# Gear help needed



## Suzuki4evr (Dec 8, 2020)

Hi guys.

I don't know where I went wrong,but I need some help. I made a set of change gears for my big lathe and I actually posted another thread about this,but I wanted to post a new thread for all to see who maybe able to see where I went wrong. Please bear with me if this is a bit long.

It is four gears and here is the configuration.


Now three gears worked out as planned, but the 57 tooth gear blank finnished with 60 teeth. NOW HOW THE HECK DID THAT HAPPEN. When I put all four gears next to each other, they still mesh but somehow the "57" teeth,that is now 60 teeth,just will not fit when on the machine.











It looks like somehow the OD of the 57 tooth gear is to big,but I can't see where I went wrong. So I will give the information I think you need to HELP me see if I made a calculation mistake.

Here is the info for the gear Module=2.
N=57
With this you are supposed to be able to get the OD for the blank and from there all the other information needed to make the gear.....right? And that gave me 118mm. Could the centre distance between the gear and Idler gear influence the OD of both gears?  And with the given chart I have wich came with my Vertex dividing head I must use a 33 hole plate and move every 22 holes to make a 57 tooth gear,but what I found very interesting looking for my mistake today is this.


What I found interesting is that to make these three divisions, for all three you need to move 22 holes on a 33 hole plate and 60 is one of them. Is that coincidence or what?
PLEASE HELP ME!!!!!!!

If any other information is needed, please let me know and I will post it tomorrow, because I don't have it with me right now.

Thanks in advance.
Michael.


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## benmychree (Dec 8, 2020)

What happened, is that 57 is a prime number, and cannot be divided without a universal dividing head with change gears, on your chart, the change gears are noted beneath the other info for 57 divisions.  I am assuming that your dividing head is not equipped to do this, but if it is, you need to use the indicated change gears, 48, 24, and 40 teeth.  Other than that, nice looking job!  On most lathes, the "banjo" that holds and positions the gears is capable of adjustment for proper mesh.


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## benmychree (Dec 8, 2020)

If you were able to make a 57 hole plate, I think you could accomplish it that way without having a universal head, I do know that the numbers of holes is limited by the relatively small diameter of B&S type plates, 39 being the highest number in the set, and the holes are pretty closely spaced at that.  On the gear that you made, since it is a small diameter for 60 teeth, the teeth would have a smaller chordal thickness that one cut with the proper number of teeth.


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## benmychree (Dec 8, 2020)

I forgot to mention earlier that this method that uses the change gears is known as differential indexing, the process gears the work spindle of the dividing head to rotate the index disc either in one direction or the other while the index crank is rotated.


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## GunsOfNavarone (Dec 8, 2020)

I would think the OD was a tad big...ran it on this calculator....indeed 118mm is correct. Above my pay scale!


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## Suzuki4evr (Dec 9, 2020)

benmychree said:


> What happened, is that 57 is a prime number, and cannot be divided without a universal dividing head with change gears, on your chart, the change gears are noted beneath the other info for 57 divisions.  I am assuming that your dividing head is not equipped to do this, but if it is, you need to use the indicated change gears, 48, 24, and 40 teeth.  Other than that, nice looking job!  On most lathes, the "banjo" that holds and positions the gears is capable of adjustment for proper mesh.


I do have a universal dividing head also,must just check if I havea all the gears,because I picked it up at the scrap yard. The banjo part on wich these gears are sitting has a fixed distance between them but can be set for the up gear clearance.


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## Suzuki4evr (Dec 9, 2020)

benmychree said:


> If you were able to make a 57 hole plate, I think you could accomplish it that way without having a universal head, I do know that the numbers of holes is limited by the relatively small diameter of B&S type plates, 39 being the highest number in the set, and the holes are pretty closely spaced at that.  On the gear that you made, since it is a small diameter for 60 teeth, the teeth would have a smaller chordal thickness that one cut with the proper number of teeth.


I  guess I coul make one using the DRO on my mill right?


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## Suzuki4evr (Dec 9, 2020)

GunsOfNavarone said:


> I would think the OD was a tad big...ran it on this calculator....indeed 118mm is correct. Above my pay scale!
> 
> 
> 
> ...


So if my gear works out with 57 teeth,the gear would mesh with the OD of 118?


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## Suzuki4evr (Dec 9, 2020)

Just got in the shop and checked if I have change gears for the universal DH. I do have the 40 & 48 but not the 24. But I have another problem. Seeing that I got the DH at the scrapyard,there is some gears and parts to fit the gears on,missing. It will take time to make all these components, so I think for this project I must make a 57 hole plate using my DRO. What do you guys think?


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## jaek (Dec 9, 2020)

benmychree said:


> What happened, is that 57 is a prime number



3 times 19?


