Spline design 1

[linares]

Hello experts,

I am in the process of designing a spline and I am using a few references to achieve that. For stress analysis I am using the Machinery's Handbook, shigley's and for tolerance and form I am using ANSI B92.1 standard.

There is one step of the process that I find troublesome. The Machinery's Handbook has a table with some "reference" stress limits (table 11), but I am uncertain as from where are those stresses derived, as I don't intend to use any of those materials. I can only assume the following:

1.- Compressive stress refers to allowed contact pressure stresses or hertzian stresses.

2.- Shear stress. Allowed shear stress.

3.- Tensile stress. These numbers are awfully low compared to the shear stresses for the same material. My guess here is that they already included the stress concentration penalty. Normally Tensile stress = sqrt(3)*shear stress.

What are your thoughts on these?

 

[tbuelna]

linares,

The stress limits given in Machinery's are extremely conservative due to the fact that the analysis approach accompanying them is greatly simplified. The contact stress calculation is a simple tooth flank contact P/A with a couple of factors applied for service, misalignment, manufacturing precision, etc. The shear stress analysis is also a simple load and area calculation applied at the pitch line, and assumes only half the teeth carry load. The internal spline tensile (bursting) stress calculation is a bit more complicated, since it takes into account the combined loads from tangential/radial forces at the tooth contact, and the dynamic radial CF forces. Like most any other structural analysis, if you want a more precise result you'll have to use a more sophisticated approach (like FEA), and use more detailed material properties.

The most important factor with splines is usually load distribution along the tooth face, and it can vary greatly. As load is applied to the spline joint the teeth deflect torsionally, and this torsional deflection tends to be greater at the end of the spline closest to the applied load. The problem becomes worse as the spline engaged length increases or if the spline has lead errors. Of course, controlled amounts of lead correction can also be used to improve spline face load distribution.

To make a long story short, the recommendations in Machinery's are probably good for the majority of spline designs.

Hope that helps.
Terry

 

[linares]

Terry,

Thank you for your thoughts. I understand what you are saying and I am on the same page as you on every aspect. I am intrigue where those reference stresses came from and how could I adapt them if not using steel. I am trying to avoid using something like FEA since my guess is that it will be really involved. I am fine with having conservative values, but if I use a non listed material from that table I feel I am shooting in the dark (unless my guesses shown in my first post are accurate).

 

[tbuelna]

linares,

If you are using metals other than steel you can find some good data in references like MIL-HDBK-5. If the two mating halves of the spline joint are made from dissimilar materials, you will need to take into account the effects of material stiffness mismatch.

Good luck.
Terry

 

[Cockroach]

You can use the same mathematical analysis for a key, as on a spline. Note that a spline is simply a multiple key, so load is similtaneously distributed over multiple faces. Is that not how the spline works? So you know your own answer, what to do for a key way?

Regards,
Cockroach

 

[tbuelna]

Cockroach,

If the spline has an involute geometry the effect of pressure angle must be considered. A keyway is closer to a straight sided spline with a 0 deg pressure angle. A positive pressure angle produces a radial force, and with larger pressure angles like those used in roll-formed splines (ie. ~45deg) the radial force can be fairly significant.

Regards,
Terry

 

[linares]

Thank you for that reference. It is very thorough. Amazing.

Cockroach, as Terry mention (but I failed too in my original post) the spline I am planning to make has an involute profile (30 degree), so it is not as simple as having just several keys, but thank you for your comment.

 

[Cockroach]

I will provide the necessary mathematical detail when off my summer vacation.

Regards,
Cockroach