Gear Hobbing Math for Helical Gears redux

After asking numerous questions myself, I think I have a couple of thoughts that might be worth sharing.


Formula for hobbing helical gears:


KCT
(CN) ± 1


K = machine index constant
C = C constant
T = number of threads on hob
N = number of teeth on gear
1 = absolute constant
M = feed constant


Sample:


K = 24
C = 35 (~0.027" feed)
T = 1
N = 34
M = 0.075
Helix angle = 16
Diametral pitch 12
Change gears = 24 to 70


Index:
24 x 35 x 1 = 840 = 24 x 35
(35 x 34) - 1 = 1189 = 41 x 29


Feed:
25 x 32
67 x 33


More coming...

A. Or punch it into Ash Gear program with machine specifics.
B. Cut teeth
But my old floppys dont plug into my computer anymore.
Thanks for sharing


Sent from my iPhone using Tapatalk

Turbowerks said:

A. Or punch it into Ash Gear program with machine specifics.
B. Cut teeth
But my old floppys dont plug into my computer anymore.
Thanks for sharing


Sent from my iPhone using Tapatalk

Click to expand...

I really shouldn't do this, but...

I went and got a sample off of the above-mentioned company's website.

Here it is:

K = 15
C = 25.6 (this was not specified, but this is what was used)
T = 1
N = 55
M = 0.075
Helix angle = 20
Diametral pitch 12

Index:
30 x 42
67 x 70

Feed:
20 x 24
28 x 43

Feed error: 0.00000088

Here is one done very quickly using the same parameters except for the C constant :

K = 15
C = 27 (this gives a little more accuracy than the above sample)
T = 1
N = 55
M = 0.075
Helix angle = 20
Diametral pitch 12

Index:
15 x 27 x 1 = 405 405 x 2 = 810 = 27 x 30
(27 x 55) - 1 = 1484 1484 x 2 = 2968 = 56 x 53

Feed:
36 x 63
80 x 75

Feed error: 0.000000099

This has an extra zero of precision. In this case it is 8.88 times more accurate.

"But my old floppys dont plug into my computer anymore."

Get an external floppy-disc drive and plug it into a USB port.

This was taken from above:

Index:
15 x 27 x 1 = 405 405 x 2 = 810 = 27 x 30
(27 x 55) - 1 = 1484 1484 x 2 = 2968 = 56 x 53

Now this is one of the things that I learned:

All numbers have an implicit denominator of 1 unless they have an explicit denominator of another size.
In the above case the C constant of 27 is equal to 27/1.
27/1 happens to be equal to 54/2.
The above formula could be rewritten as:

15 x 54 x 1 = 810 = 27 x 30
(54 x 55) - 2 = 2968 = 56 x 53

This gave the same result using 54/2 as the above did using 27. But why would you want to do this? You wouldn't in this case.

It just shows that fractions can be used as C constants. At least rational fractions that consist of natural numbers (actually, fractions made up of any combination of integers, whole numbers, natural numbers or square roots of perfect squares will always be rational).

When using rational fractions, the numerator is used in place of the traditional *C constant* and the denominator replaces the *absolute 1 constant*.

David_M said:

This has an extra zero of precision. In this case it is 8.88 times more accurate.

Click to expand...

I'm not being critical, but, umm ... it doesn't matter. That's like worrying about whether you park within 10" or 11" of the garage wall. Makes no difference in the real world. 1 on the fourth place is more than good enough.

There's lots more causes for error than the change gear index ... like unwinding the helix in heat treat. And innacuracies in the machine itself. And whether or not it was hot out that day

Actually, you don't need Ash software either. A calculator can do it nicely.

Nice job though, I'd probably use your spreadsheet because I like to mess around but .... in fact, you can do this with pencil and paper pretty easily.

EmanuelGoldstein said:

I'm not being critical, but, umm ... it doesn't matter. That's like worrying about whether you park within 10" or 11" of the garage wall. Makes no difference in the real world. 1 on the fourth place is more than good enough.

There's lots more causes for error than the change gear index ... like unwinding the helix in heat treat. And innacuracies in the machine itself. And whether or not it was hot out that day

Actually, you don't need Ash software either. A calculator can do it nicely.

Nice job though, I'd probably use your spreadsheet because I like to mess around but .... in fact, you can do this with pencil and paper pretty easily.

Click to expand...

I know you have a huge knowledge about the gear business. I certainly respect your opinion.

My point is the formulas can be greatly improved.

It's like looking through a pinhole compared to 20/10 vision. Using a whole number for the C constant allows you to use only a smidgen of the possible gear sets where using a fraction allows access to all.

And it's not just about the accuracy. This also allows you to get acceptable results when the change-gear ration seems impossibly small. I'll post an example...

This one using the rational fraction 1333/55 is 520 times more accurate that the ash sample:

Index:
(15 x 1 x 1333) / 15 = 1333 = 31 x 43
((55 x 1333) - 55) / 15 = 4884 = 74 x 66

Feed:
28 x 63
71 x 59

But, like you say, after a certain point, it is meaningless.

