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Formulae needed

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  • Formulae needed

    Background story first.

    We have a show coming up this weekend and will have two of the CNC there running under power, small XK1 and larger KX3.
    We try to do different things at the shows or it gets boring - yawn.

    This year I fancy doing a multi throw crankshaft, quite hard to do in a lathe as you need to throw the blank off centre to do the journals and can't use steadies.

    However on a mill if you time the A axis to the Z feed you can do all the journals at one setting and even employ a vee steady underneath for support.

    OK question now.
    Look at this drawing.

    Small circle denotes the crank pin and everything else is given, because I can't remove all this metal in one go I need to feed the Z down a bit then do a full rev then increase feed until it's gone full depth, in this case 20mm.

    What is the formulae of the relationship of Z [ vertical feed down ] to A [ rotary axis in degrees ] ?

    Sir John , Earl of Bligeport & Sudspumpwater. MBE [ Motor Bike Engineer ] Nottingham England.

  • #2
    Huh I could do that! Maybe with a few hundred years practice! oh well back to the plasticine. Alistair
    Please excuse my typing as I have a form of parkinsons disease


    • #3
      I can't see the pic on my phone,
      But it'll be something like a constant x sin A I think

      Will look later on a real pc <shrug>

      Just south of Sudspumpwater UK


      • #4
        (Cos(A) - 1) * 10

        But, the sign might be wrong ???
        Last edited by kitno455; 10-11-2011, 05:55 PM.


        • #5
          If you want the vertical coordinate of the centre of the small circle, relative to the centre of the large circle, and the angle A is measured from the vertical, the formula is Z = 10 * cos (A), more or less as kit said.

          Cos(theta) starts at 1 when theta is 0, goes to zero when theta gets to 90 degrees and goes to minus one when theta gets to 180 degrees.

          So since I've taken the centres as Z=0, cos starts at 1 (for top) and goes to -1 at 180 degrees (for bottom). Times it all by the radius, 10, and Bob's your uncle, or your maths teacher, whichever you prefer.

          I'm sure the barmaid down at your local can put you right on this kind of thing.
          Richard - SW London, UK, EU.


          • #6
            I think:

            Set cutter height zero at center of blank height, and centered over center in Y

            updown motion is ((10) + DOC) x cos A + 5 (Might be - DOC)
            Left right motion is (15) x sin A

            Yorkshire disclaimer:
            If you crash, you get to keep both bits

            Just south of Sudspumpwater UK


            • #7
              Why do all the math and complications ?

              Use a Woodruff Key cutter, and set the crank vertical.
              Then feed Z down, move in, and then interpolate a circle.


              Or am I missing something ?


              • #8
                Doesnt look as good
                Just south of Sudspumpwater UK


                • #9
                  John, it might be easier coding to rough out square crankpins and then only a small amount of complex coding for the final sizing. The cutter will have to be end cutting since it will be moving in the y axis as well as z as the blank rotates.

                  gbritnell posted this link on HEME for a full size crank :-


                  So it can be done!

                  If no one on the forum has done this before, I'll give it a try, but my G code experience is limited to 3 axes in Mach3.



                  • #10
                    Thanks Ian,
                    That's what we are trying to do, the bit at 1:05 to 1:16 but with a fixed vertical tool axis and interpolating in A, Y and Z at the same time.

                    I like your thinking but looking at a shaft about 8" long with 6 throws and 7 mains as a demo piece, need a long woodruff cutter for that

                    Sir John , Earl of Bligeport & Sudspumpwater. MBE [ Motor Bike Engineer ] Nottingham England.


                    • #11
                      Hey John, that's actually really easy code to do, really easy.

                      I figured out, after much frustration how it worked when I was making a square pin on the 4th axis. 1" square, .25" radiuses, and long... so it wasn't standing up.

                      Here's your line of code, assuming your 4th is along the X axis, tool height Zzero on the centerline, finish cut here, pick your Z height.

                      pick your X position.

                      G1 Y0. Z15. (just getting the cutter in place, your Y could be offset a cutter radius if you want)
                      G19 (arcs in YZ plane)
                      G2 K-10. A360. (or G3 depending on which way your 4th is rotating).

                      A simple YZ arc, and a linear A move. Yes the A is rotating, but as far as the machine is concerned its linear. Same as programming a helix. It should track all pretty like and give you exactly what you saw in that video.

                      One thing to be careful of, FEED, since you are running a YZ arc, even though you are also running an A move, it will probably want its feed in IPM or mm per minute instead of degrees per minute. Also that would be the feed speed of the arc traveled, not the speed the cutter is going through the material.

                      Good luck, sounds you get to have a lot more fun than I do.


                      • #12
                        this for the midlands ME show John?


                        • #13
                          Sussed the G19 out and just got an email back from Art at Mach3 to say Mach cannot do ellipses which is the way we were aiming but we are getting there.

                          We can hard code it from an excel spreadsheet but trying to just use a simple formulae with sub routines.

                          We'll get there one way or another, like most thing there isn't a defined right and wrong way, just many different ways, we want the simpler one.

                          Yes this is for the show, as usual it's a last minute job

                          Sir John , Earl of Bligeport & Sudspumpwater. MBE [ Motor Bike Engineer ] Nottingham England.


                          • #14
                            I go to a lot of machine shows the things I enjoy watching the most are things that are quick to make. A company brings in about 10,000. small metal pieces for making tiny little parts. They put a blank piece of metal in the vise, push a button and 1 or 2 minutes later you have a finished part. They give all the finished parts to the people that watch. You take those parts home and it makes you remember the machine. Some day you get a new job to make a special part and you need a special machine then you remember the company that made the little part you bought home from the show so you give them a call.

                            The demonstrations that take several hours are boring. You walk around the show and come back an hour or two later it is still cutting the same part. You go home and pretty soon you forget all the boring stuff you saw. Sometimes they have hand outs with photos that helps to remember and a display table with lots of different parts the machine will make.
                            Last edited by gary350; 10-13-2011, 09:22 AM.


                            • #15
                              Elipse? What have I missed? If the centreline of the milling cutter is on the vertical diameter of the crank pin, then isn't it a circular path? We want a video when you crack the problems.

                              Last edited by dvbydt; 10-13-2011, 07:18 PM.