Need Gear Train Calculation Help

Lee in Texas

Lee in Texas

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I need to know how many gears and how many teeth on each for making a miniature Universal Dividing Head. I would like to reduce 80 (or more) turns of a Sherline X table handwheel to one rotation of a spindle. The spindle is a Sherline headstock. I want to cut spiral flutes without CNC.

If I have to machine a gear bracket to make a train of 4 gears, that's OK.

Ugh. It's embarrassing to admit I don't remember high school math formulas.
 
Good question!

Let's take the case of a 10 tooth and a 20 tooth gear. If you turn the 10 tooth gear 1 turn, then the 20 tooth gears turns 1/2 turn. So 2 turns of the 10 tooth gear turns the 20 tooth gear 1 turn so the ratio is 2 to 1 (2:1)

Now let's attach another 10 tooth gear to the 20 tooth gear and then drive another 20 tooth gear with that, so another 2:1 ratio. So to get the total reduction in the four gear system, you multiply the two ratios 2:1*2:1 = 4:1 total reduction. If you add another set of the same gears you get 2:1*2:1*2:1 = 8:1 total reduction.

So choosing a set of gears that would give you an 80:1 reduction could be done several ways, for instance, a 10/80 tooth combination would give 8:1 and another 10/100 combination would give 10:1, for a total reduction of 80:1

Here is a little gear case I whipped up for a project, this one is a 16:1 reduction, 4:1*4:1, consists of two 20/80 gear combinations. The output is in line with the motor in this case. It's about 4 inches wide by 6 inches long, and just over 1 1/4 inch thick. The gears are 3/8 thick. The green and red gear are coupled together, the white and yellow gear turn independent of each other and have a thrust bearing between them.

I hope this helps

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You could also do it with a worm and worm gear from Boston Gear. Amazon has 80:1 worm gears and the descriptions tell which worm to use.


Steve Shannon, P.E.
 
Thanks. I'm not sure I've got it 100%, but I'm getting there.

I plan to mail order a variety of these:

https://www.servocity.com/html/32_pitch_aluminum_hub_gears___.html

Along with some smaller brass pinion gears.

Just out of curiosity, I used a piece of string and a cardboard tube to visualize what 1 turn in ___ inches looks like. I'll need to reduce more than 80:1 to get the look I want with the spiral flutes. BTW the whole idea is for the kits sold by Woodcraft (minus a handle that is lathe turned by the customer). I got mom started and showed her to polish up the pieces for a shaving set for my brother. She did a great job, and the faux tortoise shell acrylic is so shiny, it looks like glass. He was super surprised and impressed. Now he and I plan to make some of the same kind of things. I think fake ivory would look great as a handle for a shaving brush, razor, and stem for the holder.
 
It looks like Servo City has some reasonable prices on gears, the ones I bought for my project above, from Boston Gear was $271 for the 4 gears + 1 keyed hub.

If you need more than 80:1 ratio then a worm gear might be in your future. Using spur gears will get you there, but it might be easier using a worm gear setup. Most rotary tables have a 90:1 ratio so that might be an option, but some of the small ones are 36:1 or 72:1 so you have to watch what you buy.

Another method might be to use a stepper motor and drive the steps with an encoder attached to the hand crank, this way you could have electronic gearing with ratio changes with a flick of a switch.

I'll be looking forward to seeing some pictures of your projects, sounds interesting.
 
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I hadn't considered using the Sherline rotary table, but I also had forgotten about it already being geared down. I have one, but I would need a way to make the rotation turn 90 degrees. That is an interesting option, though.

I am wondering about a geared down motor to drive the X axis, if only for use with the divding head. With a reduction ratio of 200:1 or more, cutting 150 or so 3" long flutes is a LOT of turns.
 
I'm trying to get my head around exactly what you are doing here. Do I understand correctly that you want to cut a spiral flute around a pen barrel that makes one turn in 3 inches?

Assuming the your lead screw is a 0.200 pitch, that is 5 turns/ inch. So 3 inches * 0.200 = 15 turns. To turn the spindle 1 turn in 3 inches, you would need a 15:1 reduction between the hand crank and the spindle. That could be done with a 4 spur gear setup. Or you could use a small planetary 15:1 gearbox, or some combination of both.
 
I'm looking for 1 turn in 8-10 inches. I like the look of that better than 1 in 3 or 4.

The Sherline lead screw advances the table .050" for each turn of the handwheel/20 turns per inch. A spiral that rotates 1 time in 10 inches needs 200 turns.

That "150" number in my above post was a typo. I meant 10 flutes (or so).
 
Ahhhhh..... Makes sense now:)

Given what you want to do it seems like the easiest way would be to hang a couple of stepper motors on it, and run it with Mach3 software. Infinite gear ratios that way. You don't even have to buy the Mach3 software, the demo version will run 500 lines of code, and all you need to do that project is two lines of code, just one simple X-Y move. The steppers and drives probably cost less than the gears.

I would probably go with a stepper to power the lead screw in either case. You would get much better control over the speed.
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Whoa. I'll have to look into that. I have been wanting to go CNC, but I don't know anything about it. Maybe it's time to learn.
 
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