Proper way to calculate steps/unit for belt drive?

[MrBean]

I have a belt driven X axis, and I was wondering what the correct formula is to work out the steps/unit for Mach3?

I have always worked out the calculation as described in the Mach3 manual. Which uses belt pitch and pulley tooth counts. However the result has never been quite right when it comes to moving the actual machine. I've had to do lots of moves on the axis, adjusting the figure untill I was happy that the machine and Mach were agreed on distance travelled.

The backlash on my X axis is minimal. Not enough to account for the adjustments I had to make to the steps/unit figure in Mach.

I have seen people using dia pitch, and PI, to calculate steps/unit for belt drives.
Is that more accurate than the method I was using from the Mach manual?

Any ideas, suggestions or examples would be appriciated.

Cheers.
Regards Terry...

[martinw]

Originally Posted by MrBean I have seen people using dia pitch, and PI, to calculate steps/unit for belt drives. Is that more accurate than the method I was using from the Mach manual? Any ideas, suggestions or examples would be appriciated. Cheers. Regards Terry...

Dear Terry,

This suggestion may be entirely wrong, and if it is I apologise in advance.

IMVVVHO, the gearing ratio of pulleys as regards driver pulley and driven pulley are not quite exactly the same as the number of teeth on each pulley.

I think that what is precise is the ratios of the "pitch circle diameters" of the pulleys. These may differ a bit from the number of teeth ratio by a little bit. Enough to cause errors.

The PCD is accurate for calculating gearing.

As I said, I'm not sure on this.

Best wishes

Martin

[CNCkitsandBITS]

Hi MrBean,

I have no experience with Mach software so cannot comment on the method used. From your description I could see how it would be hit and miss.

Calculating using diameters and PI is probably the most accurate method as long as you have the instruments to measure accurately enough as an error of 0.1 mm in the diameter of a pulley is obviously a large error after PI.

Another method would be to calculate how many pulses it would take to turn the pulley an amount that was in the range of a dial indicator to measure the linear movement of the axis. Send the pulses required to the stepper and measure linear distance travelled and do your steps/ unit calculations from there.

John

[kevincnc]

The number of teeth for a ratio will give you exact results. You actually lose a little precision by using pitch diameter unless it is a whole number because of rounding error. Maybe if you show your calculations someone can find a problem.

[MrBean]

Thanks guys. Diameters is the way to go. I don't know why I couldn't see it earlier. It's obvious when you stop and think about it. The thicker the belt is, the more the outer circumference has to travel. The inner circumference changes size as it goes around the pulley. The teeth compress together, so calculating using tooth pitch is bound to be wrong, as the size changes.

Thanks again.
Regards Terry.

[MrBean]

Kevincnc. I know the tooth/pitch calculation to be the wrong one to use. I've tried it, and it's out, not by much, but it is out. The calculations weren't wrong. I was just using the wrong information to calculate from.

[Geof]

Originally Posted by martinw ..IMVVVHO, the gearing ratio of pulleys as regards driver pulley and driven pulley are not quite exactly the same as the number of teeth on each pulley...

Consider this; if you had two gears in mesh with the same number of teeth as you have on your pulleys you would be hard pressed to say that the ratio was not directly calculable from the teeth ratio. All the belt does in toothed belt drives is provide a one to one linkage between the teeth.

So the drive ratio should be the inverse of the teeth ratio.

If the number of teeth is the same the ratio is 1 to 1, if one pulley has twice the number of the other it is 2 to 1 or 1 to 2, but if one pulley has 31 teeth and the other 29 your ratio is 1 to 1.0689655172413793103448275862069ad infinitum.

Which, if the decimal does not repeat or terminate, means you have an irrational situation.

[MrBean]

Just to clear things up a bit. For reduction ratios using toothed belts, you can calculate using tooth counts. Where I was seeing an error was the actual belt that is the X axis. Basically my X axis is a continuous belt of about 2.5 metres (5mm pitch). This belt rides on a 26 tooth pulley at each end of the axis. Now if you rotate the 26T pulley one revolution, the belt should have moved 26 teeth. Which at 5mm pitch is: 130mm. This is not the case though. As you can see, if the belt were thicker the outer diameter around the pulley would be larger and the belt would have travelled further.

I think.....

[CNCkitsandBITS]

Originally Posted by MrBean Just to clear things up a bit. For reduction ratios using toothed belts, you can calculate using tooth counts. Where I was seeing an error was the actual belt that is the X axis. Basically my X axis is a continuous belt of about 2.5 metres (5mm pitch). This belt rides on a 26 tooth pulley at each end of the axis. Now if you rotate the 26T pulley one revolution, the belt should have moved 26 teeth. Which at 5mm pitch is: 130mm. This is not the case though. As you can see, if the belt were thicker the outer diameter around the pulley would be larger and the belt would have travelled further. I think.....

Not quite; the belt thickness will not come into play. The measurement needs to be taken from the inner diameter of the belt at the root of the tooth.

John

[MrBean]

It's late. I'm confused. Maybe a picture will help??

The red arrows, (not the flying team) in the picture show where the 26T pulleys are inside each end of the alu beam.

[MrBean]

Originally Posted by CNCkitsandBITS Not quite; the belt thickness will not come into play. The measurement needs to be taken from the inner diameter of the belt at the root of the tooth. John

Ok. Cheers I'll give that a go. This machine has actually been running for a few years now. The reason this cropped up is because the PC that runs Mach3, ate the config files. So I'm at square one.

When I set up originally, I fannied around for ages getting the X axis right (trial and error) because the tooth/pitch calculation as found in the Mach manual is slightly off. It didn't use DP calcs.

It's late for so many UK bods to still be online.....

Thanks.
Regards Terry.

[martinw]

Dear Terry,

The pitch circle diameter of each pulley will give you the gearing ratio.

All you have to do is is get an accurate figure for pcd from the manufacturers of the pulley. Lots of decimal points will help.

Best wishes

Martim