Spline lead variation outside of class 4-7.

[irTibo]

The ANSI B92.2M spline standard has formulas for total index variation, total profile variation, and lead variation for the spline tolerance classes 4-7. I am looking to expand past the standard for other tolerance classes. In particular, classes 0-18. The lead variation formula is the only regression I can't figure out. The formula (in micrometers) in the standard is as follows:

Class 4 0.8 * sqrt(g) + 4
Class 5 1.0 * sqrt(g) + 5
Class 6 1.25 * sqrt(g) + 6.3
Class 7 2.0 * sqrt(g) + 10

where g is the spline length in mm

The standard also states, "The lead variation is a standard tolerance grade selection from ISO 1328." I have not been able to understand its relevance to the formula, but I thought it might be of importance to mention. I also have not cross referenced this with ISO 4156 yet, as I currently do not have a copy.

I know this is an unusual question, but if anyone likes a puzzle, I'd appreciate the help in figuring out the formulas for other classes.

 

[tbuelna]

The ANSI B92 spline spec uses a different approach with regards to side fits than the newer ISO system does. The ANSI standard is limited to just a couple tolerance classes (4-7) for tooth flank fits, since this range of fits covered all of the applications these splines were used for.

The newer ISO spline spec employs the same system of fits and clearances used for things like hole/pin or bearing/shaft/housing fits. While this system is more comprehensive, it is also a bit more complicated to use. As with all ISO standards, the tolerances for fits and clearances are based on a set of equations that are intended to provide a more precise result for any given application.

On the other hand, you need to remember that when it comes to lead error of involute splines there is not much room for variation. Any involute spline with an L/D beyond 1.0 will require careful tolerance control to provide uniform loading along the tooth face. And splines having high L/D or small diameter will also require lead compensation, beyond the lead tolerances given in the ANSI or ISO standards, to prevent edge loading.

 

[irTibo]

Let me expand my original post (sorry if your eyes glaze over). I am familiar with both ISO and ANSI spline standards, and the ISO 286 tolerance standard and how it works. In the ANSI B92.2M standard, there are formulas for total tolerance, total index variation, total profile variation, and lead variation. These formulas only cover spline tolerance classes 4-7.
The total tolerance has:

Class 4 (IT6 + IT9) = 10i* + 40i**
Class 5 (IT7 + IT10) = 16i* + 64i**
Class 6 (IT8 + IT11) = 25i* + 100i**
Class 7 (IT9 + IT12) = 40i* + 160i**

The tolerance grades are from ISO 286, and the values for i* and i** are further detailed in the ANSI spline standard. If I expand these formulas, I can add the following:

Class 8 (IT10 + IT13) = 64i* + 250i**
Class 9 (IT11 + IT14) = 100i* + 400i** and so on. It gets more convoluted on the lower classes.

Total index variation has a formula for class 5 as 3.55 * L^0.5 + 9.
I found this formula buried in the text of ISO 1328, section 5.2. It gets expanded with the following:

Class Q total index variation = (3.55 * 2^(0.5(Q-5))) * L^0.5 + (9 * 2^(0.5(Q-5)))

The total profile variation formula follows a series much like the total tolerance, except using multiples of 1, 1.6, 2.5, 4, and 6.3.

The lead variation formula doesn't seem to follow any series that I can decipher.

 

[tbuelna]

irTibo-

While I can't provide an answer to your specific question, here's what I can tell you based on my experience. The class 4-7 lead variation tolerances provided in the ANSI standard probably cover 99% of applications. But if your spline design is not covered by the tolerances/fits shown in the ANSI standard, then you'll probably want to do some detailed structural analysis of the spline components, and then create a custom lead profile tolerance chart on the drawings for these parts. With splines that have large L/D ratio, you'll need to apply lead compensation to ensure uniform loading along the spline face. So the lead tolerance given in the ANSI standard is of no use for these situations.