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Objective <p>As rotor models increase in complexity, scale, and precision, the demands for efficient and accurate computational methods become increasingly stringent. Consequently, this study aims to develop an efficient and accurate framework for modeling and computation in rotor transient analysis. High-order accuracy time integration methods and automatic time-stepping strategies are considered critical for enhancing computational efficiency and accuracy. However, the discrete-time transfer matrix method, a vital transient analysis tool for rotor dynamics, has not been extensively explored in these areas. Therefore, this research focuses on addressing these gaps.</p> Methodology <p>This study: (1) replaces generalized displacements in conventional state vectors with generalized accelerations and uses the differential quadrature method to discretize the extended kinematic and dynamic equations of components, forming transfer equations and matrices. This approach leads to the development of a fixed time-stepping differential-quadrature discrete-time Riccati transfer matrix method (DQ-DT-RTMM); (2) employs the ‘displacement history curvature’ formula and curvature regularization technology of ‘maximum interval value’ to address, respectively, the implementation and timing of time-step adjustments, resulting in the development of an automatic time-stepping DQ-DT-RTMM; and (3) based on both the fixed and automatic time-stepping DQ-DT-RTMM, develops a universal solver for rotor transient analysis.</p> Conclusion <p>Numerical simulations conducted on two rotor system models reveal: (1) The fixed time-stepping DQ-DT-RTMM outperforms commonly used time integration methods in terms of computational accuracy, error convergence rate, and long-term response tracking. (2) The automatic time-stepping DQ-DT-RTMM achieves greater accuracy with fewer time steps than its fixed time-stepping version, effectively balancing the computational efficiency and accuracy. (3) The DQ-DT-RTMM solver demonstrates significant advantages in computational efficiency and accuracy over commercial finite element software for large-scale rotor system transient analysis.</p>

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Differential-Quadrature Discrete-Time Riccati Transfer Matrix Method for Transient Response in Rotor Systems

  • 期刊论文

  • 发表日期：

    2025年2月7日

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  • Kai Xie,
  • Xiaoting Rui,
  • Bin He,
  • Jinghong Wang

摘要

Objective

As rotor models increase in complexity, scale, and precision, the demands for efficient and accurate computational methods become increasingly stringent. Consequently, this study aims to develop an efficient and accurate framework for modeling and computation in rotor transient analysis. High-order accuracy time integration methods and automatic time-stepping strategies are considered critical for enhancing computational efficiency and accuracy. However, the discrete-time transfer matrix method, a vital transient analysis tool for rotor dynamics, has not been extensively explored in these areas. Therefore, this research focuses on addressing these gaps.

Methodology

This study: (1) replaces generalized displacements in conventional state vectors with generalized accelerations and uses the differential quadrature method to discretize the extended kinematic and dynamic equations of components, forming transfer equations and matrices. This approach leads to the development of a fixed time-stepping differential-quadrature discrete-time Riccati transfer matrix method (DQ-DT-RTMM); (2) employs the ‘displacement history curvature’ formula and curvature regularization technology of ‘maximum interval value’ to address, respectively, the implementation and timing of time-step adjustments, resulting in the development of an automatic time-stepping DQ-DT-RTMM; and (3) based on both the fixed and automatic time-stepping DQ-DT-RTMM, develops a universal solver for rotor transient analysis.

Conclusion

Numerical simulations conducted on two rotor system models reveal: (1) The fixed time-stepping DQ-DT-RTMM outperforms commonly used time integration methods in terms of computational accuracy, error convergence rate, and long-term response tracking. (2) The automatic time-stepping DQ-DT-RTMM achieves greater accuracy with fewer time steps than its fixed time-stepping version, effectively balancing the computational efficiency and accuracy. (3) The DQ-DT-RTMM solver demonstrates significant advantages in computational efficiency and accuracy over commercial finite element software for large-scale rotor system transient analysis.