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A little dividing head help ???

rockfish

Titanium
Joined
Aug 27, 2006
Location
Munith, Michigan
OK....... I've used a dividing head probably 2 or 3 times in more than 20 years, so every time I learn something about them, I forget it all by the next time I need to use one. I remember a friend telling me that with a 1:40 ratio dividing head, he almost always used a 18 hole plate, because he said with that plate you could do most any hole pattern with it. He wrote down some examples of how he figured the math........ for example 60. He always divided by 9. So....... 9 goes into 60, 6 times, with 6 remaining, which he put into a fraction of 6/9, then he wrote that 9 went into 18 two times, then multiplied that 2 x 6 and come up with 12................. so 6 turns and 12 holes. If you can, at all understand what I just wrote, can you explain the math ??? He's converting the fraction somehow, I faintly remember learning something about this in school about 34 years ago, but never used it again and have completely forgotten most of it.

I have three holes that I need to index on a dividing head. The first hole is top dead center, then another hole at 50 degrees from the first, then another hole 90 degrees from the first.

I need to figure out how to index this part.



Frank
 
You could trig out your 3 positions at 0, 50, & 90 degrees.


No expert on this, but you could use any hole circle that is divisible by 9 w/ a 40:1 ratio dividing head. Any plate w/ a hole circle divisible by 9 will get your circle divided into 36 divisions (every 10*). That would get you your 0, 50 & 90 degree positions. Plate circle such as 18, 27, 36, 45, etc.

To increment 10* it would be 1-1/9 turn per every 10* increment on a hole circle # divisible by 9

EDIT: This walks you through the steps: http://www.atmsite.org/contrib/JSAPP/divide/divhead.html
 
So, if I used a 18 hole plate, that would be 1 turn and 2 holes ??? Just trying to wrap my mind around the math end of it. Not my strong suit.
 
The 90* is 10 complete turns 10/40 =1/4= 90/360.

The 50* is 5 turns and 27/49(.551) as it is 5.555555555555 turns

50*=5 turns and 9.9183673 holes on a 18 hole plate.
 
50*=5 turns and 9.9183673 holes on a 18 hole plate.

Wha? calculator abuse?

(holes in plate * worm ratio ) = ( # of holes per div * desired # of div )
holes in plate = 18
worm ratio = 40
desired # or divs = 36

# holes per div = (18 * 40 ) / 36 = 20 = 1 turn + 2 holes per 10 degrees

50 deg = 5 turns + 10 holes, no significant figures required

Best, Rich
Richard McCarty, Conservation and Restoration of Antique Clocks
 
Morsetaper2's link distills it pretty well. There is no fancy math at all. With a 40:1 head, you divide 40 by whatever number of divisions you want to do.

40/36= 1 1/9, so any plate with a hole count divisible by 9 will work. 1 turn + 2 holes in an 18 hole plate, for each 10 degree move, as in the above post.

What seems to trip people up is setting the sector correctly for the holes. The plunger has to move 2 holes, so you would set the sector to span 3 holes. One for the rest position and 2 to move. And don't forget to move the sector forward after each division ;).

If you find you have a bastard division to make (recently had to make a 243 tooth gear), you can draw up a hole pattern in CAD and stick it on a plate. For the 243 tooth gear, with my 60:1 head, that's 60/243, reduces to 20/81; no 81 hole plate here, so I drew an 81 tooth hole pattern, stuck it to a plate with double face tape, and just set the plunger on the dots. Any angular error with eyeballing the plunger on the dot is reduced by a factor of 60 (or whatever your head may be, usually 40), so plenty accurate.

Any scientific calculator will convert the divided number to its lowest fractional form.
 
Since no one mentioned it, it might be one of those self-evident things that needs no explaination, or could be an a-ha moment that turns on a light for someone. Your friends magic number "9" are the degrees one turn advances the workhead with a 40:1 dividing head, 360°/40=9°.

So your job is to determine how many 9's, (full turns) it takes to rotate the work 'til there are no full turns left and to determine the fractional remainder, which must be an even divisor of the chosen ring of holes, as in Morsetaper2's,

18 hole plate: 1 full turn + 2 holes

27 hole plate: 1 full turn + 3 holes

36 hole plate: 1 full turn + 4 holes.

