Engine-Order Resonance Example

Illustrative example identifying a resonance crossing from a Campbell diagram and calculating the resonance speed for a specific engine order.

Turbomachinery5 min read

turbomachineryworked exampleengine orderresonanceCampbell diagram

Problem

A turbine blade has a first bending frequency of 620 Hz at the operating speed of 12,000 rev/min. The upstream stator row has 36 vanes, producing an excitation at engine order 36. Determine whether the EO36 crossing occurs within the operating range (10,000-12,000 rev/min) and at what speed.

Given

Blade frequency f_n = 620 Hz at 12,000 rev/min
Engine order n = 36 (from 36 stator vanes)
Operating range: 10,000-12,000 rev/min

Step 1 — Resonance speed

At resonance, the excitation frequency equals the natural frequency: f_excitation = n * N / 60 = f_n N_resonance = f_n * 60 / n = 620 * 60 / 36 = 1033.3 rev/min

Step 2 — Check against operating range

N_resonance = 1033 rev/min. This is well below the operating range of 10,000-12,000 rev/min. The EO36 crossing occurs during start-up at approximately 1033 rev/min, not during normal operation.

Step 3 — Check other engine orders

For the crossing to occur at 12,000 rev/min: n = f_n * 60 / N = 620 * 60 / 12000 = 3.1 Since engine orders must be integers, EO3 would cross at N = 620 * 60 / 3 = 12,400 rev/min (just above the operating range). This is a near-resonance that should be assessed.

Result

The EO36 resonance occurs at approximately 1033 rev/min — well below the operating range, so it is not a concern for steady-state operation. However, the blade passes through this resonance during start-up. The EO3 crossing is near the upper end of the operating range (12,400 rev/min) and should be assessed for vibratory stress.

Assumptions and limitations

The blade frequency is assumed constant at 620 Hz — in practice it varies with speed
The actual frequency at 1033 rev/min would be lower than 620 Hz due to less centrifugal stiffening
The resonance speed should be computed using the frequency at the resonance speed, not the operating speed frequency
The excitation amplitude at EO36 is not assessed — a weak excitation may not produce significant vibratory stress