# Cutting my first Miter gear



## Brian Rupnow (Sep 18, 2013)

I would like to try my hand at cutting a pair of 45 degree miter gears, similar to the ones that Swifty cut in his excellent "Article" on cutting miter gears. My cutters, (I have the full set) are 24DP and 14.5 degree pressure angle. I have some round brass stock with a maximum 1" diameter. What I HOPE to do is cut a pair of 45 degree miter gears from this 1" stock. I have Ivan Laws book "Gears and Gear Cutting" and---Holy Crap, there's a lot involved in the calculations to cut the blank, even before you start trying to cut the teeth. I am going to fumble away at this, just to see if I can actually do it or not. This is not meant in any way to upstage Swifty's thread under "Articles" on this forum. This is just a record of how I bumble through it. Don't try to follow me and build a set yourself, based on what I am doing, because I may totally screw this up. First part of the trick will be to use all of the calculations to determine the dimensions of the blank gear form.


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## Philjoe5 (Sep 18, 2013)

Good luck Brian.  Seems like many of us are on the same path, but at different mile markers.  Once I got some reasonable spur gears I thought I'd like to make some bevel or miter gears.  That's in the future though so I hope to learn from this thread.

Cheers,
Phil


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## Brian Rupnow (Sep 18, 2013)

According to Ivan Laws book, the overall gear dimension will be a resultant, based on whatever number of teeth you decide to use plus some relatively wicked geometry/trigonometry. I'm going to cheat a bit and model it in Solidworks, where by putting in the pitch circle of the small end (which will be the same as the pitch circle diameter of an equivalent toothed spur gear) and an angle of 45 degrees, the computer will calculate some of the unknowns. I COULD do it with trig, but since I have the software I will use it. I am going to guess, to get started, and use a gear with 18 teeth.


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## Swifty (Sep 18, 2013)

That's the best way to go Brian, I drew mine in CAD by putting in the PCD and then adding the addendum and dedendum, this gave me where the teeth should be, I just drew the rest around this. I searched a lot of information from gear suppliers regarding sizes for their gears, but this did not work out well. I think the main difference with purchased gears is that they are cut by a different method, making the blank sizes different.

The biggest tip that I can give you is to use a marking pen to show where the first tooth cut is, it gets confusing when you come to do the follow up 1/4 turn cuts as you have to move the mill table up or down and then cut on the correct side of the tooth.

I'm looking forward to following this thread.

Paul.


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## Brian Rupnow (Sep 18, 2013)

Some calculations showed that an 18 tooth gear was going to end up being a greater overall diameter than the 1" stock I have to work with. I messed around with the numbers until I found that a 15 tooth 24dp gear would result in an overall diameter of less than 1" so that's what I used. This is the drawing of the blank I arrived at, with a description of how I came up with the dimensions. 


 

View attachment 15 TOOTH MITER GEAR.PDF


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## Swifty (Sep 18, 2013)

Did a quick calculation Brian and I think that your bar stock is too small. With the information that you gave us in the previous posts the PCD on the small end will be 0.75", your 1" bar stock will not be big enough.

NOTE. Our posts were done at the same time, I see that you have found this out.

Paul.


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## Brian Rupnow (Sep 18, 2013)

Swifty--My old mother used to say "Great minds think alike, and fools never differ!!"--I hope you and I are in the "Great minds" category---


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## Swifty (Sep 18, 2013)

The drawing looks great Brian, does that mean that we will have gears before you go to bed tonight? 

Paul.


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## Swifty (Sep 18, 2013)

I think that in practice the undercut at the front of the gears is unnecessary, although I did include it in mine.

Just had another thought Brian, because you are cutting 15 teeth just make sure that you choose a dividing plate that allows you to shift 1/4 of a turn.

Paul.


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## Brian Rupnow (Sep 18, 2013)

Swifty--I'll have to think that one through in the morning. I go a little bit crazy with dividing plates.


