PACKINGS AND SEALS PACKINGS AND SEALS FIGURE 16-18 Power absorption and starting torque for balanced and unbalanced seals (M J Neale, Tribology Handbook, Butterworths, London, 1973.) 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 16.33 PACKINGS AND SEALS 16.34 CHAPTER SIXTEEN REFERENCES Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Units), Suma Publishers, Bangalore, India, 1986 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 Maleev, V L., and J B Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954 The American Society of Mechanical Engineers, ASME Boilers and Pressure Vessel Code, Section VIII, Division I, 1986 Whalen, J J., ‘‘How to Select the Right Gasket Material,’’ Product Engineering, Oct 1860 Shigley, J E., and C R Mischke, Standard Handbook of Machine Design, McGraw-Hill Book Company, 1986 Neale, M J., Tribology Handbook, Butterworths, London, 1975 Ratelle, W J., ‘‘Seal Selection, Beyond Standard Practice,’’ Machine Design, Jan 20, 1977 ‘‘Packings and Seals’’ Issue, Machine Design, Jan 1977 10 Faires, V M., Design of Machine Elements, Macmillan Book Company, 1955 11 Bureau of Indian Standards 12 Rothbart, H A., Mechanical Design and Systems Handbook, McGraw-Hill Book Company, New York, 1985 13 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Book Company, New York, 1994 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: MACHINE DESIGN DATABOOK CHAPTER 17 KEYS, PINS, COTTERS, AND JOINTS SYMBOLS4;5;6 a A b d d1 d2 d3 d4 dc dpl dm (or dpm ) dnom D F F , F 00 00 F2 , F2 Ft F h l L lo , so m Mb Mt addendum for a flat root involute spline profile, m (in) area, m2 (in2 ) breadth of key, m (in) effective length of knuckle pin, m (in) dedendum for a flat root involute spline profile, m (in) diameter, m (in) major diameter of internal spline, m (in) minor diameter of internal spline, m (in) major diameter of external spline, m (in) minor diameter of external spline, m (in) core diameter of threaded portion of the taper rod, m (in) large diameter of taper pin, m (in) mean diameter of taper pin, m (in) nominal diameter of thread portion, m (in) diameter of shaft, m (in) pitch diameter, m (in) force, kN (lbf) force on the cotter joint, kN (lbf) pressure between hub and key, kN (lbf) force applied in the center of plane of a feather keyed shaft which not change the existing equilibrium but give a couple, kN (lbf) two opposite forces applied on the center plane of a double feather keyed shaft which give two couples, but tending to rotate the hub clockwise, kN (lbf) tangential force, kN (lbf) frictional force, kN (lbf) thickness of key, m (in) minimum height of contact in one tooth, m (in) length of key (also with suffixes), m (in) length of couple (also with suffixes), m (in) length of sleeve, m (in) length of spline, m (in) space width and tooth thickness of spline, m (in) module, mm, m (in) bending moment, N m (lbf in) twisting moment, N m (lbf in) 17.1 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 KEYS, PINS, COTTERS, AND JOINTS 17.2 CHAPTER SEVENTEEN pressure, MPa (psi) tangential pressure per unit length, MPa (psi) maximum pressure where the shaft enters the hub, MPa (psi) pressure at the end of key, MPa (psi) diametral pitch external load, kN (lbf) resistance on the key and on the shaft to be overcome when the hub is shifted lengthwise, kN (lbf) thickness of cotter, m (in) profile displacement, m (in) number of teeth, number of splines stress tensile or compressive (also with suffixes), MPa (psi) nominal bearing stress at dangerous point, MPa (psi) shear stress, MPa (psi) angle of cotter slope, deg angle of friction, deg coefficient of friction (also with