Gear Formula

[chris mabbott]

Would anyone happen to have the formula for calculating the size of gear needed for the hour wheel?

I have a PW that is missing this gear and I would like to determine the number of teeth needed. Not sure if you could figure this out correctly with the normal gear ratio formula or if there is a special watch making calculation available :

[Bob Tascione]

Hi Chris,
This should work. I’m probably going to make this look a lot more complicated than it really is. If you jot down the numbers in place of the variables as I go through the simple process it will all be clear to you.

You’re after a 12 to 1 reduction so we’ll designate a few variables for gear tooth and pinion leaf count to work with.

a= Minute Wheel count
b= Hour Wheel count
c= Cannon pinion count
d= Minute Wheel Pinion count

Formula: (a x b) / (c x d) = 12

So since you’re solving for ‘b’ then 12 x (c x d) / a = b

Hope I got this right.
Bob

[chris mabbott]

Thanks Bob,

crystal clear and perfectly understandable, much appreciated

I’m sure it is in the Chicago school book, but there is no index in my copy, so as usual, when I’m looking for something I never find it, when I’m not, it hits my nose 😆

[tmac1956]

Chris:

There is an index in the LuLu version buts it’s not in the very back… I saw it the other day and was surprised. It’s somewhere near the back just not in the same spot as 99.9999_% of the books out there.

Just FYI…
Tom

[chris mabbott]

Thanks Tom I’ll check that out, I have the LuLu copy but I was looking in the obvious places, front & back

[daryn]

Watcha ,
To find the dimensions of the wheels and pinions and to find the size module cutter required,these calculations require metric millimeters
Firstly the distance of centres divided by the sum of half the teeth and half the leaves , this gives you the MODULE size of the gear

The outside diameter of the wheel is the MODULE x (the number of teeth +2.71)
The 2.71 is an addendum allowance to give you the actual diameter of the wheel
For pinions it’s the same but with an allowance of 1.71
Hope this helps ,
Though quite often with earlier clocks this has to be taken as a “rough guide” with modern clocks it’s fairly spot on

Daryn

[chris mabbott]

Thanks Daryn, it does, the only thing I’m not sure of is what “leaves” refers to? I think I might have an idea but would just like to confirm or deny it please

[arutha]

“Leaves” of a pinion, wheels have teeth, pinions have leaves.
Paul.

[chris mabbott]

Then I was completely waay off base 😆 Thanks Paul…

[willofiam]

Thanks guys, good info, what I am confronting in my mind is how do I know what shape and size to make the cutter if there is no example? I think I am going to the drafting table to draw out some of this, hopefully it will help wrap my head around it. I am feeling a bit dense right now. William

[daryn]

There’s a good book by j m wild “wheel and pinion cutting in horology”
There’s a set of tables in the back with dimensions etc. For making cutters , very worth a read

[tmac1956]

@Chris Mabbott wrote:

Thanks Tom I’ll check that out, I have the LuLu copy but I was looking in the obvious places, front & back

Chris:

The index turns out to be only for the section entitled “Tools and Materials of the Trade” which is of little use to the main of the book.

My mistake!

Later,
Tom

[chris mabbott]

Tom I really enjoyed that section and I spent a long Sunday morning going through that part, really interesting to see those old ads for tools and I even found out what a few of them were for

[willofiam]

Thanks Daryn, I forgot that Paul had mentioned this book to me, just ordered one. Have fun, William

[chris mabbott]

William if you keep learning this I won’t have to worry, I’ll just send you the parts I need repairing/making, obviously I will be using the forum discount code of BROTHER to receive my 80% off 😆

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