Help with calculations for my drive system...

[Astroman]

Hi all,

:help:

I have been doing some maths and trying to work out what input speed my stepper motor needs to be doing for my Star Tracker mount. In it's current form, which works out well, it takes the input stepper motor between 46 and 47sec to do one revolution. I wanted to be able to make this more accurate.

From the Stepper motor it enters a 63:1 worm drive, so for every 63 turns of the stepper motor the output of this does 1 revolution. On the worm drive I have a 15 tooth gear, this meshes to a 53 tooth gear, which has an 18 tooth gear above it. From this 18 tooth gear it meshes with another 53 tooth gear, this gear also has a 18 tooth gear above it, this meshes with another 53 tooth gear and is the final reduction. The output to my Tripod head is attached to this gear.

Now the way I see it and this is where I need confirmation, there is a 63:1 reduction of the worm, 15 to 53 gears have a reduction of 3.533333, then the 18 to 53 gears have a reduction of 2.944444. There are two of those..

So 63 x 3.533333 x 2.944444 x 2.944444 = 1929.886272364913748144 reduction. Correct so far?

Now Sidreal time is 23hrs, 56min, 4sec which is 86164 seconds.

So to do 360 degree or 1 rev, the motor needs to do

Sidereal seconds / total reduction
86164 / 1929.886272364913748144
=44.647190476365866588831940649819 sec per revolution.

Does this sound correct? It does to me since the motor input speed is very similar to what I have now, and I knew that wasn't exactly correct.

[GeoffW1]

Hi,

Yes, looks good. By punching in all the decimals and digits I could, I got 44.64722460 sec/rev, the same to 0.0001% or so :thumbsup:

Cheers

[alistairsam]

Hi,

it does look right. another way of looking at it is

if it does 1 rev in say 45 seconds, in 86164 secs it would do
86164/1 * 45 revs or 1914.756 revs

you get 45 if you do 86164/1914.756 = 45
you substitute your precise ratio and you get the result you've mentioned.


if the motor is a stepper, I'd calculate the pulse freq required considering the step angle and microsteps used and measure the input pulse freq of whichever controller you're using to see how far or close it is.
also need to consider all the backlash involved as you have several stages.

if you use 1.8 deg stepper, and use 1/8 microstepping, you'd need an input pulse as below using your reduction ratio


need to turn 360 deg of the output shaft in 86164.091 secs
Thats 0.004178075 deg in 1 sec
or
0.004178075 x 1929.886 = 8.06320844945 deg of the motor shaft in 1 sec

with 1/8 microstepping of a 1.8 deg stepper, 1 step turns 0.225 deg
or 360 deg in 1600 microsteps

you need 8.06320844945 deg in 1 sec of the motor shaft

thats 8.06320844945 x 1600 / 360 = 35.83648 steps

therefore step pulse freq should be 35.83648 Hz.

I had started a thread with a similar query, Gary and others have provided some very valuable information on various factors involved as the tracking rate is not a constant.
you'd need to track at the King rate which is a rough approximation.
http://www.iceinspace.com.au/forum/showthread.php?t=61428&page=2

all depends on what you want to do

[Astroman]

I think for widefield work <40mm it wont need to be too complex, since most of my exposures are between 30s and 5min. If I get 5 min exposure with no trail I'd be pretty happy with that...

I appreciate the extra Math you have provided also, helps when I get the new stepper driver up and running.

[alistairsam]

hi,
you mentioned that your input speed is 46 to 47secs per rev and your calculation shows you need to speed it up a bit to 44secs.
so for a 5 min exposure, your motor would complete 6.6 revs.
if the error is 2secs per rev, thats 13secs slower than it should be.
i'm not sure how much that would affect widefield imaging.
but if you correct the error, i suppose you could expose longer.

[Astroman]

I have it now set on 1 rev per 44.3 seconds, it's the closest I can get with my current driver. Once my new driver comes I should be able to get a little closer... I am doing tests now to see if I have made it better or not.

[Astroman]

The test worked out extremely well, I am able to get 5 minute subs with no noticeable movement or trailing. Here is a test picture along with a picture of the Tracker...

[DavidU]

Fabulous work ! Do you have a pic of the mechanics/electronics?

[Astroman]

Three pics of the Gears and Electrics... Simple :)