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23 comments

  • Tim Heeney

    Very logical and useful. Why not add this into the 'New Feature Requests'  and any other enhanced ability / facility that would benefit DSM.

    There it will be considered by the 'powers that be' and voted by the user community.

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  • Me Here

     Will do. Tim, I didn't know such a thing existed.

     

    Update: Done.

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  • Jacant

    Hi Buk

    This any good? You are welcome to the file.

    https://we.tl/t-Rg46HmWSFW 

     

     

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  • Me Here

    jacant,

    Yes. That looks to be excellent:

    Can you precis your method? ( If it has changed at all.)

    Your next challenge, should you choose to accept it, is to turn that into a spiral bevel with a 100mm diameter cutter at 35°.

    (Which has so far defeated my attempts.)

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  • Jacant

    I was not happy with my first attempt. The 100T gear was as I made the 30T. Nothing seemed to line up. You say you contacted 'Ovinta' about the 100T calculator? The gap between the teeth was too deep so I started a new file just to draw the 100T, this time I put a 3 point circle at 0.75mm between the teeth. Everything looked fine. So I copied and pasted the 30T gear into the new drawing. For some reason the axis points did not line up. I moved the 30T gear from it's position to be inline with the 0,0,15 point. If you look closely by selecting the 30T gear to 'Move' there are two axis points one slightly to the left. Not to sure what this means.

    How far apart are the two surfaces of the 100T gear

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  • Jacant

    Solved I think. The 30T base circle was in the wrong place.

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  • Me Here

    Interesting. According to measure, in one axis the difference is 0.0006mm or 1/6th of a micron:

    Notice the annotation on the scale line bottom right.

    I think that is what the engineers would call "within tolorance" :)

    However, in the other axis, the difference is almost 4mm, which would be more of a concern:

    With respect to the length/depth of the involute produced by the otvitna formula, but I am not yet sure how to correct it (formally), yet. I've been concentrating on finding a consistant method of modelling them in DSM for now.) I think I can diassemble the js code at the me-bac site -- which seems to produce the most accurate profiles -- and work it out from that. I hope.(Update: turns out not. He does his calculations on his server, not in the browser.)

    My instinct says that your adjustment is still leaving too much tip clearance -- Gleason's use 0.188m where M is the module, so 0.188mm in this case.

    You have roughly 3 times that at the root of the 100T and twice that in the 30T, which would make the teeth much weaker than they should be forcing an increase in the facewidth to handle a given load:

    But as you can see,  the adjustment to the root is not a one-size-fits-all affair, but rather needs to take in the size and angle of the reference cone  plus the module.

    Also, Gleason machine the tip (addendum) cone parallel to the root cone of the mating gear to minimise the risk of interference at the root end of the teeth in case of the manufacturing tolorances for the alignment adding up the wrong way. But that's a detail that doesn't affect the strenght calculation/stress analysis, so I am ignoring it until I get to have something made...if that ever comes to pass.

    A final (AFAIK) wrinkle is that Gleason would profile shift the 30T pinion positive and the 100T gear negative so as to sacrifice a little tooth strenght in the gear for some extra in the pinion. The pinions are the limiting factor strength wise and usually fail first. The amount of shift they would use for any given pairing is apparently prorietary as part of the "Gleason method".

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  • Me Here

    jacant:"You say you contacted 'Ovinta' about the 100T calculator?"

    Yes. I posted his response email in the other thread. He basically glossed over it and I didn't feel able to press him on it.

    In his code, you can see he calculates umax, but always sets umin to 0:

    	document.forms['calc'].umin.value = "0";		
    document.forms['calc'].umax.value = Math.sqrt( fTipRadius * fTipRadius / fBaseRadius / fBaseRadius - 1).toFixed(4); // sqrt( R^2/r^2 - 1)
    document.forms['calc'].ustep.value = "10";

    Which means his involute always starts at the base circle, instead of the dedendum circle.

