The Random Technical Question Thread

[pmbrunelle]

Sometimes I have quick thoughts/questions, and it would be nice to have a second opinion, but one thread per subject would clutter the forum too much.

We can post short topics there.

This does not need to be strictly Fiero-related.

[pmbrunelle]

I'll start!

This first question is for a work-related project. I have a 30 mm shaft that needs splines. It is subject to reversing torque loads. Following the DIN 5480 standard, a 30 mm shaft can have anywhere from 8 to 58 teeth.

For a given diameter, is it better to have more small teeth, or fewer large teeth?

For compressive stress on the teeth flanks, it seems like the surface area in compression does not vary much with the number of teeth.

Perhaps with large teeth, more of the tooth face is used, as there is less "waste" due to clearances for root and tip diameters.

More small teeth gives a larger and stronger root diameter to the shaft. Less material removal in hobbing for small teeth seems to be an advantage for small teeth.

What do y'all think about small/large teeth?

[zok15]

I like the concept of this thread

No expert on splines, but I believe base tooth width is related to the strength of the teeth themselves, but I imagine greater stress concentrations as teeth get larger located where the splines end results in a shearing of the shaft where it meets the splines with shock loads. In essence IDK but I wanted to contribute. Got FEA handy?

[pmbrunelle]

If we consider a tooth as beam in bending, then we can say the section modulus of the tooth is proportional to the square of the tooth's base width. The increase in strength due to the section modulus is partly counteracted by the fact that the distance to the point of force application (and hence bending moment) scales with tooth size. Therefore, bending stress calculated by the Lewis method scales with the (^-1) power of module.

In a spline, unlike a gear (with only one or two teeth loaded at a time), the smaller the teeth become, the more teeth there are to share the load; the two effects appear to cancel each other out

That being said, since spline teeth are short and stubby (with typical 30° pressure angle), my understanding is that they don't typically break in bending, making the above bending analysis moot.

I'm looking at When Splines Need Stress Control by Dudley:
https://dokumen.tips/download/link/when ... udley.html
(you can download this file for reference)

Machinery's Handbook has a section on spline stresses, but it's just Dudley's article cut-and-pasted.

Dudley suggests studying four types of stresses (copied verbatim from article):
1. Shear stresses in spline shaft
2. Shear stresses in spline teeth
3. Compressive stresses in spline teeth
4. Bursting stresses in internal spline parts

My thoughts on module with respect to each of the four stresses:

1. The bigger the teeth, the smaller the root diameter of the shaft, and the less capable the shaft is of transmitting torque.
2. Shearing is assumed to occur along the pitchline of the teeth. The cylindrical area of metal to be sheared is not a function of the number of teeth; the number of teeth simply determines among how many segments the cylindrical area is split.
3. Bigger teeth with more flank surface area can only happen with a reduction in the number of teeth, so this appears to be a wash, unless a greater percentage of the flank happens to be in contact, as I mentioned above.
4. If the OD of the female part is already small, then bigger teeth leave a thinner rim more susceptible to cracking.

I have a helper who spends much of his time doing Ansys simulations, but I'm not sure how we would simulate the contact between the imperfect male and female parts, and have reliable results. Right now he's studying something that's more straightforward, and that I know will be a productive use of his time.

Whenever published guidelines exist for analyzing something standard, I prefer to use those, while focusing the FEA type analysis on the bespoke/weird areas of the design.

[ericjon262]

I too like the idea of the thread. Unfortunately, I'm not sure I can offer much insight on the spline strength, you touched on all of my thoughts already.

[pmbrunelle]

Perhaps with large teeth, more of the tooth face is used, as there is less "waste" due to clearances for root and tip diameters.

I checked DIN 5480.

Recommended spline tolerances do become more precise as the teeth become smaller, but not proportionally with decreasing tooth size. I guess that it would not be economically feasible to manufacture splines with tolerances that scale directly with tooth size.

So, relative to the tooth size, small splines are less precise. Hence, there is more waste.

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I was also thinking that if the splined part is carburized with a certain case thickness, then depending for a small tooth, the entire tooth could be hard, or for a large tooth, the outside would be hard, retaining a tougher inside.

For my specific project, I think the part will be through-hardened, so I don't have to think about this complication.

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This question reminds me of coarse versus fine threads in screws.

[The Dark Side of Will]

Edit: I had not read your 5/17 post before I typed the below.

At the pitch diameter, for either splines or threads, each mating part has 50% of the material intersecting the "pitch cylinder". Thus slightly larger pitch diameter = slightly more material to shear before the splines or threads break. That gets balanced against the thread fit or spline tolerances, in that looser tolerances take away from the total amount of material intersecting the pitch cylinder.

As you noted, the larger minor diameter for the finer splines means that the finer splines can transmit more torque before shearing the shaft.

Would you necessarily hob the splines or broach them? If the splines can be broached, then that would tend to favor finer splines as the broaching operation would be much easier than for coarser splines.

[pmbrunelle]

The male splines on this shaft will be hobbed.

Logically, a male spline (almost?) never exists without its female mating counterpart, which will most likely be broached (wire EDM for initial prototyping).

Even though I'm not responsible for the female mating part, our customer will have to procure the female mating part, so I should make it easy for them to make/buy.