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.
A Campbell diagram (also called an interference diagram) plots blade natural frequencies as horizontal lines and engine order excitation frequencies as diagonal lines (f = n × RPM/60). Intersections within the operating speed range indicate potential resonance conditions that must be avoided.
The cantilever beam model provides a good first approximation for turbine blade natural frequencies. The blade root is essentially fixed, and the free end vibrates. For preliminary design and quick checks, this analytical model gives results within 10–20% of FEA for simple blade geometries.
A minimum 10% separation margin between natural frequencies and excitation frequencies at the design speed is typically required. Some codes and manufacturers require 15% or even 20% for critical applications. If a crossing falls within the operating range, the blade design must be modified.
Common excitation sources include:
- Nozzle passing — number of nozzle vanes × RPM/60
- Rotor harmonics — 1×, 2×, 3× running speed
- Upstream wakes — from struts, bearings, combustors
- Partial admission — arc of admission in impulse stages
At higher rotational speeds, centrifugal forces increase the effective stiffness of the blade, raising its natural frequency. This is why Campbell diagram lines for real blades curve upward slightly (not perfectly horizontal). This calculator uses a simplified model without centrifugal stiffening.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional vibration analysis and field balancing instruments for turbomachinery. Used in 50+ countries.
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.
