14 replies to this topic

[TallTanBarbie]

I'm thinking about experimenting with a 3D printed timing pulley in the 8-10 inch range with a 3-5mm belt pitch and a closed-loop stepper motor with a harmonic drive gear for a telescope drive to put on an old telescope as an experiment.  What kind of accuracy and/or error could I expect with this type of setup?

Edited by TallTanBarbie, 19 March 2025 - 10:58 AM.

[AlamoBob]

First, you probably don't even need closed loop, but consider this:

Your Harmonic Gear Reducer will probably have a backlash of ~ 20 arcseconds or less - then you have further gear reduction from your pulleys, which makes it even less.  In an open loop configuration, 1 arcsecond accuracy is easily achievable, and you will not see any jumping as your motor steps (especially if you're using micro-stepping - which is an option on almost ALL stepper controllers.).  Need finer resolution?  Drive that harmonic gear reducer with a 400 step per rev stepper instead of the usual 200 step per rev.

 

BTW, my telescope will be a test bed for this exact variety of experimentation.  I have bought a ServoCat, and it may never see use on my scope.

Edited by AlamoBob, 19 March 2025 - 10:29 AM.

[psionik]

In theory your pointing accuracy in arcseconds will be:

 

1,296,000

 

divided by

 

number of motor steps per rotation (usually 200)

 

multiplied by

 

the big number of the ratio of the harmonic gear

 

 

so if you have a 50:1 gear

 

1,296,000 / (200 * 50)

 

=  129.6 arcseconds per step.

 

This is good enough for go-to pointing but not tracking if you're taking photos.

 

The results can be improved with 2 stage gearing / belts or by microstepping the motor so that it takes more than one pulse to complete a single step.

 

The disadvantage of this setup is that without an absolute encoder on the output axis there can be built-in error.  An autoguiding setup can mitigate this.

[BGRE]

Nonsense. Thats the pointing resolution of the system not its accuracy.

Backlash isn't reduced by adding another gear or other speed reducing stage.

Some backlash is essential for gears to work.

Preloading the system is often used to eliminate the effect of backlash. 

[astrokeith]

I'm thinking about experimenting with a 3D printed timing pulley in the 8-10 inch range with a 3-5mm belt pitch and a closed-loop stepper motor with a harmonic drive gear for a telescope drive to put on an old telescope as an experiment.  What kind of accuracy and/or error could I expect with this type of setup?

I'm using 3d printed pulleys (only about 50mm diameter through) with GT2 belts, driven by harmonic gearboxes on a Nema 17 stepper. Backlash is so small as to be not measurable and each microstep is 0.2 arc seconds.

 

So, go for it!

[AlamoBob]

In theory your pointing accuracy in arcseconds will be:

 

1,296,000

 

divided by

 

number of motor steps per rotation (usually 200)

 

multiplied by

 

the big number of the ratio of the harmonic gear

 

so if you have a 50:1 gear

 

1,296,000 / (200 * 50)

 

=  129.6 arcseconds per step.

 

This is good enough for go-to pointing but not tracking if you're taking photos.

 

The results can be improved with 2 stage gearing / belts or by microstepping the motor so that it takes more than one pulse to complete a single step.

 

The disadvantage of this setup is that without an absolute encoder on the output axis there can be built-in error.  An autoguiding setup can mitigate this.

Incomplete math - it does NOT take into account any gear reduction from the Harmonic Gear reducer to the actual axis of the scope. So for the Azimuth axis, it would not be uncommon to see 19:1 reduction (1" drive wheel on a 19" ground board) taking it down to 6.8 Arcseconds per step (and 0.42 arcseconds per microstep if you're doing 16 microsteps per step).

 

In the elevation axis it's easy to achieve MORE reduction than 19:1, but that's a matter of your personal choice.

[astrokeith]

Yes, most mounts include a belt drive reduction after the main gearbox. Even the typical EQ type.

 

Microstepping is a powerful technique, but not straightforward. Torque drops off almost linearly with number of microsteps, and then at speed it gets worse. Even if not stalling the microstep to microstep accuracy can get pretty bad. (I've measured a factor 2 between adjacent microsteps!)

 

I design Dob drives, and it is relatively easy (and convenient) to introduce a 30:1 gear box and 30:1 final reduction (or similar) and get a 900:1 reduction. This reduces the need to have fine microsteps. I have always used 16 microsteps, coupled with a careful drive acceleration and deceleration. This means I can get step sizes of <1/4 arc second on the mount, plus slew speeds of up to 10 deg/sec. I drive up to 24" scopes with nema17 motors, and larger ones with nema23 motors.

 

I've switched to nema17 harmonic gearboxes recently which have very small backlash and good enough torque performance. The final drive can be also very low backlash if direct rollers are used.

[AlamoBob]

Also consider this:

 

If you use a 400 step per rev stepper, and a 100:1 harmonic gear reduction, you are down to 1.7 arcseconds per step with no further gear reduction on your pulleys or any microstepping.  From there getting to a half arcsecond is just a matter of getting a 3:1 reduction in your final drive.