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## Suzuki4evr (Dec 9, 2020)

jaek said:


> 3 times 19?


Good question.


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## Lo-Fi (Dec 9, 2020)

Do you have a 19 hole plate? 

Making a plate up with the DRO will work well. For one offs 3D printing is quite good enough if you've got that capability. Differential indexing is pretty fun, though.


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## Suzuki4evr (Dec 9, 2020)

Lo-Fi said:


> Do you have a 19 hole plate?


I do.


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## Suzuki4evr (Dec 9, 2020)

Lo-Fi said:


> Do you have a 19 hole plate?
> 
> Making a plate up with the DRO will work well. For one offs 3D printing is quite good enough if you've got that capability. Differential indexing is pretty fun, though.


So do I have it correct if I make one rotation plus one hole on the the 19 hole plate to make a 57 tooth gear?


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## Lo-Fi (Dec 9, 2020)

No, looking at it, 57 is actually a bit of an oddball case. It's not prime _itself_, but is only divisible by primes. So even with a 19 hole plate, you still can't index 57. Custom plate or differential or differential setup it is!


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## brino (Dec 9, 2020)

Michael,

Your gears look great!

Of course, it would be good to understand where the error crept in on the 57 tooth gear.

From this table you showed:



It looks like you need gears A, B  and E in the gear train to the dividing head input shaft when cutting a 57 tooth gear.



Suzuki4evr said:


> So do I have it correct if I make one rotation plus one hole on the the 19 hole plate to make a 57 tooth gear?



I don't think it's that easy......
The output depends on the ratio of the worm and wheel in the dividing head, the hole plate used, plus every other gear in the train.

If you can supply the ratio, and what plates (and gears) you do have, I can help work out other possible combinations.

-brino


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## Suzuki4evr (Dec 9, 2020)

I mentioned it in post #9. Ratio is 40:1 I think.


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## brino (Dec 9, 2020)

I didn't see it here, maybe it's in the other post you mentioned.

Anyhow, I'll go play with some numbers and look at a couple tables to see if you can get there another way.....

-brino


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## Suzuki4evr (Dec 9, 2020)

No harm done.For the universal dividing head I have the 40 and 48 gear but only one plate that goes to 39holes. But like I said there are other components I'll have to make first to be able to use the universal DH for this tipe of operation. My Vertex BS-0 DH has all the plates.


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## brino (Dec 9, 2020)

Nope. Sorry.

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

Otherwise you need to do more complex differential indexing.

If it had been a 90:1 ratio, we could have got there!
(one full turn and 22 holes on a 38 hole plate)




Suzuki4evr said:


> I must make a 57 hole plate using my DRO. What do you guys think?



That's probably the way to go.

Note to check before you start how many holes to specify.
Apparently on some DRO's you may need to specify N+1 or 58 holes _IF_ you specify both start and end angles the same......see this thread:
https://www.hobby-machinist.com/threads/do-what-i-want-not-what-i-say.84534/post-748360

-brino


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## Suzuki4evr (Dec 9, 2020)

Just to cover all the basis. Would it be possible to make a 57 hole plate on a rotary table with dividing plates?


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## Lo-Fi (Dec 9, 2020)

If the rotary table is 90:1 you'd be able to use the 19 hole plate.

To go through the maths:

We know 57 is divisible by 19. So let's take a stab at dividing with that plate. 40 turns for a complete revolution of the chuck, so 40 X 19 = 760 holes for one chuck rev. Now let's check if we can divide that by 58 and get a whole number: 760 ÷ 57 = 13.3333333. So you'd need to move 13 and a third holes each time. Not cool.

The same calc for 90:1 is 90 X 19 = 1710. 1710 ÷ 57 = 30. Ah ha! So that's one revolution and 11 holes for each move. 90:1 works here because it's wholely divisible by one of 57's factors (3). Something 30:1 would work for the same reason. It's easy to see why primes require their own plates or some trickery with differential dividing. 

Just expanding on Brino's excellent post from earlier really


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## GunsOfNavarone (Dec 9, 2020)

Suzuki4evr said:


> So if my gear works out with 57 teeth,the gear would mesh with the OD of 118?


Oh God man! I have no idea! I just happen to have a program that calcs that stuff. You did some damn nice work in my opinion, so disappointing one gear didn't work out.


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## GunsOfNavarone (Dec 9, 2020)

Lo-Fi said:


> If the rotary table is 90:1 you'd be able to use the 19 hole plate.
> 
> To go through the maths:
> 
> ...


I got a nose bleed trying to figure that out! (or more like trying to follow that.) It's like watching David Blaine levitate....


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## Suzuki4evr (Dec 10, 2020)

Lo-Fi said:


> If the rotary table is 90:1 you'd be able to use the 19 hole plate.
> 
> To go through the maths:
> 
> ...


