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Paul Alciatore
10-23-2007, 02:50 AM
OK, so you are going to cut a gear. And it is perhaps 6 or 8 inches in diameter. DP does not matter, so assume 16 or 20 if you feel it makes any difference. Individual teeth or hobbed, my question is the same.

Just how much accuracy do you need in the dividing set-up? A common spec for a dividing head or rotary table is +/- 10 to +/- 30 seconds of arc. So lets use +/- 20 seconds which is about .0055 degrees. The sine of that angle is about 9.69 X 10^-5 or 0.0000969. Multiplying by a radius of 4 for the eight inch gear you get about 0.00039" or four tenths. So your error in the placement of the tooth or a segment of the tooth's surface if hobbing is going to be +/- 0.0004" or a total range of almost a full thousanth.

But it gets worse. Lets say you are going to use CNC. Now my rotary table with a 90:1 worm has four degrees on the handwheel, and each degree is divided into 60 minutes. The vernier is used to read down to 10 seconds. So there are 60 X 4 or 240 main (one minute) divisions on the wheel. If I replace the handwheel with a stepper for CNC, then I will have 200 steps per revolution. This seems to be a common way it is done, a 200 step stepper is directly coupled to the worm shaft. So I am now stepping in 1/50 degree steps (0.02 degree). This is about four times coarser than the manual indexing which allowed resolution to the 20 second level. Doing the calculation with the sine gives me an error of about +/- 0.0014" or a total positional range of almost three thousanths.

Now, the differences between the various numbered cutters for a single DP are measured in tenths. We are an order of magnitude larger in the positional errors. If I am hobbing, then the gear will first lag and then proceed the cutter by 0.0014". This will produce a variation, a wavyness in the finish of the teeth as the hob progresses across the face. Won't it?

It seems to me that the common solution of directly coupling a 200 step stepper to a worm is an order of magnitude too coarse for proper gear forming. Am I calculating incorrectly somewhere? Are the common CNC rotaries only used for very small gears, like under a half inch diameter? Or does everyone just ignore this problem? Does the tendency of a hob to follow the proper pitch win out over the stepper's attempt at positioning? Or am I just missing something?

And please don't talk about microstepping without a complete discussion of the non-linear errors and loss of torque that can occur with that mode of operation. I personally would not recommend it.

dp
10-23-2007, 03:06 AM
Are you optimizing for least wear, least noise, positional accuracy, or running ratio?

tattoomike68
10-23-2007, 03:25 AM
It seems to me in the old books I have read that the gear maker would run the gears with other gears, oil them up and feed some lapping compound on them and run them to wear them in for a little while

Let the gears eat up the errors themselves. Smart old timers.:cool:

oldtiffie
10-23-2007, 04:14 AM
Hi Paul.

Well what a revelation that was - thanks.

As you say, there are 200 "steps" for what is a 240 "step" requirement.

As I see it both will co-incide at the 0, 90, 180, 270, 360 etc. degree marks and any differences will be cyclic (and sinusoidal? - haven't checked), and max error/differences will be at 45, 135, 225, 315 etc. degrees.

That, as you say, is with a direct-coupled 200 pulse/rev motor.

Any chance of using a 240:200 (ratio) gear-box or step pulley belt drives as this would deliver 240 "pulses" per rev at the rotab spindle.

I haver often wondered about some aspects of CNC although this one did not cross my mind until you pointed it out.

I guess similar problems may apply in say a 3mm lead-screw which "pulses" at 3.000/200 = 0.015mm (say 0.0006") where the theoretical minimum step (and maximum resolution) will be 0.015mm.

I have always been concerned about possible problems with the inertia and "pulsing" causing "mechanical hammering".

I realise that you specified direct coupling, but I have seen several set-ups on this forum where positive drive belts were used to get the required pulse ratios.

CNC is a bit of a mystery to me, but servos are not. Servos actually read the actual real position of an item to be "moved" (ie as on a DRO) and the difference between the required and the actual position are feed back to a drive controller which drives to reduce error/differences to "zero" using a "virtually" stepless and smooth drive.

I guess that CNC will have a problem if the drive "slips a cog/step" - if the belt "jumps" or "slips" and I don't know of any way CNC can detected this.

It seems to rely on "faith".

I guess that this is why CM|NC requires such high standards as regards eliminating back-lash (ball-screws etc.) and optimising "pre-loading" of bearings in, say, mill table thrust brackets.

I am advised that some CNC can compensate for any "errors" in a ball-screw etc. with an algorithm in the software,

That would (should??) not happen with servo as it is always "aware" of the position of the table/rotab etc.

I guess CNC is "cheaper and easier".

toastydeath
10-23-2007, 04:51 AM
The 200 step rotary table would indeed be too coarse for hobbing on a CNC.

Now, I am pretty unfamiliar with the accuracy requirements of gears, but I am more familiar with CNC machines and how they're put together.

For clarity: CNC just refers to the control, not the motors/screws. Most modern CNC machines use servos rather than steppers, because of the closed loop (DRO-like) behavior. You can slip a belt all day long and the CNC with a servo drive knows it hasn't gone anywhere.

Many modern CNC rotary tables are direct drive brushless servos with rotary encoders, which have no discrete steps (like a brushed servo or stepper). Even better, they have very fine control over how the table is positioned, to within a couple arcseconds. The important part is the smoothness of operation - the brushless servo is mechanically quieter and more far more consistent than a mechanical hobbing or stepper arrangement, and the encoder is accurate enough to help predict and correct any invariance in RPM. No pulsing, no hammering, just smooth, consistent movement. This is especially evident in modern optics lathes, which use the same principles but in a higher RPM capacity. Any hammering or pulsation would destroy the optical finish.

And if you don't want a whole machine, there are compact systems that can near perfectly synchronize two of these rotary tables, and you would get ideal hobbing conditions out of them. Pricey, though.

And there is my take on the matter.

oldtiffie
10-23-2007, 05:05 AM
Thanks TD.

Thanks - heaps.

With the older (very much older) servo systems I was used to - used "syncros" for error/position/difference detection - as well as velocity, acceleration and pre-retardation etc. etc. with DC or hydraulic motor power.

How is "acceleration" particularly "break-away" acceleration and pre-retardation (braking/deceleration) allowed for?

I would imagine that "stepper" control is pretty well constant speed whereas "servo" would be more variable.

Is that the case?

This is whetting my appetite - I might just get more interested in CNC yet.

Thanks Paul and TC.

Evan
10-23-2007, 06:33 AM
It seems to me that the common solution of directly coupling a 200 step stepper to a worm is an order of magnitude too coarse for proper gear forming. Am I calculating incorrectly somewhere?
...
And please don't talk about microstepping without a complete discussion of the non-linear errors and loss of torque that can occur with that mode of operation. I personally would not recommend it.
My mill is designed to use 1.8 degree steppers (200 step per rev). They drive the lead screws with a 2 to 1 reduction which is a very common system. That's 400 steps per rev. They will operate in 1/2 step mode so that's 800 steps per rev.

Half step mode on most steppers is a wash in terms of speed vs torque. Your average stepper can run at the same rpm in half step mode because it can step twice as fast while losing only a small amount of torque. Half step mode isn't microstepping. In half step mode full current is still applied to the windings. The difference is the number of windings energized at once.

Your average bipolar stepper motor rated at 1.8 degrees per full step is really a 400 step per rev motor. The motors are rated in terms of full steps per second rather than number of half steps. If it is half step driven it will still make about the same number of full steps per second with only a small loss in torque.

What it comes down to is that for the purpose of your calculations you are making an assumption about resolution that is at least a factor of 2 too coarse. If lower maximum motion rates are acceptable then it changes even more. The Z axis on my mill is driven at 4 to 1 via belt drive. That doubles again the number of steps per rev of the leadscrew to 800. Also, the torque is multiplied accordingly although the maximum leadscrew revolution rate is halved but the positioning resolution is 1600 steps per rev.

In the case of positioning a gear blank during cutting the rate of motion is not a high priority requirement. The drive to the rotary work holding apparatus (table or indexer) may be geared down considerably. A reduction of 10 to 1 is entirely workable and combined with half stepping will give 4000 steps per rev.

This is a factor of 20 higher resolution than your basic assumptions.

Paul Alciatore
10-23-2007, 10:37 AM
Oldtiffie,

Well, the 200:240 isn't the real ratio of the problem as 240 steps is whole minutes and the vernier takes it down another factor of 6 on my table for 1440 "steps".

Evan,

OK, I am aware of half stepping and yes it is a lot better than microstepping. Probably the thing to do. But, as you say, that only doubles the steps to 400 or halves the errors down to about 7 tenths in my example.

So I am still seeing a real need to gear or belt down the motor to obtain a larger number of steps/divisions. And your comments seem to agree with this. I have been reading almost everything I can on gear cutting and I guess I just wonder why there are so many examples out there in which this additional step down is not done. Just how successful are these solutions? Or are the people just making gears that look good to the naked eyd without any concern for their accuracy?

Mike,

I have heard of that "run-in" technique. I am not sure it is the way I would want to go, but I suspect it makes a superior gear. You would need another machine or setup to do the run-in. I seem to remember hearing a LONG time ago that the auto makers used this technique on transmissions. I believe they use better manufacturing techniques (probably grinding) today and for many years in the past.

As for servos, yes a servo motor can have essentially continous control, but they rely on positioning sensing devices. Those devices can be either linear or digital. If digital, as in an optical encoder wheel, then you can have a stepping effect there. Of course, they can be a lot finer than the steppers. I have seen optical encoders with 1K and even 4K slots. Or they can be analog devices which are essentially continous. But analog devices can be very expensive and will have their own type of errors. In the Army missile systems I worked with many years ago there were analog computers with sine/cosine pots that cost many thousands of dollars each. Cost/accuracy tradeoff there.

As L Ron said, TINSTAAFL.

It seems that I did not miss anything.

toastydeath
10-23-2007, 11:09 AM
oldtiffe- thanks. I'm no motion control guy, but I play one on TV.

Acceleration/deceleration rates are hard values programmed into the CNC based on motor torque and max load, so that it knows how fast to slow down each axis to properly execute a synchronized move in the worst case. I understand that there are some drives that have torque feedback and that dynamically sense the load on the motor, and synchronize the move to the slowest reacting axis - the one with the biggest load on it.

As for servos and steppers, they both have "variable" speed, but how they get it is different. I'm not going to tread too deeply there because I'm not a motion control guy (yet). While I have the basics, I really have no business explaining the interior of the two kinds of motors in any detail.

And I agree with Paul A. - the "continuous" variety of encoders are ridiculously expensive.

