Is this gear hob math correct?
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  1. #1
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    Default Is this gear hob math correct?

    Index constant: 24
    Feed constant: 0.075
    Number of teeth: 37
    Normal diametral pitch: 20
    RH helix
    RH hob; 1 thread
    Work TC
    C-constant: 25
    Helix angle: 15.999999977526763773037108877645


    Index gearing
    25 x 24 x 1 = 600; 3 x 600 = 1800 with a factor pair of (40 x 45)
    (25 x 37) - 1 = 924; 3 x 924 = 2772 with a factor pair of (63 x 44)


    Feed gearing
    0.15707963267948966192313216916398 / (25 x 0.075 x 0.27563735543996162104130573493773) =
    0.30393487109905020352781546811398
    0.30393487109905020352781546811398 = (32 x 49) / (77 x 67)

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    Hmm. Idunno offhand.
    Are you familiar with the Meshingwithgears.com forum? It is pretty good for specialized gearhead questions such as this.

    .

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    I think you need a little more precision.

    Good luck with this. Let us know how it turns out.

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    Quote Originally Posted by Yan Wo View Post
    I think you need a little more precision.

    Good luck with this. Let us know how it turns out.
    Thank you! I'll see what I can do.

    I always catch grief about excessive digits. That's what the Window's calculator outputs (and I am sticking with it)

    One of my points is:

    sin0-1(((normal cp / ((driver x driver) / (driven x driven))) / (c const x feed const)) = the theoretical helix angle produced by the feed gearing. I happen to believe this shows the error in a way that is more comprehensible than the present method. Maybe I'll show both ways (this is in software).

    e.g., input 16o and the output is 15.9999999o instead of showing an error of 0.0000345

    In my first post I went back and changed 16 degrees to what is shown to show that the error would be zero (something that wouldn't be seen too often).

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    I'm probably blind but where's the feedrate in all of this ? The feed constant is not the same as the feedrate (which you need, or the slide won't move ... ) ? You need to be able to change it, as higher helix angles need lower feedrates.

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    Quote Originally Posted by EmanuelGoldstein View Post
    I'm probably blind but where's the feedrate in all of this ? The feed constant is not the same as the feedrate (which you need, or the slide won't move ... ) ? You need to be able to change it, as higher helix angles need lower feedrates.
    Hey, EG. I hope all is well.

    It's in the c-const. Around 0.025" (rubbing territory).

    I posted this partially because people say that the feed gearing can never work out perfectly. In this case, it does (at least to 32 digits).

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    Quote Originally Posted by David_M View Post
    It's in the c-const. Around 0.025" (rubbing territory).

    I posted this partially because people say that the feed gearing can never work out perfectly. In this case, it does (at least to 32 digits).
    Have to say, I'm a little confused.

    Machine constants are, well, constant. Depends on the machine and model and doesn't change. Index constant is, with shafts at 1:1, how many turns of the hob spindle to make one turn of the work table. And the feed constant is, with 1:1 gearing, how many turns of the input shaft to equal x number of inches of slide travel. I guess in Europe it's in millimetres

    So the feed constant is set by the machine. Nothing you can do about it. To figure the feed gears for a non-diff helical you have to use the feedrate you want and factor in the feed constant to figure the proper feed gears.

    So I'm confused about what you are doing.

    Around 0.025" (rubbing territory).
    Not necessarily ... depends on the helix angle. The feed is always along the slide travel, but that's parallel to the workpiece axis. Helical teeth are at an angle to that. So .025" feed could be much more along the path of the teeth, if you get what I mean. With a really high helix angle, .025 could be double or triple what you think it is. With a 67* helix, I had the feed set as low as I could - maybe about .005"/rev ? But it was still taking great big chunks out of the part, sideways. Big for fine pitch, anyhow, this was a #3.

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    Quote Originally Posted by EmanuelGoldstein View Post
    Have to say, I'm a little confused.

    Machine constants are, well, constant.
    Edit:
    Okay, you said machine constant. The C constant is a programming constant put together from variables.

    Quoting from the book,

    "The C constant can be defined as the number of revolutions of the work spindle while the hob is fed one axial pitch of the work. It is a constant whose primary purpose is to establish a relationship between the index and feed change gears so that the correct helix angle will be cut. Mathematically it can be shown in the following equation."

    C = Normal cp / Feed rate x sin φ

    You can see where the feed rate is incorporated in the C constant.

