Starting a 60:1 gearbox

[jerrybilt]

Hopefully I'll construct a small engine before my time is out but in the mean time I need to construct a smallish gear box (about 60:1 reduction) for an astronomy project. To this end I need to cut some spur gears with the following numbers of teeth: 149 (3 off), 37, 41 and 36 teeth. The last 3 are easy to divide on the Vertex 6" rotary table but the last one presented me with a problem - Can I make a dividing plate that will divide the blank into 149 parts with a very small error ? This rotary table has a vernier that at best will resolve 20" so stepping out the numbers might prove to be too inaccurate. I had already made an index plate with 80, 72, 64, 60 and 48 holes to create lines separated at various angles eg. the 80 hole circle will create all angles in multiples of 0.05 degrees - this is my "decimal degree" divider.

The 48 hole circle will divide a circle into 149 parts with an error of 2" ... 29/48 holes

The following can also be divided, using this plate, with very small error:
59, 67 73, 79,101,107,113,127,131 and 193.

Now to doing a few trials.

Jerry

 

[Paulsv]

Wow. I obviously have a lot to learn about dividing plates!

 

[jerrybilt]

Hi Paul,

I arrived at the numbers by going backwards through the sums. The main thing is how to handle the last cut. As all the errors are adding the last tooth spacing needs to be altered by a very small amount to maintain the tooth symmetry.

Here are a couple of results:
Table - 90:1 (4 degrees/ handle rev.)

113 divisions ... 0 turns & 51/64 spaces
59 divisions ... 1 turn & 12/80 spaces

At least this plate produces much better results than if I used the RT on its own.

Jerry.

 

[Blogwitch]

Jerry,

Have you thought about using a worm and wheel, that only needs one 60 tooth gear and one worm, both could easily be made using your lathe and RT.


John

 

[Paulsv]

Is the design of the gearbox flexible at all? Could the gearbox be redesigned to use gears with a more common number of teeth? It seems to me that three gear reductions of 4:1 woul yield a 64:1 reduction (4x4x4=64). For that you could use three gear sets of say 120:30, which should be exactly achievable with dividing plates.

 

[tel]

For sheer simplicity the worm and wheel suggestion gets my vote.

 

[Ken I]

Just a couple of points

A dividing head can be differentially geared (the tailshaft drives the dividing plate) to get almost any angle or tooth numbers. Its been a long time since I used this method so look it up if you are interested (and have a suitable dividing head).

The worm gear gets my vote as well for simplicity's sake.

A word of caution - high ratio boxes (particularly worm drives) fall below 50% efficiency which makes them non-reversible. That in turn is a problem with high inertia loads - a sudden stop of the driver (motor) can lead to the intertial load applying massive loads to the gears - in most cases leading to rapid wear but even immidiate self destruction is possible.

Ken

 

[John S]

The OP states ABOUT 60:1
My guess is for astronomy he needs something stupid like 59.3573978623845662957 [ approx ] that can only be achieved with some prime numbers.

How am I doing ?

John S.

 

[jerrybilt]

Many thanks for the replies. I can answer now that the wireless is working again!
Wow talk about constructive - so much food for thought.

1. John ... Hello. The 60:1 is not really critical as minor adjustment in the motor speed can be made. The reason it is chosen is because the final shaft after this reduction needs to turn about 0.5 revolution in 12 hours and to make the numbers look nice eg 60 RPM in and 1/60 RPM out look "nice" and the "clocks" that drive the motors are easily arrived at. That 59.35397Seconds crops up if one wants to keep time using the stare (sidereal time) instead the normal solar time. Making your clock run in synchronism with the stars (instead of the sun) would be awful - ones body rythm would "go to hell in a hand basket" .

And how are you doing? Prettey good.

2. Prime numbers were chosen to try and minimise the periodic errors at this stage the next stage is to attempt a worm wheel - I have a strange feeling that this will take alot of practice on my part to get it right.


3. mklotz ... greetings.

Yes my mistake in not quoting the number of teeth in the worm wheel and yes it is 90 teeth .

