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Critical Speed Formula Calculator

Critical Speed Formula:

\[ N_c = \frac{30}{\pi} \times \sqrt{\frac{g}{\delta}} \]

m/s²
m
rpm

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1. What is Critical Speed?

Definition: Critical speed is the theoretical angular velocity that excites the natural frequency of a rotating object, like a shaft or rotor.

Purpose: It helps engineers design rotating systems to avoid resonance and potential failure at certain rotational speeds.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ N_c = \frac{30}{\pi} \times \sqrt{\frac{g}{\delta}} \]

Where:

Explanation: The formula converts the natural frequency of the system from radians per second to revolutions per minute.

3. Importance of Critical Speed Calculation

Details: Calculating critical speed is essential for preventing resonance in rotating machinery, which can cause excessive vibrations and potential failure.

4. Using the Calculator

Tips: Enter the gravity value (default 9.81 m/s²) and the static deflection of the shaft in meters. All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What happens at critical speed?
A: At critical speed, the rotational frequency matches the system's natural frequency, causing resonance and potentially dangerous vibrations.

Q2: How is static deflection measured?
A: Static deflection is the displacement of the shaft under its own weight, typically measured at the midpoint for a simply supported shaft.

Q3: Why is the 30/π factor used?
A: This factor converts radians per second to revolutions per minute (1 rad/s ≈ 9.549 rpm).

Q4: Is this formula for simple or complex systems?
A: This is for simple, single-mass systems. Complex systems may require more advanced analysis.

Q5: Should operating speed be above or below critical speed?
A: Typically, systems are designed to operate either well below (75% of Nc) or well above (125% of Nc) the critical speed.

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