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gear placement and way-basic layout question

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  • gear placement and way-basic layout question

    If I were going to place two spur gears on a plate such that they meshed, would the distance between their centers simply be the sum of half the gears' pitch diameters? That's what I gather from Machinery's Handbook.


    gear A is a 64 tooth gear having a diametral pitch of 16 meshes with gear B, a 20 tooth gear.

    Pitch Diameter of A = 64/16 = 4
    Pitch Diameter of B = 20/16 = 1.25

    So I would place their centers (4+1.25)/2 = 5.25/2 = 2.625" apart.

    And given the clearance is .157/diametral pitch = .0098, the centers need to be correct to within a a shade under .0049.

    Ok, assuming that's correct, I have a metal plate all blued up. I centerpunch a divot for the first shaft. What's the right way to locate the other shaft, assuming it has to be at some odd angle from the first (not purely vertical or horizontal?

    I'd be tempted to clamp the gears to the plate, meshed, with the teeth spaced by a few (?) thicknesses of aluminum foil, and use a transfer punch to mark the center of each gear.

  • #2
    I can't confirm that your math (formulas) are correct but assuming they are... set your compass at the distance u want and scribe a circle around the center point of the first gear. you should be able to center punch anywhere in the circle that u want your gear to be.

    I spent most of my money on women and booze, the rest I just wasted.


    • #3
      2 5/8" centre distance

      2.625" centre distance is correct. Neglect "clearance" for this set-up.

      For any centre-distance just centre-punch the first point, accurately (off a good rule will do) set a pair of dividers to 2.625" (2 5/8") apart, put one leg in the centre-punch indent and just swing an arc or circle of 2 5/8" radius with the dividers. Any point on the arc is the correct centre distance.

      If the gears were manufactured correctly, "clearance" and back-lash were allowed for and incorporated into the manufacture of the gears.

      "Gears" are not all that simple but they sure aren't real difficult either. They are often "talked up" to be more difficult than they are or need to be.

      Get the fundamentals right and you will be on your way.


      • #4
        Originally posted by tony ennis
        So I would place their centers (4+1.25)/2 = 5.25/2 = 2.625" apart.

        Ok, assuming that's correct, I have a metal plate all blued up. I centerpunch a divot for the first shaft. What's the right way to locate the other shaft, assuming it has to be at some odd angle from the first (not purely vertical or horizontal?
        If you actually know what angle the other gear is, you can use trig to figure the X and Y movements for which 2.625" is the hypotenuse.
        "People will occasionally stumble over the truth, but most of the time they will pick themselves up and carry on" : Winston Churchill


        • #5
          I suppose I should clarify a concern. How does one set calipers - or a compass - accurate to the thousandth? Regarding the clearance, am I not correct in that if the 2nd shaft is too close to the first by .005" the gears could crash?

          My rather artificial requirement of the 2nd shaft not being in the 1st shaft's horizontal or vertical was to encourage a general purpose solution - like using a compass instead of a surface plate. Of course TGTool is correct in that I will probably know one of the other sides of the triangle and as such the surface plate is also a general solution.

          Maybe my posts will be better if I get drunk first.


          • #6
            You should be able to set dividers accurately, by adjusting a micrometer or dial caliper to the required dimension, then carefully set the dividers to that gap.


            • #7
              Its a worry!!

              OK - I will assume that this is not a "try on".

              The end result will depend on three main items:
              - that the gears are correctly manufactured;
              - that the spindles on which the gears rotate are a good neat running fit in the gears; and
              - the centre distance.

              If the first two are correct, it only leaves the third (last).

              Make two "Tool-makers buttons" each the same size but not necessarily the same size/s as the spindles that the gears are to run on. Set the first to the position of the first gear. Accurately (as you can - use a micrometer) set the second so that measurement over the buttons is:
              = ((centre distance) + ((sum of the diameters of the buttons)/2))

              The positions of the centres is now set accurately.

              Put the plate with the buttons on the mill table and clamp it.

              On each button in turn:
              - use an accurate Test Dial Indicator (TDI) in your mill chuck and centre the mill spindle over the button;
              - lock the table "X" and "Y" slides;
              - remove the button;
              - use a spotting or centre drill followed by a drill, say 1/32" under-size and drill the plate;
              - remove the chuck and install your boring-head;
              - bore the hole either exactly to size or bore it say 0.010" under-size, remove the boring-head, set an accurately sized or set reamer to size and ream to size.

