TORQUE AND TENSION IN FASTENERS Machinery's Handbook, 31st Edition
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Table 4. Torque Coefficients K for Metric Hexagon Head Bolt and Nut Fine Screw Threads Coefficient of Friction
Between Bearing Surfaces, μ w
Between Threads, μ s
0.08
0.10
0.12
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.08 0.10 0.12 0.15 0.20 0.25 0.30 0.35 0.40 0.45
0.106 0.117
0.118 0.130 0.148 0.177 0.207 0.237 0.267 0.296 0.129 0.141 0.158 0.188 0.218 0.248 0.278 0.307
0.326 0.337 0.348 0.364 0.391 0.418 0.445 0.472 0.500
0.128 0.140 0.151 0.169 0.199 0.229 0.259 0.288 0.318 0.144 0.156 0.168 0.186 0.215 0.245 0.275 0.305 0.334 0.171 0.183 0.195 0.213 0.242 0.272 0.302 0.332 0.361 0.198 0.210 0.222 0.240 0.270 0.299 0.329 0.359 0.389 0.225 0.237 0.249 0.267 0.297 0.326 0.356 0.386 0.416 0.252 0.264 0.276 0.294 0.324 0.353 0.383 0.413 0.443 0.279 0.291 0.303 0.321 0.351 0.381 0.410 0.440 0.470 0.306 0.318 0.330 0.348 0.378 0.408 0.437 0.467 0.497
0.527 Values in the table are average values of torque coefficient calculated using Equations (13) and (14) for K and D w ; diameters d of 8, 10, 12, 16, 20, 24, 30, and 36 mm; and selected respective pitches P and pitch diameters d 2 according to JIS B 0207 thread standard (ISO 724). Dimension D i was obtained for a Class 1 fit without chamfer from JIS B 1001, Diameters of Clearance Holes and Counterbores for Bolts and Screws (equivalent to ISO 273-1979). The value of D o was obtained by multiplying the reference dimension from JIS B 1002 (small type series), width across the flats of the hexagon head, by 0.95. In Equation (17) , σ y is the yield point or proof stress of the bolt, A s is the stress area of the thread, and d A = (4 A s / π ) 1 ∕ 2 is the diameter of a circle having an area equal to the stress area of the thread. The other variables have been identified previously. Example: Find the torque required to tighten a 10-mm coarse-threaded ( P = 1.5) grade 8.8 bolt to yield assuming that both the thread- and bearing-friction coefficients are 0.12. Solution: From Equation (17) , calculate F fy and then solve T fy = KF fy d to obtain the torque required to stress the bolt to the yield point. σ y = 640 N/mm 2 (MPa) (minimum, based on 8.8 grade rating) A s = 0.7854(10 − 0.9382 × 1.5) 2 = 57.99 mm 2 d A = (4 A s / π ) 1 ∕ 2 = 8.6 mm d 2 = 9.026 mm (see JIS B 0205 or ISO 724) Find α ′ from tan α ′ = tan α cos β using: α = 30 ° ; tan β = l ÷ 2 π r ; l = P = 1.5; and r = d ÷ 2 = 5 mm tan β = 1.5 ÷ 10 π = 0.0477, therefore β = 2.73 ° . D K can be determined from Table 3 (coarse thread) and Table 4 (fine thread) or from Equa- tions (13) and (14). From Table 3, for μ s and μ w equal to 0.12, K = 0.164. The yield-point tightening torque can then be found from T fy = K × F fy × d = 0.164 × 30,463 × 10 = 49.9 × 10 3 N-mm = 49.9 N-m. . 1 3 86 2 15 012 9026 2997 640 5799 tan α ′ = tan α cos β = tan 30 ° × cos 2.73 ° = 0.577, and α ′ = 29.97 ° Solving Equation (17) gives the yield clamping force as follows: . . . . sec F N 30,463 fy 2 # # # ° π = + + = a k : Obtaining Torque and Friction Coefficients.— Given suitable test equipment, the torque coefficient K and friction coefficients between threads μ s or between bearing surfaces μ w can be determined experimentally as follows: Measure the value of the axial tightening
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