Accuracy

[jeff_guinn]

Dirk & Mike R,
Thanks for the spreadsheet. I entered 7.2 gear ratio,1.8 step angle,18 teeth pinions & the results are exactly twice the recommended unit values. Also, the recommended unit values for my ball screws are 2000. The screw has a .2 pitch & motor has no gearbox with a 1.8 step angle which I caculated at 1000 steps per inch. I'm totally lost & could use a good explanation.
Thanks,
Jeff

[gerald_d]

Jeff, is your system perhaps half-stepping? deleted

This old post by Ted is essential reading. There have been numerous combinations and permutations, even within the same model number, or even for different axes on the same machine.

[evan]

Brady,
PW/Pro? Is that the same as Parts Wizard Ver.2?

Evan

[Brady Watson]

Jeff,
A '.2 pitch' ballscrew is essentially moves 0.2" per revolution of the motor (200 full steps) You can also think of it as a 5 turns per inch screw, which essentially functions as a 5:1 gear reduction.

So...If you are using a .2 pitch screw in conjunction with a 7.2:1 geared stepper, then you would simply multiply the ratios together to get your final drive ratio:

5 X 7.2 = 36:1

This means that the stepper motor itself must turn 36 times in order to turn the output shaft (the screw in this case) 1 full revolution. Since there is no free lunch per se, you will get gobs of torque at the expense of speed. For instance if you were using a 7.2:1 geared PRT motor with a .2 pitch screw, (using factory PRT voltage supply) you would have a max speed of about 1 inch per second...BUT you would have a theoretical max of about 3,000 Oz-in of torque. This would be a perfect setup for a high-resolution indexer that was swinging a heavy load, but not a good choice for a Z-axis as it just wouldn't be able to keep up with the X & Y movements.

I am confused...what is your application? Is this a PR or cable tool? Why the screw?

Your unit values are the number of steps (or patial steps) needed to move the tool one inch. If you are 1/2 stepping (as Gerald points out as a possibility) then your unit values would be somewhere around 400 (200 steps per rev * 2)....1/4 stepping machines would have a unit value twice that of a 1/2 stepping PRT up around 800 or so. The size of the pinion on each axis also plays a role with your unit values. It is typical to have 25 tooth pinions on the XY axes and a 20 tooth on the Z. Stock values for a PRT with 3.6:1 boxes on the XY is about 733 steps per inch and 916 steps per inch on the Z. A 7.2:1 Z axis would have exactly 2X the number of steps per inch (so more like 1832 or so on the Z).

Confused yet?


-Brady

[Brady Watson]

Evan,
Yes. You have the option to use the regular ShopBot Inch post or Arcs_Inch in both programs. The Arcs post does circular moves in arcs...the inch post does them in very small straight movements. You can choose either post in PW2, Insignia and ArtCAM Pro. I leave it on arcs_inch all the time since it doesn't use arcs for straight moves.

-Brady

[dirk]

Jeff
It sounds like your talking about a PR machine with ball screws on the Z axis. The PR uses 1/2 steps so that is why the unit value is 2000. 200 steps x 2(halfstepping) = 400 x 5(turns per inch)=2000. Half stepping would also make unit values for other Axis 2 x different. If thats not the case post or email your recomended unit values and let me check spreadsheet for error.
Dirk

[dirk]

Jeff
Another note is the 7.2 gear ratio. Are you sure it's not a 3.6, as far as I know the 7.2 is used only on the Z and 3.6 ratios are used on other axis.
Dirk

[dirk]

I posted the question as to position accuracy on Gecko's Forum. I got the following response from Marris of Gecko Drives:


I disagree. Static microstep accuracy depends on good motor linearity
and a drive that generates accurate sine and cosine phase currents.
Unloaded accuracy routinely measures as good as +/- 0.018 degrees over
the span of a single step and +/- 3% (0.054 degrees) of cyclic error
for a full revolution.

These kind of results can only be obtained from "square" step
motors, "round" step motors are far less linear.

Load adversely affects positioning accuracy. Motor torque is
proportional to the sine of the error angle (1 full step equals 90
degrees). An error angle of 1/10 step (9 degrees) results at load
torque equal to 15.6% of holding torque. That is the limit to which
1/10th step accuracy can be maintained; at a full holding torque load
the error is necessarily 1 full step.

Dynamically things get a little more dicey. All step motors develop and
unloaded lag of 1 full step when they are running on the inverse torque
region of their speed-torque curve. This is because inductive reactance
is limiting current and current lags voltage by 90 degrees (1 full
step) in this region. The motor will be located 1.8 degrees behind the
expected location while unloaded and will stall when it lags 3.6
degrees due to applied load.

Conclusion: A 1/10th step accuracy can be relied on if the motor load
is less than 15.6% of its holding torque. This is a usable value
because a properly designed open loop step motor application should be
biased at no more than 30 to 50% of the motor's holding torque. Put
differently, a 600 in-oz torque motor develops 94 in-oz at a 1/10th
step error. This is 184 lbs of thrust when applied to a 5 TPI leadscrew.

Mariss

[Brady Watson]

"A 1/10th step accuracy can be relied on if the motor load is less than 15.6% of its holding torque." put a bit more eloquently than me saying, "Areas in between a 1/4 step position don't have a good magnetic lock, and as a result can drift..."

Thanks for posting Mariss' response...I forgot about the '15% rule'.

-Brady

[jeff_guinn]

Dirk,
Thank you for clearly answering my question about my ball screw drive.I never realized that the PR used 1/2 stepping. Yes,it is a PR model with 2 Y & 2 X steppers which are in fact geared 7.2 with a recommended unit value of 254.6479 which was exactly twice the values in your spreadsheet.
Gerald-Thanks for the response-You shouldn't have deleted it!
Brady- Thanks. As I originally stated, the ball screw motor is direct drive-no gearbox. I stayed with the ball screw because of its' accuracy,durability & compactness. As a matter of fact,I just completed building & testing a new ball screw Z axis, for another application, using a larger stepper(PK268 series).
Thanks,
Jeff