Critical Speed in Rotor Dynamics Explained

Definition: What is a Critical Speed?

A critical speed is a rotational speed that matches a rotor’s natural frequency of vibration. When a machine operates at or near one of its critical speeds, the phenomenon of resonance occurs. This causes a dramatic and often dangerous amplification of the rotor’s vibration, as even a tiny amount of residual unbalance can generate enormous centrifugal forces. Every rotor system has multiple critical speeds, corresponding to its different modes of vibration (e.g., first bending mode, second bending mode, etc.).

Why is Critical Speed So Important?

Understanding and managing critical speeds is one of the most fundamental aspects of rotating machinery design and analysis. Operating a machine at a critical speed, even for a short period, can be catastrophic. The consequences include:

• Excessive Vibration: Amplitudes can increase by a factor of 10, 20, or even more, depending on the system’s damping.
• Component Failure: The high vibration and shaft deflection can lead to bearing failure, seal damage, and rubs between rotating and stationary parts.
• Catastrophic Shaft Failure: In severe cases, the bending stresses can exceed the material’s fatigue limit, causing the shaft to crack or break.
• Safety Hazards: A machine failure at high speed poses a significant risk to personnel and surrounding equipment.

For these reasons, machinery is always designed to operate with a “separation margin,” meaning its normal running speed is intentionally kept a safe distance away from any critical speeds.

Rigid vs. Flexible Rotors

The concept of critical speed is what distinguishes a “rigid” rotor from a “flexible” one:

• Rigid Rotor: A rotor that operates *below* its first critical speed. Its shaft does not undergo significant bending during operation. These are typically slower, stockier rotors.
• Flexible Rotor: A rotor that is designed to operate *above* its first (and sometimes second or third) critical speed. Its shaft will flex and bend as it passes through the critical speeds during startup and shutdown. High-speed, slender rotors like those in turbines and compressors are flexible rotors.

Managing Critical Speeds in Machine Operation

Since it’s often not practical to design a high-speed machine that stays below its first critical speed, engineers use several strategies to manage them:

1. Separation Margin

The most common strategy is to ensure the machine’s continuous operating speed is not too close to any critical speed. A typical separation margin is ±20-30%. For example, if a critical speed is at 3,000 RPM, the machine should not be operated continuously between 2,400 RPM and 3,600 RPM.

2. Rapid Acceleration/Deceleration

For flexible rotors that must pass through critical speeds, startup and shutdown procedures are designed to move through the critical speed ranges as quickly as possible. Lingering at a critical speed allows vibration amplitudes to build to dangerous levels. A rapid pass-through minimizes the time for this amplification to occur.

3. Damping

Damping is the dissipation of vibrational energy, and it is what limits the peak amplitude at resonance. Bearings, especially fluid-film bearings, are a primary source of damping in rotor systems. By optimizing bearing design, engineers can control the vibration peak at the critical speed to a safe and manageable level.

4. Precision Balancing

The vibration at a critical speed is an amplified response to unbalance. The better a rotor is balanced, the smaller the forcing function will be, and therefore the lower the peak vibration will be as it passes through the critical speed. For flexible rotors, special multi-plane balancing techniques are required.

How are Critical Speeds Identified?

Critical speeds are identified using several methods:

• Rotor Dynamic Analysis (RDA): Computer models (often using Finite Element Analysis) are created during the design phase to predict the critical speeds and mode shapes of a rotor.
• Run-up/Coast-down Tests: The most common experimental method. Vibration amplitude and phase are plotted against speed as a machine starts up or shuts down. A critical speed is identified by a distinct peak in amplitude accompanied by a characteristic 180-degree phase shift. These tests generate diagnostic plots like the Bode Plot and Waterfall Plot.
• Impact Testing (Bump Test): Striking the rotor with an instrumented hammer when it is at rest can excite its natural frequencies, which correspond to the critical speeds.

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