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## Brian Rupnow (Sep 19, 2013)

In Ivan Laws book,  where he calculates the number of teeth on the back cone, he gives the formula 1/sin45 x 20=28.8 and then establishes that he will use a 28 tooth gear so will use a cutter appropriate for that number of teeth. He is making his calculations based on a 20DP gear with 20 teeth, and I don't know which 20 the one in his formula refers to. I am using a 15 tooth gear with a 24DP so which number should I be using in that formula?--The 15 for number of gear teeth, or the 24 for DP?


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## Brian Rupnow (Sep 19, 2013)

Okay--based on a direct measurement of my layout, the pitch diameter at the rear side of the cone looks like 0.908, which multiplied by the DP of 24 =21.8, so round it off to 22 teeth.
If I use Ivan Laws formulae and use the number of gear teeth at the small diameter of the come (which is 15t) then the formula gives 1/sin45 x 15=21.2 so I assume it must be the number of teeth on the small side of the cone that gets used in the formula.
My gear cutting charts show that for a 22 tooth gear you use a #5 cutter which cuts from 21 to 25 teeth. It is the calculated number of 22 teeth that determines which gear cutter you use, even though the gear will ultimately only have 15 teeth.


 

View attachment 15 TOOTH MITER GEAR.PDF


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## Brian Rupnow (Sep 19, 2013)

Now comes the trick part---The divider plates. My rotary table has a 90:1 ratio. My charts say that to cut a 15 tooth 24 DP gear, I can use any divider plate. 360 degrees divided by 15 teeth =24 degrees between teeth. 360 divided by 90=4 degrees rotation for each full turn of the crank on my rotary tables handle. 24 degrees divided by 4 degrees=6 full turns of the crank on my rotary table. This is fine for the initial cuts, (I think) but then I have to rotate the gear by a number of degrees equal to 1/4 of the tooth indexing angle, to do the next series of cuts. If there are 24 degrees between teeth, then 1/4 of that is 6 degrees rotation of the table. To get 6 degrees rotation of the table, I have to turn the crank on my table 1.5 full turns. I have a 20 hole divider plate. Now one full turn of the crank on a 20 hole divider plate will move the table thru 4 degrees. So--if I turn the handle thru 1 1/2 turns that gives me 1.5 x 4=6 degrees, which is 1/4 of the table rotation between gear teeth. That should mean that by turning the the crank thru one complete revolution and then advancing it another 10 holes when using a 20 hole divider plate, that I have advanced the rotary table 1/4 of the angular distance between gear teeth.


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## Cogsy (Sep 19, 2013)

I'm trying to get my head around this Brian, but I don't have a rotary table, only a dividing head. Maybe they work different, I don't know.
If they work the same, the 360 degrees divided by 90 ratio of the table = 4 degrees per rotation of the crank, as you said. So 6 full turns of the crank = 6 x 4 degrees = 24 degrees. You then need 6 degrees rotation, which equals 1.5 turns of the crank, again, as you said. Then, and this is where I get hazy, you say 1 turn of the crank now changes to 90 degrees if you use a 20 hole plate. If I disregard this statement, and use my working knowledge of a dividing head instead, you now need to go 30 holes on your 20 hole plate to equal the required 6 degrees (1.5 turns). 
I figure there must be a difference between the tools that I'm not aware of, although the info I've been googling doesn't show me what the difference is.
Feel free to let me know where I stuffed up!


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## Brian Rupnow (Sep 19, 2013)

I have just returned from having my spine pulled out thru my buttocks by the physiotherapist, and I think I have come up with the right answer to my gear question. Please have a look at post #13 and see if I have it right this time.---Brian


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## Brian Rupnow (Sep 19, 2013)

This is what may (With the grace of God) become two miter gears. Its a round piece of brass, 1" dia. x 2" long. Since I need something to hold onto with the 3 jaw chuck on my rotary table, I am going to cut a miter gear on each end of it and then split it in half.--Hopefully!!! In the background is the 20 hole divider plate.