Each turn of the hand wheel advances the table by 4 degrees.

So 29/48 turn of the hand wheel advances the plate by
(29/48) x 4 degrees = 2.41667 degrees

31/48 turn advances the plate by
(31/48) x 4 = 2.58333 degrees

Now for 149 teeth the spacing between adjacent teeth is

360/149 degrees = 2.41611 degrees

Error in the first case is 0.00056 degrees ie. ( 2.41667 - 2.41611)
Error in arc seconds = 3600 x 0.00056 = 2.0"

Error in the second case is 0.16723 degrees ie. (2.58333 - 2.41611)
Error in the second case is = 3600 x 0.16723 = 607"

After 149 steps using a dividing plate the blank would have advanced 360.0833 degrees leaving the last tooth out by 0.083 degrees now if the gear is a 1mm module the pcd is 47.43mm so the last tooth will be out by 0.07 mm or in imperial measure 0.003 inches. I could even up the error between the two gaps to 0.035mm (0.0015 inches). This is the best that I can do at home.

Will this make a huge difference? I don't know and any advice and guidance will be received with thanks.

4. Ken ... thank you for the response.

Worm gears - these are more specialised and more difficult for me to make until I get a lathe in about 6 weeks time. What little I know about gears does not include the complexities of using hobs to cut gears. I do know that some amateur astronomers/machinists use them to make the large worm wheels required and this will catch up with me sooner or later.

Differential gearing for indexing? ... Way to go! But I do not have that capability. Perhaps I may invest in one but good ones are expensive and one has to juggle getting these things and spending on the stuff that I really want to do, like build a model engine.

Inertial loads ? These can cause big problems if not handled correctly. One could get a lot of practice cutting worm gears if we chose to ter the motors to go from forwart to reverse without stopping first -- very expensive exercise!! ;D

Tel ... Hi.

At first light these Worm gears look simple but, in my books, are more complex than a simple spur gear.

Of course any ideas as to how to cut the wheel and the worm itself will be most welcome. From what I understand the wheel gear has trapezoidal teeth and the worm itself has a "type of" involute profile - how does one one cuts this ? ... Don't know.

Both worm and wheel should not have an involute profile as meshing will be a problem also backlash will have to be addressed.

All advice is welcome.

Hi Ya Paul,

Yes the gear box is flexible. Modern electronics compensates for a lot of shortcommings. But I find its best to do a good job at the outset, it is somewhat like taking a photograph if the camera is setup right in the first place there should be no need to photoshop the hell out of it. Please, please no arguments.

Whew!

Hello John,

Guess what in about 6 weeks time I will be getting a lathe so I will have a brilliant tool to use.

BTW I am still trying to decide on the size. You see I have "absolutely coveted" an engine Kit called the Economy but it has a 10.5 inch fly wheel. Now here's the problem. The most suitable lathe for me is a 10" lathe but it looks as if it is a triffle too small. The next one up is 12" and not a great more expensive but a lot more capable. I'm agonising over that one.


My Kind regards to all,

Jerry

 

[Blogwitch]

Jerry,

Once you get your lathe, do a search for cutting worm and wheels on the net, as I don't think anyone on here has shown how to do it.

It only takes a little setting up to make rather successful ones just using standard taps and single point screw cutting.

Whether this method would be accurate enough for you, only you can decide, but worm and wheel cutting can be within the realms of anyone who owns a screwcutting lathe.


John

 

[jerrybilt]

John,

Will try your suggestion. As for accuracy , until I practice on a few throw away aluminium blanks I think that I'll take what I get. Lol.

Jerry.

 

[mklotz]

Jerry,

I have to apologize for my post critical of your work. Somehow I had a massive brain fart and used 149/90 instead of the correct 90/149 to characterize the RT mathematics. Further compounding the problem, that mistake leads to numbers close to what you were getting so my error didn't immediately pop out to me.

In the interest of minimizing confusion for future readers, I've removed the offending post. Again, my apologies, and, yes, your calculations all look spot on.

