An Improved Method for Calculating Critical Speeds and Rotordynamic Stability of Turbomachinery

A number of the computer programs for rotordynamic stability and critical speed prediction in common use during recent years have been based on the works of Myklestad, Prohl, and Lund. Programs of this type, called transfer matrix programs, employ complex variables when damping or cross-coupling are included in the model. Most use an iteration scheme which at times fails to converge with sufficient accuracy on some critical speeds, and has been known to completely miss critical speeds on occasion. It is shown in this paper that by rearranging the calculations performed in a transfer matrix program, one can derive the characteristic polynomial for a complex rotor-bearing system with no loss in generality. The modeling procedures are identical for the rotor and bearing/foundations, including the effects of gyroscopics, damping, and any or all destabilizing influences which are linearized in the usual manner. With the characteristic polynomial known, critical speeds can be estimated and stability predicted with greater efficiency and with no fear of missing any modes. Such a program has been written, and a complete comparison between the two types of programs is shown.