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## Brian Rupnow (Sep 19, 2013)

Here we are with a 0.5" diameter x 0.088" deep counterbore in each end. I used a center drill in each end first because my 1/2" endmill is a 4 flute and doesn't cut right at the center.


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## Brian Rupnow (Sep 19, 2013)

Both ends are turned to a 45 degree angle, 0.141 back from the end as per the drawing. This newly exposed surface is what will actually become the "tip" of the gears after they are cut. The next step is to set things up in the rotary table. Even though there is an area of reduced diameter immediately behind the tip of the teeth, I don't have to put that in yet. If I did, it would be too difficult to hold properly in the 3 jaw chuck on the rotary table. It can be put in later.


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## Brian Rupnow (Sep 19, 2013)

Okay--I lied!!! There was one more lathe operation before I head over to the rotary table. I cut the internal 45 degree surface that runs from the front of what will become the teeth in to the .5" diameter which I put in during my first step. This wasn't a perfect match, so I put the end mill back in and cut just a tiny bit deeper until everything ran out properly with no obvious ridges left at the junction.


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## Brian Rupnow (Sep 19, 2013)

And just in case nobody thought about it--If this works the way I hope it will, these are the miter gears you need to run the governors on the Rupnow Engine.


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## Swifty (Sep 19, 2013)

Hi Brian, I'm just having my breakfast down here and reading all your latest posts. Now you know why I had to read Ivan Laws book about 4 times before I started to get my head around everything, and then I had to work with the module gear system.

You seem to have everything worked out correctly, now you can see why my earlier comment on choosing the correct dividing plate is important, an odd hole pattern will not allow you to get the 1 1/2 turn, even though it would have been OK for the main cuts.

You are now well on your way to cutting the gears, the only hard part left is when you do your second and third cuts, make sure that you cut on the correct side of the tooth. Ivan Law had a formula for working out the table rise and fall, I gave up at this stage and just adjusted the table so the cutter entered the small end of the gap precisely.

Paul.


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## Swifty (Sep 19, 2013)

And don't forget, after advancing the gear 1/4 of a turn and making all the cuts, you then have to back track that 1/4 of a turn to get back to the initial setting and then turn back 1/4 of a turn for the other cuts.

I suggest that you take the phone off the hook, lock yourself in and don't have the radio on as any distraction at this stage will get you confused.

Paul.


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## Brian Rupnow (Sep 19, 2013)

So---Here is my set-up, which at best I can only call "Buck-Shee". After getting everything set up the first time, I discovered that my "Made in India" divider plates were so large in diameter that they wouldn't fit on the spigot of the rotary table without hitting the mill table, so I had to put some 3/4" aluminum spacers under my rotary table and start over again, so that the divider plates and handle would fit in place. My mill doesn't have a particularly deep throat, so the back end of my rotary table is within a gnats ass of crushing the vertical bellows that covers the front of my column. However, I am set up, the rotary table is set at 45 degrees, (or as close as can make it). The centerline of the cutter is on the centerline of the 3 jaw on my rotary table, and I'm about to cut loose. I will cut the first set of teeth tonight after dinner, and wait until tomorrow morning (after good wife has gone to work) to start any of the tricky/funny business.


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## Brian Rupnow (Sep 19, 2013)

That seemed to go well!!! At least when I got all the way around I was cutting air, not a half tooth. It looks a bit weird, but should get better with more steps.


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## Brian Rupnow (Sep 19, 2013)

This was just too exciting to wait until tomorrow to make my final cuts. I made the second cut all the way around on all teeth, and then the third cut all the way around on all of the teeth. This necessitated raising and lowering the quill by a calculated amount, and I figured out how to make that calculation--its quite easy. --And by God, it does look good. The teeth are parallel on each side of the crest, but the gaps at the root of the teeth are at an angle, just like they are intended to be. Of course, the proof of the pudding will be seen when I cut the teeth on the other end and split the brass round into two separate gears and mount them in a pair of 90 degree bushings to see how they mesh!!!


