THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION Particular The total frictional torque for V-thread, including collar friction torque The mean diameter of collarà Substituting the value of dc in Eq (18-30a) and after simplifying 18.13 Formula d dc cos C Mt ¼ W B @ tan A ỵ c 1 cos tan ỵ dc ẳ d ỵ 1:5dị=2 M t ¼ K Fi d ð18-30aÞ ð18-30bÞ ð18-30cÞ where K is the torque factor W ¼ Fi ¼ preload, N (lbf) The torque factor tan ỵ d cos C ỵ 0:625 K ẳ B @ A c 2d À tan cos ð18-30dÞ where d2 ¼ dm Refer to Table 18-5b for K tan Wl ẳ tan ỵ ị 2Mt The eciency of square thread neglecting collar friction ¼ The efficiency formula for an angular-type thread with half apex angle and an allowance for nut or end friction on a radius rc ¼ The efficiency formula for square thread d2 tan ẳ tan ỵ d ỵ c dc tan ẳ d2 tan tan ỵ = cos d ỵ c dc tan = cos l ẵd2 tan ỵ ị ỵ c dc ð18-31Þ ð18-32Þ ð18-33Þ ð18-34Þ LOADING Lowering the load The tangential force at mean or pitch radius r2 ¼ rm The frictional torque at mean or pitch radius r2 ¼ rm The condition for overhauling for square threads Ft ẳ W tan ỵ ị Mt ẳ 18-35ị Wd2 tan ị 18-36ị d2 ỵ c dc d2 À c dc ð18-37Þ tan ! Since the flat faces of hexagonal nut is same as the diameter of washer face which is 1.5 times the nominal diameter d 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 18.14 CHAPTER EIGHTEEN Particular Formula Differential screws (Fig 18-3G) The loading efficiency of a differential screw, not including the collar friction ¼ Do tan o À Di tan i tan o þ o tan i þ i Do À Di À o tan o À i tan i ð18-38Þ Compound screws The loading efficiency of a compound screw, not including collar friction The number of threads necessary in the nut The length of nut ¼ i¼ Do tan o þ Di tan i tan o þ o tan i þ i Do þ Di À o tan o À i tan i 4W 0b ðd À di2 ị ln ẳ iP ẳ 4WP 0b d À d1 Þ ð18-39Þ ð18-40Þ ð18-41Þ TABLE 18-5c Metric mechanical-property classes for steel bolts, screws, and studsa Size range inclusive Minimum proof strength, sp MPa 4.6 M5–M36 225 400 240 Low or medium carbon 4.8 M1.6–M16 310 420 340 Low or medium carbon 5.8 M5–M24 380 520 420 Low or medium carbon 8.8 M16–M36 600 830 660 Medium carbon, Q and T 9.8 M1.6–M16 650 900 720 Medium carbon, Q and T 10.9 M5–M36 830 1040 940 Low-carbon martensite, Q and T 12.9 M1.6–M36 970 1220 1100 Property class a Minimum tensile strength, st MPa Minimum yield strength, sy MPa Material Alloy, Q and T The thread length for bolts and cap screws is L 125 > 2d þ < LT ¼ 2d þ 12 125 < L 200 > : 2d ỵ 25 L > 200 where L is the bolt length The thread length for structural bolts is slightly shorter than given above 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 Head marking THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.15 TABLE 18-5d Grade identification marks and mechanical properties of bolts and screws Identifier Grade A SAE Grade Size range (in) Min strength (103 psi) Proof Tensile Yield Material and treatment to 11 33 60 36 Low or medium carbon to 11 to 33 55 60 74 36 57 Low carbon Low or medium carbon to 11 33 60 36 SAE Grade 4 4 to 11 65 115 100 SAE Grade and to 85 120 92 ASTM A449 SAE Grade 5, ASTM A449 11 to 11 74 105 81 ASTM A449 13 to 55 90 58 C SAE Grade 5.2 to 85 120 92 Low-carbon martensite, Q and T D ASTM A325, Type 1 Medium carbon, Q and T ASTM A307 SAE Grade B to 85 120 92 11 to 11 74 105 Medium carbon, Q and T 81 Medium carbon, cold drawn E ASTM A325, Type to 11 to 11 85 74 120 105 92 81 Low carbon martensite, Q and T F ASTM A325, Type to 85 120 92 Weathering steel, Q and T 11 to 11 74 105 81 ASTM A354, Grade BC to 21 105 125 109 23 to 4 G 95 115 99 Alloy-steel, Q and T SAE Grade to 11 105 133 115 Medium carbon alloy, Q and T SAE Grade 4 to 11 120 150 130 Medium carbon alloy, Q and T ASTM A354, Grade BD to 11 120 150 130 Alloy-steel, Q and T J SAE Grade 8.2 to 120 150 130 Low-carbon martensite, Q and T K ASTM A490, Type 1 to 11 120 150 130 Alloy-steel, Q and T L ASTM A490, Type to 11 120 150 130 Weathering steel, Q and T H I 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 18.16 CHAPTER EIGHTEEN Particular The required length of engagement for adequate shear strength (assuming