    Later on in the code he calculates the "beginning and end" of the involute, and uses it to calculate the base toothe thickness:

    // distance between beginning and end of the involute curve
    var d = Math.sqrt( ( x1 - x2 ) * ( x1 - x2 ) + ( y1 - y2 ) * ( y1 - y2 ) );
    var cosx = (fBaseRadius * fBaseRadius + fTipRadius * fTipRadius - d * d) / 2 / fBaseRadius / fTipRadius;


    var basetooththickness = 2 * fTopThicknessDegrees + 2 * Math.acos(cosx) * 180 / Math.PI;
    document.forms['calc'].basetooththickness.value = basetooththickness.toFixed( 4 );

    But I don't know how to verify that calculation yet, or how to use it to set umin correctly.

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  • Me Here

    I think I've found what I looking for with regard to the umin value.

    According to the gear help page at the me-bac site ( http://www.me-bac.com/index.php?task=gear_help ) the involute curve starts not at the base circle, nor the dedendum circle, but at something they call the" Involute tooth limit diameter".

    And -- holy of holies -- they give the formula for calculating that as:

    Where:

    • α = pressure angle (usually 20°)
    • l  =
    • l<sub>0</sub>
    • y =
    • r = undefined! :(

    All of which is about as helpful as a chocolate teapot.

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  • Jacant

    The problem with trying to put a curve on each tooth is that one side of the tooth will be different from the other side . So trying to Combine them is nigh impossible. However I created a few teeth managed to Combine them and Filled all of the extra faces. I then Cut the teeth in the 'gulley' to be left with one tooth. Patterned that and Combined as in the image. It is a 30° curve however. I think I may have an even better method. With a 35° curve this time.

     

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  • Me Here

    From this limited viewpoint, that looks very clean.

    I started to look at cutting the valleys into a correctly proportioned blank by rotating a cutter through, and then replicating the cut. But when looking around for data regarding the cutting tools I happened on this simulation:

    https://www.youtube.com/watch?v=aulqG3Ioxxo 

    It was only then that I realised that in addition to the both the blank and the cutter rotating around their own axis, the cutter axis is also slowly rotating, and the cutter is advancing.

    I've since spent hours watching videos of the operation in action trying to figure out the motions involved, trouble is, they always insist on moving the camera around, and almost never show the operation from start to finish.

    There is also this simulation video which operates slightly differently in that it indexes the workpiece, and cuts each valley in a single pass that a very complex set of motions of the cutter.

    https://www.youtube.com/watch?v=UddUpq5_lJo 

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  • Jacant

    This is a very clean model with a 35° curve. However it will not work. There is 'Body Interference' on every tooth. It is the same for the 30° curve. 

     

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  • Jacant

    The 'involute' profiles from DSM, Freecad and Me-Bac look the same to me.

    I will try  the Me-Bac profile with a minus rack shift coefficient on the above model.

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  • Me Here

    jacant,

    the only problem with the DSM involute (assuming you are still basing it upon the otvinta formula) is the start = 0 value. This leaves us guessing where to draw the root. Whether that is the cause of the body interference above I am unsure, I can't tell from the viewpoint in the image above where on the teeth the interference is occuring.

    This is a (course) me-bac 30T x 1m with all the circles defined and 1 side of the otvinta involute in pink. The blue circle is the Involute tooth limit as calculated by the me-bac generator, and root radii are the DIN std 0.38M:

    Zooming in, you can see that beside that the otvinta involute is displaced radially (simple to correct by rotation once the gear is finished), the starting point is the wrong.

    The involute part of the me-bac profile stops at the blue circle, where the otvinta continues down to the green base circle. With the 30t, this discrepancy is minimal, but once you get to larger gears, like the 100Tx1, it is very different.

    Here the radial displacement is much less (more teeth smaller displacement) but the green base circle is now well inside the black dedendum circle, and far inside the blue involute limit circle:

    I'm getting the size of the limit circle from the me-bac site, but as I explained above, athough they give a formula on their help page, I am unable to interpret some of the variables. I did send them an email asking for clarification a few days ago, but I have not had a reply.

