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Shaft hertzian contact stress?

  1. Aug 19, 2008 #1

    I am trying to calculate contact stress for a shaft on a hole. The purpose of this calculation is to see if the diaphram on which the hole exists is thick enough to handle the shaft radial load. Easiest approximation would be to use a simple formula for bearing stress (stress = force / (t*d)), but more accurate approximation is required.

    A formula for cylinder on a cylinder seems to be available from many different sources, but I can't find a formula for cylinder in a cylindrical hole. The closest thing I've come up with is from Roark's Formulas 7th Edition Ch.14.4 Table 14.1 Case 2.c "cylinder in a cylindrical socket", but this equation results in a zero denominator if the cylinder and hole diameters are equal.

    Can anyone help me with this..?

  2. jcsd
  3. Aug 20, 2008 #2
    I might not quite get what you're saying, but if the cylinder and the hole have the same diameter why would the hole have any stress on it's inner diameter? Are you talking about a press fit of some sort?
  4. Aug 21, 2008 #3
    I guess I should've explained my question more clearly: a shaft is under radial load on one end, and is supported radially on the other end by a hole in a plate. I believe the plate will be under some contact stress, and it will fail if it is too thin..? The fit between the shaft and the hole is a close running fit.
  5. Aug 21, 2008 #4
    A picture would really help a lot.
  6. Aug 21, 2008 #5


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    It sounds like from what you are describing, a cylindrical hole with a rod in it with a tight fit (such that the diameters are equal) and an end load, would behave as a cantilevered beam.

  7. Aug 22, 2008 #6


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    Personally I think you are over complicating this. I would think that the bearing stress/tear out stress is what you really need.

    You shouldn't run into a 0 in the denominator for Kd because the two diameters are not equal. Kd may be very large, but it is definable.
  8. Aug 25, 2008 #7
    Here's a picture of the problem. The shaft is supported at two points by diaphragm 1 & 2, and a downward force is applied at the left end of the shaft. The point of interest is whether the diaphragm is strong enough to handle contact stress between itself and the shaft, not how the shaft would behave.

    I have decided to use the formula in Roark's with an assumption that shaft diameter is ~99% of the hole diameter. I guess this would be a conservative approximation, and Kd will not be infinite. Would this be a reasonable assumption?

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