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  • Machining measuring wheel diameters

    Given: Suspend exactly 1,000 ft. of 0.250 in. diameter, perfectly straight, stranded cable down a wellbore. At the top, pinch the cable between the faces of two flat faced wheels, each 7.6394 in. diameter. With no slippage of the cable with respect to the wheels, count exactly 500 revolutions of each wheel while pulling the 1,000 ft. of cable vertically, from the wellbore.

    Question 1: Same scenario as given, except, instead of pulling the 1,000 ft. vertically from the wellbore, have the cable contact one wheel over a 90 degree arc of it's circumference and be pulled at a right angle to the centerline of the wellbore. Now, what measuring wheel diameter would be required for it to rotate exactly 500 times for the same 1,000 ft. of 0.250 in. cable pulled?

    Question 2: Any super duper formulas for calculating measuring wheel diameters with regards to cable diameters and the arc degrees of measuring wheel contact? Our designs call for contact angles of from 80 to 90 degrees.

    G

  • #2
    ?????

    It makes no difference if it is wrapped 1 degree or 180 degrees. Why would it?

    If you are measuring the length keep in mind that 1000 feet of 1/4" cable weighs 105 lbs. As it is pulled the suspended weight grows less and so does the cable stretch.
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    • #3
      Cable stretch? ...hmm! What's the temperature at bottom of well? Top of well? Is the temp gradient constant?

      How long has cable been hanging in well?

      Boy this could get messy!
      Lynn (Huntsville, AL)

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      • #4
        Yeah...and what Evan mentioned only takes into consideration *elastic* stretch. New cable will stretch quite a bit on a permananet one-shot basis. My ATV winch instructions prescribed stretching it before it was ever used, so that can be a solution to that problem.

        So can use of some synthetic winching products that are out there now. They use Kevlar or something and are *very* lightweight and don't splinter etc. They are subject to abraision, though and do require a nice smoothly polished hawse type fairlead. They are also pricey, but are really cool stuff. If ever I need replace the cable on my winch, it will be with this stuff.

        Here is one example:

        http://www.rockstomper.com/catalog/recovery/ropes.htm
        Paul Carpenter
        Mapleton, IL

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        • #5
          Originally posted by Evan
          ?????

          It makes no difference if it is wrapped 1 degree or 180 degrees. Why would it?

          If you are measuring the length keep in mind that 1000 feet of 1/4" cable weighs 105 lbs. As it is pulled the suspended weight grows less and so does the cable stretch.
          I think what he's getting at is when its pulled straight up, the circumference of the wheel * # revs = exactly how much cable is moved, whereas when it passes over the circumference, the cable must change shape slightly, outside stretched, inside compressed- ie is the distanced moved based on the inside radius (the circumference of the wheel) or the circumference of a line somewhere in the middle of the cable - not sure what the answer is?

          Guido is this a practical question, or one of those "it be a billionth longer because of more surface area exposed to sunlight" puzzles?
          .

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          • #6
            The answer is that it makes no difference at all. The cable makes contact with the wheel at a tangent and leaves at a tangent which is a straight line. What happens in between doesn't matter. If the cable compresses on one side closest to the wheel it also decompresses the exact same amount before it breaks contact so the net effect is zero.

            Think of it this way: The cable is pulled at exactly one foot per second. Regardless of how it contacts the wheel, wrapped or not, the circumference of the wheel must rotate at one foot per second. Time x speed = distance.
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            • #7
              Just went thru this recently and it does matter for high accuracy measurements. The only solution is to calibrate against a reference length that has been mechanically measured by hand. The reference length then needs to be run thru the measuring system under working conditions and a cal factor developed.

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              • #8
                A difference can only occur if there is slip. No slip was specified.
                Free software for calculating bolt circles and similar: Click Here

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                • #9
                  Originally posted by Evan
                  A difference can only occur if there is slip. No slip was specified.
                  Like Evan said, it will make no difference. His wheel diameter has an exactly 24" circumference. One revolution of the wheel (with no slip) will meter out exactly 2' of cable, whether there is a single point contact or he has it wrapped around the wheel twice, one rev equals two feet...
                  Mark

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                  • #10
                    The internals of the cable are moving against each other if it is "uncoiling" from a pulley vs being pulled straight.

                    The stresses involved extend past the last point of contact, and I would expect a measureable difference in the vicinity of the pulley if the cable is loaded.

                    For the ridiculously fussy files:
                    Not only that, but there will be some energy absorbed in rotating the pulley, friction of wire on pulley, internal wire friction of bending, and so forth. The only place that energy comes from is added pull on the cable, which means that coming off the re-directing pulley, it will be stretched slightly more than it is before that. So measuring at the pulley has an unknown error amount, depending on how much of the stretch affects the pulley rotation.

                    As to whether that will affect the measurement? I don't know.

                    There are lots of error sources besides that. The basic stretch of the loaded cable, which is length dependent, is a big error either way.

                    Probably the accuracy is best described as "close", but not ever exact. There is no way to account for everything.

                    I think I would go for the vertical cable, and "nipping" pulleys. You can get a decent calculated correction for cable stretch as a function of load and amount of cable out. You can calibrate that system more easily than any more complex system, and have more confidence that you are really correcting for known properties of the system..
                    1601

                    Keep eye on ball.
                    Hashim Khan

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                    • #11
                      Due to compression caused by the wrap, the length payed out is less than the actual length (somewhere near the "core" ). What the magic number is for steel cable I don't know.

                      Guido shows his wheel diameter down to 0.0001" and uses the words "exactly 500".

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                      • #12
                        when the cable touches the wheel at its tangent point it will not be bent, streatched, compressed or in any other way deformed and it will be moving 2 ft per rev. ..when it exits at the top tangent (or any tangent) it has to be moving at the same speed....if it were slower there would have to be wire pilling up somewhere and if it were faster the wire would have to be stretching

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                        • #13
                          If you pay out or reel in the cable at one foot per second it make no difference whatever what happens to the cable around the wheel, it still approaches and leaves the wheel at one foot per second. With no slip the wheel must have a radial velocity of one foot per second at the circumference.

                          If slip enters the picture then everything changes but that is a different can of worms and probably cannot be calculated. There may be some rules of thumb that have been empirically determined.
                          Free software for calculating bolt circles and similar: Click Here

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                          • #14
                            Originally posted by John R
                            when the cable touches the wheel at its tangent point it will not be bent, streatched, compressed or in any other way deformed and it will be moving 2 ft per rev. ..when it exits at the top tangent (or any tangent) it has to be moving at the same speed....if it were slower there would have to be wire pilling up somewhere and if it were faster the wire would have to be stretching
                            Not quite...

                            If there is any difference of tension across the pulley, there is a difference in stretch AND THERE IS SLIP. same thing that causes your flat belt to "talk to you" under a heavy cutting load.

                            In some special cases it may be true that a pulley NOT merely contacting a straight wire gets an accurate measurement....... but in most any case there is *some* difference, even if only due to the extra tension required to supply the lost energy of bending in the cable. You cannot escape that unless you don't bend the cable.

                            Given the choice of "nipping" wheels or one that has the cable bent around it, one CLEARLY has fewer variables, so why fight it?
                            1601

                            Keep eye on ball.
                            Hashim Khan

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                            • #15
                              Just like a new bicycle, few hours using it, all the cables stretch, re-adjust, good for a year.

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