Need help with math calcs for working out a helix

[pinkpanda3310]

I've a tool post mill attached to the compound of my lathe and wanted to make a helix pattern on a tube. I've looked around for online calculators and formula's but am just getting more confused and frustrated. None of the calculations i tried was anywhere close to what i need. A picture says thousand words so here's what i'm trying to achieve...

So as you can see i'm trying to make a helix in increments / one cut at a time. The cuts on the right side in the right pic are my first cuts that were messed up calcs. I literally stumbled on the dimensions that i needed for it all to line up and still don't know the calculation. So if I use a different diameter stock it won't work out so neat right?


My set up is - stock diameter 24.94mm , compound slide 30 degrees, move carriage 15mm and roll the stock 30 degrees for each successive cut.

Does anyone know a formula i can use for different diameter stock?

 

[homebrewed]

Your helix is just a thread with a different profile so the angle won't change, as long as the effective "TPI'" of the helix you're cutting doesn't change. That also means that you will advance the carriage the same amount, regardless of the diameter of the stock.

 

[pinkpanda3310]

I'm pretty sure the angle does change with different diameter stock. See basic example below, same TPI but different diameter stock.



So I either need to change the TPI to suit the angle (preferable) or change the angle to suit the TPI. Either way I don't know what calcs i should be using.

 

[ericc]

I'm pretty sure the angle does change with different diameter stock. See basic example below, same TPI but different diameter stock.

View attachment 406567

So I either need to change the TPI to suit the angle (preferable) or change the angle to suit the TPI. Either way I don't know what calcs i should be using.

Yes, you are correct. Just "unroll" the helix, and you get a triangle. The adjacent side of the triangle is just pi*d (the diameter) and the opposite is the pitch, p. So, the angle you are looking for is arctan(p / (pi*d)).

 

[pinkpanda3310]

Okay i've slept on it and back with a fresh mind.

Pitch = distance between crests of a helix

In my case i was turning 30degrees for every 15mm so a full revolution is 360/30 = 12 . 12* 15mm = 180mm pitch

After more goggling I think the pitch diameter is just the minor diameter of a thread

Pitch Diameter = minor thread diameter

The deeper cuts i made were about 1mm but this is not super accurate.

In my case 24.94 (diameter of stock) - 2mm (1mm cut each side) = 22.94

Input those into the formula arctan(p / (pi*d))

arctan = (180 / (22.94 * 24.94))

arctan = 31.46 degrees

So my setup is technically 1.46 degrees out. I'm pretty happy that i could make that math work. Thanks for the help

One of the major things that had me confused is the "Helix Angle" is measured from the longitudinal axis not the cross section.. The following pic i thought was a drill bit but not the case, it's a toothed gear...

 

[derf]

A helix that fast is typically measured in a "lead" instead of TPI. A lead is the amount advanced in 1 revolution. A 2" lead would make a full revolution in 2" of linear travel.