1. What is Critical Speed of a Shaft?

Definition: The critical speed is the rotational speed at which a rotating shaft becomes dynamically unstable due to resonance.

Purpose: This calculation helps mechanical engineers design shafts that operate safely below their critical speeds to prevent excessive vibrations.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( N_c \) — Critical speed (rpm)
• \( g \) — Acceleration due to gravity (9.81 m/s²)
• \( \delta \) — Static deflection of the shaft (m)
• \( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The formula calculates the natural frequency of the shaft and converts it to revolutions per minute (rpm).

3. Importance of Critical Speed Calculation

Details: Operating near critical speed can cause severe vibrations leading to mechanical failure. This calculation ensures shafts operate at safe speeds.

4. Using the Calculator

Tips: Enter the shaft deflection in meters (default gravity is 9.81 m/s²). The deflection must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What causes shaft deflection?
A: Deflection results from the shaft's weight, loads, and material properties (stiffness).

Q2: How is deflection typically measured?
A: Through static deflection tests or calculated using beam deflection formulas.

Q3: What's a safe operating speed relative to critical speed?
A: Typically below 70% or above 130% of critical speed to avoid resonance.

Q4: Does this formula account for multiple critical speeds?
A: No, this calculates only the first (lowest) critical speed.

Q5: How does shaft length affect critical speed?
A: Longer shafts have greater deflection (δ), resulting in lower critical speeds.