 

[jerrybilt]

Hello Kev,,

Hey! No big issue with me.

I post stuff so that I get others with more experience to critique my work.

Being a home machinist most of the work is Independently done so forums like this are invaluable to me.

BTW One of the by products of working at home is finding answers to the question of how well am I doing, how accurate is my work. This gear cutting presented me with the problem of determining the quality of my gear cutting. I have a "nice" solution but this solution though simple will take a bit of work to implement. If anybody Is interested I could give considerable detail as to how to accomplish this task.

Regards,

Jerry.

 

[jerrybilt]

Apologies for getting the name wrong - blame it on this IPAD. Thing tries to read my mind and gets it wrong.

Jerry

 

[ozzie46]

Hello Kev,,



BTW One of the by products of working at home is finding answers to the question of how well am I doing, how accurate is my work. This gear cutting presented me with the problem of determining the quality of my gear cutting. I have a "nice" solution but this solution though simple will take a bit of work to implement. If anybody Is interested I could give considerable detail as to how to accomplish this task.

Regards,

Jerry.

I, for one, would be interested.

Ron

 

[jerrybilt]

Hello Ron,

Quick Overview

I do not know how the professional gear designers and makers measure the quality of their gear products. The obvious solution is to measure the angular spacing between each tooth of the gear and the angular thickness of the tooth at the level of the pcd then test the tooth thickness and the gap spacing for consistency. The obvious question is how to perform these measurements consistently and accurately. The solution is in three parts:

Part 1 ... Mechanical setup

The gear under test is mounted on a spindle that is rotated at a constant speed - say 60RPM or 1 rev per second. A beam of light from a slit (vertical line) shines through the teeth while the gear is rotating and a photo detector on the other side registers this " chopped " light. This output is made into a square wave (on/off) where the on time (light) represents the gap and the off time (no light) represents the tooth thickness.

Part 2 ... The electronics

The square wave obtained from the rotating gear under test is used to gate two counters that are clocked at 12,960,000 Hz or 12.96MHz. For each tooth the count in the two counters is a measure of the gap and thickness for each tooth that passes the light beam. For the clock frequencies above the angular resolution is 0.1 arc seconds. These counts are recorded in a computer memory. At the end of this stage we have accumulated a series of numbers that represent the gap and thickness of each tooth in the gear and the numbers keep repeating as long as the gear is rotated and the data taken.

Part 3 ... The calculations

So we now have a series of a pair of numbers what next? We now extract the numbers from this stream that belong to a particular tooth - this is quite simple as long the number is always from the same tooth!

Example. If the gear has 6 teeth then the sequence of tooth numbers will be

... 56123456123456123456123456123456123456 .......
Now if we start any where (say #4) and count 6 numbers then we can pick out all number pairs associated with a given tooth so:

456123 ... Rev 1
456123 ... Rev 2
456123 ... Rev 3

So you can see that one can get many measurements of the gap and thickness for the same tooth all we need to know is the number of teeth in the gear.

Now we compute the average spacing and the average thickness for all the teeth. Next we compute the average thickness and spacing for and individual tooth then calculate the standard deviation (Root mean square deviation or error ) for each tooth from the overall average. This final set of numbers should match to a high degree.

Well that's the overview Ron. If this looks OK I could do a detailed write up. Determination of periodic errors in the gear train can also be determined how? I'll have to write that down, it is only a mater of calculation but quite involved.

Jerry.

 

[ozzie46]

Thanks Jerry.

Ron

 

[Ken I]

Jerry,
I think that method will run into problems related to the width & collimation of the light source, diffusion and edge scatter.

Gears are measured various ways - for amateur use use a two wire method (use drill shanks or precision "wires") normally with contact at the PCD but can be employed at varying depths to check the profile.

There are specialist compound verniers / micrometers.

The final tests are lash and noise. (The noise test is a sod - you can assemble a gearbox full of perfect parts and still fail the noise test. Noise being both audio dB and angular G's)

Since I presume you are going to be milling these gears you are going to be off from the kind of accuracy that gearbox manufactures (like ZF) use where microns are as big as footballs.

