Dividing head math for large # of gear teeth

[LEEQ]

I am brainstorming on making a 127 tooth gear. I'm looking at the destructions for the dividing head. The example there is for a 17 tooth gear with a 17 hole dividing circle and a 90 to 1 gear ratio tool. They show you to divide 90 by 17, coming up with an answer of 5 with a remainder of 5/17ths. That would be 5 turns plus 5 holes on the sector arms of the 17 hole dividing circle. That's all hunky dory, but my number is bigger than the 90 from the gear ratio. My thoughts are to mill a 127 hole dividing plate, mount it up to the head and do the math to make it work. When I divide 90 by 127, I come up with .7086614. I'm just not sure how to turn that number into a holes in the sector arm number. Remember the gear ratio of your tool is pretty irrelevant. If it is 40 to 1, show me the math for say a 47 tooth gear with a 47 hole dividing circle with your 40 to 1 tool. I hope that makes sense. If someone can illuminate this for me with one example, I can bend it to my will from there. Thanks ahead, Lee.

 

[jwmelvin]

127 is a prime number. So you would need a dividing plate with 127 holes because you want to turn 90/127 turns on the input shaft to get the output to rotate 1/127. I think that’s right? Any time your ratio and desired count don’t have a common factor, you’d need the dividing plate to have the same number of holes as the intended gear has teeth?

 

[LEEQ]

yes as stated above I would be using a 127 hole dividing circle.

 

[LEEQ]

It looks to me like you are suggesting 90 holes in the sector arms, and to turn the crank that far every time you index a tooth. Do I understand you right? That sounds pretty good, but I'm not sure how to check it short of doing that 127 or128 times and see if I land where I started. I'm hoping to find a mathematical way to figure this problem. I'm sure that not every gear I want to cut (such as a 100 tooth gear) is going to be a prime number and demand a hole plate with exactly the same number of holes as teeth on the gear. If I can see how it's done by math, I can then fairly easily extrapolate the difference for using say a 20 hole circle for the 100 tooth gear. I'm here asking for help because I clearly can't see the forest for the trees.

 

[LEEQ]

Ok, so I'm testing your approach with a gear that's in my destruction manual chart. One that's bigger than 90. I went with 100. I put 90 over 100. I then reduced both numbers, dividing by 5, to come up with 18 over 20. I do have a 20 hole circle. That gives us an answer of 18/20ths of a turn, or 18 holes in the sector arms. This checks out with the chart. Outstanding. It would stand to reason (to me anyway) that 90 holes on a 100 hole circle would accomplish the same thing. So on my 127 that can't be reduced 90/127th's ( or 90 holes on the 127 circle plate) looks golden.

 

[tcarrington]

Another option is something you don't have - a compound dividing head. Let's let that one alone.
Everything stated above is correct. Rest assured that if you set if up correctly and step 90 holes for each tooth on a 127 hole plate, you will arrive on target, as long as you don't get caught by back lash. I would stick with this, carefully preparing the 127 hole plate. That will have some challenges.

Another option might be a list of angles down to the resolution of a rotary table - no one really likes doing that.
Finally, an electronic dividing head - more gearing and a high resolution of steps plus the automation of stepping perhaps.

 

[LEEQ]

By golly, I think you found the forest for me. I'd love other input. I'll bet there are other ways to look at this

 

[LEEQ]

I'm working with what I have, the 90 to 1 dividing function of my rotary table. I don't have the plate, but the dro on my mill will let me make the plate I want. I can always go back and add other hole patterns to it as needed too.

 

[LEEQ]

I'm also considering making the plate such that it can be mounted to the face of my rotary table with a large enough hole to accommodate my collet chuck sliding into the table's center. I'm sure I could rig up a gizmo to hold the pin/handle assembly out of the rotary table. I could direct index then. I wanted to solve the problem of simple dividing though. Any thoughts as to what's potentially more accurate? Direct indexing or simple indexing?

 

[tcarrington]

indeed - beware the spacing. you probably have up to 50 something hole plates. Some folks make a larger diameter and arm. Another path is a small pin.
Direct indexing is also good. Consider the hole placement error is divided by 90 on your dividing head. Your plate might be off a little and it won't show up after dividing by 90.