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Taper adapter help with the math

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  • Taper adapter help with the math

    i have a 7-1/4" long taper adapter the the outside is a B/S 12 but i cannot ffigure out what the inside is. the thing measures aprox:
    large end = 1.070
    small end = .895

    what offset should i set the tail stock at for a 6" long piece ?

    what is the angle from the center line to one side ? i get .691 degree.

    i tried my trig, and the google angle thing and im afraid im doing something wrong.

    i need to turn a slug of iron to fit this inside part for mounting a morse taper chuck into.

    help ?

    davidh

  • #2
    Your trig is correct.
    Gene

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    • #3
      Assumption: the center line length is 7.250". If this is the length of a side then the numbers are wrong.

      The compound angle is one-half the included angle of the taper. To reduce this to trig we find the side opposite and the side adjacent. The side opposite is the difference of the large diameter and the small diameter divided by 2. The tan of the angle is the side opposite divided by the side adjacent.

      7.250 = side adjacent
      (1.070 - .895) / 2 = 0.0875 = side opposite

      Dividing the side opposite by the side adjacent gives us the tan of the angle
      0.0875 / 7.25 = 0.01207 = tan(angle)

      We can now calculate the angle using the atan function of a calculator:
      atan(0.01207) = 0.691 degrees

      We can calculate the taper per foot to see if it matches any standard tapers:

      ((1.070 - 0.895) / 7.25) x 12 = taper per foot = 0.2896 which I don't recognize.

      The taper per inch is calculated by measuring the diameters separated by 1". This is found using a 1-2-3 block and a caliper:

      Small diameter:
      http://TheVirtualBarAndGrill.com/mac...suretaper1.jpg

      Large diameter
      http://TheVirtualBarAndGrill.com/mac...suretaper2.jpg

      Edit: Got called away before I could finish earlier post

      Once the taper per inch is known from measuring (or calculating) you can determine the tail stock offset which is:

      Offset = TPI / 2 x L where TPI is taper per inch, and L is the length.

      Calculate TPI;
      TPI = (1.070 - 0.895) / 7.25 = 0.241"

      Calculate tail stock offset
      0.0241 / 2 x 6 = 0.0724" tail stock offset
      Last edited by dp; 03-20-2009, 02:17 PM.

      Comment


      • #4
        Originally posted by davidh
        i have a 7-1/4" long taper adapter the the outside is a B/S 12 but i cannot ffigure out what the inside is. the thing measures aprox:
        large end = 1.070
        small end = .895

        what offset should i set the tail stock at for a 6" long piece ?

        davidh
        Here's a way to think about the tailstock offset. If you were making a part exactly the same length as your original, 7.250, you would set over the tailstock exactly the same amount as the difference in diameter (per side) or (1.070-.895)/2 or .0875". Since you're making a shorter part, you'd use the same proportion of offset as the proportion of length (6.000/7.250) x .0875 or .072" approx.

        The "approx" part adds one more math function, and that is a tweak of the set over to get the two parts to fit. Since you're turning your new part between centers, you can remove and remount it with confidence. Move the tailstock toward the operator so the small end will be toward the tailstock and you don't have to keep taking off the lathe dog. Check the fit of your new part against your unknown taper and keep adjusting and re-cutting as necessary.
        .
        "People will occasionally stumble over the truth, but most of the time they will pick themselves up and carry on" : Winston Churchill

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        • #5
          thanks much, i take a stab at it tonite. . . tweaking can be so much fun. .

          Comment


          • #6
            Dennis, in those photos I take it that you are laying the calipers dead flat on the block and using the difference in side widths of the block to get an accurate distance between large and small diameters. Is that correct?

            Thanks for the pictures.

            Rgds
            Michael

            Australia

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