Machinery's Handbook, 31st Edition
1660 TORQUE AND TENSION IN FASTENERS any tension and twisting in the bolt. The nut-turn angle will be different for each bolt size, length, material, and thread lead. The preceding method of calculating the nut-turn angle also requires elongation of the bolt without a corresponding compression of the joint material. The turn-of-nut method, as just outlined, is not valid for joints with compressible gaskets or other soft material, or if there is a significant deformation of the nut and joint material relative to that of the bolt. The nut-turn angle would then have to be determined empirically using a simulated joint and a tension-measuring device. The Japanese Industrial Standards (JIS) Handbook, Fasteners and Screw Threads, indicates that the turn-of-nut tightening method is applicable in both elastic and plastic region tightening. Refer to JIS B 1083 for more detail on this subject. Heating causes a bolt to expand at a rate proportional to its coefficient of expansion. When a hot bolt and nut are fastened in a joint and cooled, the bolt shrinks and tension is developed. The temperature necessary to develop an axial stress, F t (when the stress is below the elastic limit) can be found as follows: (8) t o = + In this equation, T is the temperature in degrees Fahrenheit needed to develop the axial tensile stress F t in psi, E is the bolt material modulus of elasticity in psi, e is the coefficient of linear expansion in in/in- ° F, and T o is the temperature in degrees Fahrenheit to which the bolt will be cooled. T − T o is, therefore, the temperature change of the bolt. In finite- element simulations, heating and cooling are frequently used to preload mesh elements in tension or compression. Equation (8) can be used to determine required temperature changes in such problems. Example: A tensile stress of 40,000 psi is required for a steel bolt in a joint operating at 70 ° F. If E is 30 × 10 6 psi and e is 6.2 × 10 − 6 in/in- ° F, determine the temperature of the bolt needed to develop the required stress on cooling. . , T F 30 10 62 10 40 000 70 285 6 6 # # ° = + = − ^ h^ h In practice, the bolt is heated slightly above the required temperature (to allow for some cooling while the nut is screwed down) and the nut is tightened snugly. Tension develops as the bolt cools. In another method, the nut is tightened snugly on the bolt, and the bolt is heated in place. When the bolt has elongated sufficiently, as indicated by inserting a thickness gage between the nut and the bearing surface of the joint, the nut is tightened. The bolt develops the required tension as it cools; however, preload may be lost if the joint temperature increases appreciably while the bolt is being heated. Calculating Thread Tensile-Stress Area.— The tensile-stress area for Unified threads is based on a diameter equivalent to the mean of the pitch and minor diameters. The pitch and the minor diameters for Unified screw threads can be found from the major (nominal) diameter, d , and the screw pitch, P = 1/ n , where n is the number of threads per inch, by use of the following formulas: the pitch diameter d p = d − 0.649519 × P ; the minor diameter d m = d − 1.299038 × P . The tensile stress area, A s , for Unified threads can then be found as follows: (9) UNJ threads in accordance with MIL-S-8879 have a tensile thread area that is usually considered to be at the basic bolt pitch diameter; for these threads, A d s p 2 = π ^ h ⁄ 4 . The tensile stress area for Unified screw threads is smaller than this area, so the required tightening torque for UNJ threaded bolts is greater than for an equally stressed Unified threaded bolt in an equivalent joint. To convert tightening torque for a Unified fastener to the equivalent torque required with a UNJ fastener, use the following relationship: A d d + 4 2 s m p 2 = π c m T Ee F T
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online