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Gears hobbed with ISO bolts

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  • Gears hobbed with ISO bolts

    It appears that Robint has taken his free-wheeling bolt hobs and gone home. What a pity.

    The mildly interesting part of that thread (to me at least) was the idea of using a common ISO bolt to generate gear teeth. Since the sides of an ISO thread are flat, the flanks on the teeth are involutes and should have all their advantages - conjugate action as the teeth roll on each other, constant pressure angle, ability to tolerate slight changes in mounting, etc. The distance from the tip of an ISO thread to its pitch line is 3/5 of its height, so a gear tooth generated with a thread should have a bit of clearance at the root (where the thread tip ends up), so that works too.

    Looking deeper, the dimensions of a gear tooth generated with an ISO bolt would be:

    Pb = bolt pitch (Robint used a M24-3.0 bolt when illustrating his passion here, the pitch is 3 mm)

    The pressure angle of an ISO-bolt generated gear tooth would be 30°. This large pressure angle makes the gears less efficient in transmitting force and torque, increases (by about 46% over a 20° pressure angle) the radial forces that push the gears apart and do no work transmitting motion or torque, but on the upside it allows fewer teeth on a gear before undercutting takes place (minimum of 8 teeth with a pressure angle of 30°, minimum of 17 teeth with a 20° pressure angle).

    N = Number of teeth (Robint used 28 teeth in a couple of now-deleted example photos, we'll use it here too)

    Dp = pitch diameter = diameter of the pitch circle = N * m where m = the module of the gear (1 / diametral pitch)

    Circumference of pitch circle = N * Pb = Dp * pi, so the module of Robint's gear is
    m = Pb / pi = (3 mm)/pi = 0.955 mm

    Which gives the pitch diameter as N * Pb / pi = 26.74 mm

    The addendum (distance from the pitch circle to the tip of the tooth) of a gear generated with an ISO bolt is
    a = (1/4) * sqrt(3)/2 * Pb = pi * sqrt(3) m /8 = 0.68*m,
    which is 32% shorter than the addendum of a standard AGMA gear tooth (1.0*m). The addendum diameter, the size of the blank we need to start the generation process, is
    Dp + 2*a = [N/pi + sqrt(3)/4]*Pb = 28.04 mm in our example.

    The dedendum (the distance from the pitch circle to the root of the tooth) of a gear tooth generated with an ISO bolt is
    d = (3/8) * sqrt(3)/2 * Pb = 3 * pi * sqrt(3)/16 * m = 1.02*m
    or 18.4% shorter than the dedendum of a standard AGMA gear tooth (1.25*m).

    The height of an ISO-bolt generated tooth is
    a + d = 5 * pi * sqrt(3)/16 * m
    or 24.4% shorter than a standard AGMA gear tooth (2.25*m)

    With all of this in hand, I drew a perfect ISO tooth form and the proper sized blank and rolled them together on the pitch line/circle, deleting the intersection on the blank, just like hobbing a gear, to generate the space between the teeth. An extrusion and circular pattern later, I had the gear below (the facets are due to rotations with fairly coarse 5° steps - I was interested in seeing what would happen, but not overly obsessed):


    Click image for larger version  Name:	Gear1.JPG Views:	10 Size:	7.7 KB ID:	1965984


    Click image for larger version  Name:	Gear2.JPG Views:	10 Size:	19.0 KB ID:	1965985

    So we have cute little (seriously little) involute gear teeth cut into this blank (the gear is 28 mm is diameter, about 1.10"). Two such gears appear to mesh along the pitch circle as they should (the centers of these two identical gears are one pitch diameter apart), and may be vey happy playing with other similar (same bolt pitch) gears of the same parentage.

    Click image for larger version  Name:	Gear3.JPG Views:	10 Size:	24.1 KB ID:	1965986

    The geometry of these gear teeth certainly precludes them from ever meshing with a standard AGMA gear of any common pressure angle. Even comparing to a 28T, 26.6 DP AGMA 30° gear (same pitch diameter as the gear above and no, this doesn’t exist in any catalog but you can define it and draw it, it’s the green one shown below) the flanks seem to match well but the tips and roots would prevent proper meshing.