    The other thing to note about the me-back profile, is that it is not generated using the involute formula, but rather by the simulation of the action of a rack cutter. (I was about to explain that, but I guess you already know what that means.) The rack teeth have straight sides, and it is the sucessive passes of the cutter at different angles that results in the involute curve. The positions of the rack tooth for each of the passes are shownin grey in this image from the me-bac site:

    The quality setting (course, medium & fine) just controls how many and how close to each other the passes are made. This iterative pass process is the reason the me-bac profiles are made of a series of straight lines rather than a spline. (I think FreeCAD gear module does it the same way. It is the reference method of defining a gear profile.)

    The upshot of all this is that it dawned on me what the weird movements of the cutting tools and workpieces in those videos I linked were. The cutting tools are do not have an involute profile, they have straight sides, and it is the iterative passes at slightly different angles that forms the involute surfaces of the teeth.

    Once that realisation had dawned, I made some progress myself. This is wrong in several ways, but it is accurately wrong :) and the method used to construct it worked:

    Now I'm just waiting until my brain is awake before starting over, hopefully without making the errors, and constructing a mating pair.

     

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  • Jacant

    the only problem with the DSM involute (assuming you are still basing it upon the otvinta formula) is the start = 0 value.

    Once you have created the involute from the equation, select the curve and the equation tool again. You will see that the start point is not at 0

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  • Me Here

    I really doubted this until I tried it; but you are right.

    However,that change is a really, really  miniscule amount, not near enough to correct the problem; and it has nothing whatever to do with the formula.

    I suspect that it is simply a rounding error that comes from reverse engineering the curve you drew to extract the variables values it thinks you used. That's a guess, but I think a good one.

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  • Jacant

    Sorted. No interference.

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  • Me Here

    Nice!

    Did it just need the profile shift?

    (And how complicated is your method?)

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  • Jacant

    Besides the profile shift of - 0.1. I created a 'Cutter' instead of a tooth profile for the pinion, as the tooth profiles would not line up correctly with the create pattern. 

    Create two lines in 3D as shown, use them to create a sketch plane.

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  • Jacant

    Cutter profile

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  • Me Here

    jacant,

    That looks to be a very nice (clean, relatively simple) way of producing these.

    However, what you've actually produced is a Zerol bevel gear. Ie. A special case of the spiral bevel gear, with a mean spiral angle of 0° and a cutter diameter of a gnat's under 20mm.

    The following diagram (from https://khkgears.net/new/gear_knowledge/gear_technical_reference/calculation_gear_dimensions.html Section starting "(3) Gleason Spiral Bevel Gears" ) shows the where and how of the 35° spiral angle:

    Beta-m is the mean spiral angle measured at the centre of the facewidth and from the centreline of the gear, in a plane tangential to the reference cone.

    I need to produce and test Zerol gears also, and if I can achieve the required tooth strength in the available space, then they are preferable to SBGs, as they produce no axial thrust, which simplifies the bearing arrangment considerably.

    I believe I've now cracked the generation of SBGs. I have created one pair.

    I need to a) make sure I can reproduce them consistently; b) annotate the procedure and try to simplify the steps; c) generate a gif of the meshing with body interference enabled to ensure they don't interfer anywhere in the transition from one tooth to the next.

    Hopefully, I find time overnight/tommorrow and be ready to describe the method then.

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  • Jacant

    Sorry, I got confused when you said you wanted a 35° angle, whilst looking at this image.

    Forgot to mention, both gears were produced using a 'Cutter'. The 'Blank' was created from the section of one tooth.

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  • Me Here

    You've nothing to be sorry for! You replicated that image pretty damn precisely :)

    I did label that image "Or sometime curving, but not angling (zerol):", but looking back, I could have made it clearer.

     

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