Why do standard bolts not loosen under load?

Question

The thread on a bolt runs around the shank in the form of a Helix. These flanks form roots and crests where the bolt and nut engage and maintain a certain force with which the assembly holds the "bolted joint" together, depending on the torque with which the joint was tightened. If the axial force along the joint increases, why does the bolt connection not start slipping and loosen up on its own?

Answer 1

The axial load on the bolted joint can be split into two components: The ratio between the "holding" force H along the thread Helix in the plane of the flank and the "normal" (perpendicular) force N on the flank can be expressed as the tangent of the Helix angle, H/N = tan(α). This ratio also represents the coefficient of friction along the "inclined ramp" which the helical thread represents.

In order for the bolt and nut not to slip, the Helix angle must be less than the inverse tangent of the coefficient of friction, α < atan(µ). The coefficient of friction between clean and dry surfaces of typical materials used in bolted joints can be approximated as about µ=0.1, and α < atan(0.1) = 5.7°

For example, the Helix angle of a metric M6x1 thread is atan(/π*6) ~ 3°, and ~ 3.5° for a 1/4-20 UNC thread. Even for smaller threads, the Helix angle is well under the threshold wher the joint would be able to slip under load, as long as the surfaces are kept "clean and dry" to maintain the coefficient of friction.

As a consequence, do not spray anything like WD40 on the studs when you were finally able to loosen those pesky, rusted lug nuts when you change a wheel! You risk reducing the coefficient of friction to the point where the nuts may not have enough safety margin to prevent slippage under the dynamic loads exerted on these bolted joints when you drive your car over bumpy roads!