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Stylus Force Calculations

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  • Stylus Force Calculations

    Group,

    I performed a quick calculation using equations developed by Hertz (sphere to sphere contact) to calculation how much pressure the stylus applies to an Edison Diamond Disc record for :

    1. Edison Diamond Disc Phonograph

    2. DJ style of Stylus with 0.7 mil spherical shape and 2 Grams of weight.

    3. 3.75 mil "Expert" stylus with 4 Grams of weight.

    The results were very interesting! I used the material properties of Bakelite for the Edison Disc Groove and Diamond for the stylus. The PSI (pounds per square inch) values are the "point contact" force which in turn is spread
    over the contact area.

    Results:

    1. 0.00166 sq inch contact and 72,566 PSI
    2. 0.00015 sq inch contact and 93,583 PSI
    3. 0.00046 sq inch contact and 19,902 PSI

    Conclusion : Although the actual force is spread under and around the contact area, the calculations shows that the Original Edison Design was somewhat better than using a LP style and low gram load. The reason is because of the
    non-linear relationships in the Hertz equations.

    If anyone has other results please let me know.

    Marc

  • #2
    My general intuition tells me that a perfect sphere to sphere point contact would approach infinity psi with any force applied to the stylus. So, obviously, the calculations are accounting for some deformation from the ideal sphere and not really a perfect point to point contact (unless my olde intuitions are failing me).
    .

    Craig
    "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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    • #3
      Craig,

      Yes that is true, hence the contact area.

      Marc

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      • #4
        Marc,

        Good to know that my intuitions are still somewhat intact!

        Craig
        "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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        • #5
          I would be curious what the average temperature of the tip (contact surface) of the DJ stylus is when playing a Diamond Disc record. You probably have to make an assumption about the co-efficient of friction in order to determine the energy transfer to the tip and the thermal resistance (both directions) between the record and the stylus tip and the stylus tip to the cantilever. Once you have the total energy applied to the tip, you can just run a thermal resistance calculation across the diamond. A reasonable assumption would be that the cantilever is approaching room temperature during operation and the record groove is also at room temperature. So, the entire delta T would be across the very diamond stylus itself. Fun stuff, but practical in a sense since that would help to determine the life of the diamond stylus in that application.

          Craig
          "Who put orange juice in my orange juice?" - - - William Claude Dukenfield

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