Enhanced Campbell Diagram With the Concept of H∞ in Rotating Machinery: Lee Diagram

The Campbell diagram, a frequency-speed diagram, has been widely used for prediction of possible occurrence of resonances in the phase of design and operation of rotating machinery since its advent in 1920s. In this paper, a set of new frequency-speed diagrams, which is referred to as the Lee diagram, is newly proposed, where the conventional Campbell diagram is incorporated with the concept of the infinity norm of directional frequency response matrix (dFRM) associated with a rotor with rotating and stationary asymmetry in general. The dFRM is constructed based on complete modal analysis of a linear periodically time-varying rotor model formulated in the complex coordinates. It is shown that the Lee diagram is powerful in that it can identify the modes of symmetry, rotating and stationary asymmetry, and extract only a few critical resonances out of the, otherwise, overcrowded ones without a measure of priority as in the Campbell diagram. In order to demonstrate the power of the Lee diagram in design and operation of rotating machines, three examples are treated: a typical anisotropic rigid rotor, a simple general rotor, and a two-pole generator.

[1]  Chong-Won Lee,et al.  Modal analysis of periodically time-varying linear rotor systems , 2006 .

[2]  Chong-Won Lee,et al.  Development of the use of directional frequency response functions for the diagnosis of anisotropy and asymmetry in rotating machinery: theory , 1994 .

[3]  Chong-Won Lee,et al.  Strength of modes in rotating machinery , 2008 .

[4]  Wilfred Campbell,et al.  The Protection of Steam-Turbine Disk Wheels From Axial Vibration , 1924, Transactions of the American Society of Mechanical Engineers.

[5]  D. J. Ewins,et al.  Modal analysis and testing of rotating structures , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  J. S. Rao.  Turbomachine Blade Vibration , 1991 .

[7]  Giancarlo Genta,et al.  Whirling of unsymmetrical rotors: A finite element approach based on complex co-ordinates , 1988 .

[8]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[9]  Chong-Won Lee,et al.  AN EFFICIENT COMPLEX MODAL TESTING THEORY FOR ASYMMETRIC ROTOR SYSTEMS: USE OF UNDIRECTIONAL EXCITATION METHOD , 1997 .

[10]  Chong-Won Lee,et al.  Vibration Analysis of Rotors , 1994 .

[11]  Chong-Won Lee,et al.  Modal analysis of asymmetric rotor system with isotropic stator using modulated coordinates , 2005 .

[12]  Chong-Won Lee,et al.  A complex modal testing theory for rotating machinery , 1991 .

[13]  R. Calico,et al.  Control of time-periodic systems , 1984 .

[14]  Peter Lancaster,et al.  Lambda-matrices and vibrating systems , 2002 .

[15]  F. Dimentberg.  Flexural vibrations of rotating shafts , 1961 .

[16]  Evolution of Campbell Diagram with Modal Strength in Rotating Machinery , 2007 .

[17]  Rainer Nordmann.  Identification of Modal Parameters of an Elastic Rotor With Oil Film Bearings , 1984 .

[18]  D. A. Frohrib,et al.  Instabilities of an Asymmetric Rotor With Asymmetric Shaft Mounted on Symmetric Elastic Supports , 1976 .

[19]  A. Gourlay,et al.  Computational Methods for Matrix Eigenproblems , 1973 .

[20]  Michel Lalanne,et al.  Rotordynamics prediction in engineering , 1998 .

[21]  Charles T. Hatch,et al.  Fundamentals of Rotating Machinery Diagnostics , 2003 .