Spin Doctor
10-23-2007, 11:40 AM
Lots of gear cutting questions of late. One wonders just how pricey is Boston Gear? Is the rounding up of the involute cutters needed really that much of a cost savings? Okay, I know most people here are doing this as a hobby but having cut enough gears and splines in my working life I have always had a pretty low opinion of mill cut gears. The cutter is a solution to fit a range of tooth involute profiles over its range. It might be spot on for the center of its tooth range but everything else is a compromise. A gear hob dose a better job and a gear shaper better yet. But Hobbers seem to be getting awfully expensive when not long ago they were dirt cheap. Plus witha gear hobb you can always make odd tooth number gears you might need for cutting any number of teeth. Sometimes cutting say a 127 tooth change gear for metric threading on an inch leadscrew lathe will reguire teeth that are not part of the standard change gear package. The Barber-Coleman was a Model 16-16 IIRC we had at work (rather it is still there, I'm not) had change gears we made that went from the minimum size that coud be cut for the index and feed gears, 22T to somewhere in the 80s (index gears were 10DP and the feeds 12DP, ). If one was familar with the machine one could cut the gear including all set up time in less than a half an hour. With all of the index gears we had cutting say a 49 tooth gear was simply a matter of placing a 30 tooth gear on the input shaft and a 49 tooth gear on the output shaft and fitting an idler gear between them. Practically the only time we had to compound gear the index or feed gear was for helicals. Saved a lot of time when one was cutting all new gears for a multi spindle drill head. Plus a hobber can cut more than just spur, worm and helicals. Taper splines if the machine was equipped with tangetail feed for example.

http://groups.yahoo.com/group/gearcutting/?yguid=187701020

lazlo
10-23-2007, 11:48 AM
So your error in the placement of the tooth or a segment of the tooth's surface if hobbing is going to be +/- 0.0004" or a total range of almost a full thousanth.

Since you're talking about a dividing head, you mean gear cutting, not hobbing. So each tooth, in profile, will be centered +/- 0.0004". That's more than enough to get a good mesh between gears: you're just counter-rotating a curved surface on one gear (the involute curve of the tooth) with a curved surface on the other.

The center-to-center distance between the two gears is more critical, since you want the tangents of the two involute curves to line up on the correct pressure angle for optimal performance.

lazlo
10-23-2007, 11:56 AM
I have heard of that "run-in" technique. I am not sure it is the way I would want to go, but I suspect it makes a superior gear. You would need another machine or setup to do the run-in.

I've done this to clean-up gears on old machine tools: order a precision hobbed brass, bronze, or aluminum gear from Boston gear, and mount the gear you want to clean up in a spin jig on the lathe compound, and chuck the precision gear on the lathe spindle. Carefully set the correct center-to-center distance between the two gear hubs, and then charge the precision gear with non-embedding lapping compound. Then run the gears together until the tooth flanks of the worn gear are smooth.

Norm and John might find it amusing that I read that technique from a "Geometer" (George H. Thomas) column in an ancient Model Engineering magazine.

One wonders just how pricey is Boston Gear? Is the rounding up of the involute cutters needed really that much of a cost savings?

I've bought several of the Boston Spur Gears lately. The price varies roughly linearly with the number of teeth, but a 24 tooth, 16 DP spur gear is ~\$16, and the 32 tooth spur gear is \$26.

The only problem is that the stock spur gears from Boston Gear, Martin Sprocket, Browning, etc are quite thick, and have a big hub you have to shave off.

10-23-2007, 01:58 PM
Nice problem. AGMA standards have the error budgets in chart form for their 15 classes of gearing. It's complex to look at and even more to understand fully. Basically there are several sources of gear error and they are associated with blank manufacture, tooth cutting, and cumulative errors in installation. They all have their effect and the end result is noise, vibration transmission error, and reduced life. Gear accuracy is pretty well discussed in Machinery's Handbook.

I suggest you consider a geared reduction in your stepper drive to the rotary table input. Or maybe go from a pure stepper drive to an interpolated (microstepper) stepper drive, one that's provided with encoder feed back or perhaps DC motor servo controlled. All these more elaborate schemes result in finer resolution in the drive to the equipment you're indexing. A good servo drive will resolve 4000 disinct positions in a single rotation of the servo shaft. The high precision ones are far better than that.

Depending on the quality of the rotary encoder, the quality of the servo feedback loop, the backlash and over-run of the driven devise (rotary table was offered in the OP, and the accuracy of the index on the driven devise one can theoretically index to parts of arc seconds but machinery is far from perfect.

A low cost servo drive like a Gekko or a Rutex, a rotary encoder from US Digital, the power supply, and an indexing drive like the Division Master will yield results to the limits of the rotary table for not much money. But the final index controls the angular position of the machined features. The servo takes step and direction from the index controller and converts it into a DC output controlled by quadrature feedback from the motor shaft encoder. I'm not very smart on this topic. I hope someone cames behind me and corrects my technical faux pas on this topic.

If you're cutting gears with formed milling cutters by single indexing then you won't be able to get high quality gearing from the endevor. The profile will be an involute only for the tooth count the cutter is designed for. The spread on either side of the ideal count is a diverging compromise. There are haf sizes of single indexing milling cutters but they are hard to find.

If you have need for accurate gearing, single indexing on a milling machine will make acceptable gears especially if the index is tricked up with a servo drive. Any workpiece index error will derive mostly from the worm and pinion drive and little from the servo or the electronic indexer controlling it. There is bound to be more error from cutter/work deflection, cutter wear, localized heating, chip recutting and other machine shop problems than indexing error anyway.

If you want to cut really accurate gears you have to have the equipment for it. Indexing error is only a component of the problem.

By the way; lapping usually compounds gear involute and indexing errors. Think about it. Lapping occurs when two surfaces rub together with abrasive between them. The abrasive adheres to one surface and wears away the other - or vice versa. In gears there is a point of zero rubbing velocity at the working pitchline. No lapping takes place at the pitchline; the abrasive is mashed into the surface of the metal. The pitchline laps little but the flank above and below the pitchline is subject to abrasive/rubbing. When lapping stops you wind up with a bump at the pitchline of every flank.

Lapping is not a cure-all. In high tech shops where high accuracy gears are made they make up a half dozen laps of better quality than the wotrkpiece gear material. The lap material has to be softer that the gear. Furthermore rapid axial motion is required with moderate rotation in mesh to ensure correction over the full involute. Gears lapped for accuracy may cost 2 to 5 times as much as a hobbed gear and reduce the errors to about 1/4 of as-machined. OTH, lapping gears is what ignorant shade tree mechanics do when they are stumped by noisy gearing. Once in a great while there is a small improvement and in their eyes this outshines the far larger proportion of wasted effort and ruined gearing.

lazlo
10-23-2007, 02:43 PM
lapping usually compounds gear involute and indexing errors.
...
In high tech shops where high accuracy gears are made they make up a half dozen laps of better quality than the wotrkpiece gear material. The lap material has to be softer that the gear.

Right, that why I suggested using precision hobbed brass/bronze/aluminum gears from Boston Gear, which will be much higher precision than anything you can make in the shop.

lapping gears is what ignorant shade tree mechanics do when they are stumped by noisy gearing. Once in a great while there is a small improvement and in their eyes this outshines the far larger proportion of wasted effort and ruined gearing.

I'm not sure that Geo H. Thomas qualifies as an "ignorant shade tree mechanic" :)

oldtiffie
10-24-2007, 12:12 AM
Right, that why I suggested using precision hobbed brass/bronze/aluminum gears from Boston Gear, which will be much higher precision than anything you can make in the shop.

I'm not sure that Geo H. Thomas qualifies as an "ignorant shade tree mechanic" :)

Hi lazlo.

I tend to agree with Forrest as his "oscillating-while-turning" approach does more nearly emulates the true gear hobbing/generation" process as well as removing the potential "flat" zone at the pitch line. It is not difficult to achieve. Pack/keep the "to be lapped" gear, say, 1/2 its width off the "table" and put a "return" spring" between the "driving/lapping" gear and "drive" it with a drill in an "up an down" (reciprocating) motion.

I am sure that Geo H. Thomas will be only too glad to sit under that previous "ignorant" now "learn-ed" shade tree with us all.

And FWIW, I am sure that most "Farmers" and the like here-abouts would do the same. We have lottsa "Bush Mechanics" here that get the job done too.

The "acid test" is to try it. The rest is perhaps "best guess" and perhaps "speculation".

I hope it helps.

10-24-2007, 02:12 AM
Lazlo "I'm not sure that Geo H. Thomas qualifies as an "ignorant shade tree mechanic" Maybe not but endorsing a complex and exacting technique like gear lapping as home remedy for substandard gears requires careful qualification, caveats, and detailed how-tos. The urge of the neophyte is to over-simplify: "Man! D I haveta?" and his yokel buddies are sure to egg him on.

It does not work to blob Clover brand valve lapping compound in the mesh and run the gearing iunder power for a time. That's the surest way to wreck the tooth bearing and congugate action of a gear pair as I can concieve.

Remember the rapid axial motion between lap and gear I mentioned above? You can't improve the tooth bearing without it.

J Tiers
10-24-2007, 09:21 AM
The "real" gear shaving was "crossed-axis shaving" with a gear-like tool having many cutting edges per "tooth".

The rotational axis of the cutter was "crossed", not parallel to the gear axis, so that there WOULD be axial movement and continual cutting action.

I can't imagine an abrasive process being consistent. it would seem to wear the MOST at the point of contact, and proportional to pressure. Not what you wany, I'd guess.

The idea was to make the gears act as if they had been in mesh for a while, smoothed out. But while they might be smooth, I think the form would be very questionable.

oldtiffie
10-24-2007, 10:59 AM
OK.

We've done the reality and mechanical bit.

Now, can we get back to Paul's request re. rotab and CNC?.

This is one interesting thread and I'd like to see how and where it goes.

ASAP

lazlo
10-24-2007, 12:13 PM
Now, can we get back to Paul's request re. rotab and CNC?.

OK, so you are going to cut a gear. And it is perhaps 6 or 8 inches in diameter. DP does not matter, so assume 16 or 20 if you feel it makes any difference. Individual teeth or hobbed, my question is the same.

Just how much accuracy do you need in the dividing set-up?

Since you're talking about a dividing head, you mean gear cutting, not hobbing. So each tooth, in profile, will be centered +/- 0.0004". That's more than enough to get a good mesh between gears: you're just counter-rotating a curved surface on one gear (the involute curve of the tooth) with a curved surface on the other.

lazlo
10-24-2007, 12:38 PM
It does not work to blob Clover brand valve lapping compound in the mesh and run the gearing iunder power for a time. That's the surest way to wreck the tooth bearing and congugate action of a gear pair as I can concieve.

Agreed Forrest, but that's not the procedure that Geo Thomas' advocates. As I described above, Geo Thomas advocates the use of a master gear as an involute template. As with any lap, the master gear must be constructed of softer material than the gear who's form is being corrected. The master gear is loaded with lapping compound, carefully meshed with the damaged gear, and run until the profile of the damaged gear matches the profile of the master gear.

Remember the rapid axial motion between lap and gear I mentioned above? You can't improve the tooth bearing without it.

I don't doubt that high-precision gears are lapped axially as well as radially, but that's not an option for a home-shop guy trying to get his lathe up and running.
I had a chewed-up gear in my quick change gearbox. I tried Geo Thomas' approach, and it worked fabulously.

I had four options for repair:

1. Order the gear from Clausing: \$120.

2. Buy a steel gear from Boston Gear and turn it down to the correct thickness. Machinery texts tell you to avoid steel gears in the leadscrew geartrain...

3. Cut a new gear with an involute cutter.

4. Repair the existing gear.

I chose option four: Get 'R Done.

