Metric to inch and adding belt

[LeeWay]

I built a mill using some 10 mm lead ground ball screws. The screws are in good shape. My Z axis is actually an IKO cast iron slide. The Z weighs maybe 70 pounds and I do have a 30 pound gas spring on the column.
Initially I was driving this axis direct with 495 oz steppers and 203V's on a 72 VDC PS.
I was finding if I take too much of a plunge when drilling, I would loose steps every now and then. This was easy to see.
I bout some nice 1/2" metal timing pulleys and belt from SDPS. Motor pulley has 10 teeth. Screw pulley has 20. I am running the machine in inch mode.
I measure the travel awhile back when it was in direct drive and my steps per inch settings were very close IIRC. I have all three axes set @ 5080.

This belt drive should have changed the settings to 10160. I find I have to set it at 10390 instead to get .0008" accuracy. Meaning I tell it to move an inch and it moves that much shy and twice that for two inches. Still very acceptable for me especially on the Z. I rarely even cut anything over 1/2" thick. X and Y still seem perfect @ the 5080 setting or at least this close.

My question is why the math is so far off? Well not really that far, but farther than I expected. It there an extra tooth on the large pulley that shouldn't be there? Like 10 to 19 or something? The belt is a nice one and really has no or very little stretch.

Here is the formula I used to calculate steps.

10 mm lead = 25.4 mm per inch or 2.54 turns per inch.

2.54 x 200 motor steps = 508

508 x 2 for pulley ratio of 1 to 2 = 1016

1016 x 10 microsteps = 10160 steps per inch

Why am I having to add 230 steps?

Granted I need to recheck the X and Y again because I haven't done it in awhile and I have changed lots of things around in Mach since I checked. No big deal really, just curious to see if any of you had something similar.
Any ideas? Thanks

[LeeWay]

Well...I sure am glad no one else had this problem or issue.

[ger21]

Try using the ratio of the pulleys pitch diameters, and not just using 2:1. I was going to post this the other day, but am not completely sure if that's right.

[LeeWay]

Thanks Gerry.
Not sure how to go about that either.
I did check the X and Y again and they are perfect with direct drive, so the screw counts I am using are good. The screw on the Z appears to be identical and was close to perfect as well before the belt addition.
It really isn't a problem as I mentioned before. .0008" is plenty good accuracy for what I do. I could even nail it a little closer by adding a step or two.

Here are the pulley specs anyway.

It could be that there is one groove or tooth on a pulley that is not being accounted for at a 1 to 2 ratio.

Motor pulley.

Part Number A 6A 4-10DF05012
Unit Inch
Pitch .375 (L)
No. Of Grooves 10
Material Aluminum Alloy
Belt Width 0.5
Bore Size 0.375"
Flange & Hub Configuration 2 Flanges / With Hub
Pitch Dia. 1.194"
Outside Dia. 1.164"
Overall Length 1.125"
Hub Dia. 0.88"


Screw pulley.


Part Number A 6A 4-20DF05016
Unit Inch
Pitch .375 (L)
No. Of Grooves 20
Material Aluminum Alloy
Belt Width 0.5
Bore Size 0.500"
Flange & Hub Configuration 2 Flanges / With Hub
Pitch Dia. 2.387"
Outside Dia. 2.357"
Overall Length 1.313"
Hub Dia. 1.81"




Now when I multiply the pitch diameters, it doesn't come out to exactly 1 to 2.

It comes out to 2.388" instead of 2.387". This would seem to be about the ratio that this is off.

[ger21]

That could be due to rounding errors, but I don't really know what's going on.

[LeeWay]

May also be effected by the conversion of metric to inch is something like 25.4000000003 mm per inch. My light weight oil is fatter than that tiny little 3 there on the end.
It likely is rounding errors though, Gerry. I think you might be right. That wouldn't even be noticeable on my router. Well it's not noticeable on the mill either, but I was shooting for as precise as possible. Might as well with preloaded ground ball screws.

In contrast, I think my little lathe has about 8" of backlash on the X.
Maybe not quite that much.

I bought some 3/8" precision acme rod and anti backlash delrin nuts to fix that rascal with though. Thats another thread altogether.

[WayneHill]

(Programmed/Actual) * Old Units Per = New Unit Per

No silly gear math required.

There are imperfections on every component. You are dealing with imperfect lead screws, belts, and gears that have a tolerance variation to throw your math off.

[LeeWay]

So ultimately, the math will get you close. You then may need to zero in on the actual steps per unit. That makes sense to me.
Thanks guys.