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## Brian Rupnow (Sep 19, 2013)

This is the way I calculated how far to raise or lower the quill to take the second and third cuts after the gear was first rotated 6 degrees (1/4 of the angular distance between two gear teeth).


 

View attachment 15 TOOTH MITER GEAR-SHEET-2.PDF


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## Swifty (Sep 19, 2013)

Brian, I'm just a bit nervous, you mentioned that you had parallel teeth and a tapered gap. I don't want to be negative, but I believe that you need tapered teeth and tapered gap so they mesh correctly. I had parallel teeth on one of my trial gears but it was not correct, I can't recall how I got straight teeth. The proof will be if the two gears mesh both top and bottom.

Paul.


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## Swifty (Sep 19, 2013)

I'm still thinking about things, at the large end of the gear, the tooth size at the pitch circle should match the gap size at the pitch circle. Then the teeth will mesh correctly. I see that you marked where the first cut was made, it's important when doing the second and third cuts that you have this first gap bought back to centreline and then offset 1/4 of a tooth in the direction you want. The next cuts must enter the same marked gap first off. I think I entered the wrong gap, and that's why I had straight teeth on one trial gear.

In Ivan Law's book, you will see that the sides of the teeth are all radial to the centre, and this will automatically give tapered teeth.

In my article on cutting the mitre (miter for our American friends) gears, you can see that the teeth are definately tapered in the photo.

Paul.


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## versatile (Sep 20, 2013)

Hi Brian,

I did goof around with cutting my own bevel gears some time ago as well. I found a book by Ernst Wiedmer in my universitys library. It is written in german and metric only, but the formulas are quite simmilar to the ones in Ivan Law´s book. except for he calculates the number of teeth for selecting the cutter by dividing the number of teeht of the bevelgear by the cosine of the angel. but in your case this doesn´t make any difference since it is 45 degrees ;-) 
I would like to post these formulas, but I dont know if I´m allowed to.


Well, I ended up with tapered teeth and tapered gaps just like Swifty. 

Maybe you didn´t move your blank and cutter in the opposite directions when doing the second and third cut?


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## Swifty (Sep 20, 2013)

Another thought, if you moved 1/2 a tooth this would bring the tooth on to centreline, follow up cuts either side of the tooth would make a straight tooth form as well.

Sorry, I think that you might wake up to some bad news.

Paul.


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## versatile (Sep 20, 2013)

hmm, 

I´ve been thinking about my last comment for quite some hours, but I couldnt understand why the blank and cutter should be moved in opposite directions. that way you would be cutting away the entire tooth..

I figured out I missinterpreted the image given with the formulas 

blank and cutter actually have to move in the same direction.. :wall:
Sorry for that missinformation


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## versatile (Sep 20, 2013)

hello,

I had a look at the your pictures again, especially the last one. 
I noticed that the scratchmarks of your gearcutter are not parallel to the top of the tooth. 
Seems like you got the wrong angle in either your rotary table ore your lathe compound. therefore the cuter took a deeper cut at the end of the tooth making its sides look like they were parallel..

In the second last picture you can see (especially at the teeth around the 4 o´clock position) that thei get more "pointed" towards the end. They should be the same hight throughout.


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## Brian Rupnow (Sep 20, 2013)

I THINK I got this right. Its hard to get a good picture of. Perhaps the edges of the very crest of the tooth are close to parallel, but the actual tooth cross section gets larger and larger as it moves from the center towards the outside of the blank. as far as I know, that is what I wanted to achieve.


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## gus (Sep 20, 2013)

Hi Brian and Paul,

Gus is having cold feet cutting mitre gears. Will cheat. No calculations. Copycat from "KG Gear,Japan Cataloque.
The good reason or bad excuse is I have Module 0.8 and 1.0 Metric Gear Cutters.
Paul will be reading your article on cutting these mitre gears. 
Carb done except for the soldering and needle. its weekend fishing again.