    Click image for larger version  Name:	Gear4.JPG Views:	10 Size:	45.2 KB ID:	1965987


    The geometry seems to work out, and some might be tempted to generate gears for themselves in this way but executing this idea in actual material would, I think, prove difficult. First, you’d have to find or make a perfect ISO bolt, no small task. Bolts are made of steel that is chosen and processed to make good bolts, not cutting tools, so I’d expect using bolts would be good only for soft materials such as plastics, maybe aluminum. Bolts do not come in a large range of thread pitches, so most of the teeth are going to be very small (think small modules or large diametral pitches), requiring both very precise machining and mounting.
    Last edited by DrMike; 10-15-2021, 03:19 PM.
    SE MI, USA

  • #2
    I wonder, what would happen if you used a BA thread profile? (47.5 degree flank angle) in order to tighten up the pressure angle of the resulting gear. In documenting his build of the Antikythera mechanism, Chris (AKA Clickspring) points out that the Greeks used triangular gear teeth, but they got away with it because they were transmitting almost zero power. Hence efficiency didn't enter into the picture so much as ease of manufacture.
    25 miles north of Buffalo NY, USA

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    • #3
      Originally posted by nickel-city-fab View Post
      I wonder, what would happen if you used a BA thread profile?
      A more interesting test would be to repeat the drawing using an Acme thread, say an 11 tpi.

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      • #4
        Robint appears to be very sensitive to criticism. He briefly had a thread going on H-M, but it appears to be gone and his membership deleted. Oddly enough he still has one going on PM
        https://www.practicalmachinist.com/v...-gears-395467/

        Given the general tenor on PM, it might be best to archive it before he takes his ball and goes home.
        Last edited by MrWhoopee; 10-15-2021, 02:20 PM.
        It's all mind over matter.
        If you don't mind, it don't matter.

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        • #5
          There is efficiency and there is rubbing... With and involute gear profile - the teeth roll through one another and there shouldn't be any actual rubbing.. Just point contact. Non involute profiles will wear faster. (if I understand it right.)

          Comment


          • #6
            Originally posted by MrWhoopee View Post
            Robint appears to be very sensitive to criticism. He briefly had a thread going on H-M, but it appears to be gone. Oddly enough he still has one going on PM
            https://www.practicalmachinist.com/v...-gears-395467/

            Given the general tenor on PM, it might be best to archive it before he takes his ball and goes home.
            The empty barrel makes the most noise. The over-inflated ego is the hardest to defend -- there is more attack surface.
            25 miles north of Buffalo NY, USA

            Comment


            • #7
              Both BA and Acme thread profiles are symmetric about their pitch lines. The addendum and dedendum of the resulting gears would be the same, and would leave no room for the necessary clearance at the root of the tooth. The ISO profile here is longer from pitch line to tip than from pitch line to root, and automatically introduces the root clearance in a similar way as a AGMA form tool does.

              To make it work we'd have to have a non-standard BA or Acme thread, which kind of defeats the purpose. Cutting it deeper with a standard thread would only make the situation worse since we would lose the relationships between pitch circle, tooth number, involute profile, etc.
              SE MI, USA

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              • #8
                Originally posted by skunkworks View Post
                There is efficiency and there is rubbing... With and involute gear profile - the teeth roll through one another and there shouldn't be any actual rubbing.. Just point contact. Non involute profiles will wear faster. (if I understand it right.)
                You are correct... from initial engagement through full contact to departure, the faces of properly formed and mounted involute gears roll on each other without sliding. All of the friction that might be is present is at the axle, not between the teeth.

                Note the caveat - properly formed and mounted involute gears. There is a long history of failures, frustration and study trying to achieve that goal.
                SE MI, USA

                Comment


                • #9
                  I went looking for this photo earlier this morning here but it was gone, but I found it still posted at PM.

