Radial Stress In Rotating Flywheel At Given Radius Calculator

Radial Stress Formula:

\[ \sigma_r = \rho \times V_{peripheral}^2 \times \frac{(3 + \mu)}{8} \times \left(1 - \left(\frac{r}{R}\right)^2\right) \]

Mass Density of Flywheel:

kg/m³

Peripheral Speed of Flywheel:

m/s

Poisson Ratio for Flywheel:

Distance from Flywheel Centre:

Outer Radius of Flywheel:

Radial Stress in Flywheel:

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1. What is Radial Stress in Flywheel?

Radial stress in a flywheel is the stress induced along the radial direction due to centrifugal forces when the flywheel rotates at high speeds. It's a critical parameter in flywheel design to ensure structural integrity and prevent failure.

2. How Does the Calculator Work?

The calculator uses the radial stress formula:

\[ \sigma_r = \rho \times V_{peripheral}^2 \times \frac{(3 + \mu)}{8} \times \left(1 - \left(\frac{r}{R}\right)^2\right) \]

Where:

\( \sigma_r \) — Radial stress in flywheel (Pa)
\( \rho \) — Mass density of flywheel material (kg/m³)
\( V_{peripheral} \) — Peripheral speed of flywheel (m/s)
\( \mu \) — Poisson's ratio for flywheel material
\( r \) — Distance from flywheel centre (m)
\( R \) — Outer radius of flywheel (m)

Explanation: The formula calculates the radial stress distribution in a rotating flywheel, which varies parabolically from the center to the outer edge.

3. Importance of Radial Stress Calculation

Details: Accurate radial stress calculation is crucial for flywheel design to ensure it can withstand centrifugal forces without failure, determine appropriate material selection, and optimize flywheel dimensions for energy storage applications.

4. Using the Calculator

Tips: Enter mass density in kg/m³, peripheral speed in m/s, Poisson's ratio, distance from center in meters, and outer radius in meters. All values must be positive, and distance should not exceed outer radius.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of Poisson's ratio in this calculation?
A: Poisson's ratio accounts for the material's tendency to expand or contract in directions perpendicular to the applied stress, affecting the stress distribution in the flywheel.

Q2: How does radial stress vary across the flywheel?
A: Radial stress is maximum at the center and decreases parabolically to zero at the outer edge of the flywheel.

Q3: What are typical values for flywheel material properties?
A: Common flywheel materials have densities ranging from 2000-8000 kg/m³ and Poisson's ratios typically between 0.2-0.35.

Q4: Why is peripheral speed squared in the formula?
A: The centrifugal force (and thus stress) is proportional to the square of the rotational speed, which relates directly to peripheral speed.

Q5: What safety factors should be considered in flywheel design?
A: Typical safety factors range from 2-4, considering material fatigue, operating conditions, and potential overload scenarios.