Machinery's Handbook, 31st Edition
1656 TORQUE AND TENSION IN FASTENERS Preload Adjustments.— Preloads may be applied directly by axial loading or indirectly by turning of the nut or bolt. When preload is applied by turning of nuts or bolts, a torsion load component is added to the desired axial bolt load. This combined loading increases the tensile stress on the bolt. It is frequently assumed that the additional torsion load com ponent dissipates quickly after the driving force is removed and, therefore, can be largely ignored. This assumption may be reasonable for fasteners loaded near to or beyond yield strength, but for critical applications where bolt tension must be maintained below yield, it is important to adjust the axial tension requirements to include the effects of the preload torsion. For this adjustment, the combined tensile stress ( von Mises stress) F tc in psi (MPa) can be calculated from the following: (3) where F t is the axial applied tensile stress in psi (MPa), and F s is the shear stress in psi (MPa) caused by the torsion load application. Some of the torsion load on a bolt, acquired when applying a preload, may be released by springback when the wrenching torque is removed. The amount of relaxation depends on the friction under the bolt head or nut. With controlled back turning of the nut, the torsional load may be reduced or eliminated without loss of axial load, reducing bolt stress and lowering creep and fatigue potential. However, calculation and control of the back- turn angle is difficult, so this method has limited application and cannot be used for short bolts because of the small angles involved. For relatively soft work-hardenable materials, tightening bolts in a joint slightly beyond yield will work-harden the bolt to some degree. Back turning of the bolt to the desired tension will reduce embedment and metal flow and improve resistance to preload loss. The following formula for use with single-start Unified inch screw threads calculates the combined tensile stress, F tc : (4) Single-start UNJ screw threads in accordance with MIL-S-8879 have a thread stress diameter equal to the bolt pitch diameter. For these threads, F tc can be calculated from: (5) where μ is the coefficient of friction between threads, P is the thread pitch ( P = 1/ n , and n is the number of threads per inch), and d 2 is the bolt-thread pitch diameter in inches. Both Equations (2) and (3) are derived from Equation (1) ; thus, the quantity within the radical ( ) represents the proportion of increase in axial bolt tension resulting from preload torsion. In these equations, tensile stress due to torsion load application becomes most significant when the thread friction, μ , is high. Coefficients of Friction for Bolts and Nuts.— Table 1 gives examples of coefficients of friction that are frequently used in determining torque requirements. Dry threads, indi cated by the words “None added” in the Lubricant column, are assumed to have some residual machine oil lubrication. Table 1 values are not valid for threads that have been cleaned to remove all traces of lubrication because the coefficient of friction of these threads may be very much higher unless a plating or other film is acting as a lubricant. F F F 3 tc t s 2 2 = + . P d 1 3 1 0325 + − f ⁄ . 196 231 196 . µ + . F F tc t = 2 2 − p . . d P 1 3 0637 231 + + c F F tc t = 2 2 µ m
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