Constant Velocity Gearing

http://www.majosoft.com/metalworking/html/how_to_make_a_worm_gear_reduce.html

I read about that harmonic drive description you give being used in hub reduction gears on trucks. Even though you don't have access to a lathe, the above link may give you ideas. Your worm only has one tooth, I can see no reason why it should not be constant velocity unless your drive varies. Others who are wiser will clarify I am sure.

Many thanks for your encouraging remarks.

The finer points of the exercise rely on being assured that the worm wheel will rotate smootly and a constant velocity.

Lleros

Actually, the harmonic drive you mention does not have perfect motion -- it has a little velocity ripple. I have used these drives before, and in my application, it didn't make any difference that there is a velocity ripple, and they may work O. K. in yours.

1 rev per day is great for looking at stars, but for the moon and planets you'll need one which takes their sidereal times into account. It's also very critical that your telescope align with the axis of the earth perfectly to get no distortion, which is no mean feat!

Worm drives aren't necessarily perfect either, but precision ones aren't bad at all. One of the critical pieces will be the reflected load on the motor, as it must run at a constant velocity, thereby requiring that the telescope be counterbalanced very well so that the virtually static load on the gearing and motor are at least constant.

Good luck!

Thanks for your trouble in answering.

I figured that a harmonic drive might have a ripple in its motion as the leading tooth engages and the trailing tooth disengages.

The 1 rev per day is actually 1 rev per sidereal day (time for a star to be in the same position on consecutive nights) rather than a solar day (time for sun to be in the same position on consecutuve days

I plan to run the gear train from a reasonable heavy duty motor, either a DC motor with variable tacho feedback or to use an AC induction motor by use of a stable but variable oscillator and power amplifier. In that way I can make the speed variable to follow the moon etc.

I dont know if this will be any help, but years ago I made a worm wheel in soft plastic using a fine turned bar as the pinion. the fine turned spiral on the bar acted as a great minitooth and the system worked very well - very small load capacity but very smooth and a huge reduction gearing.

Cheers JohnT

Hi,

this is a very difficult task.

A.:
To have a chance to get near the wanted performance the biggest errors have to be compensated (as more or less constant) by a suitable computer program (known as PEC or periodic error correction among the hobby astronomers.

There are two different sources of periodic errors: the radial runout of the worm and the radial runout of the wheel, both produce once per revolution sinusoidal errors.

If you have a (only) 1µm radial error in the bearings - or the location of these bearings - that guide the wheel of 75mm radius this is equivalent to 1:75000 or to 13µrad or roughly 2.5 arcsec.

As this is much more than you would like to accept you would have to implement the computerised PEC or build a bearing with a 0.1 to 0.2 µm accuracy of axis location and wheel accuracy.

This accuracy is achieved only in professional telescope mountings that are equipped with hydrostatic bearings and PEC added.

B.:
The accuracy of the gears shall be in the same class of accuracy! This too is not possible and your approach of using elastic deformation to get a smoothing is a good approach but will give only a limited improvement: n teeth that are in contact and have arbitrary location within a limited error will give an improvement of only square-root of n.

C.: Despite these difficulties your approach is wort while. Some recommendations:

Switch to the largest diameter of the wheel that you can afford. (As stated above, Nylon is much better than PE, but may be not good enough as any of the poly-amides is dissolving considerable amounts of water: changing shape and elasticity). So I would use teflon, not pure teflon because that is not mechanically stable but glass-reinforced or mica-reinforced teflon. As this is much too expensive as a big piece it would be suitable to use a metallic wheel and to mount segments of the reinforced teflon. Take a bronze to insert the center bearing.

Avoid any ball-bearings: never good enough, and if you decide to use ball-bearings try to get high-accuracy spindle bearings (look ebay) and do not mount these in a conventional manner but glue these -axially preloaded- with epoxy to shaft and housing

Better: take two (big ? 20 to 30mm diameter) high accuracy balls from ball bearing company, (grade 10 or better) glue one piece of steel tube in-between and two other steel rods to form an axis - as good as possible and later to be re-machined being guided by this bearing. Let the balls run in contact with two inside conical bronze outer parts. This will give the best possible home-made bearing: suited for 0.1 to 0.5µm runout.

There will be some more recommendations later if you like.

No more time available now.

RHABE

"I would then use a fresh piece of threaded rod for the worm."

Lleros be sure to use a rod with rolled threads rather than cut threads. Cut threads have thousands of ridges which will produce drag and irregular motion. Rolled threads are stronger and more smoothly formed and finished.

If possible reduce the number of gears and transmissions in the system. As suggested by RHABE, use the largest gear possible for the final drive. The ideal would be a very large gear driven by a single worm. The worm is driven by a ceiling fan motor which can operate at variable RPM's. This one step gear reduction yields the least amount of backlash, thus the most precision for the investment.

RHABE and others can tell you how to eliminate backlash better than I. I have heard of cutting the threads in the driven gear with a slight bias which provides zero thread interface clearance. This slight mismatch absorbs some power but has been shown to eliminate backlash.

Hi Lleros:

I Googled anti-backlash gears and found a company "Atlanta Drives" that manufactures what you may want,(WWW.Atlantadrives.com). I had seen anti-backlash gears years ago utilized in military aircraft navigation systems (pre-computer days!). They consisted of two gears mounted one on top of the other and a spring loading arrangement between the two gears. The accuracy of the "mission" depended upon the accuracy of the gear train in the device.

Good Luck and let us know how your project turns out. Come back to us for help from time to time.

Hank

Use anti backlash gears.

They are essentially a gear split in half (along their thickness) with a tensioning device. When the gear meshes with the mating gear there is no clearance between the three teeth (tooth on the anti backlash gear and the tooth in front and behind it on the other gear.

Travis

Hello,

I found your discussion on google and wondering if you have heard about new evolution step in zero backlash gear evolution. It is called twinspin and it has a new patented system. It is used widely in KUKA robots in europe. Write me an email, if u want to know more. In many tests it shows better results as harmonic drive.

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Mark

Thankyou for your contribution. In fact thankyou all who contributed to my question. Zero backlash would be important were I to need to control the speed in both directions. This is a single direction application and once the telescope has started moving (all the back lash taken up) I expect that a friction pad will suffice.

The fact that I contemplate using an Harmonic Drive is that I already have one, a brand new one, tossed out from a linear accelerator upgrade. It is designed to run a chain drive to a 6 ton gantry which operates 1 rev per minute. It is strong enough to be the main polar bearing of my forked mounted telescope. I only hope that as the teeth engage it will not show up as the star moving back and forth.

Thankyou for those who have given me hints on getting a worm to run properly. As I am limited in power tools (viz no lathe) eccentricity of both the gear and the worm will be my greatest enemy. I have since found references to "making a worm gear on a lathe" on google, and found a couple of people who have made worms for the same purpose (viz telescope) They suggest a fine threaded rod is best, greater ratio, and likelihood of constant contact by more than one thread if closely pushed together.

The articles talk of pre-gashing teeth (not Gnashing of teeth), which I cannot do. However, I figure that if I use a plastic gear that will soften with heat, I may be able to heat up the threaded rod, and run it on the face of the blank as a "rack and pinion". This may give me a chance to get the number of teeth correct and save the momentous decision of whether to accept "one big tooth ar 2 small ones" when I finish hobbing around the circunference.

I am about to leave on a holiday to Italy, and when I get back I will start production.