There are no resrictions only practicality.

Hollow shafts can be interpreted as pipe?

Must be of a material that makes sense to replace 1045 steel as the defacto standard or its equivalent. In some cases, the value is raised to 4140 or 4340 carbon steels where greater strength is required.

What material and production concept do you have in mind? ■

This is the crux of the question. There is no point in producing a design based on a hollow shaft if it is ten times as expensive to produce a hollow shaft than a solid one.

Also, you may be able to produce a hollow shaft in your production environment, but what happens out in the field if it fails? Will the end user be able to get a replacement hollow shaft quickly? Solid shafts are easier to make locally so that's what will end up being used. ■

Both bending and shear stress allowance will increase exponentially > 1:1 with increase in the shaft's OD while making the shaft's diameter a hollow with the same weight.

The bending momemt of inertia increases by the 4 th power and stress allowance is reduced by the 3rd power of the inertia, as you know.

Your idea of hollowing out the shaft center does not come without a cost. How do you expect to show a positive benefit when weighing the cost of having to make or purchase a bigger shaft which then you make hollow? Or, are you expecting to make a small shaft larger by some ballooning method?

If it could be done at no cost, then you have the clear winner!

Many mfgrs. have made a shaft system of two parts: a) solid shaft part and b) added boost of shaft moment of inertia between the pulley end disks using a pipe or heavy wall tubing. This tubing diameter is substantially larger than the shaft. This only helps reduce the end disk stresses. Its proper design and manufacturing is somewhat complex and some get it wrong. I think it finally was abandoned. ■

A little errata: the second paragraph refers to the diameter increase changing the moment of inertia by the 4th power and stress reduction by the 3rd order of the change in diameter. ■

You could start with a seamless (extruded) pipe that satisfies the shaft deflection requirements, crimp it, by heat and pressure, to the diameter, at the pulley hubs, that satisfies the bending and torsional stress requirements, then crimp further down for the required bearings and again for the drive requirements.

Such an operation called "end-pointing" is already done economically and rapidly, on a smaller scale, for idler shafts. In the case of end-pointing idler shafts the quantities for shafts of the same size are great facilitating the economics of automation.

My two cents.

Joseph A. Dos Santos ■

However, if you reduce the hollow shaft to fit through the equivalent bearing then you have lost the hollowing torsional benefit altogether. Especially if you cut a keyway to hold the drive coupling half. YOU ALWAYS FORGET THE KEYS. ■

Not that I believe hollow shafts for pulleys make sense, but the loss of torsional strength due to keys depends on the starting thickness of the pipe and the thickness at the hub, at the bearings and at the drive. The thickness may be increased with the crimping in reducing the diameter.

Better yet use shrink fittings (without keys) at the hubs and at the drive.

Joseph A. Dos Santos ■

Solid shafts are easier to supply. What about 'key ways' how do you plan on mounting your pulley and/or any bushings? ■

Mr. enfernoknight,

I repeat, keyless, shrink type locking devices; Ringfeder or Bikon type at the pulley hubs and at low speed drive couplings; shrink discs at hollow shaft drives.

Joseph A. Dos Santos ■

Dear All,

Better take a pill. There is no mfg. method to analyze the compression deformation under the shrink ring (Ringfeder type I assume). The can easily be done by FEA, but most engineers will not have access to the tools to do it.

I bet dollars to donuts that you will find a disturbing result. In principle, you need to have a hollow shaft stiff enough to push against to assure the locking mechanism performs to spec. on the shaft and hub. Your pipe will not have sufficient elastic stiffness do it. ■

The arguments against the unknown and undefined are absurd.

The shaft diameter and wall thickness (including the thickness variation at the base pipe and crimped at the hubs, bearings, drive) have not been defined. This discussion is in principle without specifics.

Calculating the shrink or interference to develop a grip, on a solid or hollow shaft, is well known and preceeds the Finite Element Method.

Joe Dos Santos ■

The discussion was about the use of practical, commercial grade pipe and the known locking device literature on its structural efficacy.

I have no interest in argument of the absurd and find this comment beyond your professional status.

I guess you would defend the absurd use of a wall thickness that was equal to half the shaft diameter even though it was absurd on principle.

I also note the endowment of the calculation method. Can it be found in Roark or Shigley or Timeshenko, with triaxial bending, torsionl and radial components? These gentlemen have a regal following on the more common methods of stress analysis. ■

Rigth at the beginning everyone, including me, expressed doubt about the practicality of using hollow shafts for pulleys.

Larry you argued that the benefit would be lost in the cost of hollowing out the shaft.

I mentioned the end pointing process, used for idler shafts, that crimps a larger diameter tube, over several steps, down to a smaller diameter at the bearing. I mentioned the economics of automation would be lost when applied to pulley shafts since the repeatable numbers are small.

So we all agree that it is likely impractical. Indeed the natural extension of the argument for a hollow sfaft is the well known propostition of stub shafts. In such a case the pulley itself is the hollow shaft. But I digress.

From that point, arguments were being made against the undefined, assuming some proportions that no one stated. It is disturbing that you propose limitations based on known, available analytcal methods. If something works the analytical methods follow. There are many ways to approach this in the ealry stages. You can build simple analytical models with appropriately conservative allowables. You can build a physical model and use strain gages, measure deflections, etc. You can use finite element analysis if you can demonstrate how close you are getting to the true solution. This requires increasing refinement of the mesh and plotting of sample stresses demontsrating the assymptotic approach to the true solution.

The basis for shrink or interference fits, with thick pipes can be found in:

- Machinery's Handbook, 26th edition, starting on page 623

- Formulas for Stress & Strain, by Roark and Young, 5th edition, starting on page 503

- Theory of Elasticity, by Timoshenko and Goodyear, 3rd edition, pages 68 thru 71

- Strength of Materials- Part II, by Timoshenko, starting on page 210

- I don't own a copy of Shigley

Application of these fits and their stresses is actually pretty predictable with the modern locking elements such as the expansion elements at the hubs and the shrink discs at the drives.

Joe Dos Santos ■

Let us not make this a discussion for arguments sake. We do agree that it is impractical. That was my only point. Pursuit of such a system, by those with some respected knowledge, was to warn the poster of potential benefits or not.

First posting acknowledged a pipe could be designed; however it would be impractical.

Second posting another comment on practicality and the past use of the double-drum concept - maybe he could research and get further pointers.

Third posting was a statement on the inability to find a computational method in any publication. I stand by that statement, acknowledging your references, which we own, as well as Ringfeder, Bikon, B-Lock; Tsubiaki (sic). I was trying to say that any triaxial treatment would likely not be found.

I disagree with you on the problem complexity on super-position, because of the deformation interactions, especially the bending on the compression of the pipe, with likely buckling at the edge of the locking mechanism in normal pipe with a thick wall thickness.

Using an interference fit analysis for a locking device is not trivial. We in fact do it when applying an FEA solution by iteration. By hand?

Go have a sip of wine, like I am here in Chile. It does wonders for the state-of-mine.

I have always had, and do have, great respect for your contributions to this industry. You sometimes are a little trying. Sometimes I am a little more trying. Maybe we take a little potion and get back the smile. ■