              There are other ways of doing it but the "jib-boring" approach has stood the test of time.

              DRO's with or without slip guages are only two others of many.

              If you want less accuracy or difficulty, move "down" from the "jig-borer" method.

              The ultimate gears will have been made by a specialist gear-maker - hobbing/shaving/shaping etc. followed by high-tech metrology (not cheap).

              It really depends on how far you want to go which may well be well in excess of how far you need to go.

              A good read of "Machinery's Hand-book" and some good books on the subject might well be a minimum pre-requisite to even beginning the job - or worrying unduly.

              I suggest that instead of theorising and worrying that you have a close look at the gears in your gear train in your lathe as well a gears in your lathe and mill geared heads - and even an outo-motive gear-box etc.

              A lot will depend on the application.


              • #8
                Originally posted by Robin R
                You should be able to set dividers accurately, by adjusting a micrometer or dial caliper to the required dimension, then carefully set the dividers to that gap.
                I beg to differ. Been there. Tried that. It is not that easy.

                Divider points (and I have a Starrett so don't tell me my dividers are not high enough quality) are approximately cone shaped. If you are working with a small distance and put them between the jaws of a mike or caliper the distance between the points will be an unknown distance smaller than the distance set on the mike or caliper. Only when the angle between the divider's legs is greater than the cone angle of the points will the actual points rest on the faces of the mike or caliper.

                And even then, it will be somewhat difficult to set the dividers to the correct distance. The slightest amount of pressure will easily close the dividers a bit while checking them this way so a very light touch is needed.

                I find the best way is to use magnifiers. At least 10X, preferably 15X or evan 20X. I like to see the points sitting centered on the edges of the mike or caliper jaws. But you must shift your viewing position to be directly over each point as you judge it's location or you will get a parallax error. And of course the divider must not move when your head does.

                Even with all of the above, it is still hard to adjust the screw/nut on dividers to the exact thousanth. And if you do, you must handle them very, VERY carefully when moving them to the work or you may easily disturb the setting you so carefully made. It does not take much of a shift in the nut's or screw's position to change the distance between the points by several thousanths. Remember that the points are at the end of the legs and the adjustment screw is in the middle at best, more likely even closer to the pivot point. It is a lever arm and any change in distance at the screw is amplifier at the points. So tenths at the adjustment become thousanths at the tips.

                I would not argue with a master machinist who says he can use dividers at this level of accuracy. But a novice or even a moderately experienced person should not expect to get thousanth accuracy with dividers without a lot of practice.

                If I were setting up two gears, I would first mount one of them and then mesh the second one with some shim stock between the teeth and use a close fitting transfer punch to mark the position of the second. Or use a short slot for the second one and adjust it during assembly. The size of the shim stock would depend on the pitch of the gears.
                Paul A.

                Make it fit.
                You can't win and there is a penalty for trying!


                • #9
                  No big deal

                  Let's put a few practicalities into this equation. We will start off with the very accurate (most are) "Machinists Rules" that are successively sub-divided into 1/64".

                  Put one point of the dividers into an etched mark on a good machinist's rule. Move the other across the rule. It is very easy to see where the moving point is.

                  First of all, 1/64" ~ 0.016" (16 thou). Halving it by eye is easy. If you are "off-centre" by 0.002" (2 thou), one side will be (0.008 + 0.002" = 0.010") and the other (0.008" - 0.002" = 0.006") a difference of (0.010" - 0.006" = 0.004") which at 1/4 of that 1/64" division is quite visible to the naked eye - better still with a loupe' or magnifying glass. There will be no (or negligible) "parallax" error as the points will be very close to the rule. So, getting it to within 0.004" is not too difficult and neither is getting it to within 0.002".

                  Transfer punches are a PITA as they must match the diameter of the bore/s very closely and the point of the transfer punch cone must be very precisely centred. Then, the chances are that the transfer punch needs to be followed up with a centre-punch and then the centre punch by a centre and/or spotting drill followed by one or more regular drills - all of which can each "wander off" bot laterally and axially and then by a reamer which will follow the drill just previous to it.

                  If I were marking it out I'd use a vernier or digital height guage (with a scribing point/edge) for accuracy or a surface guage or a scribing block and a flat plat (mill table or surface plate) with the job set up on a rotary table for the horizontal and vertical as well as any angular lines.

