Gear help needed

[Lo-Fi]

Ah, so we're dealing with a fixed centre distance. What I'd do is turn up a quick blank at the root diameter to verify. Zm - 2.5m = 109mm. If that doesn't fit with clearance you're in for some serious time with the thinking cap on.

 

[Suzuki4evr]

Ah, so we're dealing with a fixed centre distance. What I'd do is turn up a quick blank at the root diameter to verify. Zm - 2.5m = 109mm. If that doesn't fit with clearance you're in for some serious time with the thinking cap on.

That sounds like plan to me. Now I must find time to do this,because I made these gears a while ago and only git time to fit them a couple of days ago. And have a few jobs that must get done before I close up shop for the holidays. I work from home,but I must rest too and before I close, I must make time to do other maintenance on the machines. But I will keep you updated.

 

[Lo-Fi]

Time: the eternal enemy. Take it easy

Might as well turn that 60 tooth you accidentally cut down, save a bit of work.

 

[Suzuki4evr]

Time: the eternal enemy. Take it easy

Might as well turn that 60 tooth you accidentally cut down, save a bit of work.

I just measured that gear and it measured +-109.30 at the minor,so I might be good with the OD.

 

[Suzuki4evr]

I would just like to correct myself from post #30. When I said pinion gear,I meant to say idler gear.

 

[Suzuki4evr]

You need a 57-hole plate and to advance 40 holes for each tooth for a 57-tooth gear.

Hallo Brino. I have made a 57 hole plate to use for the 57 tooth gear.

Can you tell me how did get to advancing 40 holes to make a 57 tooth gear? I would just like to also understand the math behind it.

 

[Lo-Fi]

40 (head ratio)*57(holes on the plate)=2280 holes for one revolution of the chuck

Divide 2280 by the 57 index moves you want, you get your 40 holes number back out.

With indexing, the magic is ending up with a total number of holes moved for a complete chuck rotation being divisible by the number of divisions you want to index by. Why it isn't taught like this, I don't know!! Too much reliance on tables, maybe.

Really nice work on the plate!

 

[brino]

Can you tell me how did get to advancing 40 holes to make a 57 tooth gear? I would just like to also understand the math behind it.

@Suzuki4evr

Hi Michael, Sure, lets go thru it!

@Lo-Fi provides one method above that works great.....it's just not the way I think....

Note, that we could convert things to decimals along the way, but at the end we'd need to turn an ugly decimal number back into a fraction.
It's easier to just leave it as fractions thru out.

You want to cut a 57-tooth gear.
Every tooth therefore needs to be 360 divided by 57 or 360/57 degrees apart.

You said earlier that you have a 40:1 worm gear ratio in the dividing head.
So 40 turns of the input handle gives you one turn of the output shaft or 360 degrees.
Therefore each single turn of the handle gives you (360/40) degrees rotation of the output shaft.

Now we can calculate how many handle turns to get the required output rotation.
We need to divide the angle we want (angle for each tooth) by the angle we get from one full turn.
That will give us the number of turns of the handle for each tooth.

That's 360/57 divided by 360/40.
By the rules of dividing fractions we can "invert and multiply".

So it becomes 360/57 * 40/360.
Now we can cancel the two 360's (since we have one on the top and one on the bottom)
that leaves: 1/57 * 40/1 which is simply 40/57.

That tells us that the final answer is 40 holes on a 57-hole plate.

This is all available in tables. However knowing it from "first principles" allows you to work it out when you have a goofy worm ratio, or to work backwards to see what plate you'd need to make what gear, even if it's not in the table.

If anything is unclear, let me know.
-brino

 

[Suzuki4evr]

Why it isn't taught like this, I don't know!!

Well I don't know about that. Everything I know about a dividing head is what I taught myself through reading up,YouTube and this site. Thanks for your explanation on how to get to that number. Guess I haven't finished learning yet.

---

 

[Suzuki4evr]

@Suzuki4evr

Hi Michael, Sure, lets go thru it!

@Lo-Fi provides one method above that works great.....it's just not the way I think....

Note, that we could convert things to decimals along the way, but at the end we'd need to turn an ugly decimal number back into a fraction.
It's easier to just leave it as fractions thru out.

You want to cut a 57-tooth gear.
Every tooth therefore needs to be 360 divided by 57 or 360/57 degrees apart.

You said earlier that you have a 40:1 worm gear ratio in the dividing head.
So 40 turns of the input handle gives you one turn of the output shaft or 360 degrees.
Therefore each single turn of the handle gives you (360/40) degrees rotation of the output shaft.

Now we can calculate how many handle turns to get the required output rotation.
We need to divide the angle we want (angle for each tooth) by the angle we get from one full turn.
That will give us the number of turns of the handle for each tooth.

That's 360/57 divided by 360/40.
By the rules of dividing fractions we can "invert and multiply".

So it becomes 360/57 * 40/360.
Now we can cancel the two 360's (since we have one on the top and one on the bottom)
that leaves: 1/57 * 40/1 which is simply 40/57.

That tells us that the final answer is 40 holes on a 57-hole plate.

This is all available in tables. However knowing it from "first principles" allows you to work it out when you have a goofy worm ratio, or to work backwards to see what plate you'd need to make what gear, even if it's not in the table.

If anything is unclear, let me know.
-brino

Although your calculation does make some sense to my non mathematical brain,somehow Lo-Fi's method makes better sense to me. Thanks for explaining. I do wish you could have been my math teacher in high school though. Maybe I would not have just made it by the skin of my @$$.