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Wk² Inertia

  1. Apr 16, 2013 #1

    Buz

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    I have been scratching my head for a few hours now. Problem is I don't believe my calculations one bit haha.

    I have a circlular rotating disc mass (approx 80Lbs) radius of 13"

    I have 16 Blades evenly spaced on this mass(approx weight of 3.2Lbs/each) Inside radius is 13" outside radius is 21"

    I have came up with a number of 120Wk² and a number of 188Wk²

    Someone save me from pulling my hair out lol

    Thanks in advance
     
  2. jcsd
  3. Apr 16, 2013 #2

    SteamKing

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    How did you come up with these numbers? What calculations did you do?
     
  4. Apr 17, 2013 #3

    Buz

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    Thanks for response.

    26" dia. cylinder
    weight = 80Lbs
    Radius = 13.3462

    wk² = (Weight)(Gyro Radius)

    Gyro Radius = 13.3462/12 = 1.11218/2 = 0.55609/2 = 0.8341 + 0.55609 = 0.4170

    wk² = (80)(0.4170)
    wk² = 33.365

    Blades
    weight = 3.2Lbs
    In/out Radius = 13.3462/inner radius -- 21/outside radius

    wk² = 3.2(1.1121+1.75)/2
    wk² = 73.26

    sum of inertia

    Total wk² value = 106.625

    ---------------------------------

    Other Calculation

    Calculating this as a solid mass

    Weight = 131.2Lbs
    Radius = 21" / 12 = 1.75'

    wk² = (0.5)(131.2)(1.75)
    wk² = 114.8

    Which one should apply?
     
  5. Apr 18, 2013 #4

    SteamKing

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    Your calculations appear to be incorrect.

    For instance, take the 80-lb. disk, radius 13" (round numbers for convenience).

    The mass moment of inertia of a circular disk is (1/2)mR^2
    For the disk, R = 13/12 = 1.0833 ft. and m = W/g = 80/32.2 = 2.48 slugs

    MOI = 0.5 * 2.48 * 1.0833^2 = 1.458 slug-ft^2

    The moment of inertia is also equal to the mass * gyradius^2, or MOI = mass * k^2, where k = gyradius

    For the disk, k = SQRT (1.458 / 2.48) = 0.767 ft = 9.2 in.

    To add the blades to the disk, you would need to estimate the MOI of a single blade and then use the parallel axis theorem to find the MOI of the disk and blades. The MOI of a blade is going to depend on the size and shape of the blade.
     
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