suffixes) p p1 p2 pd (or P) Q R t xm z b1 SUFFIXES b c d m p s t bearing compressive design mean pin small end tensile, tangential Particular Formula ROUND OR PIN KEYS pffiffiffiffi pffiffiffiffi d ¼ 3:035 D to 3:45 D The large diameter of the pin key where d and D are in mm pffiffiffiffi pffiffiffiffi d ¼ 0:6 D to 0:7 D where d and D are in in pffiffiffiffi pffiffiffiffi d ¼ 0:096 D to 0:11 D SI ð17-1aÞ USCS ð17-1bÞ SI ð17-1cÞ where d and D are in m STRENGTH OF KEYS Rectangular fitted key (Fig 17-1, Table 17-1) Pressure between key and keyseat FIGURE 17-1 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 Above Up to Key cross section 2 20 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: IS 2048, 1962 36 Keyway radius r2 max L L max 0.16 r max r Chamfer or radius of key Length of key 0.25 0.16 t2 ỵ0.05 0.00 ỵ0.05 0.00 1.8 1.4 3 10 Tolerance on keyway depth t1 Keyway depth In shaft t1 1.2 (nominal) In hub t2 Width b Height h For shaft diameters 45 2.5 1.8 4 10 12 6 17 22 10 50 14 71 0.25 0.35 0.25 3.0 3.5 2.3 2.8 5 12 17 TABLE 17-1 Dimensions (in mm) of parallel keys and keyways 18 90 22 110 3.8 12 38 44 28 140 0.40 0.55 0.40 3.3 10 30 38 þ0.1 À0.0 þ0.1 À0.0 4.0 3.3 22 30 36 160 5.5 3.8 14 44 50 45 180 4.3 16 10 50 58 50 200 4.4 18 11 58 65 56 220 7.5 4.9 20 12 65 75 63 250 0.60 0.80 0.60 8.5 5.4 22 14 75 85 71 280 9.0 5.9 25 14 85 110 32 18 110 130 36 20 130 150 40 22 150 170 45 25 170 200 50 28 200 230 56 32 230 260 63 32 260 290 70 36 290 330 80 40 330 380 90 45 380 440 100 50 440 500 80 320 90 360 100 400 110 400 125 400 1.00 1.30 1.00 ỵ0.15 0.00 þ0.15 À0.00 140 400 160 400 180 400 1.60 2.00 1.60 200 400 220 400 250 400 280 400 2.50 2.95 2.50 10 11 12 13 15 17 19 20 22 25 28 31 6.4 7.4 8.4 9.4 10.4 11.4 12.4 13.4 14.4 15.4 17.4 19.5 28 16 95 110 KEYS, PINS, COTTERS, AND JOINTS 17.3 KEYS, PINS, COTTERS, AND JOINTS 17.4 CHAPTER SEVENTEEN Particular Formula Crushing strength The tangential pressure per unit length of the key at any intermediate distance L from the hub edge (Fig 17-1, Table 17-2) p ¼ p1 À L tan The torque transmitted by the key (Fig 17-1) Mt ¼ p1 DL2 À DL2 tan 2 The general expression for torque transmitted according to practical experience where tan ¼ p1 À p2 p1 ¼ L2 L0 Mt ¼ b1 hDL2 À 18 b1 bL2 ð17-3Þ ð17-4Þ where p2 ¼ 0, when L2 ¼ Lo ¼ 2:25D; tan ¼ For dimensions of tangential keys given here ð17-2Þ p1 h ¼ b1 Lo 4:5D Refer to Table 17-2 Shearing strength The torque transmitted by the key (Fig 17-1) Mt ¼ 1 bDL2 À 1 bL2 2 where tan ¼ The shear stress at the dangerous point (Fig 17-1) 1 ẳ 17-5ị p1 b ẳ Lo 2:25D Mt L2 bð0:5D À 0:11L2 Þ ð17-6Þ TAPER KEY (Fig 17-2, Table 17-3) The relation between the circumferential force Ft and the pressure F between the shaft and the hub F t ẳ 1 F 17-7ị The pressure or compressive stress between the shaft and the hub F ẳ blp 17-8ị The torque Mt ẳ 1 blpD 17-9ị where 1 ẳ coecient of friction between the shaft and the hub ¼ 0:25 FIGURE 17-2 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 KEYS, PINS, COTTERS, AND JOINTS KEYS, PINS, COTTERS, AND JOINTS 17.5 TABLE 17-2 Dimensions (in mm) of tangential keys and keyways Keyway Keyway Shaft diameter, D Height, h Width, b Radius, r Key chamfer, a 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 320 340 360 380 400 420 440 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 34 36 38 40 42 44 30 30 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90 95 102 108 114 129 126 132 2 2 2 2 2 2 3 3 3 3 3 4 4 3 3 3 3 3 3 4 4 4 4 4 4 5 5 Shaft diameter, D 460 480 500 520 540 560 580 600 620 640 660 680 700 720 740 760 780 800 820 840 860 880 900 920 940 960 980 1000 Height, h 