# exact gear ratio

• posted

I'm setting up rigid tapping on my mill. The encoder is ahead of the backgear so I'm wanting the exact gear ratio. I set up an encoder on both the shaft before the backgear and at the cutting tool so I could measure the turns of the spindle down to .01 revolution accuracy and took this data

Turns at tool turns at drive 1 6.1245 8 49.0573 80 490.65

163.050 1000

Is there a math wiz out there that can tell me how many teeth on the drive gear and how many on the driven gear? (integer ratio of this data)

Karl

• posted

I think you have some slip or backlash in your measurements.

• posted

No. Your numbers work out to close gear ratios, but they aren't exact. If you divide turns at drive by turns at tool, you get:

Since the more turns you've got the more accurate your results are going to be, I'll take a gues that the ratio is very close to

163:1000, but that's not the exact ratio you're asking for. What happens if you turn 10,000 at the drive?

Are you sure you've got the 'turns at drive' measurement to .0001 turn accuracy?

• posted

There's some inconsistency in your ratios. Using 163.05 : 1000 or ratio of 0.16305, I get close matches for

8/49 = 0.16327 15/92 = 0.16304

Using your ratio of 1 : 6.1245 = 0.16304, 15/92 is a good match.

• posted

We can probably assume that the spindle drivetrain of his mill does not contain a 1000 tooth gear. 16:100 perhaps? It sounds like the back gear has perhaps a 2 stage reduction? What is the ratio when not in back gear?

• posted

As asked, your question has an infinite number of answers. There are an infinite number of ratios of integers that can yield a value of

1/6.1245 = 0.163279.

That said, plugging 0.163279 into my RFRAC program (see my page), we find that that number can be approximated (using continued fractions) by the integer ratio 8/49 with an accuracy of 0.008%. Thus whatever gears are actually mounted, their tooth counts should come close to being some multiple of 8/49, e.g., 16/98, 24/147, etc..

If you want a more accurate approximation than 0.008%, download the program - one of its inputs is the desired accuracy of approximation.

Regards, Marv

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• posted

No, I claimed .01, but i found the encoder I had temped in could move 1 or 2 degrees. I didn't want it too rigid, its not made to be clamped in a vice and bolted to an endmill holder.

Karl

• posted

...

I might have known you'd be the one to figure it out. Surely you didn't just guess this ratio. How'd you do it?

Karl

• posted

No way this is a substitute for Marv's method, but you could just use a spreadsheet. Set up a column going from 1 to 100 (more if you want) and multiply your fraction by each number in turn. It should be quick enough to spot the close matches: here's a section

47 7.674113 48 7.837392 49 8.000671 50 8.16395 51 8.327229 52 8.490508
• posted

First one can be by inspection. 6.1245 is about 6 and one eighth, or 49/8.

Generate a table in Excel using input gear teeth from 1 to 100, dividing those values by .16305 and you'll see 15/92 or multiples are the best match....

• posted

Karl

Put the turns numbers in an excel spread sheet, divide, format to display as a 3 digit fraction, 15/92, solved

CarlBoyd

• posted

"newshound" wrote: No way this is a substitute for Marv's method, but you could just use a

^^^^^^^^^^^^^^^^^^^^^ I came to the conclusion that it is 49/8, using a similar method. I used the average ratio in Townsend's list, which was .163118, and then set up a chart assuming thew small gear had 1 tooth, 2 teeth, 3 teeth... etc until I came to 8 teeth, which gave me 49.04 on the large gear. Continuing the process, I didn't come to anything close until 16/98.09. This tells me that it has to be one of those two, or a multiple, which would be out of reasonable range.

There may be a mathematical reason to get a weighted average from Townsend's numbers, but what I did produces a pretty solid conclusion.

• posted

Also I think that if the encoders don't have a common denominator with the gears the ratios will never be exact and you will just be trying to find the most likely gear teeth numbers based on the data and what gear teeth numbers are sensible for the application.

• posted

I asked about .0001 because that's the accuracy of the numbers you gave.

• posted

I used MathCAD. No doubt others will provide more erudite approaches.

• posted

Excuse my ignorance, but if you are tapping, the tap is going to self feed once it gets started. Don't you only need to concern yourself with the depth of the tap prior to the spindle reversing?

Seems to me that that would then be a function of the number of revolutions rather than the speed that the tap is turning. (unless you are going too fast in which case you will hear the snap and then call on your reserve of magic words!)

• posted

...

