ABSTRACT
The assembly torque of a fastener is consumed by two mechanisms: friction-free bolt stretching and overcoming friction. Useful work is done when the contacting surfaces slide relative to each other up the inclined planes formed by the thread surfaces. A portion of the applied torque on the bolt head creates normal forces on the threads to stretch the bolt. The balance of the bolt torque overcomes thread friction and under-head friction. The assumed linear torquetension relation is a simplification of the actual behavior. More complicated models reflect the effects of thread friction, bolt head friction, and the helix and thread flank angles. The following equations [12, pp. 758-762] characterize the external bolt torque, T, required to tighten or loosen a fastener:
where
F = the bolt tension (lb, N) T, = the torque to tighten (in.-lb, N · m) T1 = the torque to loosen (in.-lb, N · m) e = the thread flank angle (de g) a = the helix angle ( deg) fn =the friction between the bolt head and the flange (dimensionless) d" =the mean diameter of the head bearing face (in., m) f, =the bolt thread coefficient of friction (dimensionless) d, = the mean thread contact diameter (in., m)
These equations can be rewritten in the form
(3)
(4)
(5)
A mathematical expression for the nut factor can then be written in the form
For small lead angle u and low thread friction, the nut factor can be expressed as [13, p. 224]
K = dnfn + d,j; d, tan u w w cos e + w (7)
The torque-tension equations show that the input torque is divided into three components. First, the applied torque must overcome friction between the bolt head and the flange acting at diameter d" with a coefficient of friction fn· Second, the applied torque must also overcome the thread friction forces acting at mean thread diameter d, with thread friction coefficient j;. The balance of the applied torque does the useful work of stretching the bolt.
