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I have a 40 turn dividing head with the 3 standard plates. The 80 tooth gear is easy but the 75 tooth one has me baffeled to say the least. Without going to a CNC with a 4th axis what are my choices?
Which "standard plates", Brown and Sharpe or Cincinnati? If you have one with 15 holes then 8 holes per tooth is the way to go (that would be B&S), if you have a 30 hole plate, (Cinci) then 16 holes. Part of the problem today is that import manufacturers aren't sticking to tradition, and the tables for dividing heads don't work with their tools. I use an Excel spreadsheet that gets around the problem.
It is all about prime factors. 75 = 3 x 5 x 5. Those are the prime factors of 75. You must have all of these prime factors in either the basic ratio of your table or head or in the hole circle. Since 40 = 2 x 2 x 2 x 5, you only have one of the three prime factors there, one 5. The other two (the 3 and the second 5) must be in the hole circle. The simplest circle with 3 and 5 is 3 x 5 = 15.
To find the number of holes you must jump for each division, first multiply the basic factor of the table (40) times the number of holes in the circle you will use (15). 40 x 15 = 600. Then divide that number by the number of divisions needed; 600 / 75 = 8. You jump 8 holes. If the number of holes given above is greater than the number of holes in the circle, divide that number by the number of holes in the circle. Stop when you have reached a whole number dividend and have a whole number for the remainder. The whole number dividend is the number of turns you must use and the remainder is the number of additional holes per division. Example using the 40:1 head and the 15 hole circle: 40 x 15 = 600 total holes per one rotation. If you want 12 divisions (2 x 2 x 3) you divide 600 by 12 and get 50 holes. That is more than the 15 holes in the plate so 50 / 15 = 3 with a remainder of 5. You would use three whole turns and an additional five holes for each of the 12 divisions.
For the 75 division, you could use a circle with any whole number multiple of 15: 15, 30, 45, 60, 75, etc. Of course, with more holes, you would have to jump by a larger number of holes for each division. A 45 hole plate would give 40 x 45 = 1800 holes. 1800 / 75 = 24 holes per division.
Don't know why you have to jump through all those hoops Paul. dividing head ratio /divisions required gives the ratio. 40/75 = 8/15 or 16/30 . eight holes on a fifteen circle or sixteen holes on a 30 circle. end of story. Peter
The difficult done right away. the impossible takes a little time.
75 divisions is rather well-behaved, with an exact simple indexing solution of 8/15 and its equivalents. The approaches discussed here are fine when there is a solution, but an exact simple indexing solution doesn't always exist. In the Brown & Sharp system, for example, there are exact simple indexing solutions only up to 50: for 51 there is none. For 51 divisions, however, there is an exact compound indexing solution, 10/15 + 2/17. Accounting for all the exact simple indexing solutions and the exact compound indexing solutions still leaves divisions that can't be done. The first of these encountered is 53, but compound indexing movements of 26/29 + 19/31 will give 52.99926 divisions. That would be closer than the precision our machines can usually achieve, so approximate indexing solutions are often quite acceptable.
Developing these solutions would be difficult, but it isn't necessary because it has been done for the Brown & Sharp system and published in Machinery's Handbook, 25th Edition and later (up to 250 divisions) and HSM magazine in 1997 (up to 400 divisions). The 1997 HSM articles are republished in Projects Eight. That work was never extended to other dividing systems, but it could be if there were sufficient demand.
Rich Kuzmack
Pi = 355/113 . . . to less
than 85 parts per billion!
I have a 40 turn dividing head with the 3 standard plates. The 80 tooth gear is easy but the 75 tooth one has me baffeled to say the least. Without going to a CNC with a 4th axis what are my choices?
Thanks
Pete
You now have the justification so this is your chance to buy another tool - 'division-master'.
john
John
I used to be indecisive. Now I'm not so sure , but I'm not a complete idiot - some bits are still missing
Don't know why you have to jump through all those hoops Paul. dividing head ratio /divisions required gives the ratio. 40/75 = 8/15 or 16/30 . eight holes on a fifteen circle or sixteen holes on a 30 circle. end of story. Peter
Peter, you are quite right, it does work. Lets see for the 73 divisions mentioned above: 40/73 gives 40 divisions on a 73 division plate.
But it does not help to explain WHY it is that way. So if you don't understand the idea behind it and mix it up six weeks or months from now and try 73 holes in a 40 division plate you will get a ruined part. If you understand the ideas behind the process, you can correctly figure it out any time in the future and get it right. I very strongly prefer understanding a process to just brute memory of a procedure that works without understanding.
The 73 hole example is better understood if you do realize that 73 is a prime number and it absolutely requires a separate plate with that number of holes or a multiple thereof. You can not get an exact division of 73 parts from any combination of most standard plates if they do not include a 73 hole circle. Without this understanding, many would waste time searching for such a solution when none exists.
Understanding vs. Brute Memory
Paul A.
SE Texas
Make it fit.
You can't win and there IS a penalty for trying!
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