that the load is distributed over the threads in contact) Neglecting the radial clearance between threads, or allowance at the major and minor diameters and considering the threads as a series of collars the equation for thread engagement The normal length of thread engagement as per Indian standard Formula lc ẳ nPF A lescrewị ẳ lenutị ẳ ð18-42Þ nPF d1 t1 ðscrewÞ ð18-43Þ nPF dt ðnutÞ ð18-44Þ leNðminÞ ¼ 8:92Pd 0:2 SI ð18-45aÞ SI ð18-45bÞ SI ð18-46aÞ SI ð18-46bÞ where leN , P, and d in m leNðminÞ ¼ 2:24Pd 0:2 where leN , P, and d in mm leNmaxị ẳ 26:67Pd 0:2 where leN , P, and d in m leNmaxị ẳ 6:7Pd 0:2 where leN , P, and d in mm Note: If leN has to be between the limits, the length of the thread is said to be normal ðNÞ If leN has to be below the minimum level, length of thread is said to be short ðSÞ If leN has to be above the maximum level, length of thread is said to be long ðLÞ Eccentric loading The load on bolt 1, Fig 18-5 (panel a) The general expression for the load carried by ith bolt, Fi The maximum load on the bolt, Fig 18-5(b) F1 ẳ Fll1 la b cos ị ẳF 2 2 l1 ỵ l2 ỵ l3 ỵ l4 4a2 ỵ 2b2 Fi ẳ F Fmax ẳ The maximum load on the bolt, Fig 18-5(c) 2lða À b cos ị 2a2 ỵ b2 ịi 2Fla ỵ bị 2a2 þ b2 Þi " 2Fl a þ b cos Fmax ẳ 18-47ị 18-48ị 18-49ị 1808 i # 2a2 ỵ b2 Þi 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 ð18-50Þ THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION Particular 18.17 Formula FIGURE 18-5 Fastening of a flanged bearing Fastening of a bracket Bracket with no preload Fll1 2 ỵ l2 ỵ l3 ị 18-51ị F2 ẳ Fll2 2 2l1 ỵ l2 ỵ l3 ị 18-52ị F3 ẳ Fll3 2 2l1 ỵ l2 ỵ l3 ị 18-53ị F1 ẳ Tensile load taken by the bolts, Fig 18-6(a) 2ðl1 Shear stresses (i) If shear load is taken completely by the lug, shear load on lug is given by F1 ẳ F 18-54ị (ii) If shear load is taken completely by the bolt shear load on each bolt is given by Fb ẳ F i 18-55ị (iii) If shear load is shared equally between the bolt and the lug F1 ẳ F 18-56ị Fb ¼ F 2i ð18-57Þ Shear load due to the eccentricity e, Fig 18-6(b), in each bolt is given by Fex Fei ẳ P i2 xi 18-58ị where xi ẳ distance between the center of bolts and the center of the particular bolt Resultant shear load Fex Fr ¼ Fb or Fb ị ỵ P i2 xi 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 ð18-59Þ THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.18 CHAPTER EIGHTEEN Particular Formula FIGURE 18-6 Preloaded bracket Preloaded bracket Compression stress in contact area between the bracket base and the wall, Fig 18-6(c) c ẳ iFi Ac 18-60ị Bending stress due to eccentric load, Fig 18-6(d) 0b ¼ Mb c1 Flc1 ¼ Ic Ic ð18-61Þ Resultant compressive stress in the contact area 0c ¼ iFi Mb c1 iFi Flc1 À ¼ À Ac Ic Ac Ic ð18-62Þ Tensile stress in any individual bolt is given by 0b ¼ Fi Mb cb þ Ab Ic ð18-63Þ Fi > Mb c1 Ac iIc ð18-64Þ With a 25% margin on the preload to account for overloads, condition to avoid separation of the base and wall Fi ẳ 1:25Mb c1 Ac iIc 18-65ị Bolt load taking into consideration 25% margin on the preload to account for overloads Fb ẳ 1:25Mb c1 Ac Mb cb ỵ iIc Ic ð18-66Þ Condition to avoid separation of the base and wall 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 With an additional horizontal load Fh , the preload Fi is given by 18.19 Formula Fi ¼ 1:25Mb c1 Ac Fh ặ iIc i 18-67ị where (ỵ) is used when Fh is away from the wall and (À) when Fh is toward the wall 1:25Mb c1 Ac Fh Mb cb Fh Ab ặ ỵ ặ iIc i Ic Ac With the addition of a horizontal load Fh , the bolt load is given by Fb ¼ Moment on the bracket Mb ẳ Fl ặ Fh e0 18-69ị M x F i ẳ P1 2i xi ð18-70Þ ð18-68Þ Shear loads Shear load due to the eccentricity e in each of the bolts with no horizontal load where M1 ¼ Fe À Mb c1 p a2 ỵ b2 16Ic P 0:25Mb x0i c1 A2 b À Ic A c ð88-70aÞ where x0i ¼ distance of the center of a particular bolt to the center of the base of the bracket Shear load due to eccentricity e in each of the bolts with a horizontal load, Fh M x F i ¼ P1 2i xi ð18-71Þ where " 0:25Mb c1 Fh p a2 ỵ b2 ặ M1 ẳ Fe Ic Ac Ab À Ac Vertical applied load due to the friction component of the preload Fv ¼ Condition for the nonexistence of the support for the shearload F