Helical cutting gear selection

[martinprecision]

Hi,

I am setting up a mill to cut spiral fluting on a 24" rifle barrel.

I have a PM949 mill and a BS2 dividing head from Precision Matthews.

The BS2 came with 12 gears with the following tooth count.

• 100, 86, 72, 64, 56, 48
• 44, 40, 32, 28, 24, 24

In looking through several sources, it seems to me the proper way to determine the gears needed to drive the spindle on the dividing head from the table lead screw is to do the following:

Determine the pitch of the helix (S), which is the length of one full spiral = length of the barrel	S=24"
Determine the value for use as (Ls), which is the TPI of the table lead screw (1:5) multiplied by the gear ratio of the dividing head (40)	Ls = 8
Resolve fraction to two factors
Raise each factor to higher terms that match available gears

If I use those gears A (64 tooth) / D (32 tooth) and B (72 tooth) / C (48 tooth) as shown below do not mesh regardless of configuration.

To my knowledge, there is no option that will get me an exact match based on the gears provided with the dividing head. I have tried going up and down in teeth for different gears and came up with one combination that meshed and created a 24.5" spiral which was very close to the 24" goal. The math did not work out for me when trying to reverse engineer.

As far as I can tell, none of the gear combinations that were an exact match are physically possible and are limited to those in green.

Am I going about determining which gears should be used correctly, and am I making any incorrect assumptions?
What adjustments should I make to create a 24" spiral in this instance?
Recommendations for how to approach this best in the future.

Thanks

 

[markba633csi]

I would guess nobody at the factory has ever checked this- I could be wrong
The variable here is the distance from the table screw to the div head input shaft- it's too far
You could add an idler gear to bridge the gap- figure a way to mount it and a shaft for it
Idler gears don't change the ratio like compound gears do

 

[Lo-Fi]

Yep, idler gears are your friend here, having gone through this myself. Don't forget the change of direction with an odd number of idlers, of course.

You may find this video of mine interesting:

 

[benmychree]

Instead of fussing over the math, look up the tables in Machinery's handbook, or the B&S book, Practical Treatise on Milling and Milling Machines, they show every possible gear combination for every lead that can be cut with the standard change gears.

 

[benmychree]

Having perused the Holy B&S book I see that their leads stop at 20.050", so it would seem that additional change gears would be required, or perhaps the change gears could be directly to the dividing head spindle, as I have done occasionally.

 

[benmychree]

Having perused the book again, I see that the available lead using direct spindle drive would need to be .625", and the table does not go down to that, so that one would have to use the short lead attachment and gear for a lead of 5" if I remember correctly, the attachment has a reduction ratio of 8:1, and that would give a lead of 25" exactly, indexing could be done by disengaging the gear train possibly, and yes, I do have the short lead and feed reducing attachment and have used it.

 

[martinprecision]

@Lo-Fi, I found your video shortly before posting. It has some great information.

@benmychree I created my own table of sorts. Thanks for sharing.

The chrome piece on the mill prevents the gears and mounts from working in my situation. It cannot be removed since it is supporting the feed screw on this side of the mill.

I will keep working on it.