I made a mistake on my post about the rotary table. I forgot to put the word "NO", infront of dividing plates. There is NO dividing plates for the rotary table.   So the same question apply.


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## Suzuki4evr (Dec 10, 2020)

brino said:


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


Lo-fi,now that you gave GunsOfNavarone a nose bleed,can you confirm that no matter how I achieve getting a 57 hole plate that my OD of 118mm is correct and that when I sit with a 57 tooth gear in my hand, that it should now mesh with my the 95 tooth gear on the lathe?


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## jaek (Dec 10, 2020)

You can totally do this on a rotary table, it'll just be a minor hassle.

This is a spreadsheet I threw together with the angular offsets for each of the 57 holes. Just print it out, cross of each row once you drill it.


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## Suzuki4evr (Dec 10, 2020)

jaek said:


> You can totally do this on a rotary table, it'll just be a minor hassle.
> 
> This is a spreadsheet I threw together with the angular offsets for each of the 57 holes. Just print it out, cross of each row once you drill it.


Thank you for this awsome spread sheet. Now there is one more option.


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## Lo-Fi (Dec 10, 2020)

Lol! Yep, spot on with that. Zm + 2m = (57*2)+(2*2) = 114+4 = 118

With the right diameter and wrong tooth count, you've not technically cut a module 2 pitch gear, so the mesh won't be perfect. Is the mesh adjustable by moving the banjo? Or is this a fixed relationship? Difficult to see from the photos. It kinda looks like you've run out of banjo adjustment rather than it being purely a meshing issue?

A pic of the lathe without the gears mounted could be quite handy


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## Suzuki4evr (Dec 10, 2020)

The banjo is not the problem here. As you can see here the pinion gears and the driven gear is on a set distance where as you set the play between the drive and pinion gears.


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## Lo-Fi (Dec 10, 2020)

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.


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## Suzuki4evr (Dec 10, 2020)

Lo-Fi said:


> 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.


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## Lo-Fi (Dec 10, 2020)

Time: the eternal enemy. Take it easy  

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


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## Suzuki4evr (Dec 10, 2020)

Lo-Fi said:


> 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.


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## Suzuki4evr (Dec 10, 2020)

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


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## Suzuki4evr (Jan 20, 2021)

brino said:


> 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.


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## Lo-Fi (Jan 20, 2021)

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!


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## brino (Jan 20, 2021)

Suzuki4evr said:


> 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


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## Suzuki4evr (Jan 20, 2021)

Lo-Fi said:


> 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.


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## Suzuki4evr (Jan 20, 2021)

brino said:


> @Suzuki4evr
> 
> Hi Michael, Sure, lets go thru it!
> 
> ...


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 @$$.


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## Suzuki4evr (Jan 21, 2021)

So I made the gear. Don't get it,don't understand it and don't know what to do. I now have a 57 tooth gear. The gears mesh on the table.


But the overlap by about 2mm on the lathe. The 95 tooth gear OD must be 194mm,and it is,but it is like something is still too big.


The center distance is set,you can't change it. It according to calculations it must be 152mm,and it measures 150, so there lies the 2mm I am talking about. So now the only thing I can do in my opinion is to make afset pin so I can adjust the big gear.


I guess about 2mm offset would be fine or what do you guys think I must do with this whole situation?


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## Lo-Fi (Jan 21, 2021)

Your numbers are right for module 2. I don't know if we discussed this before, but there is such a thing as "profile shifting", which results in smaller or larger gears for the same module and tooth count but with longer or squatter teeth. Either that's the case or the machine was manufactured incorrectly with the centre distances being off. I'd try turnin down the gear a couple of mm and re-cutting your 57 undersize. It won't be _correct_, but it's a small difference. I cut a 41 tooth M1.5 gear on a blank meant for 39 teeth because i fluffed up my differential indexing (forgot an idler gear) and it works just fine.


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## Suzuki4evr (Jan 21, 2021)

Lo-Fi said:


> Your numbers are right for module 2. I don't know if we discussed this before, but there is such a thing as "profile shifting", which results in smaller or larger gears for the same module and tooth count but with longer or squatter teeth. Either that's the case or the machine was manufactured incorrectly with the centre distances being off. I'd try turnin down the gear a couple of mm and re-cutting your 57 undersize. It won't be _correct_, but it's a small difference. I cut a 41 tooth M1.5 gear on a blank meant for 39 teeth because i fluffed up my differential indexing (forgot an idler gear) and it works just fine.


So what you are saying is basically turn the OD down from 118 to say 116 to gain the 2mm needed and re-cut the teeth? I was also thinking of maybe making an offset bush wich slips onto the pinion pin that I can fasten with a setscrew to the pin and then make a slightly larger bush for the gear. Could that work?


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## brino (Jan 21, 2021)

The gear sure looks great!