Thinking of it in that way, prepares you to use Screwmachines 60:1 or any other ratio head by the simple 360°/ratio= degrees per turn. 9 is not always the answer.:)

Bob
 
Hint: don't count holes when setting a sector, count spaces. For example, the 18 hole circle should be thought of as an 18 spaces circle. If you count spaces you are far less likely to make a mistake, because the first space is never zero, but the first hole is.
 
Srewmachine has it right.

Dividing heads are very easy.
40:1
18 hole plate
60 divisions = 40 /60 = 4/6= 12/18 That is 12 holes on a 18 hole circle.

Next: 4 divisions
40/4 = 10 full turns

Next 6 divisions
40/6 = 6 turns and 4 holes on a 6 circle or 12 holes on a 18 circle.

Next: 72 divisions
40/72 = 5/9 =10/18 = 10 holes on a 18 hole circle.

If you have more than one plate you need to find a number that goes into any number on your plate.
But it is always 40 divided by the number of divisions you are looking for.

Sample: 46 divisions
40/46 = 20/23 = 40 holes on a 46 circle or 20 holes on a 23 circle.
With the exception of some prime numbers where you have to use a gear ratio for indirect dividing.

You need to find a number that can be divided into both - 40 and the number you are looking for.
There are many other ways to do it - just plain knowing your fractions.
But remember - bring your left sector pointer up against the index pin and than count the hole you need to move.

Ps.: On a 60 : 1 head it is always 60 divided by the number you want.

If you have a Machinist Hand book - it's in there. Also gives you the setting in degrees for your dividing head.
 
I go about this from the other end. I want an initial hole, and one at 50°, and one at 90°. Center the piece under the drill chuck. Move table one pitch radius. Drill initial hole. The method below uses units to guide us. Remember, in fractions you can divide the numerator and denominator by the same number and it doesn't change the fraction value. So 3/12 can be changed by dividing the top and bottom by 3, to get 1/4. Same for units. If I have x work turns I want, and I know that there are 40 plate turns per workpiece turn, I can multiply x workpiece turns by 40 plate turns/workpiece turn. We can divide the numerator and denominator both by 1 workpiece turn to get the answer in plate turns. The point is, just as you can eliminate common factors, you can eliminate common units in fractions.

We want to turn the work piece 50° by turning the index plate a certain number of turns.
50° is 50/360ths of the work turning a whole circle.
40 turns of the plate (whatever plate you have) is the work turning a whole circle

50/360 workpiece turns times 40 plate turns per workpiece turn = 40*50/360 plate turns = 2000/360=100/18 = 50/9 plate turns.
50/9 is five, with a remainder of 5/9.
That is, 50/9 whole plate turns is 5 plate turns, plus 5/9.
This is the same as 5 plate turns, plus 10/18ths.
So the 50° hole is obtained with 5 plate turns, plus 10 holes.

If the 90° is in the same direction as the 50° hole (that is,the holes are at 0°, 50°, and 90° as opposed to 0°, 50°, and negative 90°, that is 270°) then you need 40° more. This is then an additional
40/360*40 = 1600/360=160/36=80/18=40/9 plate turns
This is 4 with a remainder of 4. So you turn the plate 4 complete plate turns, plus 4/9 of a turn
Same as 4 complete plate turns, plus 8/18ths.
4 turns plus 8 holes.

If the 90° is really a negative 90°, I'd continue in same direction (actually, I'd start with the -90 hole, then go 90 to the 0 hole, then another 50 to the 50 hole). But to get to 270 from the 50 degree hole you'd need an additional 220 degrees

220/360 times 40 = 880/36 = 110/9, or 12 whole plate turns, plus 2/9th, or 12 plate turns plus 4 holes in the 18 hole plate.

This is a little different than Bob Campbell's approach, but you can see that it works out the same: for the 50° turn, you divide 50° by 9° and get five turns, which moves youu 45°. The additional 5 degrees you get with the product 5 degrees(work) * 18 holes/9 degrees(work), and you get 10 holes. Or, rather, 10 spaces moved. Same result as above.
 








 
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