                  This is Robint's gear. Compare it to the CAD drawing above of what it was supposed to look like, if his methods actually worked.

                  The only similarities I can see is that there are some tooth-like things on it. They are certainly not involute teeth, even at this resolution. Actually, it was this photo that got me to look at exactly what these teeth could be if they were cut correctly.

                  Click image for larger version  Name:	Robins gear.jpg Views:	0 Size:	88.3 KB ID:	1966030
                  Last edited by DrMike; 10-15-2021, 03:14 PM.
                  SE MI, USA

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                  • #10
                    Originally posted by DrMike View Post

                    You are correct... from initial engagement through full contact to departure, the faces of properly formed and mounted involute gears roll on each other without sliding. All of the friction that might be is present is at the axle, not between the teeth.

                    Note the caveat - properly formed and mounted involute gears. There is a long history of failures, frustration and study trying to achieve that goal.
                    If I understand correctly, one of the most efficient forms ever, was invented by clockmakers in using the "lantern" style of pinions against cycloidal teeth. No real power transfer, but great efficiency in terms of low friction.
                    25 miles north of Buffalo NY, USA

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                    • #11
                      I've been casually following along with the concept of free-hobbing. I have only the most basic familiarity with gear cutting, but two things occur to me.

                      1. It might be possible to single-point a cutter using a tool with a profile different from the standard 60º to produce a gear that is compatible with standard 20° PA gears.

                      2. Lacking indexing capability, it should be possible to gash the blank using a bolt-circle calculator to generate the x,y coordinates.
                      https://littlemachineshop.com/mobile/bolt_circle.php
                      It's all mind over matter.
                      If you don't mind, it don't matter.

                      Comment


                      • #12
                        .... you’d have to find or make a perfect ISO bolt, no small task. Bolts are made of steel that....
                        No, but a thread tap is & does.


                        Footnote: DrMike, i find the software and brain you are using intriguing; I might PM you later with a gear question unrelated to this thread
                        Last edited by Dr. Rob; 10-15-2021, 02:56 PM.

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                        • #13
                          Someone mentioned an ACME thread. That is very close to the form for a hob, and seems to be a much better choice if limiting to "already made" sources of a hob. Of course, an actual hob form could be made for the purpose.
                          2730

                          Keep eye on ball.
                          Hashim Khan

                          Everything not impossible is compulsory

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                          • #14
                            Originally posted by nickel-city-fab View Post

                            If I understand correctly, one of the most efficient forms ever, was invented by clockmakers in using the "lantern" style of pinions against cycloidal teeth. No real power transfer, but great efficiency in terms of low friction.
                            don't think I buy that. There is sliding so friction vs an involute. A lantern is basically a completely undercut epicycliod gear....they were used because they were cheap to make. Better clocks used cut and lapped/polished pinions. The subject is very completely covered in Davis's Gears for Small Mechanism which is a fantastic reference for watch and instrument wheels/gears. I could go read Davis and be more sure of the matter, but frankly at the end of the work week, the whole thing is so bloody dull I doubt I'd make it to dinner
                            Last edited by Mcgyver; 10-15-2021, 08:54 PM.
                            in Toronto Ontario - where are you?

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                            • #15
                              Thanks for the heads-up and the book reference. I'll have to look it up. Totally *not* an expert on that stuff.

                              Originally posted by Mcgyver View Post

                              don't think I buy that. There is sliding so friction vs an involute. A lantern is basically a completely undercut epicycliod gear....they were used because they were cheap to make. Better clocks used cut and lapped/polished pinions. The subject is very completely covered in Davis's Gears for Small Mechanism which is a fantastic reference for watch and instrument wheels/gears. I could go read Davis and be more sure of the matter, but frankly at the end of the work week, the whole thing is so bloody dull I doubt I'd make to dinner
                              25 miles north of Buffalo NY, USA

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