Eigenvalue perturbation in drivetrain analysis and optimization

The optimization of the dynamic behavior of drive systems often involves targeted modifications of the system characteristics. Structural and parametric modifications are used to satisfy the constraints of the dynamic requirements. However, many optimizations are still achieved by intuition or parameter variations, even though more streamlined and easy-to-implement tools such as the eigenvalue perturbation method are available. In this article, the eigenvalue perturbation method in the form of an eigenvalue sensitivity analysis is used to efficiently optimize the dynamic behavior for two different use cases using different optimization measures. This paper demonstrates, how eigenvalue perturbation theory can efficiently optimize drivetrain dynamics by systematically modifying system parameters. Two case studies show how eigenvalue sensitivity analysis achieves targeted frequency shifts to avoid resonances: (1) adapting shaft stiffness and control parameters in a torsional drivetrain, and (2) optimizing structural modifications in a wind turbine bedplate. The study introduces the eigenvector tensor product as a weighting matrix, identifying key parameters for effective redesign. Compared to conventional parameter studies, this method enables precise control over system dynamics with minimal computational effort, making it highly applicable for vibration mitigation and drivetrain optimization.