Steady-State Response Analysis of an Uncertain Rotor Based on Chebyshev Orthogonal Polynomials

The performance of a rotor system is influenced by various design parameters that are neither precise nor constant. Uncertainties in rotor operation arise from factors such as assembly errors, material defects, and wear. To obtain more reliable analytical results, it is essential to consider these uncertainties when evaluating rotor performance. In this paper, the Chebyshev interval method is employed to quantify the uncertainty in the steady-state response of the rotor system. To address the challenges of high-dimensional integration, an innovative sparse-grid integration method is introduced and demonstrated using a rotor tester. The effects of support stiffness, mass imbalance, and uncertainties in the installation phase angle on the steady-state response of the rotor system are analyzed individually, along with a comprehensive assessment of their combined effects. When compared to the Monte Carlo simulation (MCS) method and the full tensor product grid (FTG) method, the proposed method requires only 68% of the computational cost associated with MCS, while maintaining calculation accuracy. Additionally, sparse-grid integration reduces the computational cost by approximately 95.87% compared to the FTG method.