A back-up wrench or back-up spanner is placed on the bolt head to prevent bolt rotation when the nut is being tightened. Once the bolt is tightened and the nut is then attempted to be tightened, the whole nut-bolt assembly can spin without further tightening occurring at a torque lower than the initial tightening torque. The concern sometimes expressed is whether or not this is a problem?
When a nut is tightened, the torque applied to the nut can be split into three components. The torque needed to stretch the bolt (the thread extension torque); the torque needed to overcome thread friction; and the torque needed to overcome nut face friction. The torque needed to stretch the bolt and the torque needed to overcome thread friction is transmitted through the bolt shank and is reacted by the bolt head. Whether a backing spanner is needed depends whether the torque needed to rotate the bolt head is greater than the torque being transmitted up the bolt shank. This torque is the sum of the torque needed to stretch the bolt plus the torque needed to overcome thread friction. If the reaction torque provided by friction grip of the bolt head on the joint surface is greater than the torque being transmitted up the shank, then the bolt will not rotate and the nut would tighten the assembly.
This is illustrated in the image shown above. If the reaction torque is less than the torque being transmitted up the shank, rotation of the whole bolt-nut assembly would occur. A back-up wrench would then be needed for the nut to be tightened.
To clarify with an example. Consider the situation in which a M20 property class 10.9 bolt is tightened to 500 Nm. The coefficient of friction under the nut face and in the thread is 0.12. Such a torque and friction combination would result in a bolt load of 160 kN. Below is a pie-chart showing this situation.
If the friction condition under the bolt head is the same as under the nut face, in the above case, a backing spanner would be needed to prevent the bolt head from rotating. This is because the torque needed to overcome thread friction (203 Nm) plus the torque needed to stretch the bolt (63 Nm) is greater than the torque that the bolt head is capable of reacting (234 Nm). That is, 203 + 63 = 266 Nm is greater than 234 Nm. In this case to tighten the nut, a backing spanner would be needed to prevent the bolt from rotating. The backing spanner would react a torque of 266 - 234 = 32 Nm.
Once the bolt was fully tightened to the 500 Nm, the backing spanner could be released. Assuming no change in the friction conditions, if the nut was then attempted to be tightened without the backing spanner, the whole nut-bolt assembly would rotate at a torque of 468 Nm. (Since both the nut face and bolt head would rotate needing a torque of 234 Nm each.) Being able to rotate the nut-bolt assembly at a lower torque than the tightening torque does not indicate that there is necessarily a problem with the assembly.
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