    You know this stuff WAY better than me.

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    Are you sure you want to make a 37 teeth gear?

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    Quote Originally Posted by David_M View Post
    Okay, you said machine constant. The C constant is a programming constant put together from variables.

    Quoting from the book,
    That's the Barber-Colman manual, yes ? I think they're the only ones who do it this way. I've never understood how they can call something a "constant" when it includes a variable. I just call it the feedrate ...

    In normal English, a constant is what's built into the machine.

    You know this stuff WAY better than me.
    Not on this one, I hate doing this. It's a last last last resort, when you can't figure any other way. No fun, in all caps.

    But better than not being able to do it at all

    If your software can figure different C numbers easily, that'd be useful. It's kind of a pain in the rear to do it manually. You might even consider a calculation from linear feed to up-the-tooth feed ? That's what we really care about. (Better be up the tooth because if you try climb cutting doing this, you'll be crying over a broken hob after the very first part.)

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    Quote Originally Posted by EmanuelGoldstein View Post
    That's the Barber-Colman manual, yes ? I think they're the only ones who do it this way.
    I believe it is any machine that uses the minus 1 tooth / plus 1 tooth method when calculating the index gears.

    You might even consider a calculation from linear feed to up-the-tooth feed ? That's what we really care about. (Better be up the tooth because if you try climb cutting doing this, you'll be crying over a broken hob after the very first part.)
    I think I know what you mean. Write it, so you input the number of gashes in the hob (and on second thought, the hob diameter), then the program calculates the feed per hob tooth based on anything that affects it like the helix angle, number of gear teeth, et al. Then you always get 0.003" per hob tooth if that is what you specified.

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    Quote Originally Posted by David_M View Post
    Write it, so you input the number of gashes in the hob, then the program calculates the feed per hob tooth based on anything that affects it like the helix angle, number of gear teeth, et al. Then you always get 0.003" per hob tooth if that is what you want.
    I just meant the feedrate along the axis of the tooth (or however you want to put it.) You're never going to get a feedrate like a mill because hobbing is different from milling ... even with a generally-accepted feedrate of x number, as the hob enters the tooth the chip thickness is really low, then in the middle it's large, then again on exit it drops back to nothing. So chip thickness even with the same feedrate is all over the map.

    What I was thinking tho is, if your feedrate (slide movement) is, for example, .040/rev, on a spur gear that really is .040/rev. But on a helical, it will be more because the tooth is at an angle so the actual cut will be longer. One should recalculate the feedrate to get the true feedrate along the tooth, but I bet most of us just fake it. If it were quick and easy to get the feedrate along the tooth that you want, that could be nice.

    I think it is any machine that uses the minus 1 tooth / plus 1 tooth method when calculating the index gears.
    Method is the same but no one else I can think of calls it a 'constant'. But the real use for that is not cutting prime teeth - it's cutting helicals without a differential. Or cutting anything on a Cleveland. Beefy bastards those are, but what a pain in the neck to set up !

    At least that's true on older machines, not sure if anyone does that anymore tho, with CNC you just type in a number

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    Quote Originally Posted by EmanuelGoldstein View Post
    ...because hobbing is different from milling ...
    Hobbing is a neat process until the helix angle gets high like your 67-degree worms or these High Helix Angle Crashing Hobbs - Is feed speed my issue? (practicalmachinist.com). Then it can turn into a gnawing, chiseling, clawing operation.

    I looked in my G&E book, and C is referred to as C and not C constant, just as you thought.


    Edit: To be fair, Jason in the link did a great job under challenging circumstances.
    Last edited by David_M; 06-27-2021 at 03:33 AM.

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    Quote Originally Posted by EmanuelGoldstein View Post
    If software can figure different C numbers easily



    Above is using 30 to 80 change gears. The left/right buttons gives access to dozens if not hundreds of different gear combinations.

    I worked for Union Camp/International Paper in their bag machine shop. Our shop cut all the gears for all of their printing presses located nation wide with many locations. Besides all of the bought printing presses, we built numerous ones ourselves.

    The first thing that I did when I went to work there was to write the gear-hob software. Griffin gear in Roebuck, SC, was used to check leads to make sure the program worked correctly. We cut around 300 to 600 helical gears a year. Several thousand in the time, I was there with no issues. Every index set was always exact.
    Last edited by David_M; 06-28-2021 at 05:33 AM.


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