Electronic gearing, check my math.

[MattH]

I've had to gear down my drive on my CNC plasma build as I was struggling to tune my servos tight enough for a clean cut, I also wanted to up my acceleration.
To this end I had a set of 5:1 low backlash planetary gearboxes to suit the servos I am using which I have now fitted.

Before the servos were driving the ballscrews with a 2:1 toothed belt reduction i.e. 24T on Servo and 48T on screw and the screw had a pitch of 25mm per revolution.

This meant that one revolution of the servo amounted to 12.5mm of linear movement.

I have now added the gearboxes but at the same time changed the belt reduction to 1.33:1 i.e. 36T on gearbox and 48T on ballscrew.

This means that 1 revolution of the servo amounts to 3.75mm of linear movement.

All this is well and good until you factor in the 10,000 pulses needed to turn the servo 1 full revolution.
This means that the pulses per mm in the software ends up as 2666.66 reoccurring.
This fractional number then causes compound movement error.

To combat this there is an option in the servo drives for electronic gearing i.e if you put a gear number of 2 in then instead of needing 10K pulses per revolution it will only need 5K.
Further to this you can add a denominator to allow for fractions i.e. a gear number of 5 and denominator of 2 would give a electronic gear of 2.5 so 4K pulses instead of 10K.

Anybody still following / reading?

Good.

So my total drive reduction with a 5:1 gearbox and a 1.33:1 pulley reduction is 6.66:1 which drives a 25mm pitch screw.
So 10,000 pulses * 6.66 = 66,666.66... (pulses) / 25 (screw pitch) = 2666.66...

2,666.66... Pulses per mm is a bad number.

If I put a Gear number of 100 and a Denominator of 75 into the drive I get an electronic gear reduction of 1.33...

So 10,000 / 1.33... = 7500 pulses per motor revolution.

7,500 pulses * 6.66... (gear ratio) = 50,000 (pulses) / 25 (screw pitch) = 2,000

2,000 Pulses per mm is a good number.


All this means that my maximum speed has dropped from 37.5M/min to 11.25M/min.
The top cutting speed of my Hypertherm 45xp is around 8M/min on 1.5mm steel so plenty of headroom for that and I have solid and tight acceleration of 3000mm per second per second.

Can anyone see any glaring error/s in my math?

 

[Hood]

...
This means that the pulses per mm in the software ends up as 2666.66 reoccurring.
This fractional number then causes compound movement error.....

You sure? I know you are not using Mach but the way Mach works, from what I recall, is that it will move to the nearest full step of the commanded position but it will not accumulate. My X axis on the plasma has a fractional number and I have absolutely no problems with accuracy/repeatability.

 

[MattH]

You might be right, I'm using UCCNC and I haven't actually looked into it.

But if I can cancel out the fractional gearing in the servo drive and then use a whole number then that's going to make it nice and neat.

 

[Seadog]

Your maths seems fine to me.

 

[MattH]

Of course it occurs to me after writing that long post that there's a simpler way of looking at it.

The 36t - 48t belt reduction is what causes the problem, so a electronic gear ratio of 48/36 will cancel it out.

The 100/75 is exactly the same but using the same numbers makes the whole thing clearer.

 

[Hood]

Although you may have introduced slight errors with the double calcs anyway, not that it will matter
Never been a huge fan of electronic gearing personally but I do use it on the Z axis of the plasma to keep the THC happy

 

[Spark plug]

Would simplest solutions not be, removing the fractional gearing, by replacing for example the pulley on the ball screw with either a 40t or 32t giving a hearing of 1.2:1 or 1.5:1 respectively.

 

[MattH]

Would simplest solutions not be, removing the fractional gearing, by replacing for example the pulley on the ball screw with either a 40t or 32t giving a hearing of 1.2:1 or 1.5:1 respectively.

Is that simpler than entering two numbers into a servo drive?

Anyway I can’t change the 48t as it’s part of a rotating nut arrangement.

 

[Hood]

Is that simpler than entering two numbers into a servo drive?

Anyway I can’t change the 48t as it’s part of a rotating nut arrangement.

Bit off topic but was just wondering if you ever got the O ring and if so did it help?

 

[Spark plug]

Is that simpler than entering two numbers into a servo drive?

Anyway I can’t change the 48t as it’s part of a rotating nut arrangement.

It certainly won’t be easier but it seems the root cause of the issue is the 1.33:1 gearing, so if you could remove the awkward ratio would this remove the issue?

 

[MattH]

It certainly won’t be easier but it seems the root cause of the issue is the 1.33:1 gearing, so if you could remove the awkward ratio would this remove the issue?

Yes it would, but unfortunately it was not something I considered when I ordered the pulleys and belts.
It's not really an issue, I put the electronic gear settings into the drives earlier and it's all working like a charm.

 

[Spark plug]

Yes it would, but unfortunately it was not something I considered when I ordered the pulleys and belts.
It's not really an issue, I put the electronic gear settings into the drives earlier and it's all working like a charm.

I always think more from a mechanical perspective than software.

 

[MattH]

Bit off topic but was just wondering if you ever got the O ring and if so did it help?

It remains to be seen.

I haven't been able to get a Hypertherm part replacement but I did order and fit an equivalent metric size.
At the time of the Orings arriving is when I ran into the problems with the first set of electronics.

Once the servos were replaced I started on performance testing again which was all 2mm steel and showed that I needed to reduce the gearing.

On the thin stuff the bevel looked better but it's hard to tell.

I was waiting on two belts for the X axis so I have been doing all my gear testing on just the Y axis. Those belts showed up today so hopefully tomorrow everything will be put back together.
Once I have proven the new gearing then i can chuck some thicker plate on and test the bevel issue.

Fingers crossed.

 

[MattH]

I always think more from a mechanical perspective than software.

TBF there's no mechanical issue with the 1.33:1 reduction, it's just it left me with a fractional number in the software.