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 Width, b Radius, r Key chamfer, a 138 144 150 156 162 168 174 180 186 192 198 204 210 216 222 228 234 240 246 252 258 264 270 276 282 288 294 300 5 5 5 6 6 6 6 6 6 6 8 8 8 6 6 6 7 7 7 7 7 7 7 9 9 9 Notes: (1) The dimensions of the keys are based on the formula: width 0.3 shaft diameter, and thickness ¼ 0.1 shaft diameter; (2) if it is not possible to fix the keys at 1208, they may be fixed at 1808; (3) it is recommended that for an intermediate diameter of shaft, the key section shall be the same as that for the next larger size of the shaft in this table Source: IS 2291, 1963 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 KEYS, PINS, COTTERS, AND JOINTS TABLE 17-3 Dimensions (in mm) of taper keys and keyways Shaft Key Above Up to and including 10 12 17 22 30 38 44 50 58 65 75 85 95 110 130 150 170 200 230 260 290 330 380 440 10 12 17 22 30 38 44 50 58 65 75 85 95 110 130 150 170 200 230 260 290 330 380 440 500 Width, b (h9) 10 12 14 16 18 20 22 25 28 32 36 40 45 50 56 63 70 80 90 100 Height, h 8 10 11 12 14 14 18 10 25 22 25 28 32 32 36 40 45 50 Keyway in shaft and hub Chamfer or radius r1 , 0.16 — 0.25 — 0.40 — 0.60 — 1.00 — 1.60 — 2.50 Keyway width, b (D10) 10 12 14 16 18 20 22 25 28 32 36 40 45 50 56 63 70 80 90 100 Depth in shaft, t1 Tolerance on t1 Depth in hub, t2 1.2 1.8 2.5 3.0 3.5 4.0 5.0 5.0 5.5 6.0 7.0 7.5 8.5 9.0 10.0 11.0 12.0 13.0 15.0 17.0 19.0 20.0 22.0 25.0 28.0 31.0 ỵ0.05 0.5 0.9 1.2 1.7 2.1 2.5 2.5 2.5 2.9 3.4 3.3 3.8 4.8 4.3 5.3 6.2 7.2 8.2 9.2 10.1 12.1 11.1 13.1 14.1 16,1 18.1 ỵ0.10 ỵ0.15 Tolerance on t2 Radius, r2 , max 0.16 ỵ0.1 0.25 0.40 ỵ0.2 0.60 1.00 ỵ0.3 1.60 — Source: IS 2292, 1963 17.6 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 2.50 KEYS, PINS, COTTERS, AND JOINTS KEYS, PINS, COTTERS, AND JOINTS Particular 17.7 Formula The necessary length of the key l¼ The axial force necessary to drive the key home (Fig 17-2) Fa ẳ F ỵ F ẳ 22 F ỵ F tan 1.60 1.59 1.60 1.54 0.20 1.50 0.30 Max Min Max Min amax rnom c dh6 2.00 1.94 0.25 2.00 0.35 2.00 1.99 2.01 2.00 1.50 2.44 0.30 2.50 0.40 2.50 2.49 2.51 2.50 2.5 3.00 2.94 0.40 3.00 0.50 3.00 2.99 3.01 3.00 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 1.50 1.46 0.20 Max Min Source: IS 549, 1974 a dh10 1.5 dnom 2.00 1.96 0.25 2.50 2.46 0.30 2.5 3.00 2.94 0.35 TABLE 17-17 Dimensions (in mm) for solid and split taper pins Source: IS 2393, 1980 dh11 1.61 1.60 Max Min dm6 1.5 TABLE 17-16 Dimensions (in mm) for cylindrical pins 4.00 3.95 0.40 4.00 3.92 0.50 4.00 0.63 4.00 3.98 4.01 4.00 5.00 4.95 0.63 5.00 4.92 0.63 5.00 0.80 5.00 4.98 5.01 5.00 6.00 5.95 0.80 6.00 5.92 0.80 6.00 6.00 5.98 01 6.00 8.00 7.94 1.00 8.00 7.91 1.00 8.00 1.60 8.00 7.98 8.02 8.01 10.00 9.94 1.20 10 10.00 9.91 1.20 10.00 2.00 10.00 9.98 10.02 10.01 10 12.00 11.93 1.60 12 12.00 11.89 1.60 12.00 2.50 12.00 11.97 12.02 12.01 12 Nominal diameter, dnom , mm 16.00 15.63 2.00 16 16.00 15.89 2.00 16.00 3.00 16.00 15.97 16.02 16.01 16 20.00 19.92 2.50 20 20.00 19.87 2.50 20.00 3.50 20.00 19.97 20.02 20.01 20 25.00 24.92 3.00 25 25.00 24.87 3.00 25.00 4.00 25.00 24.97 25.02 25.01 25 32.00 31.90 4.00 32 32.00 31.84 4.00 32.00 5.00 32.00 31.96 32.02 32.01 32 40.00 39.90 5.00 40 40.00 39.84 5.00 40.00 6.30 40.00 39.96 40.02 40.01 40 50.00 49.90 6.30 50 50.00 49.84 6.30 50.00 8.00 50.00 49.96 50.02 50.01 50 KEYS, PINS, COTTERS, AND JOINTS 17.21 KEYS, PINS, COTTERS, AND JOINTS 17.22 CHAPTER SEVENTEEN Particular The axial stress in the sleeve Formula ¼ TORQUE The shear due to twisting moment applied For the design of hollow shaft subjected to torsion F 2 ðd3 À d2 ị 2d3 d2 ịdm Mt ẳ d d m Refer to Chapter 14 