Campbell diagram

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A Campbell diagram plot represents a system's response spectrum as a function of its oscillation regime. It is named for Wilfred Campbell, who introduced the concept.[1][2] It is also called an interference diagram.[3]

Analytical Campbell Diagram for a Simple Rotor

In rotordynamics

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In rotordynamical systems, the eigenfrequencies often depend on the rotation rates due to the induced gyroscopic effects or variable hydrodynamic conditions in fluid bearings. It might represent the following cases:

 
Campbell Diagram of a steam turbine. Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to safely ignore it.
  1. Analytically computed values of eigenfrequencies as a function of the shaft's rotation speed. This case is also called "whirl speed map".[4] Such a chart can be used in turbine design.
  2. Experimentally measured vibration response spectrum as a function of the shaft's rotation speed (waterfall plot), the peak locations for each slice usually corresponding to the eigenfrequencies.

In acoustical engineering

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In acoustical engineering, the Campbell diagram would represent the pressure spectrum waterfall plot vs the machine's shaft rotation speed (sometimes also called 3D noise map).

References

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  1. ^ Campbell, Wilfred (1924). "Protection of Steam Turbine Disk Wheels from Axial Vibration". Transactions of the ASME: 31–160.
  2. ^ Meher-Homji, Cyrus B.; Erik Prisell (2005). "Dr. Max Bentele---Pioneer of the Jet Age". Journal of Engineering for Gas Turbines and Power. 127 (2): 231–239. doi:10.1115/1.1807412. Archived from the original on 2013-02-23. Retrieved 2010-07-27.
  3. ^ Nelson, F. C. (2007). "Rotor dynamics without equations" (PDF). International Journal of COMADEM. 10 (3): 2. Archived from the original (PDF) on 2015-09-24. Retrieved 2012-10-01.
  4. ^ Logan, Earl Jr (2003-05-01). Handbook of Turbomachinery (Mechanical Engineering, No. 158) (2 ed.). CRC Press. ISBN 978-0-8247-0995-2.