Torque needed to rotate shaft in pipe?

[iokast]

I have a shaft within a pipe, all horizontal. Shaft diameter is 2.875" and pipe inner diameter is 5". Shaft and pipe length is 650 ft. Shaft weight is 2500 lb.

I need to determine the torque needed to begin rotating the shaft. The coefficient of static friction between the shaft and the pipe is 0.3

T = I * a
T = F * Rs
Fr = Cf * Fn

T = torque
I = moment of inertia
a = angular acceleration
F = force
Fr = force of friction
Rs = radius of shaft = 2.875/2/12 = 1.4375/12 = 0.12 ft
Rp = radius of pipe = 5/2/12 = 2.5/12 = 0.208 ft
Cf = coefficient of friction = 0.3
Fn = force normal to shaft = 2500 lbf
L = length of shaft and pipe = 650 ft

What I have so far is:

Fr = 0.3 * 2500 = 750 lbf
T = 750 * 0.12 = 90 ft-lbf

So 90 ft-lb is what needs to be overcome according to this.

This is bothering me because it does not take into account the inertia equation or the surface area of contact between the shaft and pipe. Wouldn't a greater surface area result in a greater amount of friction acting against motion. What do I use for angular acceleration in the inertia equation?

Can someone please get me on the right track here?

 

[Nidum]

This is a very difficult calculation to do .

You can't do a simple friction torque sum on a shaft that long and with that amount of running clearance .

Would take pages to explain why but basic problem is that the shaft is very unlikely to simply sit at the lowest point in the tube and rotate true about it's own axis .

 

[iokast]

Appreciate the response. I knew there must be more to it.

Making a lot of assumptions do you know of a way to get a general ballpark solution? I know the maximum amount of torque I can generate on the shaft so if it's order(s) of magnitude off I will know whether it is feasible to do.

 

[Nidum]

(1) Can you tell us any more about this project ?

(2) Have a look at oil well drilling technology - this commonly involves very long shafts running in tubes .

 

[haruspex]

This is a very difficult calculation to do .

You can't do a simple friction torque sum on a shaft that long and with that amount of running clearance .

Would take pages to explain why but basic problem is that the shaft is very unlikely to simply sit at the lowest point in the tube and rotate true about it's own axis .

I suspect the problem is not intended to be that difficult. It does not matter that it will not sit at the lowest point. I would interpret the question in terms of applying a gradually increasing torque until sliding starts. We can calculate where the shaft will be in the pipe at that time.

(2) Have a look at oil well drilling technology - this commonly involves very long shafts running in tubes .

I would have thought that involved much smaller clearances, which would indeed raise complications, particularly for a horizontal shaft subject to bending under its own weight.