Dimensionality reduction method based on energy order distribution for multi-nonlinearity-coupled rotor-bearing system

Gas turbine rotors are complex dynamic systems with high-dimensional, discrete, and multi-source nonlinear coupling characteristics. Significant amounts of resources and time are spent during the process of solving dynamic characteristics. Therefore, it is necessary to design a low-dimensional model that can well reflect the dynamic characteristics of high-dimensional system. To build such a low-dimensional model, this study developed a dimensionality reduction method considering global order energy distribution by modifying the proper orthogonal decomposition theory. First, sensitivity analysis of key dimensionality reduction parameters to the energy distribution was conducted. Then a high-dimensional rotor-bearing system considering the nonlinear stiffness and oil film force was reduced, and the accuracy and the reusability of the low-dimensional model under different operating conditions were examined. Finally, the response results of a multi-disk rotor-bearing test bench were reduced using the proposed method, and spectrum results were then compared experimentally. Numerical and experimental results demonstrate that, during the dimensionality reduction process, the solution period of dynamic response results has the most significant influence on the accuracy of energy preservation. The transient signal in the transformation matrix mainly affects the high-order energy distribution of the rotor system. The larger the proportion of steady-state signals is, the closer the energy tends to accumulate towards lower orders. The low-dimensional rotor model accurately reflects the frequency response characteristics of the original high-dimensional system with an accuracy of up to 98 %. The proposed dimensionality reduction method exhibits significant application potential in the dynamic analysis of high-dimensional systems coupled with strong nonlinearities under variable operating conditions.