I carefully followed Geo Thomas' directions, bought a 32-tooth precision-hobbed brass gear from Martin Sprocket, built the spin jig in Geo Thomas' article, and the tooth flanks came out perfectly. The lapped gear is running in my lathe, and is noticeably quieter than the stock gears (which were not chewed up). I wish now that I had taken pictures :)

http://i164.photobucket.com/albums/u15/rtgeorge_album/geometer.gif

lazlo
10-24-2007, 12:45 PM
I can't imagine an abrasive process being consistent. it would seem to wear the MOST at the point of contact, and proportional to pressure.

My understanding is that with an involute tooth profile, the pressure is consistent as the teeth slide past each other across the pressure angle:

"The [involute] design keeps all contact between gears in a flat plane as the teeth mesh in and out. The contacting surfaces are always perpendicular to the plane of contact, so the dominant contact forces (in a well lubricated system) are always parallel to the plane."

John Stevenson
10-24-2007, 03:52 PM
.

But it gets worse. Lets say you are going to use CNC. Now my rotary table with a 90:1 worm has four degrees on the handwheel, and each degree is divided into 60 minutes. The vernier is used to read down to 10 seconds. So there are 60 X 4 or 240 main (one minute) divisions on the wheel. If I replace the handwheel with a stepper for CNC, then I will have 200 steps per revolution. This seems to be a common way it is done, a 200 step stepper is directly coupled to the worm shaft. So I am now stepping in 1/50 degree steps (0.02 degree). This is about four times coarser than the manual indexing which allowed resolution to the 20 second level.

.

towards the bottom where it discusses the Hoffman head and the max error of 0.008 degrees which is far from your 0.02 degrees.

.

lazlo
10-24-2007, 04:32 PM
Hi John,

towards the bottom where it discusses the Hoffman head and the max error of 0.008 degrees which is far from your 0.02 degrees.

"John Stevenson, who runs an engineering business in Nottingham, UK, has been using DivisionMaster to drive this Hoffmann dividing head, which he has fitted with a MEMA 42 size 9A/phase stepper:

This Hoffmann dividing head has a 40:1 gear ratio between the motor and the output spindle.

[John] was cutting four 27-tooth gears simultaneously. Bottom right shows the display of DivisionMaster at this point - the actual position is 93.330 degrees. The theoretical position should be 93.333 degrees;

John said that the positional error on any one of the 27 moves was never more than 0.008 degrees."

Neat setup John!
How were you measuring the positional accuracy versus the display position on the DivisionMaster (which was just adding up the step count)?
Were you comparing the 40:1 vernier reading with the DivisionMaster display?

oldtiffie
10-24-2007, 05:59 PM
My understanding is that with an involute tooth profile, the pressure is consistent as the teeth slide past each other across the pressure angle:

"The [involute] design keeps all contact between gears in a flat plane as the teeth mesh in and out. The contacting surfaces are always perpendicular to the plane of contact, so the dominant contact forces (in a well lubricated system) are always parallel to the plane."

lazlo.

That gif file animation shows the (20 deg or what-ever) pressure angle pretty well except that it appears that the points of contact are over the full depth (addendum + dedendum) where-as the contact point/plane on a true involute generated on and from the pitch circle is between the addenda only. It is correct with a close(r) look which only emphasises the need for "clearance" at the dedenda (between the pitch circle and the base/bottom of the cut). But it also neatly shows that if the wear is excessive that "crowning" can occur (used to be common in fibre cam-shaft drive gear trains in cars here for a while).

It - indirectly - shows that the PA is composed of, and can be resolved to, its components of: torque (at right angles) to the line connecting the centres of mating gears and thrust (along that line between centres) - friction is neglected. The "useful" component is "torque" and the "lost" component is "thrust". This, in turn tends to illustrate that there are "losses" in all gear trains - even with friction neglected.

The "jerkiness" of the gif file might also show the state of mesh if the actual "pulse" amplitude in a CNC drive is too "vigorous" and the "frequency" too low to be "absorbed".

In think that it - again indirectly - shows the need for the axial oscillation required for "grinding" as stated in a prior post (13) by Forrest Addy and discussed in the following posts.

And again, indirectly, the gif file makes a very good case for helical gearing.

A very effective graphic.

I am enjoying this thread - keep it up.

Thanks.

oldtiffie
10-24-2007, 06:16 PM

towards the bottom where it discusses the Hoffman head and the max error of 0.008 degrees which is far from your 0.02 degrees.

.

John.

Thanks - heaps.

I read that several times and it cleared up a lot of my "vague" ideas, misconceptions and questions - very well.

I have both those "Vertex" 6" and 8"" rotabs and I knew they were better than just "pretty good".

Truly extraordinary!!

It also neatly emphasised that "laboratory" and "German/Swiss" (looking) shops with brand new gear is NOT a pre-requisite for such precision and that "ordinary" (HSM-type?) shops CAN and DO achieve extra-ordinary things - with the "right" operator/machinist.

That should give new heart and confidence for those that might think they need "something better" to "do better". Perhaps a change of focus is all that is required in lots of cases - here/me included!!

I look forward to the continuation of this thread.

Thank you.

oldtiffie
10-24-2007, 06:20 PM
Agreed Forrest, but that's not the procedure that Geo Thomas' advocates. As I described above, Geo Thomas advocates the use of a master gear as an involute template. As with any lap, the master gear must be constructed of softer material than the gear who's form is being corrected. The master gear is loaded with lapping compound, carefully meshed with the damaged gear, and run until the profile of the damaged gear matches the profile of the master gear.

I don't doubt that high-precision gears are lapped axially as well as radially, but that's not an option for a home-shop guy trying to get his lathe up and running.
I had a chewed-up gear in my quick change gearbox. I tried Geo Thomas' approach, and it worked fabulously.

I had four options for repair:

1. Order the gear from Clausing: \$120.

2. Buy a steel gear from Boston Gear and turn it down to the correct thickness. Machinery texts tell you to avoid steel gears in the leadscrew geartrain...

3. Cut a new gear with an involute cutter.

4. Repair the existing gear.

I chose option four: Get 'R Done.

I carefully followed Geo Thomas' directions, bought a 32-tooth precision-hobbed brass gear from Martin Sprocket, built the spin jig in Geo Thomas' article, and the tooth flanks came out perfectly. The lapped gear is running in my lathe, and is noticeably quieter than the stock gears (which were not chewed up). I wish now that I had taken pictures :)

http://i164.photobucket.com/albums/u15/rtgeorge_album/geometer.gif

Hi lazlo.

That article was one good read.

Thanks.

10-24-2007, 06:48 PM
That animated illustration is wonderful and demostrates a point Buckingham makes time and again: rolling action takes place only at the pitch line. Above the pitchline the action is "approach" and below it's "recess." Some specialised gear manufactiuring like enlarged addendum technique produces all-aproach action on the gear and all recess on the pinion. That's because the effective rolling cylinder (the pitch line) is at of below the root of the pinion.

That tiny distinction reprents the rock on which gear lapping theory breaks requiring extraordinary technique and care must be taken in lapping gears to preserve the tooth form and the transverse geometry.

Thus my derisive terms like "shade tree" and "yokel" when applied to people who apply the lapping technique commonly used on gearing in the expectation of producing smooth meshing accurate gearing.

The article reference has too small a print for me to read. I'll have to import it onto something that will will allow me to do so. I'll comment later.

I submit that a few minutes with swiss pattern files and some thin slip stones would restore defective but salvageable gears to usability in less time and mess.

Imagine an array of abrasive particles ialong the flank of the illustrated gears. Which will experience a rubbing action and which will be simply rolled over with no net radial motion? For lapping to take place there has to be relative motion between the tool and the work. Thus the gear teeth are preferentially lapped above and below the pitchline and not at the pitchline itself. This will appear as a difference in texture in the lapped tooth flanks between the pitchline itself and the sliding portion of the gear tooth.

And for the recond 0.0004" tooth to tooth indexing errors will be pretty noisy if run at any speed. The pair will mesh but the noise will drive you bananas.

John Stevenson
10-24-2007, 07:04 PM
Hi John,

John said that the positional error on any one of the 27 moves was never more than 0.008 degrees."

Neat setup John!
How were you measuring the positional accuracy versus the display position on the DivisionMaster (which was just adding up the step count)?
Were you comparing the 40:1 vernier reading with the Division Master display?

Just taking the reading off the division master as gospel.
I have no way of counting on this table now the big motor has been fitted so it's just send 10 steps or whatever and hope it gets there :D

I have done some largish count gears, one for a telescope that had something like 259 teeth, can't remember now it was ages ago but it was a weird one and when I went back to the first tooth it didn't remove any material.

One thing no one has mentioned but errors in a decent system don't stack up. The idea is to compute the nearest step and division and then play catchup at each position.
That's why it's only possible on the Division master to have 0.008 degrees of error as it adds and subtracts per position.

Personally I feel that although this thread is attracting a lot of interest it's hypothetical in the home shop due to machine and cutter limitations not allowing you to get anywhere near the errors that show in theory.

If you look at a gear that has been professionally hobbed by precision machines from someone like Boston, Ash Gear, HPC etc if you twist this in the light you will see a spiral band traveling thru the gear.

This is because the feed is constant as the blank is turning. In truth the feed needs to feed, then stop for one blank revolution, then feed again etc.
This would be too slow and expensive so they compromise and use a constant feed.
The result being that the tooth width varies by a small amount depending on where it's measured in relation to feed.

Even so these are made and sold by the tens of thousands and go into all forms of motive power.

Somebody mentioned the difference between tooth counts on a cutter.
The number on a cutter is only accurate for the lowest count so a 21 to 26 tooth cutter will only do a 21 accuratly.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/gear21_26.jpg

Not a good pic but this is a 21 and 26 tooth gear superimposed on each other as 1 Mod or 25.4 DP.
There is already an 0.08 mm error if you cut a 26tooth gear with the recomended cutter.

And we won't even start to mention run out, loose gib strips, the wind off the Serengetti and the curvature of the earth.

.

oldtiffie
10-24-2007, 10:08 PM
Just taking the reading off the division master as gospel.
I have no way of counting on this table now the big motor has been fitted so it's just send 10 steps or whatever and hope it gets there :D

I have done some largish count gears, one for a telescope that had something like 259 teeth, can't remember now it was ages ago but it was a weird one and when I went back to the first tooth it didn't remove any material.

One thing no one has mentioned but errors in a decent system don't stack up. The idea is to compute the nearest step and division and then play catchup at each position.
That's why it's only possible on the Division master to have 0.008 degrees of error as it adds and subtracts per position.

Personally I feel that although this thread is attracting a lot of interest it's hypothetical in the home shop due to machine and cutter limitations not allowing you to get anywhere near the errors that show in theory.

If you look at a gear that has been professionally hobbed by precision machines from someone like Boston, Ash Gear, HPC etc if you twist this in the light you will see a spiral band traveling thru the gear.

This is because the feed is constant as the blank is turning. In truth the feed needs to feed, then stop for one blank revolution, then feed again etc.
This would be too slow and expensive so they compromise and use a constant feed.
The result being that the tooth width varies by a small amount depending on where it's measured in relation to feed.

Even so these are made and sold by the tens of thousands and go into all forms of motive power.

