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  • Working out taper

    Hi all
    i am hoping someone can help me in how to work out how many deg to set cross slide to turn a JT0 taper the sizes are Large end 0.2500” small end 0.2284” and 0.44” long.
    thanks in advance Dell

  • #2
    It might be easier to set the compound slide to 1 degree 24 minutes and 18.8 seconds.
    Kansas City area

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    • #3
      Assuming the length is axial and not the side of the taper, the angle is 5.66822 degrees, so the cross slide would have to be set at 2.83411 degrees. That angle would be impossible to set even on the taper turning attachment I use, which is 10 times as accurate than any cross slide.
      The only way I can think of for a close setting would be to already have the JT0 male and use a dti exactly on the centre line to set the angle running against the taper.

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      • #4

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        • #5
          arctangent [(0.25 - 0.2284) / (2 * 0.44)] = 1.406 degrees
          Regards, Marv

          Home Shop Freeware - Tools for People Who Build Things
          http://www.myvirtualnetwork.com/mklotz

          Location: LA, CA, USA

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          • #6
            I cannot get anything like those figures. I first did the calculation from a metric start, and got 2.82411 degrees per side, and then from the op's imperial figures and got 2.81044 degrees.I will find out where I have erred, eventually. My figures are exactly double the other results, so I must have forgotten to halve the difference when subtracting the small end from the large end.
            1.406 degrees is still almost impossible to set on any lathe without a lot of juggling of the set angle.
            Last edited by old mart; 03-13-2021, 04:41 PM.

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            • #7
              Originally posted by old mart View Post
              I cannot get anything like those figures. I first did the calculation from a metric start, and got 2.82411 degrees per side, and then from the op's imperial figures and got 2.81044 degrees.I will find out where I have erred, eventually. My figures are exactly double the other results, so I must have forgotten to halve the difference when subtracting the small end from the large end.
              Included angle. 2.864 Deg.

              Any error is due to metric angle dimension conversion.
              Last edited by Bented; 03-13-2021, 04:44 PM.

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              • #8
                Note that the difference between Bented's result (1.4321 deg) and my result (1.406 deg) is the fact that I used the 0.2284 specified in the OP and Bented used 0.228. That 4 tenths, if it's real, makes a difference. Of course, 1.4321 - 1.406 = 0.0261 deg = 1.566 arcmin is probably impossible to set on a compound.
                Regards, Marv

                Home Shop Freeware - Tools for People Who Build Things
                http://www.myvirtualnetwork.com/mklotz

                Location: LA, CA, USA

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                • #9
                  As mklotz has written above, the formula is Deg = Tan-1 [(Dmax - Dmin) / 2L]

                  In this case, Dmax is 0.2500, Dmin is 0.2284, and L is 0.44.

                  So I too make the answer 1.406°. And if you can set your compound slide accurately to a thousandth of a degree you have a lathe of quite astonishing precision! As Old Mart writes, using a DTI to match the compound to an existing taper is the only practical way of getting it accurate.

                  Incidentally, when making the above calculation, it does not matter whether the measurements are metric or imperial—as long as they are all in the same system you will get the same answer. If you don't, you've made a mistake.

                  Bented, no offence, but assuming the OP's figures are correct for a JT0 taper, your diagram has an incorrect diameter for the small end, and your angle is wrong.

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                  • #10
                    Originally posted by Mike Burch View Post
                    As mklotz has written above, the formula is Deg = Tan-1 [(Dmax - Dmin) / 2L]

                    In this case, Dmax is 0.2500, Dmin is 0.2284, and L is 0.44.

                    So I too make the answer 1.406°. And if you can set your compound slide accurately to a thousandth of a degree you have a lathe of quite astonishing precision! As Old Mart writes, using a DTI to match the compound to an existing taper is the only practical way of getting it accurate.

                    Incidentally, when making the above calculation, it does not matter whether the measurements are metric or imperial—as long as they are all in the same system you will get the same answer. If you don't, you've made a mistake.

                    Bented, no offence, but assuming the OP's figures are correct for a JT0 taper, your diagram has an incorrect diameter for the small end, and your angle is wrong.
                    The spec I see for the Jacobs "0" taper is: large end 0.2500", small end 0.22844", length 0.4375"
                    Not splitting hairs here. I too have limits with my lathe compound setting abilities.

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                    • #11
                      arctangent [(0.25 - 0.2284) / (2 * 0.44)] = 1.406069 degrees
                      arcsine [(0.25 - 0.2284) / (2 * 0.44)] = 1.406492 degrees

                      difference = 0.000492 - 0.000069 = 0.000423 deg = 1.5 arcseconds = 7.4 microradians = 7.4E-6 radians

                      which is a really, really tiny angle. If you aim your laser gun at a target 1,000 yards (3.6E4 inches) away and have that much pointing error, you'll miss the bullseye by 0.267 inches.

                      Conclusion: For almost all self-holding taper calculations, the distinction between sine and tangent can be ignored; measuring, much less setting, angles that small is the domain of specialized high tech laboratories, not machine shops.

                      And, yes, you don't set up a lathe for turning self-holding tapers by dialing in an angle on the compound or taper apparatus. You use a DTI on a master gauge.
                      Regards, Marv

                      Home Shop Freeware - Tools for People Who Build Things
                      http://www.myvirtualnetwork.com/mklotz

                      Location: LA, CA, USA

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                      • #12
                        And, yes, you don't set up a lathe for turning self-holding tapers by dialing in an angle on the compound or taper apparatus. You use a DTI on a master gauge.
                        Or at least start with an existing arbor held between centers. Or if you don't have an arbor then turn a stub so it runs true and tighten your drill chuck onto it and read off the ID with a DTI for as far in as it will reach. Note that you want to do this on the far side if doing it with an ID.
                        Chilliwack BC, Canada

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                        • #13
                          When setting up PITA angles on the lathe, I use two indicators: one measures the axial length travelled, the other measures the offset as if the part were a right triangle. It can be a bit fiddly, but I believe it's the best way.
                          25 miles north of Buffalo NY, USA

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                          • #14
                            Originally posted by Mike Burch View Post

                            Bented, no offence, but assuming the OP's figures are correct for a JT0 taper, your diagram has an incorrect diameter for the small end, and your angle is wrong.
                            No offence taken, simply used the number supplied but left out the 4th decimal position as .000X degrees is a bit much for the home shop

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                            • #15
                              I found that to get an accurate MT2 taper with a taper turning attachment and using a length bar and dti needed a Morse taper socket to actually get a fit that was feeling like right.
                              Having a chuck with the JT0 in it and feeling the fit as you make fine adjustments to the compound is probably the best way to go. It will take patience and several trys, so allow a little extra length for the end to be machined as each recut will shorten the workpiece.

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