# Understanding Belt Calibration Numbers

Posted by avayan
 Understanding Belt Calibration Numbers November 10, 2012 11:02AM Registered: 14 years ago Posts: 27
Well, I am printing but the output is not perfect. In this case, a mm on either axis does not come out as a mm. This is OK for stuff like the whistle, but when going into gears, perfection is a must.

I found Triffid Hunter's Calibration manual which was extremely useful: [reprap.org]

His equation makes sense to me: # microsteps/mm = # steps/rev * # microsteps/step * # teeth/mm(belt pitch) * rev / # teeth (number of teeth on the pulley)

On my X Axis I have a 17 teeth GT2 pulley. Why did I chose such a weird teeth number? I think because of the stepper motor shaft, if I recall. Anyway, what this gives me is 200*16/2/17=94.117.

On my Sprinter firmware I placed 94.117 but when I run the cube I get 19.76mm width.

So 2 questions:

1. Is 19.76 what I am supposed to get? Or differently phrased, are these 3D printers supposed to be dead-on, or are differences of this sort expected?

2. When I specify a number such as 94.117 on the firmware, will the decimal fraction portion play a role, or is this information lost?

My Y axis is even worse, but that one is my mistake as I went with a 40 DP belt. I should have of course chosen the same belt for both axis. Oh darn "reuse of what I had available"...

JIQ
 Re: Understanding Belt Calibration Numbers November 10, 2012 06:00PM Registered: 11 years ago Posts: 2
The formula will get you close to the correct calibration, but does not account for small changes in the effective belt pitch as it bends around a small pully. Now that you are close try:

new_steps = current_steps * expected size / actual size

To compute a new steps per mm for your next print.

Good luck getting the error down to a reasinable tolerence and repeatability
Jack
 Re: Understanding Belt Calibration Numbers November 10, 2012 09:10PM Registered: 12 years ago Posts: 108
Interesting... when I built my printer, I used really large GT2 pulleys chosen specifically to get a nice round number of steps per mm (32 teeth, which comes out to 50 steps per mm with 1.8 deg @ 1/16). When I take the calipers to a print, I'm off by about 1% - 2% each dimension. I always figured it was because of slicing issues and wobbling, and completely ruled out the possibility of updating my steps per mm.
 Re: Understanding Belt Calibration Numbers November 11, 2012 06:47PM Registered: 13 years ago Posts: 313
avayan Wrote:
-------------------------------------------------------
> On my X Axis I have a 17 teeth GT2 pulley. Why did
> I chose such a weird teeth number? I think because
> of the stepper motor shaft, if I recall. Anyway,
> what this gives me is 200*16/2/17=94.117.
>
> On my Sprinter firmware I placed 94.117 but when I
> run the cube I get 19.76mm width.
>
> So 2 questions:
>
> 1. Is 19.76 what I am supposed to get? Or
> differently phrased, are these 3D printers
> supposed to be dead-on, or are differences of this
> sort expected?

There are numerous error sources and getting 19.76 when printing a 20 mm cube is already pretty good. If you forget backlash (which is one of the most common errors, and which you can't correct by adjusting the steps-per-mm parameter) the printer will move exactly the amount given by the calculation, with no need for manual calibration from printed part measurements. Doing a manual calibration from measurements would only make sense if you're sure that all other errors have already been eliminated.

You could try printing a 100 mm long calibration piece, if there is an error in the steps-per-mm value, it should show five times the error you saw in the 20 mm cube. If it shows only an error of similar magnitude, it's something else.

The pulley diameter doesn't matter, only the tooth count and the actual belt pitch (I guess there could be some deviation in the pitch, it's not like the belts are infinitely accurate).

> 2. When I specify a number such as 94.117 on the
> firmware, will the decimal fraction portion play a
> role, or is this information lost?

I believe that Sprinter and Marlin use floating point calculations so the decimals are correctly taken into account.
 Re: Understanding Belt Calibration Numbers November 11, 2012 07:30PM Registered: 13 years ago Posts: 972
1. Another source of inaccuracy can be the belt path not to be perfectly horizontal.
2. Decimal part is taken into account by the firmware.
 Re: Understanding Belt Calibration Numbers November 11, 2012 08:12PM Registered: 13 years ago Posts: 1,611
I'm not sure measuring printed parts is the best way to accurately set the X and Y axis steps per mm, because you will get a false reading if your extrusion is even slightly inaccurate, and it will be worse the smaller the 'calibration' object you print.

I use the calculated value first. I use 1.8 degree motors (200 steps per rev) and 16 x micro stepping with 9-tooth printed pulleys and T5 belt. This gives me a step per mm of (200*16)/(9*5) = 71.1111 which I put in as the steps per mm for X and Y. Then I check this by measuring the actual movement of the axis, using digital calipers, over a decent distance, like 100mm. For example, measure from a fixed point on the frame to the x carriage, in line with the x axis. Move the X axis 100mm with G1 X100, then remeasure, and calculate the difference.

This is where I, too, have a slight problem with the calculated steps per mm from the pulley formula. When I ask for 100mm, the carriage moves 99.75mm. At first I thought this might be because the tension in the belt was stretching it, but it's actually the other way around; it implies the belt pitch is 4.9875mm. This is, possibly, within manufacturing tolerances - it is only 25 microns per 5mm (0.5%) - or it could be that belt manufacturers expect more tension to be applied to the belt than I give it, to stretch it slightly. Or, more likely, something else in the system is causing this very small variation. So the formula isn't wrong, it's just that any initial assumption, or subsequent measurement, can't be taken too literally and/or may be prone to error.

Either way, the message here is that, for really accurate part sizing, you need to calibrate your X and Y axes more accurately than with printed parts - there may be other factors effecting it that you may not be aware of, and adjusting the steps per mm to resolve one problem may actually cause others. That's not to say you can't accurately calibrate a reprap, just that you need to think it through.

(Edited for mistakes, clarity.)

Edited 1 time(s). Last edit at 11/12/2012 06:45AM by droftarts.
 Re: Understanding Belt Calibration Numbers November 12, 2012 06:15AM Registered: 14 years ago Posts: 27
Wow! Thanks all for this great information! I have been using the calipers too, but was under the impression that measuring the parts was the expected method. If a slight variation is expected, then I am more than happy.

I did change my X Axis belt so it is the same as the Y Axis. Having two different belts should definitely be frowned upon ;-)

JIQ
 Re: Understanding Belt Calibration Numbers November 12, 2012 09:33AM Admin Registered: 17 years ago Posts: 7,881
Quote

The formula will get you close to the correct calibration, but does not account for small changes in the effective belt pitch as it bends around a small pully.

No that does not generate any error. Imagine the pulley moves one rev: exactly that number of teeth of belt is paid out on one side and taken in on the opposite side, so the carriage moves the number of teeth times the pitch. The exact pitch depends on the belt tension though.

The fact the plastic shrinks probably has more effect on object dimensions.

[www.hydraraptor.blogspot.com]
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