Test to see how rational fraction C constants work with limited change gears:

Using 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80 change gears (21)

15 index const
0.075 feed const
20 degree ha
12 dp
~.025 feed rate

for:
55t 1537/55 worked
56t 125/4 worked
57t 95/3 worked
58t 779/26 worked
59t 1633/59 worked
60t 1007/36 worked

all with <= 0.0000x error

with no answers for whole number C constants

David_M said:

Test to see how rational fraction C constants work with limited change gears:

Using 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80 change gears (21)

Click to expand...

This part is cool. I can't tell you how many times I've worked up a set of change gears about six times, ... this'll do ! umm, nope, no 89 tooth gear. Okay, how about this ? nope, only have one 61 toother. Well, maybe this .....

Gets frustrating

Can you deal with, like, two 60's and such ? Frequently people will have duplicates of some sizes.

p.s. generally you wouldn't have much below 30 .... too small. And you try to have all the primes you can because otherwise you're fucked cutting a prime # teeth gear. Usually index, feed and diff gears are the same.

Can you do that trick where you cut a spur prime without the prime change gear, by setting up the index for a helical with one extra tooth, then backing it up with the lead ?

Yes, it allows you to input up to 7 dupes for each gear.

I have another program written for primes. I'll post an example.

30-90 change gears. 32/60 for the feed.

After thinking about it, this isn't what you are talking about is it?

David_M said:

After thinking about it, this isn't what you are talking about is it?

Click to expand...

I think possibly you show excessive decimal places, my eyes hurt

I didn't figure it out, but is that going to give me 127 teeth and a 0* helix ? If so, pretty good ! Common ordinary old change gears in that setup.

Except for one thing ... will only work on a 14-15 or D. Differential on all the other Barbers is really rare. Can you figure it non-differentially ?

Oh wait. Probably won't work on a D either. They don't have feed gears. Rats. On a G&E or similar should work but on a Barber we have a problem, Houston ...

I'm going to reduce all those long strings of decimal numbers at some point. It just helps me to debug right now.

Yes on the 127t with 0.00001 degree helix angle.

The G&Es use a different formula, but I have one for them.

I don't think the helical program would be good for prime spurs as is, but using a different method for a prime 127t without the aid of a differential:

Index constant: 24

Index gearing:
41 x 47
103 x 99

gives an error of 0.0055598 degrees using .05 thousandths feed. Just under a tenth of a thousandth per inch of gear thickness.
I believe this is a lead of 64,751" Any double checkers out there?

This is another thing that I learned

I know that some people do helical gears this way:

24 = index constant
69 = number of teeth to hob
36 = calculated C constant to give desired feed rate
1 = hob threads

24 x 36 x 1 = 864
(69 x 36) - 1 = 2483

Now, instead of playing around to find two composite numbers that will give factor pairs equal to available gears
(like this:
24 x 37 x 1 = 888 = 24 x37
(37 x 69) -1 = 2552 = 58 x 44 ), they divide 864 by 2483. Then use a *ratio to 4 gear converter*.

864/2483 = 0.3479661699556988

Picking from the results of the software, gets:

46 x 61
96 x 84

If you have the change gears and they fit the machine, they are perfectly good to use. The only problem is that the C constant needs to be corrected to the index change gears so that it can be used for calculating the feed gearing.

This program corrects the C constant:



With this, your C constant is corrected so that the Index gearing is now perfect (using the fractional method mentioned earlier). So, instead of using 36 (this would compound the feed error) you would use 35.974358974



p[SUB]n[/SUB] / 36 x 0.075 x sin ψ = 0.28350007

p[SUB]n[/SUB] / 35.974358974 x 0.075 x sin ψ = 0.28370214

0.28370214 - 0.28350007 = 0.000202 (this is the error caused by using the incorrect C constant)

0.000202 is 13 times worse than the suggested maximum error of 0.000015 found in the Barber-Colman manual.

This uses C in fraction form (1403/39) instead of the decimal approximation 35.974358974:

0.26179938779915 / ((1403 x 0.07500000 x 0.34202014332567) / 39) =
0.283702141870079046637697
0.283702213279678068410463 = (39 x 47) / (91 x 71)
Feed Error: 0.0000000714095990217727659
Feed Change-Gears:
39 x 47
91 x 71

David_M said:

After asking numerous questions myself, I think I have a couple of thoughts that might be worth sharing.


Formula for hobbing helical gears:


KCT
(CN) ± 1


K = machine index constant
C = C constant
T = number of threads on hob
N = number of teeth on gear
1 = absolute constant
M = feed constant


Sample:


K = 24
C = 35 (~0.027" feed)
T = 1
N = 34
M = 0.075
Helix angle = 16
Diametral pitch 12
Change gears = 24 to 70


Index:
24 x 35 x 1 = 840 = 24 x 35
(35 x 34) - 1 = 1189 = 41 x 29


Feed:
25 x 32
67 x 33


More coming...

Click to expand...

How can i diatuinguish the c constant