Somebody mentioned the difference between tooth counts on a cutter.
The number on a cutter is only accurate for the lowest count so a 21 to 26 tooth cutter will only do a 21 accuratly.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/gear21_26.jpg

Not a good pic but this is a 21 and 26 tooth gear superimposed on each other as 1 Mod or 25.4 DP.
There is already an 0.08 mm error if you cut a 26tooth gear with the recomended cutter.

And we won't even start to mention run out, loose gib strips, the wind off the Serengetti and the curvature of the earth.

.

Thanks John.

You make your excellent points very well and in your own inimitable way.

All points noted - particularly the final ones.

Keep it up.

Tops.

Paul Alciatore
10-25-2007, 03:11 AM
Wow, great discussion.

Lets see. Someone assumed I was talking about milling a tooth at a time since I mentioned a RT. Actually, I am talking and asking about rotary indexing in general: both for single tooth and for hobbing. When hobbing it is recommended that the gear be driven at the correct rate instead of allowing the cutter to turn it. That is only suggested when a odd or prime number of teeth are needed and the shop does not have the proper change gear.

In reality, I want to set up to make gears. I am tending toward hobbing as it is more versitile and as Forrest and others have said, it is more accurate for all tooth counts. I am thinking of using a worm gear and a stepper to allow me to produce gears of any tooth count without the necessity of having a pre-existing gear of that count for the gear train. Let the electronics handle the primes.

I agree with Forrest when he says that the errors will come from a variety of sources. But one must tackle each of these sources in turn and I am asking about the accuracy needed in the gear train. I find it easy to believe that the indexing head John referred to is three times better than my Chinese made table. I simply used that table in my example because it is what I am most familiar with. If I buy/construct a machine or rig up a setup for a mill, I would probably purchase a high quality worm and worm wheel for the best accuracy I can get. It would also be more compact than my table.

As for the idea of just purchasing the gears from Boston or another commercial source, there are two good reasons for not going that route. One, Boston and the other stock gear suppliers do not stock all tooth counts. Two, I find their prices a bit high for what you get. If you are trying to make a product at a low price, you can not just pay the going rate for everything in it.

Yes, the question is theoretical. But it also has practical consequences. I believe Forrest has answered my original question. No, I am not missing anything. My analysis seems to be essentially correct and if anything, it does not go far enough. If I use a 72:1 or a 90:1 worm and a 200 step motor, I still need at LEAST another 10:1 reduction in the chain. 50:1 or 100:1 would be better.

Thanks to all for the excellent discussion.

oldtiffie
10-25-2007, 08:26 AM
Paul mentioned getting a better rotab. I have the 6" and 8" "Vertex" mentioned in the link John Stevenson gave at:
http://www.jeffree.co.uk/divisionmaster/examples.html

Pics of my "Vertex" rotabs follow:
http://i200.photobucket.com/albums/aa294/oldtiffie/HF45-5.jpg

http://i200.photobucket.com/albums/aa294/oldtiffie/HF45-6.jpg

Both are really excellent rotabs and the worm ratios on both are 90:1.

Maximum indexing error is 1 arc minute.

The 8" with its larger indexing plates (3) indexes directly from 2>100 - the 6" with its smaller and only 2 plates is not as comprehensive but its very good for its size.

Of course (non-CNC-ed) rotabs can use the manual hand-wheels which are calibrated (vernier) to read directly to 5 arc minutes and to interpolate even closer for gears etc. to be cut manually if the number is beyond the capacity of the dividing plates.

Marv Klotz has an excellent utility for setting the hand-wheel for any ratio and any number of divisions/holes/teeth etc. in the even that the dividing plates will not be able to do the job. A dividing head only has the indexing facility as the hand wheel indexing is not provided.

OK - so much for the "mechanicals".

In a previous post John Stevenson was hobbing spur gears on a horizontal mill with a direct coupling (CNC-type belt/s as I recall) between the (horizontal) arbor (and tooth cutter) and the "universal" dividing head . IIRC the cutter was a spiral like a "toothed worm" which acted as a gear generator. As the arbor was running and driving the dividing head the "X" feed was engaged as well and the gear was generated. I don't recall if the dividing head was rotated on the table an amount equal to the helix angle at the Pitch circle of the spiral cutter (which acted as a hobbing cutter) - but I would expect that it was.

I can see how worm-wheels (and worms) and helical gears can be done as well.

So it seems that there may be several "ways to go".

I can understand how a full 2x- or 3x-axis CNC set-up could do the job as also - and MUCH better - as in the pics of link provided by John - using either a horizontal mill and a dividing head or a vertical mill with a stub arbor and a rotab. with the dividing head and the "X" feed all direct-coupled for/in CNC.

It would be most imprudent not to take John Stevenson's "caution/s" (post 28) into account so as to remain "practical" and realistic with our expectations.

I hope there is a lot more "mileage" in this thread yet as it is a real "goodie".

oldtiffie
10-25-2007, 09:05 AM
I was following up a link from another thread when I cam across this link to Boston Gear which has a 5.5 Mb pdf down-loadable file for those that might like to "brush up" on "gears" from one of the leaders in the field.
http://www.bostongear.com/products/open/theory.html

I haven't had time to down-load it yet (slow ADSL feed and its late) but I will do in the morning (if I remember) - should be a good read.

I hope it helps.

J Tiers
10-25-2007, 09:13 AM
Hey, if you like gadgets, no reason at all to avoid the whole system you mentioned.

But if you want to "cut gears" gears that will work fine and are not for stealthy submarines, Lexus trannys, etc, you will do fine to have a dividing head and a set of cutters.

In that case, cut the cackle and start cutting.

If you obtain a dividing head with external drive capabilities, and are willing to set up a drive off your mill axis drive, you can hob and so forth with a similar setup using the DH.

The inaccuracy of cutting that comes from the DH will not be a particular factor given the precision of the rest of the setup.

And, a small error of "depthing" the mating gears will totally wash out any accuracy issues in many applications, adding a huge (relatively) looseness and backlash to the system.

John Stevenson
10-25-2007, 09:41 AM
JT,

We have a winner.

11 out of 10 and anything off the top shelf.

.

oldtiffie
10-25-2007, 09:44 AM
Hey, if you like gadgets, no reason at all to avoid the whole system you mentioned.

But if you want to "cut gears" gears that will work fine and are not for stealthy submarines, Lexus trannys, etc, you will do fine to have a dividing head and a set of cutters.

In that case, cut the cackle and start cutting.

If you obtain a dividing head with external drive capabilities, and are willing to set up a drive off your mill axis drive, you can hob and so forth with a similar setup using the DH.

The inaccuracy of cutting that comes from the DH will not be a particular factor given the precision of the rest of the setup.

And, a small error of "depthing" the mating gears will totally wash out any accuracy issues in many applications, adding a huge (relatively) looseness and backlash to the system.

Good practical post JT - as usual.

I agree with you 100% as that is the way I would go as I like that method as I am used to it, and like yourself, I get "good-enough" results. Any better required, I get a specialist gear Company to do it.

I only used the "all mechanical" approach to try and show what is possible the "Old" (read "non/pre-CNC") way/s - as you say.

But I reverted back to CNC as that is the main intent of the thread that Paul OP-ed.

And I "stayed up" and down-loaded that Boston Gear pdf file at:
http://www.bostongear.com/products/open/theory.html

Its a damn good read and "gathers all the threads together" - as you'd expect from Boston Gear. It was a great read.

Lew Hartswick
10-25-2007, 09:52 AM
Aint DSL great 25 sec to download that . It'l take me a day or two to
...lew...

lazlo
10-25-2007, 11:31 AM
Someone assumed I was talking about milling a tooth at a time since I mentioned a RT. Actually, I am talking and asking about rotary indexing in general: both for single tooth and for hobbing.

Hi Paul,

We're mixing and matching indexing errors for various methods of gear cutting.

If you're cutting gears with an involute cutter, you're using a dividing head, which usually has a 40:1 worm, or a rotab, which usually has a 90:1 worm. So your error calculation of +/- .0004" applies to the rotab, but that indexing error is probably twice as high for a dividing head.

But most importantly, you can't hob on a rotab or dividing head: you need a pair of synchronized spindles, like on the Helix gear hobber or Stevo's Eee-lec-tronik hobber. Then the indexing error is dependent on whatever reduction drive you have on the workpiece side. I vaguely remember that Steve used a 20:1 industrial right-angle gearbox for his hobber, so that indexing error would be entirely different than the gear cutting he did with the Hoffman dividing head.

the positional error on any one of the 27 moves was never more than 0.008 degrees.

Assuming Paul's original calculations are correct, .0055 degree error for a 90:1 rotab translated into 0.0004" indexing error. So John's .008 degree error works out to an indexing error of +/- .00058".

And for the recond 0.0004" tooth to tooth indexing errors will be pretty noisy if run at any speed. The pair will mesh but the noise will drive you bananas.

I'm a little confused there Forrest -- almost every gear cut in a home shop in the last 100 years was cut with a gear cutter in a dividing head, and they seem to work fine??:confused:

If .0004" tooth center error will drive you bananas from the noise, John's gears , with .00055" tooth center error should be even worse, but it seems like John has a lot of happy customers? :)

Evan
10-25-2007, 11:39 AM
This discussion brings to mind how relaxed the specs are for most gearing applications. John mentioned making a gear for a telescope. I would be interested to know how it turned out in practice. The pointing accuracy required for astrophotography can be orders of magnitude more demanding of the gear set than common applications. Gear noise isn't an issue as in this application the gears are moving at clock speeds. Tooth flank errors are an issue as they will result in periodic errors that repeat every tooth. This has the effect of pointing the telescope incorrectly as the tooth gradually passes through the incorrect part of the involute form.

To give some idea of the accuracy required the positional accuracy of my double arm camera drive is on the order of no more than 1 arc second error both immediate and cumulative over two hours. This has been verified empirically by studying the images obtained on a long exposure and determining the actual spot size of resolved objects. For this device I rejected gearing as being unable to provide the required accuracy and instead used a screw drive. It acts in effect as a segment of a very large worm gear having an effective diameter of 22 inches.

To give some idea of how this compares to the best worm gears an 11" Byers worm gear set is specified as being accurate to 5 arc seconds and costs over \$1000. The low error that I achieved is due to the use of a screw drive instead of a gear. The accuracy of the screw is the accuracy of the lead screw used to make it. This is further divided by the number of rotations required to produce a rotation, in the case of my drive with a 20 tpi screw it is approximately 691 turns or the equivalent of a worm gear with that many teeth.

How does this pertain to this discussion? What it means is that larger rotary tables with more teeth on the worm are usually more accurate than small ones. The angular error produced by size independent tooth shape error is divided by the radius of the wheel. The larger the radius given a tooth profile error that is the same despite wheel size the less effect it has on positioning accuracy. Also, the more teeth there are the more accurate the positioning. This means the higher the ratio the more accurate it is since more teeth mean smaller errors per tooth. More teeth also means a less demanding involute profile that approaches a straight sided tooth as the number climbs above 60 -100 teeth per gear.

Going back to my screw drive it is essentially a rack driving a rack. Both the screw and the nut have "teeth" with a straight sided profile which eliminates profile error from consideration.

