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GEM mount gear reduction

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#1 nimaajhep

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Posted 23 June 2021 - 04:19 PM

I'm planning on using gear reduced stepper in combination with a worm gear for driving a GEM mount.
With 32 microstepping and a typical 200 steps for the stepper it seems like a reduction of 200 gives a 1 arcsec resolution. But most commercial mounts have reductions of around 700.
Does anyone know the reason for the overkill?



#2 photoracer18

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Posted 23 June 2021 - 05:47 PM

The greater the reduction of a given motor the greater the torque output.  Just like in the rear-end of car the greater the reduction the more torque it makes. It also smoothes the steps out I think. And that includes the worm gear reduction.



#3 Couder

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Posted 23 June 2021 - 06:08 PM

The greater the reduction of a given motor the greater the torque output.  Just like in the rear-end of car the greater the reduction the more torque it makes. It also smoothes the steps out I think. And that includes the worm gear reduction.

you're correct - think if you turned the motor shaft one revolution every few seconds instead of turning it 200 increments for the same time, it would be much smoother look through the eyepiece. 



#4 nimaajhep

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Posted 23 June 2021 - 07:13 PM

thanks for the quick response. That makes sense. Although I thought that if the telescope is weight balanced the torque output wouldn't be really an issue at 200x ratio but perhaps smooth slewing might be affected. I guess the thing to do is to balance this against slewing speed as higher ratios result in slow slewing for ordinary nema 17 steppers and slow slewing could be annoying.



#5 Bruce in Michigan

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Posted 28 June 2021 - 05:52 AM

The equatorial axis moves across the sky at approximately 15 arc seconds per second of time. So, with your resolution of 1 arc second per step, you will have 15 moves per second. Motion pictures use 24 frames per second because engineers determined through testing the this is the slowest refresh rate possible without the eye beginning to perceive a jerky motion. So moving to a greater resolution through gearing would be beneficial.



#6 macdonjh

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Posted 28 June 2021 - 07:28 AM

Although I thought that if the telescope is weight balanced the torque output wouldn't be really an issue at 200x ratio but perhaps smooth slewing might be affected. 

The mount will need torque to get the scope/counter weight load moving, and to stop it again.  If the load is balanced and moving at a constant speed, the torque requirement will be minimal, but not zero (friction has to be overcome).

 

I asked once about the torque output of the servo motors Losmandy uses (prior to the Maxxum motors, so a long time ago) and I think I was told 2 oz-in, which is a tiny amount of torque: 1/96 of a ft-lb.  A huge gear reducer is needed to make any practical output.



#7 Geo.

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Posted 28 June 2021 - 02:45 PM

Think you're confusing reduction with resolution. They are related but you haven't collected all the data you need.

 

So here an example of what you need.

 

Xnumbers.jpg

 

http://www.stellarjo...alculations.xls

 

Here I'm going to fit a 359 tooth Byers worm wheel to a cave mount. I'm going to use the highest resolution stepper I can, an $11 NEMA 17 with a 0.9° step angle. There will be a belt drive between the motor and the worm. It will have a 20 tooth pulley on the motor and a 40 tooth on the worm or a two 2:1 reduction.

 

So our overall reduction is:

 

2:1 X 359:1 or 718:1

 

Our step motor has a native resolution of 400 steps/revolution. If we operate it at 32 µstep/step it is:

 

400 X 32 or 12800 µsteps/revolution. Due to our 2:1 belt drive reduction it must complete 2 revolutions to advance the worm wheel one tooth or 0.9972222°. -0.0000473718° off an actual a sidereal "degree." We'll let the microcontroller take care of the error.

 

Tracking resolution is calculated, 3600/((Stepper-Steps X (µsteps) X belt reduction X Worm gear reduction)/360). The estimate is determined by a complicated formula. Best to download the spreadsheet and see it.

 

Hope this helps.

 

 



#8 nimaajhep

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Posted 28 June 2021 - 03:41 PM

The equatorial axis moves across the sky at approximately 15 arc seconds per second of time. So, with your resolution of 1 arc second per step, you will have 15 moves per second. Motion pictures use 24 frames per second because engineers determined through testing the this is the slowest refresh rate possible without the eye beginning to perceive a jerky motion. So moving to a greater resolution through gearing would be beneficial.

That's a good point I didn't take into account the number of steps per second.

 

Tracking resolution is calculated, 3600/((Stepper-Steps X (µsteps) X belt reduction X Worm gear reduction)/360). The estimate is determined by a complicated formula. Best to download the spreadsheet and see it.

Thanks the spreadsheet helps. I hadn't realized that there's a formula for estimated resolution besides what you would obtain from naively calculated reduction. I looked at the formula in the spreadsheet but can't really tell where it comes from.

 

In the end I've decided to go with a gear reduction of 1120 based on parts that are available to me. I think that this should provide adequet resolution for my purposes.



#9 Geo.

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Posted 29 June 2021 - 08:18 AM

For AP we like to see >9000 µsteps/degree. If I were to directly connect my stepper to my worm, thus removing the intermediary reduction (GR1), the µsteps/degree drops to 12764.4444 and estimate tracking resolution to 0.58 arcsec/second. The trade off is that a 5°/second slew rate only requires 300RPM from the motors. Steppers loose torque fairly quickly at higher speeds.

 

trq VS sPD.jpg

 

The spreadsheet is a good tool to run "what ifs."

 

Howard Dutton, a CN member, who created the OnStep firmware and designed many of the motor controllers, ran tests on different step motors to come up with the constraints used in the Tracking Resolution formula. His results seem to be born out in practice. 


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