I'm setting up the machine for rigid tapping on the large taps. Put the tap right in the collet. To do this, you slave the Z-axis to the spindle. For example, for a 3/4 x 10 tap, the spindle will move down 0.100" inches for every revolution of the tap.

The machine can also hob gears. With a 4rth axis, advance the gear blank one tooth for every one revolution of the spindle. This is the reason I needed the extreme accuracy, it takes 1000s of turns of the spindle to make one gear. For tapping, 20 turns is a lot.

Karl

• posted

A slide rule is an amazing tool for guessing gear ratios ratios, just set up the ratio and look across the slide for matching integers ;)

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• posted

Way to go!!!! Not too many of us left. :-) ...lew...

• posted

My attempt using Excel

163.05 1000 6.13308801

541 3318.001 3318 -1.1E-06 1.13E-06

278 1704.998 1705 5.52E-06 5.52E-06 556 3409.997 3410 5.52E-06 5.52E-06 263 1613.002 1613 -8.2E-06 8.16E-06 526 3226.004 3226 -8.2E-06 8.16E-06 571 3501.993 3502 1.18E-05 1.18E-05 511 3134.008 3134 -1.6E-05 1.56E-05 293 1796.995 1797 1.78E-05 1.78E-05 248 1521.006 1521 -2.3E-05 2.35E-05 496 3042.012 3042 -2.3E-05 2.35E-05 308 1888.991 1889 2.89E-05 2.89E-05 481 2950.015 2950 -3.2E-05 3.19E-05 323 1980.987 1981 3.89E-05 3.89E-05 233 1429.01 1429 -4.1E-05 4.08E-05 466 2858.019 2858 -4.1E-05 4.08E-05 338 2072.984 2073 4.81E-05 4.81E-05 451 2766.023 2766 -5E-05 5.03E-05 353 2164.98 2165 5.65E-05 5.65E-05 218 1337.013 1337 -6E-05 6.05E-05 436 2674.026 2674 -6E-05 6.05E-05 368 2256.976 2257 6.42E-05 6.42E-05 383 2348.973 2349 7.13E-05 7.13E-05 421 2582.03 2582 -7.1E-05 7.14E-05 398 2440.969 2441 7.78E-05 7.78E-05 203 1245.017 1245 -8.3E-05 8.31E-05 406 2490.034 2490 -8.3E-05 8.31E-05 413 2532.965 2533 8.39E-05 8.39E-05 428 2624.962 2625 8.96E-05 8.96E-05 443 2716.958 2717 9.48E-05 9.48E-05 391 2398.037 2398 -9.6E-05 9.57E-05 458 2808.954 2809 9.98E-05 9.98E-05 579 3551.058 3551 -0.0001 0.0001 473 2900.951 2901 0.000104 0.000104 488 2992.947 2993 0.000109 0.000109 188 1153.021 1153 -0.00011 0.000109 376 2306.041 2306 -0.00011 0.000109 564 3459.062 3459 -0.00011 0.000109 503 3084.943 3085 0.000113 0.000113 518 3176.94 3177 0.000117 0.000117 549 3367.065 3367 -0.00012 0.000119 533 3268.936 3269 0.00012 0.00012 548 3360.932 3361 0.000124 0.000124 361 2214.045 2214 -0.00012 0.000124 563 3452.929 3453 0.000127 0.000127 534 3275.069 3275 -0.00013 0.000129 578 3544.925 3545 0.00013 0.00013 173 1061.024 1061 -0.00014 0.00014 346 2122.048 2122 -0.00014 0.00014 519 3183.073 3183 -0.00014 0.00014 504 3091.076 3091 -0.00015 0.000152 331 2030.052 2030 -0.00016 0.000157 489 2999.08 2999 -0.00016 0.000164 158 969.0279 969 -0.00018 0.000177 316 1938.056 1938 -0.00018 0.000177 474 2907.084 2907 -0.00018 0.000177 459 2815.087 2815 -0.00019 0.00019 301 1846.059 1846 -0.0002 0.000198 444 2723.091 2723 -0.00021 0.000205 143 877.0316 877 -0.00022 0.000221 286 1754.063 1754 -0.00022 0.000221 429 2631.095 2631 -0.00022 0.000221 572 3508.126 3508 -0.00022 0.000221 557 3416.13 3416 -0.00023 0.000233 414 2539.098 2539 -0.00024 0.000238 15 91.99632 92 0.000245 0.000245

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