John Stevenson
10-25-2007, 11:50 AM
I'm a little confused there Forrest -- almost every gear cut in a home shop in the last 100 years was cut with a gear cutter in a dividing head, and they seem to work fine??:confused:

If .0004" tooth center error will drive you bananas from the noise, John's gears , with .00055" tooth center error should be even worse, but it seems like John has a lot of happy customers? :)

WOT ?:confused:
Can you speak up, I'm a little bit deaf................................

.

lazlo
10-25-2007, 11:53 AM
Stop it John -- I just spit up my coffee :D

oldtiffie
10-25-2007, 07:23 PM
WOT ?:confused:
Can you speak up, I'm a little bit deaf................................

.

Well John, there may be a cure for that.

Jist gotta 'av "faith".

'owzit werk?

Loik diss.

All a da "hear, hear"s zn "greats", "Wow!"' 'nna da loik 'r' just comment 'n' 'currijm'nt.

Yeh? Zo?

Well you neels on ya neez darn 'n frunt ov wun uv' deez "goo-rooze" wiv dere "magic powaz" 'n' face skywud 'n diss "goo-roo" puts iz 'andz on yer 'ed, looks skywud 'n sez "hear hear" as a command 'sted uv a comment an lo 'n beyold ya 'eernz OK 'gin.

QED

Paul Alciatore
10-26-2007, 03:41 AM
Evan,

Interesting mechanism (your telescope drive). Perhaps you have neglected the factor of two in your calculations. R = 11, D = 2*R = 22, C = pie*C = 69.11, and finally Thread (or tooth) Count = 20*C = 1382.3

I am curious about your design. Your photo is a bit dark so I can't see the precise details. And my copy of Photoshop is not working at present (for brightness/contrast correction). But I am assuming your screw is straight, not curved with an 11" radius. If so, then the distance traversed along the screw is a chord of the circle, not the length of an arc. For small angles the difference is slight and the drive should work well. In fact, it is a drive that has been published many times in various amateur astromony pubs. But, as the angle gets larger, the difference will become progressively larger in a non linear manner. A two hour exposure would require the camera to traverse an angle of 2*360/24 or 30 degrees. At 30 degrees, the difference in length between the arc and the chord will be quite significant. So it does not make any sense that you could get one arc second accuracy over that long of an exposure. Would you care to comment on this?

I do have to agree that any gear of a practical size for amateur telescope equipment would be incapable of one arc second accuracy. Using your 11" radius (22" diameter) example, a one arc second displacement at the 11" radius would be about 0.00005" or 50 millionths. This may be possible but would cost many thousands of dollars per gear. But the same calculation applies to your mechanism. Now, a screw-nut combination will give somewhat of an averaging effect in that several threads are in contact at any given time and this will reduce some of the errors in the mechanism. But I really have to wonder if you have truely achieved this level of accuracy over such a relatively large distance. How did you produce this thread and nut?

You do not give any specs on the optics of your camera. If you are using a digital imaging device, it would have perhaps 1500 to 2500 pixels per inch. Lets go with the 2500. So each pixel would be about 0.0004" and the C-C distance between pixels is the same. Doing the reverse calculation for the angle, you would have to have a focal length of at least 82.5 inches to get one arc second resolution with such an imaging device. Film would give different results but would be comparable. And the lens/mirror would have to have at least a 4.5" diameter. That would be an f18 system and I doubt you have such a slow camera. I would suspect at least f10, more likely f8 or so. That would increase the lens/mirror diameter to about 8 or 10 inches. A size that is quite normal for amateur and some professional equipment, but is this the type of instrument we are discussing?

For many decades telescope makers and astronomers have delt with the inaccuracies of the available gears. That is why big telescopes and even medium sized telescopes have guide scopes attached to them. A junior astronomer or in more recent times a photocell (or imaging device) based automatic tracking system tracks a bright star near the object the main scope is photographing and makes continous, small corrections to the main scope's position. The gear/motor based tracking system only provides approximate tracking. In some scopes the tracking system uses an off-center star in the main scope's field. And I am sure modern scopes also add computers to the loop. But, this is how arc second and better tracking is achieved. a coarse system that approximates the needed position and a correction system (manual or automated) that does the fine correction.

PS, I don't presently have any need for gears that are that accurate. I am interested in making good, servicable gears with as little time and effort as possible. In other words, a compromise. I plan to CNC the process so I can set up one or more blanks on the arbor, zero the cutter, hit start and let the computer do the work. I plan to use a computer drive for the blank rotation (and other motions) so I do not have to have gears of every prime tooth count available for the gear train.

oldtiffie
10-26-2007, 04:56 AM
Paul.

Good post re. Evan's set-up.

There is at least one Swiss theodolite - "Wild" Model T1 - that is used for geodetic work that has a transit at least - and possibly the alidade - that will get to 6 arc second (direct) and 3 arc seconds interpolated (probably 2 or beter with a good instument and Surveyor).
http://www.mohaveinstrument.com/NewFiles/T1E.html

I would expect that some of the modern Total Stations would have that capacity or better. But so far as I know, that is for "static" work and not "tracking".

I would expect that Observatories and their tracking systems and telescopes would be of an extremaly high order of accuracy and photography.

Is that so?

What is the state for radio telescopes?

I will be very interested to read Evan's response.

Evan
10-26-2007, 05:21 AM
Paul,

The device is a double arm drive, not a simple tangent arm drive. The geometry is very different and produces nearly perfect circular motion over a range of 30 degrees before it starts to diverge.

However, Type 4 drives are quite another story. Their performance is truly astonishing. While the table rounds off errors to whole are seconds, a careful calculation using Alain Hairie's beta = 2 shows that his drive will track to 0.005 arc second for half an hour! At the end of an hour, it is still good to 0.159 are second. The last column illustrates how a slight variation of Hairie's ratio, to beta = 2.186, can push the "perfect" tracking all the way to two hours, as long as we are willing to relax our expectations in the middle of the exposure. Now the worst error occurs near the 90-minute mark, and it amounts to just 0.8 are second!

See here: http://hometown.aol.com/davetrott/page17.htm

My drive is a modified type 4 drive. As for the accuracy I reported I have taken some liberty in describing it. The atmosphere will exhibit about 15 arc seconds change in refractive error over a one hour change in declination so that swamps any attempt to track more accurately than that. Even so, using the drive I was able to unambiguously image objects to magnitude 13 using just a 50mm camera lens in excellent conditions. It was previously thought that the limiting magnitude for such a lens was about magnitude 11 to 11.5 so I was able to show that with suficiently accurate tracking that it is possible to do much better. All of my testing was done using professional film and a diffraction limited lens on an SLR camera. I should point out that the motor that drives it is driven by a crystal controlled oscillator inverter that is calibrated to better than 1 part per million using a reference only 2 steps removed from NIST.

You are right that I left out the factor of two in the above calculation. Rest assured that I did not when I designed it. :)

Evan
10-26-2007, 05:30 AM
Tiffie,

The observatories and nearly all large telescopes use closed loop tracking systems so drive accuracy isn't a factor for them. What they are most concerned with is pointing accuracy, a somewhat different matter.

oldtiffie
10-26-2007, 08:06 AM
Tiffie,

The observatories and nearly all large telescopes use closed loop tracking systems so drive accuracy isn't a factor for them. What they are most concerned with is pointing accuracy, a somewhat different matter.

Thanks Evan - last 2 posts.

I guessed that about the observatory as I'd expect that they would be using high-order scales (super DRO type??) to determine where they are and where they want to be in absolute terms as well as tracking rates and excellent predictors, rates monitoring etc.etc. I'd expect that would be servo-controlled for smooth running and to not have to rely on "mechanisms and mechanics" etc. The tracking and movement would need to be superb to maintain high orders of positional accuracy as well as low order "hunting" and "over-shoot".

That tracking/positioning/recording set-up of yours must be "something else".

Also FWIW, the scales on the "Wild" T1 theodolite are etched on glass and are a "microptic" system that "double-checks". It is etched on a scale that is about 3" in diameter. Just imagine how accurate the etching processes were - and even more so, the systems for checking them for compliance. My theodolite is a Japanese 20 arc second micropotic job (very good optics) that can with some care can reasonably easily get down to about 10 and at a "push" 5 arc seconds and come back almost spot on over almost a Kilometer and at least 4 change or station points. My "Red-Mini" EDM (elec distance meter) is calibrated to 1 ppm +/- 3mm. Both are 30 years old but have not been used in 10 years.

Also the much admired early jig-borers with such incredible accuracy had glass scales as well.

The combination of mechanisms and optics in the sort of stuff you and Paul are talking about is almost unimaginable.

oldtiffie
10-26-2007, 08:34 AM
As orders of magnitude seem to be required here, why are we only discussing spur gears.

I'd have thought that moving onto spiral/helical/hypoid gears and the like would have been better suited and perhaps incorporate "anti-back-lash" and perhaps some sorts of "smoothing" device/s would improve things.

I'd have thought that "wind-up" ("stored torque"??) would be an issue too as are friction, stiction, inertia and what-ever else. This which while of most concern in dynamic states is still a concern in static states.

I see no mention of countering the "back-lash" (no matter how small) in the hobbing processes as I'd guess that the roatab or what-ever can "rattle around" within its "back-lash/slackness" etc. and possible needs some sort of "brake" or "drag".

Locking or clamping spindles of rotabs and dividing heads is a matter of course when "hand milling" but I've seen no mention of it in the "continuous" cutting methods - ie CNC - either or both "step" and "servo". Is it needed? If not - why not? And if so, how is it either effected or countered?

And the best gears in the world are negated if the fixing/connection to or "sliding over" shafts and keys are not of a very high oder as well. I have seen this quite well over-come by using accurately gound involute splines matched (selected fit/lapped) broached internal slines on moving parts. The hydraulic shrink fit gave an absolute and excellent connecting between a shaft and a part to be fivxed to it. Getting them apart without the equipment to reverse the hydraulic shrinking - ie to re-expand the mated/joined parts - was all but impossible.

As I understood it, Evan did allude to a servo mechanism being able to over-come many of these short-comings were-as "stepping" may be quiet dependent on it.

Paul Alciatore
10-26-2007, 10:25 AM
Evan,

The double arm mount looks like an extremely clever idea and I am sure it is correct in principle. But my comments about the actual achievable accuracy still stand. You still need an extremely accurate screw and nut, not to mention the flatness of the surface on which the point of one lever slides on the other. And the shape and smoothness of that sliding poing. Consider that the arm with the camera is moving faster than the arm with the screw. Any errors in flatness on the screw arm will be amplified in the motion of the camera arm.

And a 50mm diameter lens (2") could never resolve to arc second accuracy. That's basic physics and why telescopes have large diameter lenses/mirrors. You can check out the resolving power and many other factors with the Stellafane telescope comparison calculator page.

http://stellafane.org/atm/atm_select_scope/atm_scope_calc.htm

A 50mm diameter lens is difraction limited to 2.25 arc seconds. I have followed camera lens tests for years and can assure you that actual production lenses will almost never reach their theoretical limit. They are made for general photography, not astronomy. (The eyepiece numbers are of no concern here so if anyone tries this you can just leave the original eyepiece numbers or enter other reasonable ones.)

