Unit Values for the 7.2:1 PRS-Alpha Motors

[richards]

I'm totally confused about how the unit values for the PRS-Alpha motors were derived. For example, my PRT-Alpha has a factory default Unit Value of 1273.2395. That number is easy to compute. If we multiply the pitch diameter of the pinion gear we find the distance travel by the axis per revolution of the stepper motor. Next, if we divide that number by the gear ratio of the stepper motor we find the true distance traveled per revolution of the stepper motor's shaft. Next, we divide that number by the steps per rotation of the stepper motor to find the distance per step. Next we divide 1" (were're using inches for this example) by the distance per step to get the required steps per inch. Finally, we multiply the steps per inch by the Unit Value Multiplier to get the value of the Unit Value for that axis. So, running that equation for the PRT-Alpha we get:

1 / (1 X PI / 1 / 1000) X 4 = 1273.2395

That's exactly what the default number should be.

For my modified PRT-Alpha that has a 3:1 belt driven gear box, the numbers are:

1 / (1 X PI / 3 / 500) X 4 = 1909.8593

With my 20 toothed pinion gear, 3:1 belt drive, 500 steps per stepper revolution and 4X default multiplier, 1909.8593 is the Unit Value gives me exactly one inch of axis movement on my machine.

Now we come to the PRS-Alpha with a 7.2:1 gearbox, a 30-toothed pinion gear (I assume), 500 steps per revolution and a 5X multiplier. Running the numbers gives us:

1 / (1.5 X PI / 7.2 / 500) X 5 = 3819.1863

However, the published Unit Value for that machine is 2482.8171. If I change the number of steps from 500 per revolution to 325 per revolution, I get 2482.8171.

When I looked on the Oriental Motor web site and browsed the AS98AA-T7.2 motor, I could only find 500, 1000, 5000 and 10000 as the permitted steps per revolution for their stepper drivers.

Is there an explaination? (Please don't spare my feelings. If my math is faulty, please tell me.)

EDITED: The racks on my PRT-Alpha have 20 teeth per inch. The 20-tooth pinion gear (standard for the PRT-Alpha) has a pitch diameter of 1-inch. On that same machine a 30-tooth gear has a pitch diameter of 1.5-inches, which is 30 / 20 = 1.5. Also, when I modified my machine to use a 3:1 belt drive, I had to change the factory default of 1,000 steps per revolution on the Oriental Motor stepper driver to 500 steps per revolution to keep the Unit Value below 3,000 - as per the recommendations from those who advised me from Shopbot. (By the way, their recommendation works perfectly with my configuration.)

[Brady Watson]

You have mail.

-B

[richards]

Brady,

Thanks for the email. Now I can sleep knowing that I haven't lost all math skills.

-----------------------

For those who might be interested, Brady simply wrote that the new software has some nifty features that require a different computation to derive the Unit Values. He didn't tell me what that computation might be, but I am relieved to know that there was nothing wrong with my math and that the published Unit Values are not a typographical error.

[curtiss]

Hope this helps...

The numerical value of ð truncated to 50 decimal places is:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

[richards]

Curtis,
That might be good enough for government work, but we're talking CNC routers! Wouldn't it be better to put in a little more effort and compute PI so that we can get a little more accuracy? ;>)

[pfulghum]

Her's the first 1000 places... THAT should work provided you don't go the the 50:1 gear ratio with 1000 steps/rev with more that a 30 tooth pinion.

3.141592653589793238462643383279502884197169399375 10
58209749445923078164062862089986280348253421170679
82148086513282306647093844609550582231725359408128
48111745028410270193852110555964462294895493038196
44288109756659334461284756482337867831652712019091
45648566923460348610454326648213393607260249141273
72458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094
33057270365759591953092186117381932611793105118548
07446237996274956735188575272489122793818301194912
98336733624406566430860213949463952247371907021798
60943702770539217176293176752384674818467669405132
00056812714526356082778577134275778960917363717872
14684409012249534301465495853710507922796892589235
42019956112129021960864034418159813629774771309960
51870721134999999837297804995105973173281609631859
50244594553469083026425223082533446850352619311881
71010003137838752886587533208381420617177669147303
59825349042875546873115956286388235378759375195778
18577805321712268066130019278766111959092164201989

[curtiss]

Sorry about only having the first 50 decimal places.... my daughter worked it out in a few minutes,

I would guess some of the other numbers are being provided by "grown ups"

[richards]

Pat,
I'm surprised that you didn't catch the obvious error in line twelve where '53921' is mistakenly written instead of '53821'. Remember, remember, remember - garbage in, garbage out! That little mistake could have ruined the cut! ;>)

Edited: Sorry about the delay in responding but my wife and I were enjoying an afternoon drive up through the eastern part of your state. We stopped to walk along the Snake river just below the American Falls Dam. That spot is now part of a state park. Back when I was a boy working summers in Idaho moving sprinkler pipe, that part of the beach was part of the farm on which I worked. What a truly beautiful state you live in.