17-41ị 17-42ị Taper joint and nut F t ẳ d2 c ð17-43Þ The bearing resistance offered by the collar F c ¼ 2 ðd À d2 Þ ð17-44Þ The diameter of the taper d2 d2 > dnom ð17-45Þ The tensile stress in the threaded portion of the rod (Fig 17-8) without taking into consideration stress concentration FIGURE 17-8 Tapered joint and nut Provide a taper of in 50 for the length (l À l1 Þ Knuckle joint The tensile stress in the rod (Fig 17-9) The tensile stress in the net area of the eye Stress in the eye due to tear of t ẳ 4F d 17-46ị t ẳ F d4 d2 ịb 17-47ị tn ẳ F bd4 d2 Þ 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 ð17-48Þ KEYS, PINS, COTTERS, AND JOINTS KEYS, PINS, COTTERS, AND JOINTS Particular 17.23 Formula FIGURE 17-9 Knuckle joint for round rods Tensile stress in the net area of the fork ends F 2aðd4 À d2 Þ ð17-49Þ tr ¼ F 2aðd4 À d2 Þ ð17-50Þ Compressive stress in the eye due to bearing pressure of the pin e ¼ F d2 b ð17-51Þ Compressive stress in the fork due to the bearing pressure of the pin c ¼ F 2d2 a ð17-52Þ Stress in the fork ends due to tear of Shear stress in the knuckle pin i ¼ ¼ 2F d2 The maximum bending moment, Fig 17-9 (panel b) Mb ¼ The maximum bending stress in the pin, based on the assumption that the pin is supported and loaded as shown in Fig 17-9b and that the maximum bending moment Mb occurs at the center of the pin b ¼ The maximum bending moment on the pin based on the assumption that the pin supported and loaded as shown in Fig 17-10b, which occurs at the center of the pin Mb ¼ The maximum bending stress in the pin based on the assumption that the pin is supported and loaded shown in Fig 17-10b b ¼ ð17-53Þ Fb ð17-54Þ 4Fb d2 ð17-55Þ F b a ỵ approx:ị 43b ỵ 4aÞF 3d2 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 ð17-56Þ ð17-57Þ KEYS, PINS, COTTERS, AND JOINTS 17.24 CHAPTER SEVENTEEN Particular Formula COTTER The initial force set up by the wedge action F ẳ 1:25Q 17-58ị The force at the point of contact between cotter and the member perpendicular to the force F H ¼ F tan ỵ ị 17-59ị The thickness of cotter t ẳ 0:4D 17-60ị The width of the cotter b ẳ 4t ¼ 1:6D ð17-61Þ Cotter joint The axial stress in the rods (Fig 17-10) Axial stress across the slot of the rod ẳ ẳ 4F d 2 d1 17-62ị 4F À 4d1 t ð17-63Þ Tensile stress across the slot of the socket ¼ The strength of the cotter in shear F ẳ 2bt 17-65ị Shear stress, due to the double shear, at the rod end ẳ F 2ad1 17-66ị ẳ F 2cðd4 À d1 Þ ð17-67Þ 4F À d1 Þ ð17-68Þ Shear stress induced at the socket end The bearing stress in collar Crushing strength of the cotter or rod 4F 2 ðd3 À d1 Þ À 4tðd3 d1 ị c ẳ d2 F ẳ d1 tc FIGURE 17-10 Cotter joint for round rods 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 ð17-64Þ ð17-69Þ KEYS, PINS, COTTERS, AND JOINTS KEYS, PINS, COTTERS, AND JOINTS Particular Crushing stress induced in the socket or cotter The equation for the crushing resistance of the collar 17.25 Formula c ẳ F d4 d1 ịt 17-70ị Fẳ 2 ðd2 À d1 Þ c ð17-71Þ Shear stress induced in the collar ẳ F d1 e 17-72ị Shear stress induced in the socket ¼ F d1 h ð17-73Þ The maximum bending stress induced in the cotter assuming that the bearing load on the collar in the rod end is uniformly distributed while the socket end is uniformly varying over the length as shown in Fig 17-10b b ¼ Gib and cotter joint (Fig 17-11) The width b of both the Gib and Cotter is the same as far as a cotter is used by itself for the same purpose (Fig 17-11) The design procedure is the same as done in cotter joint Fig 17-10 FIGURE 17-11 Gib and cotter joint for round rods FIGURE 17-12 Coupler or turn buckle Fd1 ỵ 2d4 ị 4tb2 17-74ị Threaded joint COUPLER OR TURN