                  I can quite comfortably and repeatedly set a mill spindle axis over a line or intersection of lines within 0.002"

                  Its a matter of knowing what your tolerances and allowances and limits are and where your errors are of might be and acting and making informed judgments accordingly.

                  If the real requirements of or the gears is not too rigorous, I suggest that even badly meshed gears in the lathe gear-train rattle away in a dusty environment without a lot (or any) care and lubrication and by and large they do very well.

                  It is not uncommon for the pitch circles of gears to be eccentric to the bores and they oscillate in and out of mesh from "good" to "not so good". Set a pair of gear-train gears and set the back-lash and see if it is the same all the way through a complete rotation of each gear.

                  Oh dear - what to do?

                  Answer: bugger all. If it works its probably OK.

                  If you are cutting gears on a mill with the standard sets of gears for each DP and numbers of teeth, the only one that will be pretty accurate will be the first one in the set - even that is a compromise and the compromise gets bigger (worse?) the further up the number of teeth for each cutter you go. If you are plunging straight in for depth with your milling cutter using machine dials you are really trusting to luck unless you measure the gears against table in "Machinery"s Handbook" - or the like - using either a set of gear calipers or wires (2 or 3) with a micrometer. Seeing that the gear profile is concentric and symmetrical is another concern.

                  And that is not all of it - by far.

                  But in practical terms in many shop projects, most of it can be disregarded - up to a point.

                  I will not get into set-up and machine rigidity as common sense will soon identify any potential problems as well as their "fixes".

                  Why the diversion into gear-cutting when the topic is about setting gears up super-accurately?

                  Easy - because they are interdependent.

                  Just keep a sense of reality and perspective as well as a cool head and you will be OK most times.


                  • #10
                    Looking at the OP Tony this is a hypothesis? Machinery's calcs are based on a perfect world and we all know it ain't. This is why for super accuracy (??) one of the centres is either slotted or fitted with an eccentrically adjusted pivot. If you've ever watched the Discovery Channel's "How do they do it" or "How it's made" on ball races, the varying tolerance the individual balls are made to has quite a wide band.

                    Just remembered the Anti-backlash gears for "Important" drive systems,but they are usually lightly loaded. You want to play with the centres? make a depthing tool similar to the watch/clockmakers, but it has one fixed pivot with a hardened centre and a clampable sliding one in a slot in a piece of bar. Mount the gears, interpose a shim for clearence, clamp and bonk the pins on the plate you're marking.

                    Regards Ian
                    You might not like what I say,but that doesn't mean I'm wrong.


                    • #11
                      All these are good answers, but if your gears are running on pins fixed in the plate, make one of them say 30 thou eccentric, then you have a way of adjusting out any error.



                      • #12
                        Originally posted by Richard Wilson
                        if your gears are running on pins fixed in the plate, make one of them say 30 thou eccentric, then you have a way of adjusting out any error.
                        Very good advise.
                        "Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did."


                        • #13
                          Hi all

                          I know onlty what I was exposed to in gear class many moons ago...

                          1.)I must be misunderstanding a statement in the original post... Spur gears must have parallel axes otherwise, they will not make correct contact on the tooth faces. Parrallelism of the shafts is, IMHO as important as backlash.

                          2.) optimum backlash will improve the vibvration and noise from the gears meshing and reduce slop when loads are applied and removed, but are quite forgiving unless you're working with super high speed or horsepower.

                          3.) there has been no mention of the use of chalk on the good machinists rule to make the setting of dividers easier. Rubbing chalk into the division marks will make setting the dividers considerably easier.

                          My $.02 cdn
                          Design to 0.0001", measure to 1/32", cut with an axe, grind to fit


                          • #14
                            Off hand if youre using a center punch to locate the holes, a dress-
                            makers tape will be accurate enough to locate the other hole. :-)


                            • #15
                              I'm not in Tiff's class of precision, however....
                              presuming you are not using exotic alloys, a couple of NIB magnets make a sort of toolmakers button setup on the mill, using coax indicator or edge finder and some trig.

                              You may be surprised by the tolerances on these things.
                              I checked a pack of 5 ($2 AUD) and they varied by less than .01MM in dia and thickness.
                              (by Moore and Wright mic.)
                              Just got my head together
                              now my body's falling apart