Stress Analysis of Involute Splines 6

[PFMD]

I am designing an involute spline with a fillet root. I want to do a simple analyis to see if the stresses are even in the ball park before I hand off to finite element person. Seems like line contact stress at pitch diameter to check the bearing stress is good. And potentially a shear stress at the ptich diameter is good too. I have dimensions and load, just need to know what I should do as far as hand calcs. This would be a shaft with external splines, and a driven gear sort of arrangement. Suggestions would be appreciated on hand calcs.

 

[CoryPad]

You have identified the two common ones.

 

[dinjin]

Use the same technique that is used for a gear to give
you a rough guideline. What did you mean by "seems like".
Is this a wild guess? I would use the simple Lewis equation for a rough estimate. You have to layout the spline tooth to calculate a Y factor.

 

[PFMD]

Thanks CoryPad and dinjin. I have never analyzed a gear tooth (or spline tooth), so the Lewis Equation was a new one on me. The two analysis' I suggested seemed obvious though. I have the "Gear Handbook" by Dudley, and remarkably enough the index does not even have a listing for stress, but I did find the Lewis Formula thanks to your help.

Remember: "If it ain't broke, fix it until it is"!

 

[tbuelna]

PFMD,

Detailed analysis of splines is not that simple. And how you approach the analysis is very dependent upon what conditions the spline operates in and how carefully the spline and its mate are manufactured. What is the torque the spline must transmit, what is it made from, and how many load cycles does it see?

If the spline is well supported, accurately manufactured, has a L/D ratio below 1.0, has adequate back-up shaft structure, and is properly lubed, then its torque capacity will likely be determined by its resistance to fretting at the tooth contact. Unless your spline geometries are very unusual, then the spline will not fail in root shear, or fracture failure propagating from the fillet area. It will fail from surface initiated fractures propagating out from the contact faces. The classical spline failure mode is due to these fractures originating from tooth surface pits caused by trapped metallic debris producing surface fretting or corrosion. That is not a condition that you can evaluate for with an FEA model. And most likely, your FEA model would show big, fat margins for both root fillet stresses and tooth shear stress for a spline designed for contact limits.

If your spline is susceptible to misalignment during operation, or has a L/D ratio greater than 1.0, then you will need to manufacture the spline with some degree of lead correction or crowning to compensate for torsional wind-up and edge loading.

I design lots of high-performance involute splines for aircraft that are carburized and require unlimited fatigue life. For these oil lubed splines, the spline is designed so that it has a constant flow of oil along the teeth to flush away any debris, has an L/D below 1.0, and the spline is designed for a simple face contact stress (ext. spline OD - int. spline ID X the number of teeth) below 5 KSI. This limit may seem overly conservative, but experience has shown that oil lubed splines designed to this limit will last forever.

Regards,
Terry

 

[mfgenggear]

terry

****nice I gave you a star****

Lee

 

[PFMD]

Thanks for the info, Terry. I did a line contact stress analysis on my teeth, and found that the stress levels were about 3X too high for the material I was using. Yeah, that is different than fretting, but still a failure mode. The material in question (G10) was being considered because it has lousy thermal conductivity (K), which is desireable for this application. But it is way too soft. G10 is the material used for making circuit boards. If that sounds bizzare, so be it, because so is the application, a lab type of end use. Next up on the lousy K list is Titanium. Is there anything that can be done to Titanium, that you are aware of, to reduce or eliminate fretting? This application has a finite life. I can set that life to like 10k or 100k cycles, and/or change out the splined gears at some point, like when the teeth are showing signs of problems. One rpm is fast for this application, no dynamic (instantaneous) loading.

 

[tbuelna]

PFMD,

Titanium can definitely be used for one half of a spline joint, but not for both. Since it has a very nasty habit of galling.

Non-metallic resins (like Torlon or Vespel) make an excellent mate for a hard metal spline. They are not susceptible to fretting, have amazingly good mechanical properties, and machine very well. These materials are commonly used as splined inserts for aircraft gearbox accessory drive shafts. They are designed to have the spline teeth shear out in case of seizure of the driven accessory device, thus preventing damage to the rest of the accessory drive system. I've seen these resin inserts last for over 10,000 hours of service.

The best and most simple guideline I can recommend for designing a metal spline joint, is to try to make the male spline with a harder finished surface than the female spline. Contacting metal materials with a significant difference in hardness have a much lower tendency to fret and gall.

Good luck.
Terry

 

[Tmoose]

Do you need the spline for blind assembly, sliding during operation, or ???

 

[hoyle]

I used to work at a company that designed very large gearboxes, 40,000 HP and a 20 year life, not uncommon. Previous to this I had always wondered how you specified the design of splined shafts/couplings as I had never seen anything other than the guidelines in Machinery’s Handbook.
I expected this company would have the definitive piece of literature and /or software to design splines. I was wrong; they used the guidelines in Machinery’s Handbook! I transferred the numbers and tables into Excel.