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.