1. What is Critical Speed of a Shaft?

Definition: The critical speed is the rotational speed at which a shaft becomes dynamically unstable due to resonance, causing excessive vibrations.

Purpose: This calculation helps mechanical engineers design shafts that operate safely below their critical speed to prevent resonance and potential failure.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The formula calculates the natural frequency of the shaft and converts it to RPM. The critical speed occurs when the rotational speed matches the shaft's natural frequency.

3. Importance of Critical Speed Calculation

Details: Operating near critical speed can cause catastrophic failures. This calculation ensures shafts are designed to operate at least 20% above or below their critical speed.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What causes static deflection in a shaft?
A: Static deflection results from the shaft's own weight and any static loads applied to it.

Q2: How do I measure static deflection?
A: It can be measured experimentally or calculated using beam deflection formulas based on the shaft's material, dimensions, and loading.

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

Q4: Does this formula work for all shaft types?
A: This is the simplest formula for a uniform shaft. More complex shafts may require advanced calculations.

Q5: How does shaft diameter affect critical speed?
A: Larger diameter shafts generally have higher critical speeds as they're stiffer (less deflection).