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.).