Surface Grinder CNC Notes

Controlling the Z axis

Option A - Stepper motor

Using a stepper motor with 1.8 deg steps will give a resolution of 200 steps in full step mode per rotation. This would require a 46:1 reduction to achieve the desired 0.5um resolution on a 5mm lead screw.  Cons: discreet steps, not sure if this will be an issue, holding torque goes down with reducing step size.

Option B - Servo

With a servo motor using dual loop position feedback control will make more sense since steps are no longer discrete. The dunker motor I have had lying around for years, seems like a good fit. 23:1 gear ratio with a 100ppr encoder, without using the linear encoder as additional feedback this will give a resolution of 9200 steps or 0.543 um. Quick estimation with Bresenham algorithm, gave the following approximations for 0,001um increments. But i would like to hit them exactly...well in theory at least.

1	0,000543
2	0,001087	0,001
3	0,00163
4	0,002174	0,002
5	0,002717
6	0,003261	0,003
7	0,003804	0,004
8	0,004348
9	0,004891	0,005
10	0,005435
11	0,005978	0,006
12	0,006522
13	0,007065	0,007
14	0,007609
15	0,008152	0,008
16	0,008696
17	0,009239	0,009
18	0,009783	0,01
19	0,010326
20	0,01087	0,011
21	0,011413
22	0,011957	0,012
23	0,0125

This made me research the possibility of using dual loop feedback, seems common in commercial machines.

LinuxCNC supports it out of the box

http://wiki.linuxcnc.org/cgi-bin/wiki.pl?Combining_Two_Feedback_Devices_On_One_Axis

http://linuxcnc.org/docs/2.7/html/man/man9/offset.9.html

This great explanation https://granitedevices.com/wiki/Dual-loop_feedback_position_control

Gave me another idea, just use Elm Chan SMC3 Velocity control mode with LinuxCNC, feeding position from Heidenhain encoder to LinuxCNC, which controls the SMC3 servo in velocity mode.
http://elm-chan.org/works/smc/report_e.html

Writing Software for CNC Applications

Need to synchronise the spindle to the C axis? Or implement an electronic gearbox reduction for a lathe? Stepper on a rotary table? Or just plot a circle on XY planes? all of these implementations have a few common problems to solve, one of which is to coordinate the movement of two or more axis. Since each axis might have different resolution and or require fractional advance of that resolution to accomplish the desired motion. Most open and closed source implementations seem to make use of some sort of  Bresenham's line algorithm here, to deal with the resulting error.

void main () {
   double y0 = 0.00;
   double dy = 0.0125; // 5mm / 100x4
   double dx = 23; // gear ratio
   double k = (double)dy / (double)dx;

    double y = (double)y0;
    double yi = 0.0000;

    for (int x=0; x<23; x++)
    {
        y += k;

        if ((y+0.0005) > yi) // error larger than 0.0005? increment yi
        //if ((int)(y+0.5) > yi)
        {
            yi=yi+0.0005;
        }
      printf("%02d %02f %02f\n", x, y, yi );
    }

}

Let us look at Gear ratios, the concept of accurate synchronized electronic reduction gears for the lathe made me think. Why not use closed loop phased locked control?

1) decode position pulses to direction and 4x steps,

2) Multiply step pules by M an then divide by N. 

3) feed the resulting pules directly to a stepper which can act as the divider

To implement this one would require a PLL for multiplication. Using this method should make it possible to implement any gear ratio without error.  I have implemented this on Arduino making use of the internal clocks and one external PLL 4046. The lock and capture range now determine the spindle speeds. The solution runs entirely on hardware no software is required once the counters have been set. It is abit more complex than this, since direction needs to be accounted for. But here is the gist of it. I then found commercial industrial solution doing exactly this at http://www.motrona.net/encoder_divider.html