BUCKLE Strength of the rods based on core diameter dc , (Fig 17-12) d c t ð17-75Þ The resistance of screwed portion of the coupler at each end against shearing F ¼ ad ð17-76Þ From practical considerations the length a is given by a ẳ d to 1.25d for steel nuts 17-77aị 17-77bị The strength of the outside diameter of the coupler at the nut portion a ¼ 1:5d to 2d for cast iron F ẳ d1 d ịt F¼ 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 ð17-78Þ KEYS, PINS, COTTERS, AND JOINTS 17.26 CHAPTER SEVENTEEN Particular Formula 2 ðd À d2 Þt The outside diameter of the turn buckle or coupler at the middle is given by the equation F¼ The total length of the coupler l ¼ 6d ð17-79Þ ð17-80Þ REFERENCES Maleev, V L., and J B Hartman, Machine Design, International Textbook Company, Scranton, Pennsylvania, 1954 Shigley, J E., and L D Mitchell, Mechanical Engineering Design, McGraw-Hill Book Company, New York, 1983 Faires, V M., Design of Machine Elements, The Macmillan Company, New York, 1965 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College Cooperative Society, Bangalore, India, 1962 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986 Juvinall, R C., Fundamentals of Machine Component Design, John Wiley and Sons, New York, 1983 Deutschman, A D., W J Michels, and C E Wilson, Machine Design—Theory and Practice, Macmillan Publishing Company, New York, 1975 Bureau of Indian Standards 10 SAE Handbook, 1981 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: MACHINE DESIGN DATABOOK CHAPTER 18 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION SYMBOLS5;6;7 Ab Abr Ac Ag Ar A d d2 d1 dc dm ¼ d2 D D1 D2 Db Di Do e Eb , Eg F Fa Ff Fi Ft h area of cross section of bolt, m2 (in2 ) area of base of preloaded bracket, m2 (in2 ) core area of thread, m2 (in2 ) loaded area of gasket, m2 (in2 ) stress area, m2 (in2 ) shear area, m2 (in2 ) nominal diameter of screw m (in) major diameter of external thread (bolt), m (in) pitch diameter of external thread (bolt), m (in) minor diameter of external thread (bolt), m (in) mean diameter of thrust collar, m (in) mean diameter of square threaded power screw, m (in) diameter of shaft, m (in) major diameter of internal thread (nut), m (in) minor diameter of internal thread (nut), m (in) pitch diameter of internal thread (nut), m (in) diameter of bolt circle, m (in) inside diameter of a pressure vessel or cylinder, m (in) mean diameter of inside screw of differential or compound screw, m (in) mean diameter of outside screw of differential or compound screw, m (in) eccentricity, m (in) moduli of elasticity of bolt and gasket, respectively, GPa (Mpsi) permissible load on bolt, kN (lbf ) tightening load on the nut, kN (lbf ) applied or external load, kN (lbf ) final load on the bolt, kN (lbf ) initial load due to tightening, kN (lbf ) preload in each bolt, kN (lbf ) tangential force, kN (lbf ) thickness of a pressure vessel, m (in) thickness of a cylinder, m (in) 18.1 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 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.2 h2 ho CHAPTER EIGHTEEN thickness of the flange of the cylindrical pressure vessel, m (in) depth of tapped hole (Fig 18-1), m (in) FIGURE 18-1 Flanged bolted joint i I K K l lc lg L Mb Mt n p pc P t t1 W o , i c i , o a b 0b number of threads in a nut number of bolts moment of inertia of bracket base, area (Fig 18-6), m4 or cm4 (in4 ) constant (Eq (18-4a)) stress concentration factor lever arms (with suffixes), m (in) distance from the inside edge of the cylinder to the center line of bolt, m (in) lead, m (in) required length of engagement of screw or nut (also with suffixes), m (in) gasket