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## Brian Rupnow (Sep 20, 2013)

Ahhh---Sweet Success!!! The gears seen to mesh perfectly. This isn't something I would rush to do again, but I'm surprised at how easy it actually is. I don't really need them for anything---I just wanted to see if I could do it. If any of you have been considering cutting your own miter gears, then rush out and buy a copy of "Gears and Gearcutting" by Ivan Laws, read thru my thread, and have a look at the excellent article Swifty did in the "Articles" section of this forum.--The top picture is actually a video and the bottom two are just pictures-Brian


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## Philjoe5 (Sep 20, 2013)

Congratulations Brian, nice work.  Thanks for posting

Cheers,
Phil


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## Swifty (Sep 20, 2013)

Congratulations Brian, I'm so happy for you. When you mentioned earlier that the teeth were parallel, I got very worried. I hope I didn't upset you with my concern.

Paul.


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## Swifty (Sep 20, 2013)

Gus, you cannot use the dimensions that appear in gear catalogues, they use a different method of cutting and the blanks would be too small for you to use. They all seem to use the PCD at the large end of the gear, whereas we use it at the small end.

If you need blank sizes, let me know the module and number of teeth and I will send you a blank drawing.

Paul.


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## Brian Rupnow (Sep 20, 2013)

Swifty--If you hadn't posted your "how to" in the "articles" section, I would never have been brave enough to try this.


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## canadianhorsepower (Sep 20, 2013)

Nice work Brian Thm:Thm:

are you going to put them on your motor??


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## Brian Rupnow (Sep 20, 2013)

Luc--No--I have gears on my motor already. I just made these ones to see if I could. I have set them up in a small frame with knurled shafts and they will go up on my "Bragging Wall". How is the work on your engine progressing?


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## Cogsy (Sep 20, 2013)

Congrats on your success Brian. I may well attempt my own, once I get an appropriate cutter. I'd rather spend the money on the cutter and learn a new skill than buy gears.


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## JAndrew (Sep 21, 2013)

Mr. Rupnow,

Congrats on the gears! Was just wondering what the green goo was on your final mesh test picture? I'm assuming its some kind of Loctite? I'm just wondering the specifics of it for future reference.

Thanks in advance!
-J.Andrew

P.S. Thanks for taking the time to post all these pictures. It's real helpful to us not-so-experienced guys.


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## canadianhorsepower (Sep 21, 2013)

Brian Rupnow said:


> Luc--No--I have gears on my motor already. I just made these ones to see if I could. I have set them up in a small frame with knurled shafts and they will go up on my "Bragging Wall". How is the work on your engine progressing?


 
I'll be spending the hole day on it Sunday so the crank, gear,
and push rod support should be finish. I'm happy that my contract is ready.
the kind of play a trick on me when I was done and delivered they realized
the the email asking for double the order wasn't sent.:fan:
but all of it was delivered yesterday, today is brooming time 
and back at it tomorow


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## Brian Rupnow (Sep 21, 2013)

JAndrew said:


> Mr. Rupnow,
> 
> Congrats on the gears! Was just wondering what the green goo was on your final mesh test picture? I'm assuming its some kind of Loctite? I'm just wondering the specifics of it for future reference.
> 
> ...


 That green goo is Loctite. #638 for "slip fits" and #648 for press fits. The stuff is absolute magic in a bottle.--and it can be separated with application of some heat if you ever have to separate the joint.


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## RichD (Sep 22, 2013)

Good Job Brian!
RichD


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## ddmckee54 (Oct 4, 2013)

The way he cuts the gears may not be exactly kosher, but check out this guy cutting miter gears with home made equipment.

http://woodgears.ca/reader/pekka/routerlift.html 

Don


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