1. ## Threaded thin walled cylinder diameter change with torque

I am not an engineer, just a tinkerer.

I am looking for a formula that can determine the change of the inner diameter of a tube when a threaded nut is torqued on.

Best example I can think of is on a rifle barrel with a threaded muzzle. When a muzzle device is threaded on and torqued, at some point, the rifle bore (inner diameter) constricts.
Is there a formula so I can predict the change in inner diameter based on the torque applied?

2. I think what you want is the deflection due to external pressure hoop stress.

https://www.engineersedge.com/calcul...o_18_15451.htm

Which that deflection with a straight thread torque is going to be very-very minimal.

3. Unfortunately, I am basic member and cannot see that link.

4. It is minimal, but enough where torquing a muzzle device say more than 30 ft lbs, the pin gage taht previously fit the bore is now stuck and held in place by the bored that has decreased.

I was thinking it was from the pressure applied to the threads. So when the muzzle device is threaded on and butts up against the shoulder, any more torque now engages the threads in an axial direction. I've seen calcs on thread shearing regarding minimum thread engagement, etc.

What I am thinking is that as more of this axial stress is applied to the threads, specifically the male threads on the barrel, some pressure is directed inward due to the 60° threads thus creating the deformation decreasing the diameter of the barrel bore.

As I said, Im not an engineer so I may be way off and using wrong terms.

My goal is to predict the amount of torque that will begin to decrease bore size on different thread diameters (1/2-28 vs 5/8-24, etc.)

5. So far I have found info on typical bolt/nut fastener interactions, but not threaded cylinders just yet.

I am leaning toward a function of Poisson's Ratio and Hoo's Law. Basically we need to look at the tensile strength of the threaded portion of the barrel. Then determine the stress and strain applied to the barrel as we tighten the muzzle device. The barrel will "stretch" with this tightening as it is elastic. There is a range of the elasticity of the steel before it fails and becomes plastic. In that range of elasticity, Poissons ratio comes into play and the inner diameter decreases. In theory, because the elasticity slope is linear, should be able to calculate X torque = Y decrease in diameter.

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