فرکانس طبیعی پره توربین و بررسی کمپبل

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.