[astrokeith]

Also consider this:

 

If you use a 400 step per rev stepper, and a 100:1 harmonic gear reduction, you are down to 1.7 arcseconds per step with no further gear reduction on your pulleys or any microstepping.  From there getting to a half arcsecond is just a matter of getting a 3:1 reduction in your final drive.

Sorry Bob, I think you made a maths error?

 

without micro stepping your 400 step (0.9 deg) stepper and 100:1 is 0.009 deg or 32.4 arc seconds. 

[AlamoBob]

Sorry Bob, I think you made a maths error?

 

without micro stepping your 400 step (0.9 deg) stepper and 100:1 is 0.009 deg or 32.4 arc seconds. 

Yeah, I keep doing that.
Who knows where I came up with that figure?  Not starting the calculation from scratch, I would guess.

[TallTanBarbie]

Yes, most mounts include a belt drive reduction after the main gearbox. Even the typical EQ type.

 

Microstepping is a powerful technique, but not straightforward. Torque drops off almost linearly with number of microsteps, and then at speed it gets worse. Even if not stalling the microstep to microstep accuracy can get pretty bad. (I've measured a factor 2 between adjacent microsteps!)

 

I design Dob drives, and it is relatively easy (and convenient) to introduce a 30:1 gear box and 30:1 final reduction (or similar) and get a 900:1 reduction. This reduces the need to have fine microsteps. I have always used 16 microsteps, coupled with a careful drive acceleration and deceleration. This means I can get step sizes of <1/4 arc second on the mount, plus slew speeds of up to 10 deg/sec. I drive up to 24" scopes with nema17 motors, and larger ones with nema23 motors.

 

I've switched to nema17 harmonic gearboxes recently which have very small backlash and good enough torque performance. The final drive can be also very low backlash if direct rollers are used.

What about the accuracy of 3D printed parts?  I was also considering using a PGFUN NEMA 17 harmonic drive, how accurate are these?

 

I'm trying to get a 3600:1 overall gear ratio as you would with a conventional worm gear but with 72:1 GT3 3D printed axis pulleys and a 50:1 off the shelf harmonic drive.  

Edited by TallTanBarbie, 22 March 2025 - 09:06 PM.

[astrokeith]

I’m not familiar with that harmonic drive so can’t comment.
Most 3d printers are inherently accurate. Enough for our purposes anyway.

[psionik]

Incomplete math - it does NOT take into account any gear reduction from the Harmonic Gear reducer to the actual axis of the scope. So for the Azimuth axis, it would not be uncommon to see 19:1 reduction (1" drive wheel on a 19" ground board) taking it down to 6.8 Arcseconds per step (and 0.42 arcseconds per microstep if you're doing 16 microsteps per step).

 

In the elevation axis it's easy to achieve MORE reduction than 19:1, but that's a matter of your personal choice.

Yes, it does.  50:1

 

The output of the harmonic gear IS the axis.  The OP didn't specify any gearing or belts afterward.

[Spinwiz]

What about the accuracy of 3D printed parts?  I was also considering using a PGFUN NEMA 17 harmonic drive, how accurate are these?

 

I'm trying to get a 3600:1 overall gear ratio as you would with a conventional worm gear but with 72:1 GT3 3D printed axis pulleys and a 50:1 off the shelf harmonic drive.  

When you go with these massive reduction ratios you can run into an issue with the stepper having to be ran too fast in an area of operation where torque drops off rapidly.  While it will vary with stepper I'd be careful about going much above 400 RPM.   That might sound like a lot but divided by  3600 that might mean 1 tenth of an RPM which is real slow if want to slew to a new position.

[luxo II]

Not true.

 

If you look at stepping motor specs they usually state a "maximum pull-in rate", this is the max step frequency at which the motor can go from stationary to rotating, in one step - at its rated voltage. For the types of motors often used here, this is often about 1,000 full steps/sec.

 

There are two approaches to going faster - much faster.

 

The first is to use acceleration/deceleration - ie ramp the step rate smoothly from near zero to a very high value, and then decelerate smoothly. If the acceleration is not overly aggressive speeds 5X the pull-in rate can be achieved - and without missing steps or stalling. And by the way. this is exactly the technique used by Synta in the Synscan mounts - you will hear them accelerate/decelerate smoothly.

 

The second approach is much more brutal - and poses a safety hazard - and requires an understanding of the motor winding as an inductor at high step frequencies. Basically:

 

As the step rate increases the motor winding behaviour is increasingly that of an inductor - its impedance increases, reducing the current flow, and at the same time generating significant back-EMF spikes. If you treat the motor as a constant-power device, ie dissipating a constant amount of heat from the winding, it implies increasing the voltage applied to the winding with increasing frequency - using a constant-current power supply. Using this approach I have seen motors with windings rated for 4V running at as much as 30,000 steps/sec - with over 50V DC applied to the winding. There are two issues with this, however:

- the back-EMF spikes generated from the windings can exceed several hundred volts and is lethal; and

- if the motor stalls the inrush current will vaporise the winding in milliseconds.

Edited by luxo II, 26 March 2025 - 03:44 AM.