] 25.81 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 ELEMENTS OF MACHINE TOOL DESIGN 10 12.5 16 20 25 31.5 40 50 2500 2000 1600 63 80 D C C’ D’ 1250 1000 630 800 Body cross-section Sheet thickness s, s2 mm Qz,2 mm2 0.4 250 (a) Pz II 2.5 6.3 20 3.2 25 32 40 6.3 12.5 10 E’ s E Qz 63 hz 40 500 C’ ’ B1 25 I’ III ’ B2 315 0.2 C bo onv dy ers cro ion ss- lin sec e fo tion r Q I 200 125 s h1 80 (b) PA d1 (U1) Q1 d2 (U2) 50 hz s Q2 s1 31.5 40 10 16 25 100 160 250 25 63 160 250 100 630 1000 25 63 40 400 10 16 20 80 200 315 31.5 125 50 200 80 1250 2000 3150 50 31.5 500 800 315 500 125 Press tonnage rating Prat tonnes 63 400 250 160 250 100 40 63 400 630 1000 1600 2500 16 100 160 40 25 10 160 500 20 50 80 125 315 800 31.5 12.5 31.5 12.5 200 50 200 20 125 80 E’ 12.5 K’ E A 16 250 50 63 80 10 s d (U) Drawing force Pz,A tonnes 100 D 0.3 B C 400 160 0.8 0.6 0.5 1.6 25 15 2.5 G H G’ 40 0.8 0.63 0.5 20 31.5 G F’ z,A 50 ’ A2 40 31.5 400 C ro s s-s tio ec IV q tio n A Drawing ratio βN F L’ G’ 50 H’ 63 80 16 00 50 15 00 00 30 00 000 250 600 000 500 150 000 000 300 000 0000 500 2 1 2 1 100 63 re-drawing Work A 12 Drawing Or m.kg or mm.tonnes A ’ A1 2.5 2.24 25 20 1.8 16 1.6 12.5 Blank height h1 mm 1.4 10 1.2 M’ 630 1000 1600 6.3 Blank cross-section Q1 mm2 Body drawing stress Kz = Z(A) σB kg/mm2 — Mean drawing diameter d, d2, mm; — Mean body circumference U, U2, mm; — Mean drawing diameter d, mm; — Drawing force Pz, tonnes; — Limit line for rational utilisation of press-working capacity; — Work path hz,2 (mm) of cylindrical bodies FIGURE 25-44 Calculation chart for deep drawing and redrawing (a) Deep drawing with blank holder (b) Re-drawing of body Courtesy: Heinrich Makelt, Die Mechanischen Pressen, Carl Hanser Verlag, Munich, German Edition, 1961 (Translated by R Hardbottle, Mechanical Presses, Edward Arnold (Publishers) 1968) Equations and Examples: (Fig 25-44) Force and work requirements for deep drawing and re-drawing: The body cross sectional area Qz ¼ Us ¼ ds mm2 where d ¼ mean diameter of the drawn parts, mm U ¼ mean circumference of the drawn part, mm s ¼ sheet thickness, mm The maximum draw force ¼ Pz ¼ Qz zB =1000 tf where z ¼ drawing factor ¼ y ln N =F ¼ ln N = ln ... 0. 19 0. 19 0.25 0 .31 0 .38 0.44 0.50 0. 69 0.81 1.00 — 0.06 0.06 0. 09 0. 09 0. 09 0. 09 0. 09 0. 09 0.12 0.12 0.16 0. 19 0. 19 0.28 0 .38 0.50 — 0. 03 03 0. 03 0. 03 0.06 0. 09 0. 09 0.12 0.16 0. 19 0. 19 0. 19. .. 64 23 31 – – – 31 – – 31 33 33 41 8 2 16 16 13 16 13 16 11 31 – 5 – – 116 – 16 16 16 13 16 13 16 11 116 116 18 57 15 57 – – – – – – – – – – – – – – – – – – 8 8 2 4 – – – 27 31 W L 31 31 33 33 41... 8 4 216 8 2 11 31 6 31 6 31 31 33 4 31 4 8 13 13 11 13 21 41 4 – – – – – – – – – – 1 13 13 15 15 17 17 21 21 211 16 211 16 33 33 35 35 4 4 21 45 8 4 – – – – – – 4 51 4 61 4 31 53 4 71 4 61 61 61