thickness, m (in) length of bolt nut to head (Fig 18-2), m (in) bending moment, N m (lbf in) twisting moment, N m (lbf in) factor of safety pressure, MPa (psi) circular pitch of bolts or studs on the bolt circle of a cylinder cover, m (in) pitch of thread, m (in) thread thickness at major diameter, m (in) thread thickness at minor diameter, m (in) axial load, kN (lbf ) helix angle, deg respective helix angles of outside and inside screws of differential or compound screws, deg friction angle, deg half apex angle, deg coefficient of friction between nut and screw coefficient of collar friction respective coefficient of friction in case of differential or compound screw efficiency stress (normal), MPa (psi) allowable stress, MPa (psi) bending stress, MPa (psi) bending stress due to eccentric load [Eq (18-61)] allowable bearing pressure between threads of nut and screw, MPa (psi) 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 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION c d w a w 18.3 compressive stress, MPa (psi) design stress, MPa (psi) working stress, MPa (psi) applicable shear stress, MPa (psi) allowable shear stress, MPa (psi) permissible working shear stress, MPa (psi) SUFFIXES vertical horizontal v h Particular Formula SCREWS The empirical formula for the proper size of a set screw d¼ The maximum safe holding force of a set screw F ẳ 54;254d 2:31 D ỵ mm where D in mm ð18-1Þ SI ð18-2aÞ USCS ð18-2bÞ where F in kN and d in m F ¼ 2500d 2:31 where F in lbf and d in in Applied torque Mt ¼ 0:2Fa nominal diameter of bolt) 18-3ị Ff ẳ KFa ỵ Fi 18-4ị Gasket joint (Fig 18-2) Final load on the bolt E b Ab L 7 where K ẳ 4Eb Ab Eg Ag ỵ L lg Refer also to Table 18-1 for values of K FIGURE 18-2 Gasket joint 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 ð18-4aÞ THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.4 CHAPTER EIGHTEEN Particular Formula TABLE 18-1 Values of K for use in Eq (18-4) Type of joint K Soft, elastic gasket with studs Soft gasket with through bolts Copper asbestos gasket Soft copper corrugated gasket Lead gasket with studs Narrow copper ring Metal-to-metal joint 1.00 0.90 0.60 0.40 0.10 0.01 0.00 According to Bart, the tightening load for a screw of a steamtight, metal-to-metal joint F ¼ 2804:69d SI ð18-5aÞ USCS ð18-5bÞ SI ð18-6aÞ USCS ð18-6bÞ SI ð18-7aÞ where F in kN and d in m F ¼ 1600d where F in lbf and d in in Tightening load for screw of a gasket joint F ¼ 1402:34d where F in kN and d in m F ¼ 8000d where F in lbf and d in in Cordullo’s equation for the tightening load on the nuts F ¼ w ð0:55d À 6:45 Â 10À3 dÞ where F in kN, w in MPa, and d in m F ẳ w 0:55d 0:036dị USCS 18-7bị where F in lbf, w in psi, and d in in Bolted joints (Fig 18-2) The flange thickness of the cylinder or pressure vessel j h2 ¼ 1:25d to 1:5d < 1:1h to 1:25h 18-8ị The bolt diameter d ẳ 0:67h to 0:8h ð18-9Þ Circular pitch of the bolts or studs on the cylinder cover to ensure water and steamtight joint pc ¼ 7d for pressure from to 0.33 MPa (0 to 48 psi) as per American Navy Standards ð18-10Þ pc ¼3:5d for pressure from 1.2 MPa (175 psi) to 1.37 MPa (200 psi) 18-11ị pc ẳ 3d 18-12ị for tight joint 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 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION Particular The average stress for screw for sizes from 12.5 to 75 mm 18.5 Formula av ẳ 490:33 d SI 18-13aị USCS ð18-13bÞ where av in MPa and d in m av ¼ 2;800;000 d where av in psi and d in in d ẳ 17;537:4d ỵ 11 for rough joint SI 18-14aị USCS 18-14bị s ẳ 33;828:9d ỵ 17:3 for faced joint SI Unwin’s formula for allowable stresses in bolts of ordinary steel to make a fluidtight joint