You still did not mention the focal length of that lens. As I said, film will have different characterists from an electronic image pickup. Different films will differ and you are into the old speed vs. resolution delema. Fast films tend to have lower resolution and high resolutions films are relatively slow. But the resolution numbers are going to be in the same ballpark as the electronic devices. And, truth be known, the electronic devices have similar problems/compromises. So my comments about focal length needed also still stand. Of course, you could have a secondary lens (focal length extender) that produces a longer effective focal length. But that would also add optical abberations and probably further blur the image.

I am sure you have a very good system. I just highly doubt that it is anywhere near arc second capable. Either optically or mechanically.

oldtiffie
10-26-2007, 10:31 AM
Well, well.

This just gets "betterer and betterer".

I've learned lots here and am looking forward to more of the same.

oldtiffie
10-26-2007, 11:03 AM
In a previous post I mentioned the Wild T1 theodolite.

One of the members who repaired and set these items up was kind enough to PM me and suggest that I should check out the Wild T4, which I did,

WOW!!!!!!!!!!!!

The impossible is not only possible but it exists with the Wild T4.

If you want to see what you aspire to as regards accuracy and performance for a lot of "stuff" and "things", Astronomy included check this out (University of New South Wales (Australia) and the theodolite was "donated"!!!:
http://www.gmat.unsw.edu.au/currentstudents/ug/projects/f_pall/html/t21.html

And when you pick first yourselves up from the floor and then your sagging/gaping jaws you might work your way through this "Google" post:

And to the forum member who advised me on this matter - my sincere thanks.

Evan
10-26-2007, 12:08 PM
You still need an extremely accurate screw and nut, not to mention the flatness of the surface on which the point of one lever slides on the other. And the shape and smoothness of that sliding poing. Consider that the arm with the camera is moving faster than the arm with the screw. Any errors in flatness on the screw arm will be amplified in the motion of the camera arm.

And a 50mm diameter lens (2") could never resolve to arc second accuracy. That's basic physics and why telescopes have large diameter lenses/mirrors. You can check out the resolving power and many other factors with the Stellafane telescope comparison calculator page.

The first arm carries the second arm via an abec 5 bearing that rolls on a piece of polished tool steel. It's polished to optical flatness. That part is easy. As for the screw thread that part isn't that hard either. The nut engages the screw over a range of about 8 threads and the screw and the nut were lapped together over the entire length of the screw. The screw is SS and the nut is brass. The possible single thread periodic errors are lapped out by the lapping process as the two were lapped in both directions with the screw reversed half the time. Also, the inaccuracy in the lead screw on the lathe that made the nut is divided by the ratio of the leadscrew tpi and the screw tpi which is 2.5 to 1. Since the screw is very short compared to the leadscrew any cumulative errors due to wear in the leadscrew are extremely small.

On the matter of resolution, I am well aware of the math surrounding the subject and have pointed it out here more than once. The Raleigh Limit doesn't apply to imaging a single point source. It determines the ability of an optical system to resolve two or more such sources as separate entities. That is not the issue here. Regardless of the resolving power of the lens it will still provide an image of a point source such as a distant star. With an ideal lens the image contains about 84% of the light in the central airy disk and the remainder is distributed in the surrounding diffraction rings. It is nonetheless an image of the source. The only thing that changes with changes in resolving power is the apparent size of the image on the imaging media.

Where the drive accuracy comes in is the ability to accurately track the source thus insuring that as much light continues to fall on the same part of the imager during the exposure. You will note I did not make any claims regarding resolving power. The ability of my system to capture images two orders of magnitude below the accepted limit even applies to a poor lens as what drive accuracy provides is improved location of the light on the same spot during the entire exposure. This is where the spot size provides information about the drive accuracy. The less accurate the drive the more the light is spread over the imager and the poorer the quantum efficiency in capturing the photons on any particular element of the imager. That in turn limits the lowest magnitude of the image that may be captured.

By providing highly accurate tracking my drive insures that the light strikes the imager in the same place during the entire exposure. This in turn makes it possible to image weaker light sources than if the image is drifting across the imager because of tracking error.

Again, I make no claims of arc second capability for the optics, only the drive tracking.

Paul Alciatore
10-27-2007, 05:52 PM
The first arm carries the second arm via an abec 5 bearing that rolls on a piece of polished tool steel. It's polished to optical flatness. That part is easy.

OK, I take optical flatness to be in the 50 micro inch range. That would work, I guess.

As for the screw thread that part isn't that hard either. The nut engages the screw over a range of about 8 threads and the screw and the nut were lapped together over the entire length of the screw. The screw is SS and the nut is brass. The possible single thread periodic errors are lapped out by the lapping process as the two were lapped in both directions with the screw reversed half the time.

Again, errors can be reduced by such processes, but there are many types of error and no process with a single screw and nut will take care of all of them.

Also, the inaccuracy in the lead screw on the lathe that made the nut is divided by the ratio of the leadscrew tpi and the screw tpi which is 2.5 to 1. Since the screw is very short compared to the leadscrew any cumulative errors due to wear in the leadscrew are extremely small.

What? If you have a 10 TPI lead screw (I am using a round number for simplicity) and are cutting a 25 TPI thread that is a 2.5:1 ratio. Now, if the 10 TPI lead screw is 0.001" too long per inch (a generous error) then the 25 TPI thread you are cutting will be the same amount too long or 0.001" per inch. I don't see where there there would be any reduction in the error as measured on a linear basis. Now, on a per thread basis, yes the error would be less. 0.001"/10TPI = 0.0001" per thread while 0.001"/25 TPI = 0.00004" per thread. But we would be more concerned with the error per unit of length, not the error per thread.

As for errors over longer distances, distances which exceed the 8 thread length of your nut and the length of the half nut in your lathe, neither the reduction in the cutting process nor the lapping process you mentioned above would have a lot of effect on them unless the lapping were carried out to an extreme extent.

On the matter of resolution, I am well aware of the math surrounding the subject and have pointed it out here more than once. The Raleigh Limit doesn't apply to imaging a single point source. It determines the ability of an optical system to resolve two or more such sources as separate entities. That is not the issue here.

The resolutin of a single point and the ability to separate two such sources may not be identical, but they are closely related. If an optical system is unable to resolve two points that are one arc second apart it is because each of those point sources are each imaged as a blurred disc with diameters that overlap. Now, I know it is not completely that simple as the difraction rings are also there and they also combine with each other and with the central discs. And there is a whole range of images possible from two completely distinct central discs with difraction rings that don't even touch each other, through various figure eight blendings, down to a single central disc with a single set of difraction rings that are for all purposes completely circular. If I recall correctly the Raleigh limit falls somewhere in the figure eight blend range. It is not a sharp division. BTAIM, the Raleigh limit is perhaps the most popular measure of the resolving power of a system for whatever reasons. It is not the only measure, but it does speak volumes. If a "single point" object is displaced by an amount less than the Raleigh limit it is very doubtful that you will be able to measure that displacement with any degree of accuracy in the optical system. It is also doubtful that you could even see the motion (with the eye or any instrument that you posess).

So my point is that you have absolutely no way of determining or verifying that your drive is actually as accurate as your theory suggests that it may be. At least not with anything you have described here.

Where the drive accuracy comes in is the ability to accurately track the source thus insuring that as much light continues to fall on the same part of the imager during the exposure. You will note I did not make any claims regarding resolving power. The ability of my system to capture images two orders of magnitude below the accepted limit even applies to a poor lens as what drive accuracy provides is improved location of the light on the same spot during the entire exposure. This is where the spot size provides information about the drive accuracy. The less accurate the drive the more the light is spread over the imager and the poorer the quantum efficiency in capturing the photons on any particular element of the imager. That in turn limits the lowest magnitude of the image that may be captured.

I believe you are extrapolating a bit too much from spot size. From the information given, I am sure that your tracking error is far smaller than the ability of your camera to resolve. You could probably double the tracking error and not see any difference in the images provided the other conditions are the same. I would also suspect that atmospherics would play a far greater role in the spot size.

As for the ability to capture objects that are two orders of magnitude less than accepted standards for similar systems, well that does attest to your skil and knowledge in constructing the system. It also points to good atmospherics at your location. You definitely could not do that from the middle of Central Park in NY City or from smog prone LA. One of the biggest advantages in astrometric observations is the "seeing" conditions. And it perhaps points to other factors as well. I am sure your drive is highly accurate but I am just a bit skeptical about the actual level of that accuracy. One arc second is a difficult goal for any mechanics.

Evan
10-27-2007, 08:23 PM
Paul,

The resolving ability of the optics doesn't enter into the question. The resolving ability only determines the size of the airy disc and the associated diffraction rings. All optical systems will produce the exact same result from a point source with the only difference being the size of the image on the sensor. This assumes diffraction limited optics. If the optics are not diffraction limited then more light will be distributed in the diffraction rings and they may be blurred or out of round.

If the optics are diffraction limited then with perfect tracking the result is a round image. Only the size of this round image depends on the resolving ability of the optics. This has nothing to do with the ability of the optics to resolve anything in terms of arc seconds of separation, simply that the image wasn't dragged across the sensor during the exposure. The very important point about this effect is that the ability to resolve any resulting distortion of the round image IS NOT related to the optics but to the resolving power of the imaging media or sensor. That is an independent variable. That is the reason I used Fuji Superia Professional film. It has extremely high resolving power, much greater than the optics.

In order to determine if the image has been dragged by inaccurate tracking the negative is examined at high magnification. The 50mm f2 lens I have is diffraction limited. It has very good optics. Any distortion of the round image near the center of field will be due to something besides the lens. Fuji Superia has perhaps 10 or 20 times the resolving ability of a 50mm lens so it is easily able to show the effects of image displacement during an exposure even if the amount of displacement is well below the resolving ability of the lens. The image will not be round. This has nothing to do with the size of the image the lens formed, only that movement of the image occurred relative to the film plane.

Once again, I reiterate that the limits on the resolving power of an optical system are the limits of what it can distinguish as separate entities. It is not a limit on what it can image. A perfect example is this astrophoto I took with my Nikon 4300. This was taken with only the camera's own lens with the camera mounted on my double arm drive.

It is a sequence of three photos showing a transit of Ganymede across the face of Jupiter with Callisto in the lower left. The shadow of Ganymede is clearly imaged even though the apparent size of the shadow is below Dawe's Limit of the lens on the Nikon. That is because Dawe's limit is not a limit on what can be imaged. There is no such limit except the ability to collect sufficient light to expose or activate the media or sensor. With a modern CCD the quantum efficiency can be as high as 80 to 90 percent meaning that even a single photon can be detected.

Callisto is identified in the lower left and the arrow from it to Ganymede delineates the orbital plane of the moons. I used an orrery program for Jupiter to verify that a transit was in progress, which it was.

http://vts.bc.ca/pics3/gtransit.jpg

The primary verification of the drive's accuracy was performed by means of a series of exposures taken at Mt. Kobau in 2002. This is the site of the annual star party and is considered the best accessible observing location in Canada.