Automotive gearboxes are typically hobbed, induction hardened / tempered, ground - and in some cases superfinished. All of which are well outside the scope of anything you can do at home.

Milled / hobbed gears are "noisy" - if you are tracking a telescope with this that noise will appear as cyclical irregularities in the pan speed - small to be sure but when your target is lightyears away can be significant.

Regards,
Ken

 

[jerrybilt]

Hi Ken,

Thankyou for taking the time to respond.

Re: Problems mentioned

Looking at the points in order:

Colimation is not a problem as one could employ a readily avaible low powered laser as the light source - suitably dimmed ofcourse.
Diffusion and light scattering will not be much of an issue over this very short path of about 20mm separation.

Yes diffraction round the edges has an effect together with the size of the photo diode. The effect of the detector size is to slow up the signal from the detector because the shadow of the tooth passes gradually over the detector until it is fully illuminated add to this the diffraction effect which is to further slow up these rise and fall times. This presents no problems as a simple circuit cleans up these edges making them ready for the gating circuit. To give you a feel for the numbers:

The times are measured from when the signal levels go from 10% of the low level to 90% of the high level. So the rise time of the detector output might be of the order of an interminable 1 micro-second, the simple (treshold) circuit "cleans" this up to a more "respectable" 10 to 15 nano-seconds - BTW this is also quite easily measured.

Noise Tests?

Brilliant! Isn't it amazing that using words like "listen to" open up a whole new ways of looking at things ? Many moons ago I tested out a gear box (very expensive!) to see how the gear train was organised and how well it performed - the word listen fits very well. I found a picture of the results and I can post it here, if you like, but you will first have to tell me how to post a pic. Doing this exercise for a single spur gear gives about the same amount of pain. What would be very interesting to see is how things change when the gear box is subjected to various types of load.

1 micron accuracy ?

If I so much as thought of getting machines capable of that accuracy it will cause an immediate divorce - 0.02 mm or 20 microns is the very best I can muster. Even my class 2 gauge blocks are only good to 1 micron. And yes my main capability is via a milling machine/rotary table and tail stock.

Automotive gear boxes - I find it amazing how these pieces of complex machinery are so relativly cheap. Chaps who make model V8 engines at home may make one but definitely not me.

Re gear boxes for trackuing - the random variationd don't seem to present much of a problem its the periodic errors that cause much pain. Some gears of chinese origin are really sad but it is amazing what some complex electronics does to over come the deficiencies. Here is the problem: in my case a 60kg rotating load must maintain its pointing to better than 10 arc secs over a period of about 4 hours, the electronics reliably detects deviations of 0.1 arc secs.

Hope that's not too long winded?

Jerry

 

[Ken I]

Jerry,
O.K. I can see how your electronics will "clean up" and microseconds are as "big as footballs" to astronomers who measure to Femtoseconds.

Even so 0.1 acrcseconds ! - I'm into robotics and with 20 bit encoders we can resolve to 1/1048576 of a motor revolution via a 50:1 harmonic drive (or 98:1 cyclo) to resolve to 0.025 arcseconds or 0.0126 arcseconds.

Are you going to resolve at input or output level ? resolving at input level does not compensate for the vargaries of the gearbox, output level is less accurate (for the same method) by the ratio so its a sort of a lose-lose situation.

With robotics we rely on high resolution backlash free gearboxes - which are monumentally expensive.

We often junk cyclo gearboxes because they have developed too much lash - but are otherwise still good - try a local robotics shop and see if you can't scrounge an old box off them.
You might also be able to scrounge a few non-functioning encoders that you might still coax some data out of - just an idea.

A cyclo gearbox is a complete gearbox & bearing package - very compact - entire robots stand on them - ideal for driving any "turret" sort of application.

Robots by Yaskawa-Motoman, ABB, Fanuc & Kawasaki (market share order) are your most likely bets.

Ken