ð18-14cÞ where d in MPa and d in m d ¼ 6030d ỵ 1600 where d in psi and d in in where d in MPa and d in m d ẳ 3070d ỵ 2500 USCS 18-14dị where d in psi and d in in TENSION BOLTED JOINT UNDER EXTERNAL LOAD Spring constant of clamped materials and bolt (Fig 18-3A) The basic equations for deflection (), and spring constant (k) of a tension bar/bolt subject to tension load 1 ẳ ỵ k k1 k 18-15aị ẳ Fl AE 18-15bị kẳ The spring constant or stiness of the threaded and unthreaded portion of a bolt is equivalent to the stiffness of two springs in series F AE ¼ l ð18-15cÞ The effective spring constant/total spring rate in case of long bolt consisting of the threaded and unthreaded portion having different area of crosssections, the clamped two or more materials of two or more different elasticities which act as spring with different stiffness sections in series 1 1 ẳ ỵ ỵ ỵ ỵ kelf k1 k2 k3 kn ð18-15dÞ Spring constant of the clamped material km ¼ Am Em Deff Em ¼ l l ð18-15eÞ Spring constant of the threaded fastener l l lt l l ẳ t ỵ ẳ t ỵ unt kb At Eb Ab Eb At Eb Ab Eb 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 ð18-15f Þ THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.6 CHAPTER EIGHTEEN Particular Formula FIGURE 18-3A FIGURE 18-3B Bolt joint diagram due to external load acting on the joint Approximate effective area of clamped material Am ¼ ðD À d Þ eff where Deff d lt lunt ¼ effective diameter, m ¼ round bolt of diameter equal to shank, m ¼ threaded length of bolt, m ¼ unthreaded portion of bolt length, m PRELOADED BOLT (Fig 18-3B) The external load Fa ¼ Fab ỵ Fam The bolted joint in Fig 18-3A subjected to external load Fa is such that the common deflection is given by ¼ The load shared by bolt The resultant/total bolt load 18-15gị Fb Fm ẳ kb km Fab ẳ 18-15hị kb F kb ỵ km a Fb ẳ Fab ỵ Fi ẳ Fi ỵ kb ẳ 18-15iị kb F ỵ Fi 18-15jị kb ỵ km a ẳ CFa ỵ Fi The resultant load on the clamped material Fm ¼ Fab À Fi ¼ Fi À km ẳ 18-15kị km F Fi 18-15lị kb ỵ km a ẳ CịFa Fi where C is called the joint constant or stiffness parameter Fm ¼ portion of load Fa taken by member/material, kN Ft ¼ preload, kN 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 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.7 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION Particular The joint constant or stiness parameter Formula kb kb ỵ km C¼ or The preload to prevent joint separation occurs when Fm ẳ Fao ẳ 1ỵ km kb 18-15mị Fi ẳ CịFao The external load required to separate joint C¼ The tensile stress in the bolt Preload under static and fatigue loading as per the recommendation of R, B and W,a and Bowman where Fao ¼ external load that cause separation of joint b ¼ Fi 1ÀC Fb CFa Fi ẳ ỵ At At At 18-15nị 18-15oị where At ¼ tensile stress area, m2 or mm2 0:75Fp for reused bolt connections Ft ¼ 0:90Fp for permanent bolt connections ð18-15pÞ where Fp is proof load, N The proof stress load that has to be used in Eq (18-15p) Fp ẳ At sp 18-15qị where sp ẳ proof strength, taken from tables 18-5c and 18-5d sp % 0:85sy The load factor n¼ Fao Fa The load factor guarding against joint separation nẳ Fi Fa Cị or Fao ẳ nFa 18-15rị 8-15sị GASKET JOINTS For design of gasket bolted joint Refer to Chapter 16 under Bolt loads in gasket joints PRELOADED BOLTS UNDER DYNAMIC LOADING The mean forces felt by the bolt The alternating forces felt by the bolt a Fmn ẳ Fal ẳ Fb ỵ Fi Fb À Fi Russel, Bardsall and Ward Corp., Helpful Hints for Fastener Design and Application, Mentor, Ohio 1976, p 42 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 ð18-15tÞ ð18-15uÞ THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.8 CHAPTER EIGHTEEN