Tangential Stress In Rotating Flywheel At Given Radius Calculator

Formula Used:

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

Mass Density of Flywheel (ρ):

kg/m³

Peripheral Speed of Flywheel (V):

m/s

Poisson Ratio for Flywheel (u):

Distance from Flywheel Centre (r):

Outer Radius of Flywheel (R):

Tangential Stress in Flywheel (σₜ):

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1. What is Tangential Stress in Flywheel?

Tangential Stress in Flywheel is the stress experienced by the flywheel when the direction of the deforming force is parallel to the cross-sectional area, also called as shearing stress. It occurs due to rotational forces and varies with radial position.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for material properties, rotational speed, and radial position to calculate the tangential stress distribution in a rotating flywheel.

3. Importance of Tangential Stress Calculation

Details: Accurate tangential stress calculation is crucial for flywheel design to ensure structural integrity, prevent failure due to rotational forces, and optimize material usage while maintaining safety margins.

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 rotating flywheel.

Q2: How does tangential stress vary with radial position?
A: Tangential stress is maximum at the center and decreases towards the outer radius, following a parabolic distribution pattern.

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, depending on the material type.

Q4: Why is peripheral speed squared in the formula?
A: The stress is proportional to the square of peripheral speed because both centrifugal force and resulting stress increase quadratically with rotational speed.

Q5: What safety factors should be considered in flywheel design?
A: Typical safety factors range from 2-4, considering material properties, operating conditions, and potential dynamic loads beyond the calculated static stress.