Strength of Large Diameter Threads

[Kartoffelbri]

Hi all,

I have been assigned the task to calculate the strength of threads for the hydraulic cylinders my company manufactures. I have started doing some research and have found several guide formulas and methods to find shear area, length of engagement, force resulting in failure and so forth, but every equation or source seems to specify it applying to fasteners. The cylinders produced here are sized quite a bit larger compared to the average fastener and so I am not sure if these equations still apply. We make cylinders with up to a 3 foot diameter as far as I know or even bigger, but on average they have about a 1 foot diameter. I know in the mechanical engineering world there are many instances where one specific calculation has different equations needed to solve it based on the existing parameters. Is this one of those instances or is it a one equation fits all situations type circumstance? And if these equations do not apply for larger diameters, what equations do I use, as I cannot find them?

On another note, I see several formulas to derive the force that will result in failure of the thread based on the tensile strength of the thread material, but I do not see any equation explicitly stating how to find the acting/working stress on the thread so that I can have a representation of a safety factor. In this case, since I am working with hydraulic cylinders, I should be able to find the resultant force based on the operating pressure and the inner diameter of the top stage of the cylinder. Once I have found that, I just divide that by the shear area of the thread to find the working stress on the thread correct?

Brian

 

[JBA]

I don't know what level of pressure your components for which your components are designed; but, below are some general factors to be considered in your stress analysis

Specifically for very high pressures for cylinder threads there is one item that I have not found generally addressed in standard thread design calculations and that is "thread dilation", ie. the expansion of the outer threaded cylindrical component created by the circumferential loading stress from the wedging effect of the contact angle of the threads. This expansion both adds to the circumferential stress of the external component wall but also can, if not prevented by a sufficient compensating wall thickness on the external cylinder in the region of the threads, reduce the contact surface of the internal and external thread and reduce the effective shear area below that at threads' root.

In all cases the effective pressure area used for calculating the pressure tensile loading should always be based upon the outside diameter of the joint seal.

When determining an acceptable tensile stress, either for an internal thread or external thread of a hollow threaded internal component an appropriate stress concentration factor due to the notching of the V thread must also be included. Note: for thread designs using acme style threads this is less of an issue but in both cases the radius and finish at the throat of the thread must taken into consideration in selecting the appropriate stress concentration factor.

 

[OCR]

I have been assigned the task to calculate the strength of threads for the hydraulic cylinders my company manufactures.

I suppose you've already looked here... ?

 

[Kartoffelbri]

Thank you for the replies!

JBA, the circumferential stress would be my next step to consider as I have not even gotten to that yet. The stress concentration factor would only apply to the bending stress of the threads however, correct? And are the threads always going to fail in shear prior to bending? That is an interesting point, as almost all of the analyses I have found involve fasteners or threaded components that do not have an internal pressure and therefore wouldn't account for thread dilation due to the wedging of threads. I would not have thought of the reduction of effective shear area due to thread dilation; that would then drastically increase the stress that the threads are under. Thank you for the note on calculating the effective pressure. I'm a recent graduate and have been hired by a company that gets all its structural companies from elsewhere and I have no one previous work or foundation to base anything off and no one to walk me through or help. So thanks for your patience and sorry for all the questions!

OCR, I have already taken a look through that website.

Thanks again!

 

[JBA]

With pressure vessel threaded connections, apart from the thread dilation issue and thread shearing (due to lack of adequate number of thread engaged between the the two components, is the tensile stress at the root diameter of the bottom inside thread of the cylinder (the x-sectional area between the thread and the cylinder outer wall); and, in the case of a hollow inner component, the throat of the upper most thread and the bore of that component. This is where the "V" notch concentration stress factor must be taken into consideration, both as to the radius and finish at the base of the "V".

 

[Baluncore]

There are two effects that counter the reduction of thread contact due to the thread profile ramp.

If you consider a small cube of material in the wall of a cylinder, the internal hydraulic pressure provides twice the hoop tension as the axial extension. That is why tubes tend to split lengthwise under excess pressure, why welded seam pipe is cheap and why stainless steel tube, helically wound from a narrow strip and welded is significantly stronger than the straight welded seam tube.

Where a heavy female threaded outer coupling is screwed onto a lighter cylinder tube, the internal male threaded cylinder will expand against the outer coupling more than the tube stretches axially against the thread profile. The radial thread angle will probably be 30° which allows the tube to expand more than the axial profile ramp reduces contact against the outer coupling with the 60° axial angle. So the threads should engage more under pressure, not less.

 

[JBA]

In the case of threaded tube closures/plugs, a bore on the internal plug may small or nonexistent; and, therefore there will be little or no compensating effect to the expansion of the tube due to the ramping effect of the thread angle.

 

[Baluncore]

In the case of threaded tube closures/plugs, a bore on the internal plug may small or nonexistent; and, therefore there will be little or no compensating effect to the expansion of the tube due to the ramping effect of the thread angle.

That may be true of solid internal blanking plugs screwed into threaded holes, where the hydraulic pressure can enter the thread contact and open the thread contact. But on the other hand, for internally honed hydraulic cylinder tubes that run sliding pistons, and screw into a base or more solid external end cap, the expansion of the relatively thin wall cylinder tube is an advantage and is very important in the analysis. That is why they are built that way.

 

[JBA]

All points well taken, my main concern was not so much thread separation as the fact that the longitudinal loading all on its own on either a threaded plug or cap style end connection results in a wedging effect that results in an additional hoop stress in the external wall component that should be included in the components wall thickness evaluation.

At the same time, many, maybe most, large high pressure cylinder manufacturers simply choose to use either bolted flange or tie bolt retained end covers and avoid the threaded connection issues altogether. Either of which may be a better solution than threads for @Kartoffelbri's application.

 

[Baluncore]

Either of which may be a better solution than threads for @Kartoffelbri's application.

Not quite. I have just come in from tightening the tie bolts on a hydraulic cylinder, so I could not let the opportunity pass. With tie bolt cylinders, where the ends of the cylinder tube rest on a rubber seal in grooved end plates, internal hydraulic pressure provides hoop stress, but not axial stress in the cylinder wall. All the axial tension is carried by the bolts, which stretch and so reduce pressure on the rubber end seals at just the time they need to seal. The resulting hydraulic actuator is heavier than necessary because the lazy cylinder could do the work of the unnecessary tie bolts. If an externally threaded cylinder has threads that do not go deeper than half the wall thickness, the strength will not be significantly reduced since the axial stress is half the hoop stress and the threads are perpendicular to the axis, and contained by the cylinder end cap.