Calculations involving torque

[Rizkyffq]

Homework Statement

For Project

Relevant Equations

Torque Equation

Hello guys, i need some enlightenment (help) to solve this problem , maybe someone here have mastered physics or engineering can help me to break this problem !
I already tried to seek the answer, but i face dead end and really frustating because of it .

So the problem is "how to get calculation / equation for calculate torque (delta torque) on "Multi Lobe Torque Ring (MLT Ring)" as picture above.

Name of thing above is MLT Ring "blue coloured", it is installed inside Casing/Tubing threaded for oil well, and the main function of this ring is to boost value of torque on Casing/Tubing, so it can endure more torque with it.
From that explanation we know that there two kind of torque on it, torque of the casing/tubing threaded and torque of ring.
The reference/book that designed/made/fabricated this "MLT Ring" is just explaining how they get number of ring torque in very common,

Different with torque of Casing/Tubing, it has reference equation to get exact number of it torque,

Above is equation to get torque of casing/tubing, initially i think this equation will be the same equation to calculating how much torque on ring because as you see, between ring and casing/tubing they are connected in one line, but i tried and it is not same as the table.
In this book also has already table of both torque, for casing/tubing and ring but what i need is the exact explanation or philosophy why they get that number, from where ?

Material of ring : L-80 (yield strength 80.000 psi)
OD : 2-3/8"
ID: in the table

Maybe someone here want to help me to solve it
If you have any question because of this post unclear explanation/any deeper definition, free to ask

 

[Valkarie]

Thanks & Regards !The equation you provided is the correct equation to calculate the torque of the casing/tubing. To calculate the torque of the MLT ring, you need to consider the geometry of the ring and the friction between the ring and the casing/tubing. The friction force can be determined by multiplying the normal force (due to the weight of the ring) by the coefficient of friction between the two surfaces. Once you have the friction force, you can calculate the torque of the MLT ring by multiplying the force by the radius of the MLT ring.