A question of Scale.....

Hi All

I have been wondering lately how accurate we have to be when setting the Scale for our machines.

I want my machine to be as accurate as possible so I have been using a scale with 14 decimal points. I have no idea if this detail is actually required so here I am.

On my machine I have Module 1 racks, 4:1 reduction, 30 tooth pinions powered by 640 OzIn Nema 34 Steppers. My controllers are AM882's powered by a 70V Toroidal power system set to 8 Microstepping. Also in the mix is a Mesa 5i25 and 7I76. My current software is PathPilot 2.14. The machine itself has a working area of 2400x1200.

With that knowledge just how accurate can I be? Would I need smaller pinions (I have a bunch of 24 tooth available if needed)?

This is my current Scale setting for all axis: -1725.81113657584232 It is negative because non-negative goes backwards, yes I probably have the drives all wrong but this was the easiest way to fix.

Anyone have any input on the accuracy expectations versus Scale setting?

Cheers
Bruce

You need a known length like a long stack of gauge blocks. Indicate the face of one side and set zero.

Then rapid to the other end and check that face. Go the same direction so backlash isn't a factor.

Accuracy has many components, on a 2400 mm steel table for example you would have a ~.3 mm shift at the end of travel with a 10C temperature change. Even 6 digits of scale setting is way beyond what is typically needed.

I would expect backlash, stiction, expansion with temperature, and flex to be the major
contributions to position errors

Have you measured the backlash/repeatability with an indicator?

Anyone have any input on the accuracy expectations versus Scale setting?

Theory: The choice of scale value determines the digital granularity (steps per motor revolution) of control, because scale is defined as the inverse of granularity per turn. Choose that control granularity to be upper-limited "some fraction" of the total mechanical imprecision (a statistical, analog "granularity" if you will) following the motor, and lower-limited by the speed goal of the motor vs the available bandwidth of the control signal (how fast you want the top speed of the motor to go, divided by how fast you can step). "Some fraction" is at most the Nyquist criterion of 0.5, but often pessimistically taken as 0.1. This is a "weakest link" analysis, similar to how in circuit theory, parallel resistor networks have to be calculated as the inverse of the sum of the inverses.

For example, if the mechanism (im)precision is 0.001in, then you want steps certainly no larger than 0.0005in (by Nyquist), or no larger than 0.0001in (by cautious pessimism). Finer steps that these will not yield any precision-performance benefit, and compete against the speed-performance imposed by stepping bandwidth. Larger steps than these will lose control of physical precision. This is an "impedance matching" analysis, similar to how in circuit theory, impedance governs the efficiency of power transfer.

Choose the step size with all that in mind, then divide the travel per turn of the motor by that step size, and that's the scale value. To continue the example, if you are a pessimist and choose 0.0001in granularity, and if the motor turns translate into 0.1in of motion, then the scale value is 1000 = 0.1in/0.0001in. Competing with that will be the step-rate bandwidth and speed goal; if the step bandwidth is 10 kHz, then the speed will be limited to 0.1in/sec = 10000 Hz * 0.0001in.

Theory Verses Praxis

Best Scale vs Precision vs Speed vs Torque vs Budget

In Europ SORRY ballscrew 1605 means 5mm/revelution)
Steppers 200steps / rev // TIMED 400 -800 1600...
as on a Timingbelt 20/25 teeth it means 1,25 Gear Ratio you are with Halfstepping at
BEST Speed ,Best Precision , Max Torque
Best Speed means 0,01mm (0,00039in) Per step the MAX Speed you can go saying 12000mm/min or 500IPM as off 100000 Latency
Best Precision 0,01mm (0,00039in) Per step the Min Your Messurment system takes CALIBER
MAX Torque as of Halfstepping brings the Best of your Power to Stepeper (( 10Times the Stepper Voltige Rate Requirerd 5V/48V )

soy your Hardware shoudt be optimised
NOT the DIP Switch of the DRIVER
to get BEST

I'm not a machinist but as Racedirector is a fellow Aussie it would be well worth his while getting your hands on the "Engineers Black Book" by Sutton Tools and review the tolerance tables for shafts and holes. The tightest seems to be a H6 code which is 0.000 to -0.006 on shafts 1-3mm in diameter. But when you get up to 18-30mm shafts, the same H6 tolerance is 0.000 to 0.013.

Remember that a micron is 0.001 mm . A human hair is about 75 microns wide and the finest merino wools are around 16 microns. A red blood cell is about 5 microns wide.

So then you need to ask yourself would a smear of blood only one cell thick affect your engineering outcome? Could you run your fingers over this in the dark and feel it? Would your bloodied shaft no longer fit ? I suspect not.

So if we can only comprehend a measurement up to 0.001 mm, If your device units are millimetres 14 decimal places is a bit overkill when in our climate a steel table can vary 1mm in length from winter to summer.