Free Engineering Tool
Turbine Blade Natural Frequency & Campbell Check
Calculate the first-mode natural frequency of a turbine blade (cantilever beam model) and check for harmonic crossings within the operating speed range using a simplified Campbell diagram.
Results
Cantilever Beam Natural Frequency
A turbine blade can be modeled as a cantilever beam fixed at the root. The natural frequencies are:
- λn — eigenvalue: λ₁ = 1.8751, λ₂ = 4.6941, λ₃ = 7.8548
- E — Young’s modulus (Pa)
- I — second moment of area (m⁴) = b·h³/12 for rectangular cross-section
- ρ — material density (kg/m³)
- A — cross-sectional area (m²) = b·h
- L — blade length (m)
Campbell Diagram
The Campbell diagram plots blade natural frequency (horizontal lines) against engine order excitation lines (diagonal lines: f = n × RPM/60). Intersections within the operating speed range indicate potential resonance.
A minimum 10% separation margin between natural frequencies and excitation frequencies at operating speed is generally required.
Mode Shape Ratios
| Mode | λn | fn / f₁ ratio | Character |
|---|---|---|---|
| 1st | 1.8751 | 1.000 | First bending |
| 2nd | 4.6941 | 6.267 | Second bending |
| 3rd | 7.8548 | 17.55 | Third bending |
Given: L = 500 mm, thickness h = 12 mm, width b = 80 mm, Steel (E = 200 GPa, ρ = 7850 kg/m³)
I = 80 × 12³ / 12 = 11,520 mm⁴ = 1.152 × 10⁻⁸ m⁴
A = 80 × 12 = 960 mm² = 9.6 × 10⁻⁴ m²
f₁ = (1.8751² / (2π)) × √(200×10⁹ × 1.152×10⁻⁸ / (7850 × 9.6×10⁻⁴ × 0.5⁴)) = 0.5596 × √4892
f₁ ≈ 39.1 Hz
⚠️ Note: This is a simplified uniform cantilever beam model. Actual turbine blades have tapered profiles, twist, shrouds, platform effects, centrifugal stiffening, and temperature-dependent material properties that significantly affect natural frequencies. Use FEA for detailed design.
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Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
