Calculating Average Tangential Stress for Non-Uniform Rotating Disk

In summary, the average tangential stress for a nonuniform thickness rotating disk can be calculated using the above equation, which takes into account the variable thickness of the disk and the density and speed of rotation.
  • #1
xanderlinkz
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Assumed a disk loaded with external pressure Po, internal Pressure Pi and rotating at the speed ω.
I'm sure that average tangential stress for uniform thickness rotating disk can be calculated using equation below :

σ avg = (PiRi/Ro-Ri) - (PoRo/Ro-Ri) + (ρω^2) / 3(Ro^2+RoRi+Ri^2)

Ro = outer radius
Ri = inner radius
ρ= density

now if the disk have nonuniform thickness (e.g. L1,L2,...,Ln) and Rn as the radius for each interface of two segment (thickness variable).
How do we calculate the average tangential stress for this case?

I would really appreciate any kind of help, i will gladly describe further information if necessary.
and sorry for my bad grammar, English is not my native language. thank you very much.
 

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  • #2
The average tangential stress for a nonuniform thickness rotating disk can be calculated as follows: σ avg = (PiRi/Ro-Ri) - (PoRo/Ro-Ri) + {[ρω^2]/3 [Σ(Li/2)(Rn+1^2-Rn^2)]} + {[ρω^2]/3 [Σ(Li/2)(Rn^2-Rn-1^2)]}where Ro = outer radius Ri = inner radius ρ = density Li = segment length Rn = radius of each interface of two segments. Note: The summations are over all the segments.
 

FAQ: Calculating Average Tangential Stress for Non-Uniform Rotating Disk

What is the formula for calculating average tangential stress for a non-uniform rotating disk?

The formula for calculating average tangential stress for a non-uniform rotating disk is:

σavg = (ω^2 * R^2 * mavg)/Iavg

Where σavg is the average tangential stress, ω is the angular velocity, R is the radius of the disk, mavg is the average mass per unit area, and Iavg is the average moment of inertia per unit area.

How do you determine the average mass per unit area for a non-uniform rotating disk?

The average mass per unit area for a non-uniform rotating disk can be determined by dividing the total mass of the disk by its total surface area. This can be calculated by integrating the mass density function over the entire surface area of the disk.

What is the significance of calculating average tangential stress for a non-uniform rotating disk?

Calculating the average tangential stress for a non-uniform rotating disk is important in determining the strength and durability of the disk. It allows engineers and scientists to understand how much stress the disk can handle before it may fail or break. This information is crucial in designing and manufacturing safe and efficient rotating disks for various applications.

Can the formula for calculating average tangential stress be used for uniform rotating disks as well?

Yes, the formula for calculating average tangential stress can be used for both non-uniform and uniform rotating disks. In the case of a uniform rotating disk, the mass and moment of inertia per unit area will be constant, resulting in a simplified formula:

σavg = (ω^2 * R^2 * m)/I

Where m is the mass of the disk and I is the moment of inertia of the disk.

Are there any simplifying assumptions made when using the formula for calculating average tangential stress for a non-uniform rotating disk?

Yes, there are a few simplifying assumptions made when using this formula. First, it assumes that the disk is rotating at a constant angular velocity. It also assumes that the mass and moment of inertia per unit area are constant. Additionally, it assumes that the disk is thin and has a uniform thickness. These assumptions may not hold true for all real-world scenarios, but the formula can still provide a good estimate of the average tangential stress for a non-uniform rotating disk.

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