It is frustrating that after all your work it doesn't fit right.

I agree that your blank diameters look good, for module 2:
the 95 tooth gear the OD should be 194mm and it is!
the 57 tooth gear the OD should be 118mm and it is!
Also, the centre-to-centre distance should be 152mm, just as you say.
(I used: https://www.mechanicdrive.com/spur-gear-calculation)

I would double check:
1) the gear cutter (usually a set of 8 cutters to cover the range of small gears up to a rack; was the proper cutter used for the both gears?)
2) the tooth depth the gears were cut to; maybe the teeth are a little too shallow?

As you already proposed, maybe you can come up with some alternate arrangement for mounting them (offset axle, additional banjo, ....)

This is a head-scratcher!

-brino


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## Lo-Fi (Jan 21, 2021)

Yeah, you got it. It's not correct, but it would work alright. 

The offset bush is probably a better idea if it's practical and doesn't mess up the mesh with something else. Keep us posted! Brino is right, it's certainly a head scratcher.


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## Suzuki4evr (Jan 22, 2021)

brino said:


> The gear sure looks great!
> 
> It is frustrating that after all your work it doesn't fit right.
> 
> ...


I went through your checklist a few times before starting to make the gear and everything was fine. I have a couple of jobs to do this morning and then I will take a run at making the offset bush. I think that would be the easiest and quickest. If that doesn't work,well then I will go with making the 57 tooth gear smaller.


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## Suzuki4evr (Jan 22, 2021)

Lo-Fi said:


> Yeah, you got it. It's not correct, but it would work alright.
> 
> The offset bush is probably a better idea if it's practical and doesn't mess up the mesh with something else. Keep us posted! Brino is right, it's certainly a head scratcher.


It really is a head scratcher,but will keep you posted.


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## Suzuki4evr (Jan 26, 2021)

So what I did in the end was the following. I made the ID of the gear larger from 28mm to 35mm because I had to go bigger on the sentrifugale bush's OD therefore I had to go bigger on the gear bushing.


My first attempt was a failure bcause I made the offset to small at 2mm,I had to go a little over 4mm offset total for it to work. You can see the difference in the pic below.


I drilled a small hole on the side of the centrifugal bush that went over the pin just to have something to use to move the gear into place. There is a set screw on the bush to fix it into place.


And FINALLY they mesh.


And here is what the fuss was all about. I only made these change gears just to be able to make greas grooves on backhoe bushing,wich I do a lot. I am now able to make the grooves at 1/2" TPI when I use my imperial setting and that is perfect for the grooves needed. The bush is about 2" long so the groove makes a full rotation. 




I just have one issue and that is that the gears are very clunky and noisy. The higher the spindle speed the noisier it becomes. I don't know why because the gears now mesh perfectly. But it doesn't really bother me because I really only going to use these gears for the grooves at the lowest spindle speed and then it is quiet. I don't really see me using the other pitches on that table,never have before.

Lo-fi and Brino thanks for assisting me with this,you two guys really helped me think here. If I left someone out......I am sorry.

Thanks for viewing. 
Michael


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## Lo-Fi (Jan 26, 2021)

Nice one!! That's what we're collectively here for  

The mesh looks a little on the tight side, which might explain the noise. A little backlash is always good.


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## Suzuki4evr (Jan 26, 2021)

Lo-Fi said:


> Nice one!! That's what we're collectively here for
> 
> The mesh looks a little on the tight side, which might explain the noise. A little backlash is always good.


On the pic it looks tight,but believe me there is enough backlash, I tried it tight and loose,but there is still this clunky noise of gears.


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## Suzuki4evr (Jan 26, 2021)

I would think that it is noisy because of too much clearance/backlash or am I wrong?


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## brino (Jan 26, 2021)

@Suzuki4evr

Michael, very nice save on that eccentric bushing.
That is a very clever solution!

....and wow I never thought of using 1/2 TPI threads for lubrication grooves.
It looks like that should work great.

Well done!

-brino


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## Suzuki4evr (Jan 26, 2021)

brino said:


> @Suzuki4evr
> 
> Michael, very nice save on that eccentric bushing.
> That is a very clever solution!
> ...


Glad I could give you an useful idea. I am very very happy with the outcome of the grooves. Just need to sort out the noisy gears,but it's not a big issue.


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## Suzuki4evr (Jan 26, 2021)

brino said:


> eccentric bushing.


There is the word I was looking for.


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## Suzuki4evr (Jan 27, 2021)

Lo-Fi said:


> little backlash is always good.


Tried your suggestion and there was a lot less noise. Thanks again


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## Jim F (Jan 27, 2021)

Suzuki4evr said:


> Tried your suggestion and there was a lot less noise. Thanks again


a piece of paper folded in half for double thickness is a good gauge for backlash.


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