High-Precision Algorithm for Rotor Critical Speed and Unbalance Response Calculation

This paper presents a high-precision algorithm for calculating rotor critical speeds and unbalance responses, primarily based on the transfer matrix method. The transfer matrix method serves as a mathematical tool for describing linear systems, representing the relationship between system inputs and outputs in matrix form. Through implementation of this method, our algorithm achieves more accurate computation of rotor critical speeds and unbalance responses, thereby facilitating improved design and optimization of rotor systems. The computational approach involves constructing state vectors at each rotor station and propagating them through sequentially multiplied transfer matrices. Key functions include handling gyroscopic effects, bearing stiffness variations, and mass unbalance forces. Notably, our algorithm demonstrates not only high precision but also computational efficiency, making it suitable for practical engineering applications. The implementation features optimized matrix operations and eigenvalue solvers for rapid critical speed determination, with the unbalance response calculation incorporating complex phasor analysis for vibration amplitude and phase prediction.