What is a flexible rotor?

A flexible rotor operates above one or more of its critical speeds, so it deforms during rotation. The unbalance distribution changes with speed as different mode shapes are excited. Examples include turbine shafts, large generators, and high-speed compressor rotors.

What is ISO 21940-14?

ISO 21940-14 provides procedures for evaluating balance quality of flexible rotors. It addresses the additional complexity of modal unbalance and specifies tolerance criteria for each significant mode shape.

How does flexible rotor balancing differ from rigid rotor balancing?

Rigid rotors need only 2-plane balancing (low-speed). Flexible rotors require N+2 planes for N modes, with speed-dependent correction. Each mode has its own unbalance tolerance based on the modal mass and the mode's critical speed.

What is modal unbalance?

Modal unbalance is the component of unbalance that excites a specific bending mode of the rotor. Each mode acts like an independent SDOF system with its own effective mass. Total balance requires addressing each significant mode.

How many correction planes do I need?

For N flexible modes, you need N+2 correction planes. For example: 1 mode → 3 planes, 2 modes → 4 planes, 3 modes → 5 planes. Plane locations should be chosen to effectively influence each mode shape.

Free Engineering Tool — #029

Flexible Rotor Balancing Tolerance

Calculate per-mode unbalance tolerance for flexible rotors per ISO 21940-14. Enter rotor mass, maximum speed, balance grade, and number of flexible modes.

ISO 21940-14Modal BalancingPer-Mode Tolerance

Results

Total Permissible Unbalance (ISO 21940-11)

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Per-Mode Tolerance

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Specific Unbalance (Eccentricity)

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Correction Planes Needed

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Angular Velocity ω

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Total Permissible Unbalance

Same as ISO 21940-11 (rigid rotor baseline):

Per-Mode Tolerance Distribution

For flexible rotors, the total tolerance is distributed among the rigid body mode (low-speed) and each flexible mode. A common engineering approach:

Where N is the number of flexible modes + 1 (rigid body mode). Each mode receives an equal share of the total unbalance budget.

Correction Planes

For N_flex flexible modes, the minimum number of correction planes is:

Example — Gas Turbine Rotor

Given: m = 500 kg, n = 8000 RPM, G2.5, 2 flexible modes

ω = 2π × 8000/60 = 837.76 rad/s

e_per = 2.5 × 1000 / 837.76 = 2.984 μm

U_total = 2.984 × 500 = 1492 g·mm

Per-mode = 1492 / 3 = 497 g·mm (3 modes: 1 rigid + 2 flexible)

Planes needed: 2 + 2 = 4 correction planes

⚠️ Note: The equal-distribution model is a simplified approach. In practice, modal mass participation may differ, and actual tolerances should be verified by rotor dynamics analysis.

Flexible Rotor Balancing Tolerance — ISO 21940-14 | Free Online Tool

Published by Nikolai Shelkovenko on February 15, 2026 February 15, 2026

Results

Total Permissible Unbalance

Per-Mode Tolerance Distribution

Correction Planes