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Steps per inch calculations

Official support for products purchased from the BuildYourTools.com and BuildYourCNC.com sites, and the book "Build Your Own CNC Machine (Technology in Action)" by Patrick Hood-Daniel and James Floyd Kelly.

Steps per inch calculations

Postby lkohnke » Wed Nov 10, 2010 4:37 pm

I have some problems with my calculations on steps per inch. I'm running a Blacktoe 2x4 v4 chain drive with Mach3. Everything is tight, square, flats ground...

X axis has 9 tooth drive gears which equates to 1422.222 s.p.i.
Y axis has an 11 tooth gear which I believe calculates to 1163.636 s.p.i. right?
At first I was running both x and y axis at 1422.222 by mistake and was cutting ovals where I should be cutting circles. When I plugged the 1163.636 into the y axis the ovals got worse, more elongated. Judging from that, I subtracted 1163.636 from 1422.222 and got 258.586. Then I added that 258.586 to 1422.222 and got 1680.806. So I plugged 1680.806 into the y axis in mach3 and was cutting what I believe to be perfect circles. It appears to work, but it doesn't make sense according to the formulas. Any insight as to where I'm off? What steps per inch do you guys run your x and y axis at for comparison?
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Re: Steps per inch calculations

Postby Awesomeness » Wed Nov 10, 2010 6:47 pm

BuildYourCNC.com wrote:Let's go ahead and do the math to determine the resolution (steps per inch). A standard stepping motor provides 200 steps per revolution (1.8 degrees per step). It's never recommended to set a driver for full step, so let's assume that the drivers are set to 1/16 microstepping for the stepping motors that are to drive the chain (not the lead screw). I generally recommend 1/16 for microstepping roller chain drives. There will be 16 steps for each full step. Simply multiply 200 steps per revolution by 16 and you get 3200 total steps per revolution. The sprockets that I use on this machine has 9 teeth. At the pitch of 1/4 inch, one entire revolution will yield 2.25 inches. Since we are looking for step per inch, we already know how many steps there are in one revolution, so all we need to do is divide the 3200 steps with the number of inches in one revolution (2.25 inches). So, 3200 steps per revolution divided by 2.25 inches is 1,422.2222 steps per inch.

For the lead screw, I recommend 1/4 microstepping. So, 200 steps per inch multiplied by 4 steps (per full step) is 800 steps per revolution. With lead screws, the math is a bit reversed since the mechanism is actually increasing the resolution. The lead screw, as mentioned above, yields 2 turns per inch. Since we are going the other way and the mechanism is multiplying the resolution, we need to multiply the steps per revolution by the number of turns per inch (2). So, the product of 800 and 2 is 1600. Another way to think about this (similar to the roller chain math) is to divide 800 by the number of inches in one turn, which is 1/2 inch. so, 800 divide by .5 gives us the same answer, 1600 steps per inch. you can increase both the roller chain and lead screw numbers by increasing the microstepping. Make sure to understand the torque at higher settings.


So...

((200 motor steps per revolution) * (16 microsteps per step)) / ((1/4" pitch per tooth) * (11 teeth per revolution))
= (3200 microsteps per revolution) / (2.75 inches per revolution)
= 1163.6363 steps per inch

Now, if you're saying 1680 is cutting nearly correct, you really only have 4 things in this formula to examine. Not rocket science, just have to work through it.
- Your motors are not 200 steps per revolution.
- You're not using 1/16 microstepping.
- Your gears are not 1/4" pitch per tooth.
- You do not have 11 teeth per revolution.
- (Bonus) You have a modifier applied in software, such as Mach3, to dynamically alter the output on one axis.
- (Bonus) Something is just not functioning as designed (e.g. breakout board is bad, wires are cross-talking, etc.).
If you don’t have time to do it right, when will you have time to do it over?
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Re: Steps per inch calculations

Postby lkohnke » Wed Nov 10, 2010 8:37 pm

- Your motors are not 200 steps per revolution.
- Your gears are not 1/4" pitch per tooth.
- You do not have 11 teeth per revolution.

All parts were purchased through Build Your own CNC as a package so I believe they are correct.

- You're not using 1/16 microstepping.
Double checked, microstepping is 1/16 which leaves us with the bonuses...

- (Bonus) You have a modifier applied in software, such as Mach3, to dynamically alter the output on one axis.
- (Bonus) Something is just not functioning as designed (e.g. breakout board is bad, wires are cross-talking, etc.).


I'll try hooking y axis to different outputs on the breakout board. Signal wires are totally separate from power wires so that should eliminate cross talk? It seems to make the most sense that the glitch is in the software at this point so I will go through that with a fine-toothed comb and report back if I find any solutions.
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Re: Steps per inch calculations

Postby Awesomeness » Wed Nov 10, 2010 8:40 pm

Swap the x and y axis wires, and see if the problem moves to the other axis.
If you don’t have time to do it right, when will you have time to do it over?
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Re: Steps per inch calculations

Postby lkohnke » Wed Nov 10, 2010 9:33 pm

One thought... If it works as is... do you see any potential problems in just running as is?

P.S. I dig WOW as well.
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Re: Steps per inch calculations

Postby Awesomeness » Wed Nov 10, 2010 9:40 pm

Not theoretically, but I think the method you arrived at the math solution is flawed. It doesn't feel right that you would subtract to get the difference, when the formula is all about multiplying and dividing between ratios. (Yes, I understand multiplication is repetitious addition.) It's important to understand why it worked, and if it is really correct or if it's just a close guess that happens to be right by coincidence. Personally, I couldn't let that go.
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Re: Steps per inch calculations

Postby jeff » Sun Nov 14, 2010 5:40 pm

Wouldn't the setting be the same for all Blacktoe's, like they all have the same chain and gears as long as they are ordered from Patrick? Mine has the 24 pitch chain, and the 9 tooth axle gears, and the 20 tooth idler gears. Also can a value such as " 1600.5 " be added in the motor tunning box with any effects?
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Re: Steps per inch calculations

Postby Awesomeness » Sun Nov 14, 2010 5:49 pm

He says he has 11-tooth sprockets. Mine are all 9 tooth. There's no way to tell what other things may be different. If we were all using the same parts, then our numbers would be the same, but he's not. (The number of teeth on the idler gears is irrelevant.)

What you put in for the steps per inch will have an effect. The computer is counting on you to know how many pulses it needs to send in order to move 1" in your drawing. So when it reads "cut a 1 inch line" in the g-code, if you have the number right it cuts correctly, if it's too small it cuts small, and if it's too big it cuts big. It's basically the same as scaling.
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Re: Steps per inch calculations

Postby lkohnke » Wed Nov 17, 2010 8:23 pm

Woot! The original-original calculations were spot-on! The x and y axis were reversed however Doh! Everything works great now AND makes sense.
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Re: Steps per inch calculations

Postby snooprob » Fri Jan 20, 2012 2:36 am

It is also worth noting that is you use Mach3, it will automatically fine-tune your steps/inch via a wizard. Check out section 5.5.2.3 in the manual.

http://machsupport.com/docs/Mach3Mill_I ... Config.pdf

You pick an axis, tell mach 3 how far to move it, ie 10", then input how far it actually moved.
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