One of the images taken was this photo of M31, The Great Galaxy in Andromeda. This was with a 50 mm f2 lens with an exposure time of about 12 minutes. M31 is well away from the pole so it provides a good test for tracking ability.

http://vts.bc.ca/pics3/m31.jpg

The image was analyzed by enlarging it with a 4800 dpi slide scanner directly from the negative. I have reversed it so it looks more familiar. A very small region, too small to delineate above, was examined and correlated to a rescaled image of the same region from the Skycat II survey. The lables indicate the locations of objects from the Skycat survey and the apparent magnitudes of each. The fuzzy blobs are the images on my negative. They are blobs because of the low resolving power of a 50 mm lens but the lens still collects the light and forms images nonetheless.

As can be seen there is no trailing of the images even at this high magnification. Also, it is clear that 13 and even 13.9 magnitude objects were imaged in this astrophoto. That is completely at odds with the popular wisdom that says a 50mm lens can only image to a depth of 11 or 11.5 magnitude. The reason I could image this deep is because of accurate tracking. Also, the scale of the image is well quantified by the Skycat survey so estimating the spot size of my images is easy. You can see that if the 13.9 mag image had been trailed even slightly it would not have been sufficient to expose the film.

http://vts.bc.ca/pics3/maglim139.jpg

I will mention that I received an award for mechanical excellence from the jury which included the director of the Arizona state observatory as well as an experienced machinist.

oldtiffie
10-28-2007, 03:00 AM
All very well and good.

I am enjoying the discussion thus far but to bring it back to "Gear-Cutting: Accuracy of Dividing" (the title of this thread) for a moment and a bit of a reality check for the "great unwashed" (me for certain - any others?).

As I see it, the accuracy we are talking about here seems to centre on 1 arc minute (3,600 of 'em in 1 arc degree).

ArcTan (or arcsine - both the same) of 1 arc minute is Atan 1/3,600 deg = atan 0.0003 deg = 4.8481 x E-6 (that is 4.8481 per 1 million) = 4.8481mm per kilometer (there are 1,000,000 mm per Km.).

A 1" "spread" (ie a 2" diameter circle) on a rifle target at 100 yards (3,600 inches) is Atan 1/3600 = 0.0003 = 0.0159 arc degree = 0.0159 x 60 = 0.9549 arc minutes x 60 = 57.2958 arc seconds.

So the relative order of accuracy that Paul and Evan are discussing is about 58 times as accurate as a 1" target spread (2" circle) at 100 yards.

That is seriously accurate.

But is gets better as the mechanism that the camera or recording media/method is mounted on must move in 2 ordinates - traverse (left-right) and elevation (up-down) so that the vector and rate at the orientation of the vector (or part of circle) must both be of greater accuracy than the mechanisms that drive each of the traverse and elevation to get 1 arc second accuracy at the recording media apparatus.

So far as I can see the position at any time is done by "dead-reckoning" (ie "where it should be" as opposed to "knowing where it is" (by comparing the actual position/s of the mechanism/s with where they are/were predicted to be). So there may well be errors that are neither known nor measured.

This seems to be analogous to the CNC "stepping" procedure as it is in the mechanisms discussed.

It it were in a "servo" system where the error between "predicted" and "actual" position's could be determined (at much better than 1 arc second resolution), the inaccuracies inherent in any mechanism/s might be largely eliminated or accounted or "corrected" for.

This "error" determination can be similar to a rifle shooter measuring and correcting according to error measured by eye and "experience" and "correcting" the rifle line of sight and reducing the error accordingly - or even a car driver using the steering wheel and mechanism to correct for any error between where the car is pointing and the direction he wants to point it in.

[Edit1]
Now to relate 1 arc minute to the 11" radius of Evan mechanism (see Evan's pics).

My relevant paragraph said:
ArcTan (or arcsine - both the same) of 1 arc minute is Atan 1/3,600 deg = atan 0.0003 deg = 4.8481 x E-6 (that is 4.8481 per 1 million) = 4.8481mm per kilometer (there are 1,000,000 mm per Km.).

So, taking one of pail's points re. the difference/s between arc length and chord(al) length, I will assume that they are the same at mid-travel of Evan's screw/nut - that is the "sweet-spot".

So the accuracy required to be maintained at the point where the nut moves the rest of the mechanism (that drives the recording device/s) is to be better than 11" x (4.8481 x E-6) = 0.0000533" (1/2 of 1 "tenth of a thou") so as to maintain 1 arc minute at the recording device.

Also as I understand it, the CNC "stepper" method is an "open loop" system where-as the "servo" method is a "closed loop" system which will have quite a problem accurately picking up that order of error (say "1/2 a tenth" or better at 11" radius) even with the very best of "DRO/pick-up" methods I would think.
[End edit1

[Edit 2]
Now to relate the maximum error at the driving screw of Evan's apparartus (ie 0.0000533" (1/2 of 1 "tenth of a thou") in terms of "turns" of the 20dpi thread (= lead of 1/20 = 0.05000").

0.0000533/0.05000 = 0.0011 = 1/938.0863 turns x 360 = 0.3838 degrees = 23.0256 arc minutes = 1,381.54 arc seconds.

So for a movement of 0.0000533" along the screw by the nut the screw must be moved 0.0011 (say 0.001 = 1/1,000 of a single turn) which approxiamtes to 0.001 x 360 = 0.36 degrees which as it is say 1/1,000 turn requires a maximum "step" (and minimum resolution) of 1,000/turn of the screw.

I hope some-one checks this in case I've got "lost" or "lost it" - whic sure can happen.

So WTH did I do it? 'cos I wanted to; and to see how the mechanisms are required to "perform".

[End of edit 2]

I hope this helps.

Evan
10-28-2007, 11:41 AM
Tiffie,

The drive only has one degree of freedom. The axis of the drive is aligned with the polar axis of the Earth and the drive then turns at the sidereal rate. Provided the alignment is correct and the motor turns at the right speed the rest that we are concerned with is only periodic errors. The main possible long term cumulative errors in the double arm drive is the length of the drive arm and the length of the drive screw.

I shall digress for a moment. I have repeatedly found that the ordinary machinst is accustomed to thinking in terms of thousandths of an inch (or the metric equivalent). Working to specs below that level is considered precision machining and going much below that level is rare.

On the other hand the astronomical instrument community is accustomed to thinking in terms of fractional wavelengths of light. A good telescope mirror will have a shape that is accurate to 1/8 wave of light or better, perhaps much better such as 1/20 wave accuracy.

The machinist in general simply isn't accustomed to dealing with the level of accuracy and precision that is considered ordinary and every day by the astronomer. What the astronomer considers as ordinary the machinist thinks of as extraordinary.

One arc second of accuracy isn't extreme or all that difficult to obtain. The controlling factors over the long term aside from polar alignment are the radius of the drive arm and the rotation rate of the motor. The Earth rotates at a rate of about 15 arc seconds per second. This is an easy to understand human scale quantity. Most of us can count out seconds with reasonable accuracy and a 1/15 of a second is not an incomprehensibly short period of time.

My drive is powered by a 117 vac synchronous motor, not a stepper. In order to maintain one arc second accuracy over 2 hours it must not gain or lose any more than 1/15 of a second in 2 hours. That is no challenge at all and a dollar store quartz watch is at least that accurate. My drive is powered by a crystal controlled inverter that has better than 100 times greater timing precision than is required.

The drive screw is 20 tpi. It rotates at .5 rpm or 180 degrees per minute. That's not hard to understand and appreciate. One can do quite well in actual practical terms turning the screw by the hand crank with reference to the second hand on a watch. In two hours it will have turned 60 times covering three inches or a total of 21600 degrees of rotation of the screw. A one arc second error over two hours will produce a .2 degree position error of the crank handle. Think of it as a clock. This is easy to quantify and measure as I can easily let the drive run disengaged for days if need be to check the rotational accuracy.

The circumference of the "virtual" worm gear is ~70 inches. 2 hours represents 108,000 arc seconds of Earth rotation. That requires that the drive screw length be accurate to 5 decimal places. Or, it would if it weren't possible to compensate.

The one variable that I cannot control is the actual length of the drive screw as generated by the lathe. That however is easily compensated by adjusting the length of the drive arm until no visible tracking error exists. A more subtle adjustment exists in the double arm drive and that is the relationship of the two axes of rotation of the individual arms. By adjusting the relative spacing of these axes the tracking rate of the driven arm can be changed in parts per million.

I use a variety of techniques to measure and quantify dimensions and motion. My favorite methods are optical. A simple method is to attach a laser to the moving part and project the beam along a long base line. In my basement shop I have available a 30 foot long hallway that makes this easy to do. What is an 11" arm becomes a 700 inch arm by projecting the beam on a first surface mirror at the far end.

The real difficulty is the polar alignment. That can present a problem and is the most likely source of error. The amount of error it produces depends on where in the sky the camera is pointed. The error is greatest when pointed 90 degrees from the polar axis and near zero when in line with the axis. To assist in polar axis alignment I made a special "polarscope" from one half of a binocular. Without going into details it makes polar alignment relatively easy. I also developed a polar alignment calculator that can be used to assist in polar alignment in the field.

http://vts.bc.ca/astrophoto/finder.jpg

http://vts.bc.ca/astrophoto/k%20finder.jpg

 Note that the calculator doesn't work upside down. Sorry. :)

oldtiffie
10-29-2007, 03:27 AM
Good post Evan.

For a while I was afraid that I might have to brush up on my Calculus and spherical geometry - thankfully not as it would be a non-event as it is (from) all too long ago.

My only concern really - given that the drive system has been proved to "work" at those rates and tolerances - was that despite - or because - of the lead-screw having been lapped etc. etc. it had not had a check accuracy calibration "run" on it to determine whether there were any errors, and if so how many, where and of what magnitude as regards "turn" and "travel/displacement" for that lead-screw along its operating length.

Perhaps with slip-guages and TDI etc. and very accurate rotation of the lead-screw.

I daresay that software can account or allow for these errors and process any information/data accordingly and/or adjust the "turning" of the screw accordingly.

Marv Klotz has such a utility if I recall correctly (haven't checked - just relying on memory).

The main reason I asked about this is that I hear/see a lot of "stuff" about the high orders of accuracy and virtual lack of back-lash between the nut/s and screw in a "ball-screw assembly. I would be surprised if ball-screws did not come with a test certificate as in guage (slip/"Jo") blocks as has been mentioned both my Cameron Kelloug and laslo (the name of USA testing authority is forgotten) so that the user can adjust the CNC accordingly. But having said that, I would be more concerned at getting similar results when the screw was installed in the machine (lathe, mill etc.).

The "linkage" set you use seems to be very "elegant" indeed for that level of accuracy in traversing - the more so as there seems to be no computer-control or CNC or the like - other than the oscillator which I suppose could be equated to a very sophisticated "up-market" modern-day "tuning fork".

Given the adverse comment re. your ability not so long ago re. a thread with a topic along the lines of "Who is a machinist" - or some-such, I'd say that anybody who is foolish enough now to question your "Machinist" "cred" can justifiably expect a "spray" - and that you are more than qualified to "give" that "spray".

Evan
10-29-2007, 08:05 AM
The "linkage" set you use seems to be very "elegant" indeed for that level of accuracy in traversing - the more so as there seems to be no computer-control or CNC or the like
There is no reason that open loop control cannot provide the required level of accuracy when applied to a motion that must be consistent and invariable. This applies in the case of the double arm drive which is the invention of Dave Trott who teaches as a professor of astronomy at the University of Colorado.

