Torsional strength in a hollow steel body with milled slots 3

[GeoDrilling]

Hi everyone,
I am trying to figure out how to determine the torsionsal strength of a hollow body/tube with slots milled in it. The tube is a downhole drilling device and the slots contains expandable reamer elements that stick out sideways into the borehole wall (underreamer). When drilling, a torsional force is acting on the body, twisting the body so the reamer elements get jammed (they pop out and in on hydraulic pressure). I have read with interest the comments by electricpete, zekeman and others, but have not quite found somethindg directly applicable.

A typical tool is between 4" and 16" OD, 2" to 4" ID and there are three slots milled in each tool. The slots are 1/4 to 1/3 of the circumference and are from 1 to 2 feet long. The steel is normally alloy, yield 135 ksi.

Thanks and regards

 

[BobM3]

Longitudinal slots, right? It's strength and not stiffness your're after, right? If so, for 3 slots (and assuming the reamer blades don't contribute to the strength of the tube), you would have 3 beams each seeing bending loads and torsional twisting. A solid tube would of course only see the twisting.

 

[GeoDrilling]

Hi BobM3, that is right. The net result is 3 beams seeing both bending and twist. The reamer parts should not contribute to the strength as they would jam mid way through the opening (they are milling their own space in an undersized wellbore, so they must be free to move)

I thought it might be possible to calculate it as one big tube, but remove the proportionate amount that represents the slots for the moment of inertia. But, then I get a linear curve and I think the curve should be more logarithmic. If the three beams are long enough, they will twist very quickly.

I have enclosed a picture that shows a similar tool, with three slots and the cutters inside.

Thanks

 

[prex]

IMO you should treat the slotted part as an open section in torsion. For it you can calculate the torsional constant and the torsional modulus. As far as stress is concerned, of course the slotted portion will govern. If you are after the rotations, you'll simply add up the rotations of the slotted portion and of the solid one.
Sure the result will be equivalent to three beams in bending with clamped ends, but seeing this as a torsion problem seems simpler to me.
And of course buckling considerations could govern upon the strength of the device.

prex

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[GregLocock]

Torsional stiffness is tricky, I'd be tempted to jump straight into FEA after deciding that a few different hand calcs gave indicative answers only. If the slots were longer in proportion than the one in the pdf then I'd be more confident of a handcalc giving a good answer.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Tmoose]

If I was sure that the jamming was not a result of cutting swarf getting in there, I think I'd need either lots more wall thickness (not really possible looking on that picture), or strategic clearance to avoid binding, or both.

 

[gwolf2]

I think a simple medium density TET mesh with pressure loads on the contact faces of the slots would tell you a lot. Watch out for higher than expected stress concentrations on the ends of those sloping slot ends.

gwolf

 

[ornerynorsk]

Not quite answering your original question, but the Russians began ultr-deep and under-reaming operations in 1970. Have you looked at how their down hole tools are contructed.

 

[GeoDrilling]

Thanks guys,
Yes, underreaming has been industry practice for years. Today, underreaming is going through a renaissance as it is used more and other purposes than before. That results in requirements that are way beyond what was seen in the past. We are trying to construct underreamers that can drill past 5.000 feet in a single run.

The main design problem is cutter blocks and lifespan and the only solution is longer cutterblocks with higher density PDC cutters. The next problem is that the pockets to fit the cutterblocks become longer and jamming due to torsional twist is the result. In many cases, the torsional twist is so high that the material yields. If the cutterblocks are jammed in expanded position, you cant get out of the hole and the customer will flip.

Anyway, a number of your comments has put me on the track again, so thanks all of you!