Understanding a Flexible Rotor

Definition: What is a Flexible Rotor?

A flexible rotor is a rotor that deforms or bends due to centrifugal forces when operating at or near its critical speeds. Unlike a rigid rotor, which can be balanced at a low speed and will remain balanced throughout its operating speed range, a flexible rotor’s unbalance distribution changes as its shape changes with speed. This means that balancing a flexible rotor is a significantly more complex process.

As a general rule of thumb, a rotor is considered flexible if its maximum service speed is 70% or more of its first bending critical speed.

Why Do Flexible Rotors Behave Differently?

The key to understanding a flexible rotor is the concept of critical speeds and mode shapes.

• Critical Speed: This is a rotational speed that matches one of the rotor’s natural frequencies. At this speed, the rotor experiences resonance, and any small amount of unbalance is greatly amplified, causing the rotor to bend.
• Mode Shape: This is the characteristic shape that the rotor bends into as it passes through a specific critical speed. The first critical speed has a simple half-sine wave shape, the second has a full sine wave shape (with a node in the middle), and so on.

When a flexible rotor spins up, the location of the “heavy spot” (center of mass) shifts due to this bending. An unbalance that exists at low speed may be in a completely different effective location at high speed. Therefore, a simple two-plane balance performed at low speed will not be sufficient to ensure smooth operation at the service speed or during transit through the critical speeds.

Balancing Flexible Rotors

Balancing flexible rotors is a specialized task that requires advanced techniques and equipment, as outlined in standards like ISO 21940-12. The goal is not just to balance the rotor for one speed but to ensure it runs smoothly across its entire operating range, including passing through its critical speeds.

Common techniques include:

• Modal Balancing: This is a powerful technique where each bending mode is treated as a separate unbalance problem. Correction weights are strategically placed in multiple planes along the rotor to specifically counteract the forces generated by each mode shape. For example, to correct the first mode, weights are placed at the center of the rotor where the bending is greatest. To correct the second mode, weights are placed on either side of the central node.
• Influence Coefficient Method (Multi-Speed, Multi-Plane): This involves running the rotor at several different speeds (including near the critical speeds) and using trial weights in multiple correction planes. The data is used to build a complex matrix of influence coefficients that describes the rotor’s response. A computer then solves this matrix to determine the optimal set of correction weights for multiple planes simultaneously.

This process typically requires a high-speed balancing machine that can safely operate the rotor through its critical speeds and sophisticated software to perform the necessary calculations.

Examples of Flexible Rotors

Flexible rotors are common in high-performance machinery, including:

• Large steam and gas turbine generators
• High-speed turbocompressors
• Long, slender shafts and rollers in paper machines
• High-speed machine tool spindles

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