Particular The stress due to the preload Fi The fatigue safety factor by using modified Goodman criterion The alternating component of bolt stress Formula i ¼ Kfm Fi Ai ð18-15vÞ nf ¼ se ðsut À i ị se m i ị ỵ sut a 18-15wị a ẳ Fb Fi kb Fa CFa ẳ ẳ 2At kb ỵ km 2At 2At 18-16aị The mean stress m ẳ a ỵ The factor of safety according to the Goodman criterion nẳ Fi CP Fi ẳ ỵ At 2At At sa a 18-16cị sa ẳ sm Fi At sm ¼ sut À sa se Solving of Eqs (18-16c) and (18-16d) simultaneously sa ẳ sut 1ỵ 18-16bị Fi At sut se sy sy ẳ max m ỵ a The factor of safety on the basis of yield strength n¼ For specification of SAE, ASTM and ISO standard steel bolts ho ¼ 1:25d in steel castings ð18-16eÞ ð18-16f Þ Refer to Tables 18-5c and 18-5d The depth of tapped hole (Fig 18-2) ð18-16dÞ 18-16gị 18-16hị ho ẳ 1:50d to 1:75d in cast iron 18-17ị ho ẳ 1:75d to 2d in aluminum 18-18ị The distance l from the inside edge of the cylinder to the center line of bolts (Fig 18-2) l ¼ 1:25d to 1:5d 18-19ị The diameter of bolt circle Db ẳ D1 ỵ 2d 18-20ị The safe load on each bolt F ẳ A r d 18-21ị The number of bolts iẳ D2 p b 4F 18-22ị Another expression for the number of bolts iẳ Db pc 18-23ị 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 THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION Particular 18.9 Formula TABLE 18-2 Approximate bolt tension and torque values TABLE 18-3 Load and working stress for metric coarse threads Minimum bolt tension Equivalent torque Bolt size, mm kN lbf kN m lbf ft 12.7 15.9 19.6 22.2 25.4 21.6 31.8 51.2 76.9 113.9 139.7 189.1 225.4 286.9 11,500 17,300 25,600 31,400 42,500 50,600 64,500 1.353 2.442 4.835 6.374 9.620 13.013 18.289 1,000 1,800 3,570 4,700 7,090 9,600 13,500 Major diameter, d, mm Stress Design stress, w area, Ar , MPa psi mm2 kN 16 20 24 30 36 42 48 56 0.016 0.025 0.035 0.056 0.082 0.112 0.147 0.203 2.97 667 5.59 1,260 9.59 2,160 18.04 4,060 30.89 6,940 48.35 10,870 71.10 16,000 111.80 25,130 18.9 22.8 27.2 32.2 37.1 43.1 48.3 55.2 2,740 3,300 3,950 4,670 5,380 6,250 7,000 8,000 Permissible load lbf Stress in tensile bolt Seaton and Routhwaite formula for working stress for bolt made of steel containing 0.08 to 0.25% carbon and with diameter of 20 mm and over Applied load w ẳ CAr ị0:418 18-24ị Refer to Table 18-2 for bolt tension and torque values and Table 18-3 for w Fa ẳ CAr ị1:418 18-25ị where C ¼ 7:8 Â 108 (5000) for carbon steel bolts of u ¼ 414 MPa (60 kpsi) ¼ 23:3 Â 108 (15,000) for alloy–steel bolts ¼ 0:33 Â 108 (1000) for bronze bolts The values of C inside parentheses are for US Customary System units, and values without parentheses are for SI units Rotsher’s pressure-cone method for stiffness calculation of Fastenera The elongation of frustum of a cone (Fig 18-3C) ¼ Fa 2t tan ỵ D dịD ỵ dị ln 19-25aị Ed tan 2t tan ỵ D ỵ dịD dị The spring stiness of the frustum kẳ Fa ẳ Ed tan 2t tan ỵ D dịD ỵ dị ln 2t tan ỵ D ỵ dịD dị a ð18-25bÞ Courtesy: Shigley J E and C R Mischke, Mechanical Engineering Design, 5th Edn., McGraw-Hill Publishing Company, New York, 1989 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 ... 12 12 — 17 17 17 — 22 22 — 30 30 — 8 10 10 10 — 12 12 — 17 17 — 22 22 22 — 30 30 — 38 38 — 10 10 12 12 12 16 17 17 17 22 22 22 30 30 30 30 38 38 38 38 38 38 10 12 12 17 17 17 17 22 22 22 30 30 ... so 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 3. 5 Pin diameter, d 7. 629 9. 32 4 10 .37 9 12. 736 14.460 17.478 20 . 738 22 .484... 10.5 52 12. 105 15.5 52 19.116 20 .5 52 22. 265 25 .5 52 27 .30 8 28 .31 6 30 .5 52 32 . 34 0 35 .5 52 37 .36 5 38 .38 7 40.5 52 42. 38 4 45.5 52 48. 424 50.5 52 52. 4 13 55.5 52 58.448 60.5 52 62. 434 65.5 52 62. 464 70.5 52 72. 449