need help calculating my accuracy? not sure if i did this correctly

rack and pinion set up
info
30 tooth spur gear 20 deg pressure angle, pitch dia. 1.5"
gear ratio 7.2:1

calculations

1.5x 3.14159...=4.71238898 inches for every rotation of spur
4.71238898 /7.2 gearratio=.654498469 inches of axial movement per rev

gecko step (2000) 0.654498469 /2000=.000327249 inchs pers step

I think it (4.712 x 7.2)/2000 = 0.01696 inches per step. And that would be the precision, not the accuracy. :)

I think it (4.712 x 7.2)/2000 = 0.01696 inches per step. And that would be the precision, not the accuracy. :)

how do you calculate acurracy of machine?

You measure it when it's done. Accuracy is what it can actually do, not just what it's supposed to do.

I think it (4.712 x 7.2)/2000 = 0.01696 inches per step. And that would be the precision, not the accuracy. :)

how to get better precision, seems like high number, what a typical
4x8 machine about to do/ get.

I think I made a mistake, and you were right in the first place. Sorry about that. :) It is .0003 inches per step.

I think I made a mistake, and you were right in the first place. Sorry about that. :) It is .0003 inches per step.

If so, thats the first one I have seen. ;)

Just to add some info, your increment of motion (one step) is .00327...so you cannot be more accurate than that. But more important are:
1. Backlash or lost motion
2. Springiness- deflection under load
3. Squareness of your system - don't want to make parallelograms
4. Straightness of BOTH axes
5. Perpendicularity of your Z axis to the other two
6. Following error of your servo system
7. Absolute accuracy of the computations from the CNC

Jack C.

Since I am working on a rack and pinion system, I will add a related question

I see a lot of recommendations for rack suppliers, mostly standard steel, boston gear, and atlanta drives. Some of the obvious specs are the same (Example, 14.5 or 20 degree pressure angle, 20 teeth per inch or module 1 - 1.5, etc), but the pricing can vary quite a bit.

Has anyone actually found a way to compare the precision of these various racks? I may not be using the terminology correctly, but what I am trying to understand is how to compare the motion achieved ONLY due to the quality of the rack manufacturing itself. In ball screws, there are distinct methods of determining this, such as 0.001 inch per foot of travel, etc. I assume that in a rack, not every tooth is perfectly cut, nor is the spacing, which is fine - but - how to compare / decide ?

Edit - Yes, I realize that split pinions will improve the motion control, etc. If someone has a vendor for a split pinion that can mount directly on a 1/2 in shaft (mine, not theirs), I would love to hear about it. Ideally, about a 1 inch pitch diameter, about 20 - 25 teeth on the pinion, nominal 14.5 degree pitch angle. That is the goal, but I am open to other specs in the 1 in / 25mm dia. range.

you can achieve a spit pinion by using 2 pinion one in series with each othere. Just like the link from altanta drives, but one will be your drive pinion
the other is setup to take out the backlash ....on the opposite leading edge of the rack tooth, Ie let say 2-3 inches behind your drive pinion.

Its the same concept just moved back afew teeth to best utilize the 1/2 track in a series fashion rathere than 2 pinions in parallal. The trick is the one pinion will be your drive pinion other will require adjustable slider to tune out the backlash... think of it as pinion mounted in a dovetail pocket slide with a adjustable screw.

Eloid - That is an interesting concept - never thought of that approach. I will have to think through the implementation aspect some more.

Edit - Eloid - I suddenly can picture your setup and it is so straight forward - great simple but solid concept for implementation.


Were you able to gain some clarity on how to spec rack "quality" ? I am still lost on that aspect. Basic sizing I now understand, but not quality ratings / tooth size / space control.

I've seen those anti-backlash spur gears, with 20 degree pressure angle at http://sdp-si.com/