Prime number division without gearing?

[talvare]

Thanks RJ. I think the light bulb just came on !

Ted

 

[RJSakowski]

If you assume a 50% of hole diameter space between holes, the bolt circle for a 127 hole pattern would be about 60 x the hole diameter. For a 1/4" hole, that would require a 15" bolt circle. That's the reason for multiple rows or the spirals.

 

[Bob Korves]

Deleted

 

[markba633csi]

What you are missing Ted is the gear ratio of the head itself usually 40:1 but sometimes a different ratio like 72 or 90 to 1
Mark

 

[talvare]

Ted, that requires a plate with the 127 holes and an indexing setup to engage them. That would be "plain indexing." It would work fine, but the plate has to be available (which they are not) or shop made, which you might be able to do on your CNC BP, but most of us cannot. One of the issues is the size of the dividing plate with a single row of 127 holes and the 1/8" hole size that people here are suggesting, along with a relatively large space between holes. I have no idea why a 1/16" hole size could not be used, or a pin tapered to a cone point. There is not much rotary stress on the plate when drilling a hole or cutting a gear, and the spindle should be locked anyway for each cut. But again, all of that would need to be fabricated. I do not think the spaces between holes need to really be large, there only needs to be enough meat there to keep the dividing plate from being fragile if dropped.

Bob,

Ya, my brain wasn't working very well this morning (nothing new for me). My theory would work fine if the dividing head was a 1:1 ratio . I figured that a single row of 127 holes could be done with 1/8" holes on a 8" diameter plate with about .070 of material between holes. The dividing plates I have only use 1/8" holes. I agree that there really shouldn't be any stress on the pin if the spindle is locked.

Ted

 

[Karl_T]

Karl, if you start at the innermost hole on one spiral, your next hole has to be at 255.12º from the previous one (for 90:1 gearing). Which hole will that be on your plate?

There are five spirals, move four each time, or one less than current position each time. I'd suggest a magic marker to keep track of the hole that was already used. wipe it clean when done.

Talvare: A dividing head is geared down. This one 90 times. So, you go around 90 times on the crank to move the head one revolution. This is so you can move very accurate small amounts.

 

[British Steel]

Gentlemen,
I am truly quite ignorant when it comes to the complexities of dividing heads so if I'm not understanding something here I would appreciate a little education. It seems to me that in this particular case where we are dealing with a prime number that the easiest and simplest dividing plate would be one with a single row of 127 holes. I don't understand how the ratio of the dividing head even comes into play. It seems to me that the pin would just be advanced to the next hole on the plate in succession until all 127 equally spaced cuts had been performed. What am I missing ?

Thanks

Ted

Not ignorant, you have an enquiring mind, that's the opposite of ignorant

A 127-hole plate would be simplest IF you had one - they have to be pretty big, as the holes can't overlap... It's not standard provision with dividing heads/rotary tables, probably for that reason?

The worm ratio dictates how many holes you have to go each time around the plate - simply put, if you did have a 127-hole, you'd step around the ratio-number of spaces and you'd get a perfect 127 division - so 40 spaces on a 40:1, 90 on a 90:1 etc.

If that seems illogical, for a full turn of the workpiece you need [ratio] turns around the plate, if you have [divisions] holes then for that full turn of the workpiece you have [ratio] x [divisions] spaces to pass, to dividing by [divisions] you get [ratio] hole spaces - if you wanted 2 x [divisions] (e.g. cutting a 254 tooth gear), you'd have to pass [ratio] divided by 2 spaces, so 45 on a 90:1 dividing head, 20 on a 40:1.

I hope that makes sense, rather than confuses!

Dave H. (the other one)

 

[4GSR]

The high number plate I have with the 127 hole pattern is on a 6.875" dia hole circle. Hole diameter is .093" and the web between holes is approximately .080". That's a lot of holes!

 

[benmychree]

The high number plate I have with the 127 hole pattern is on a 6.875" dia hole circle. Hole diameter is .093" and the web between holes is approximately .080". That's a lot of holes!

Yes, a lot of holes, and how to divide them for drilling????? It's the old one about the chicken and the egg; which came first? The probable answer is differential indexing likely came first and with it, the ability to divide prime numbers.

 

[Bob Korves]

Bob,

Ya, my brain wasn't working very well this morning (nothing new for me). My theory would work fine if the dividing head was a 1:1 ratio . I figured that a single row of 127 holes could be done with 1/8" holes on a 8" diameter plate with about .070 of material between holes. The dividing plates I have only use 1/8" holes. I agree that there really shouldn't be any stress on the pin if the spindle is locked.

Ted

I actually deleted the post you responded to, Ted, because I also realized that we would not likely be using a 1:1 ratio setup, and if we were, it would not be so accurate. The 40 or 90 or whatever to 1 is where the potential accuracy comes from. You were too quick to read my post...