He says this about my implementation of his invention:

This is the double-arm "barn door" drive which I invented many years ago. To get the complete story on this innovation read my original article (http://hometown.aol.com/davetrott/page17.htm)from Sky and Telescope magazine Feb.1988 and the follow-up article in April 1989 . There are MANY web pages about this invention:
...
Evan Williams' Page (http://vts.bc.ca/astrophoto/astro.html) has the most precise version of this mount ever constructed to my knowlege. Check them out!

It (open loop control) also applies to the positioning of a dividing head or for that matter any motion control application where the positioning required is predictable in advance. Within reason, any degree of accuracy may be achieved subject to various trade-offs.

The use of closed loop servo control primarily serves to increase speed, not accuracy. It is still subject to the limits imposed by the resolution of the position detection system. Those limits are only a difference in type, not kind.

The main difference between stepper and servo methods of control is that with steppers you are operating "blind". This means the foremost priority must be to insure the system actually does what it is commanded to do. To do this the system must be robust enough to overcome all forseeable forces that would cause lost motion. This is not a practical difficulty, it can easily be solved with money.

The servo system operates by allowing for lost motion. It does so by keeping track of it and compensating. When the required motion and end point is predictable the servo does not offer any inherent increase in accuracy, merely speed. At some point the extra complexity and cost of a servo becomes cheaper than the extra cost of providing the required open loop robustness of a stepper.

oldtiffie
10-29-2007, 09:17 AM
Thanks Evan.

Now let's get back to making gears on a mill - in a HSM work-shop.

That is or seems to be the required outcome and challenge raised by Paul Alciatore in and since his OP.

Now back to the "Vertex" rotabs used in the article about John Stevenson and how he addressed the problem in a work-shop and under conditions that many HSM's can relate to and which apply in many HSM work-shops.

I checked my specs on my "Vertex" rotabs (6" and 8"). Both are 90:1 ratio and have a maximum actual and accumulated rotary error of 1 arc minute.

It is assumed that the usual grades of gear-cutters will be used on a milling machine arbor - either vertical (as in the case of many of us) or horizontal (as was the case with John Stevenson's excellent demonstration -as it will no doubt be by others).

I am going to assume that we will be cutting spur gears using the "X" feed with the clamps applied to the "Y" and "Z" drives.

A dividing head or rotab "on end" can be used.

The process can be either "hand/manual" or "CNC".

I will presume that the DH/rotab will be indexed by CNC and the "X" feed to be CNC-controlled.

So far so good.

One problem is that a lot seem to assume that the arbour-mounted cutter is precisely "true and symmetrical" to its bore and that the cutter teeth profiled do not "wobble" side-ways. Those teeth are "as formed" prior to heat treatment and distortion - if any - is not normally eliminated or adjusted for. Sure, the "front" of the teeth are "trued-up" in the post heat-treatment grinding processes - but the profiles are not. So even with careful "in-feeding" the tooth-space "as cut" will widen and the tooth-width will be narrowed.

Even if all as discussed previously is a "non-event" and is "OK" there must be a problem with the tooth profile - all-be-it very small - if the teeth being cut are not at the bottom of the "number" range for that cutter.

Now that raises a problem as to the accuracy of a "gear-caliper" reading even when the "in-feed" is correct.

Reducing the in-feed to get the "caliper reading" "Correct" will only enlarge the effective Pitch and base circles as well as the full-depth circle.

I suspect that there is no real way of either generating a "perfect" gear in such conditions, nor measuring it accurately. But, as has been said previously, many "acceptable" gears have been made under these conditions for many years.

I would be the first to concede that "acceptable" is a very subjective term in use in place of what should be a lot more or very "objective" term/s.

"Hobbing" with a cutter with a DP - if "inch" - or Mod(ular) if metric the same as is required on the gear to be hobbed is a much more accurate proposition that can be determined with a gear caliper.

As I understand it, the making of a spur (or helical) gear requires that the DH or Rotab (as the case may be) is required to be "off-set/rotated" on the mill table so that the "line" of the teeth to be cut and the hob are coincident.

One of the concerns I have is that the cutter will be progressively cutting wider and deeper with more "length of cut" - the cutter is a multi-tooth form tool after all.

I hear little of sharpening these cutters so I presume that the cutter is always new or "as new". After all we wouldn't use cutters that were not sharp and would over-load the whole process - would we?

In fact I hear little or virtually no mention of resharpening of milling cutters at all?

How do most HSM's sharpen/re-sharpen milling cutters? I guess that not all of us own or have the use or access to a Tool and Cutter grinder.

Cutters mounted on arbors are notorious for not running true - at all - or as accurately as cutter mounted in a good set of collets. I know that some get it right every time - but I'd doubt that all do. And if they don't they will not only not get optimal "performance" from their cutter/s but uneven wear and sharpness as well.

So how does all this affect the accuracy of gears (say spur gears) in such a HSM shop environment?

If it does - how does it and how is it countered or remedied?

And does it?

John Stevenson
10-29-2007, 10:14 AM
So how does all this affect the accuracy of gears (say spur gears) in such a HSM shop environment?

If it does - how does it and how is it countered or remedied?

And does it?

The limitations I have found are not in cutter design, steps per inch or the electronics but rigidity of the setup.

Most DH or rotabs don't have bearings that can fully handle the loads incurred. Most have never seen a thrust bearing and rely on a basic tailstock for support.

I have even seen some designs where the worm and wheel is outboard of the bearings.

The gearbox I use on the hobber is a commercial gearbox and the normal bearings have been replaced by angular contact bearing but even so on a large gear say a 6.400" diameter 127 tooth cut in steel I would only describe the finish as commercial.

This is all based on a 1 -1/4 tonne Victorial horizontal mill.
To improve this I will have to increase rigidity either by increased diameter arbours and roller rests supporting the blank behind where it's cutting or thow about 3 more tonnes at the setup.

.

oldtiffie
10-29-2007, 10:42 AM
The limitations I have found are not in cutter design, steps per inch or the electronics but rigidity of the setup.

Most DH or rotabs don't have bearings that can fully handle the loads incurred. Most have never seen a thrust bearing and rely on a basic tailstock for support.

I have even seen some designs where the worm and wheel is outboard of the bearings.

The gearbox I use on the hobber is a commercial gearbox and the normal bearings have been replaced by angular contact bearing but even so on a large gear say a 6.400" diameter 127 tooth cut in steel I would only describe the finish as commercial.

This is all based on a 1 -1/4 tonne Victoria horizontal mill.
To improve this I will have to increase rigidity either by increased diameter arbours and roller rests supporting the blank behind where it's cutting or throw about 3 more tonnes at the setup.

.

Thanks John.

A very concise and precise "reality check".

I rather suspected that as I've always had problems with this sort of load - which may seem small - but definitely is not. The problems were largely to do with the arbour, its size and straightness, the clearances between the cutter and the arbor, the arbor and "hanger" journals, the journals and the hanger bearings and last and by no means least the effectiveness of the arbor spacer rings. And if the job develops a "thrum-thrum-thrum...... etc.) a real "hammering" effect sets in which may cause chatter and cutter failure or work-piece hardening or all three.

I have only got a HF-45 vertical mill which is OK so far as it goes but I am limited to using a stub arbor (which is a cantilever and not a mid and end-supported shaft/beam) in my quill which is just about the worst of all worlds. It would be OK for but limited to small light-load minor gear jobs for those reasons as well as those you gave.

I am considering making an emulation of the "hangers" on a/your horizontal mill. It is to be fitted to my vertical column slide dove-tail. It's a "make-do/band-aid/fudge" job but hopefully it will improve things somewhat.

Any advice re. using "normal" cutters, hobbing and gear calipers etc?

Will be very much appreciated.

John Stevenson
10-29-2007, 04:04 PM
These are very handy for measuring gear teeth.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/hidden/gear%20caliper.jpg

A lot easier to read than the old fashioned vernier type as some of these had short reach scales and were limited to 0.005" steps instaed of the usual 0.001 scales.

As is usual for digital calipers they can be zeroed on a known master gear and the material to move is read off directly.

.

lazlo
10-29-2007, 07:53 PM
Hi John,

These are very handy for measuring gear teeth.

Do you sell these digital gear calipers? I looked on your Ebay store, but can't find them.

I'd love to get a set of those! :)

Thanks,

Robert

John Stevenson
10-29-2007, 08:00 PM
No I picked a set up when I was over in China last for my own use.

.

lazlo
10-29-2007, 08:18 PM
You stinker! :D

I figured as much: I Googled for "digital gear caliper" and the only hit that I found is a web page hosted off of Alibaba (the Chinese Distributor Network) that's dead:

www.xbef.com/5390.html

So.... can you or Gert get these exported to the West?

Joel
10-29-2007, 08:37 PM
IIRC, the infamous 800watt used to have some listed at a very good price, but he doesn't seem to have any right now.

Here is a digital on eBay:

http://cgi.ebay.com/Digital-Gear-Tooth-Calipers-New-In-Box_W0QQitemZ200148304699QQihZ010QQcategoryZ1504QQ rdZ1QQssPageNameZWD1VQQcmdZViewItem

There are also 2 Starrett vernier styles on eBay, one with a current bid of \$60.

lazlo
10-29-2007, 09:22 PM
Oh geez, I did a search on "gear caliper" but didn't think to search for the plural. Thanks Joel!!!

oldtiffie
10-29-2007, 10:06 PM
These are very handy for measuring gear teeth.

http://homepage.ntlworld.com/stevenson.engineers/lsteve/hidden/gear%20caliper.jpg

A lot easier to read than the old fashioned vernier type as some of these had short reach scales and were limited to 0.005" steps instaed of the usual 0.001 scales.

As is usual for digital calipers they can be zeroed on a known master gear and the material to move is read off directly.

.

Thanks John.

The makers and designers of those digital calipers are very very clever and innovative people.

It is the inevitable outcome of up-grading to modern technology. I like it.

You raise a very interesting point as regarding "referencing" to a "master gear". They too are available - but as always - at a cost. Its a matter of just how much "master" you want for your money I guess - that is provided that the user has or uses or references to a "Master" at all.

I can see that they would be useful with accurately "hobbed" or "shaved" and "ground and/or lapped" gears.

Given that the standard arbor-mounted gear cutters are not that accurate - even at the "bottom" of their "range" where they more closely approximate the true tooth form - I'd be more than a little surprised if "perfection" was realistically achievable with those cutters.

The hob is very close to a rack form indeed - and in better "class" gear-cutting very very close indeed.

I would guess that they'd be be used as an adjunct to a very high quality digital-optical comparator as well.

Just keeping those calipers "square" in at least two planes (three?) would be a challenge.

I do like the "fine" adjustment/s which are "tops" but missing on most "ordinary" digital calipers but which were quite the usual on the better vernier calipers. (It would solve a lot of the "problems" if used on digital calipers).

Great care would be needed to ensure that "burrs" etc. were cleaned off and did not compromise the "readings".

But as is the general case with digital calipers, there is or will be an "acquired art or skill" required to get the best out of them.

A great post - thanks.

Paul Alciatore
10-31-2007, 10:15 AM
I have even seen some designs where the worm and wheel is outboard of the bearings., Sir John