Modal Parameter Identification of Electric Spindles Based on Covariance-Driven Stochastic Subspace

Electric spindles are a critical component of numerically controlled machine tools that directly affect machining precision and efficiency. The accurate identification of the modal parameters of an electric spindle is essential for optimizing design, enhancing dynamic performance, and facilitating fault diagnosis. This study proposes a covariance-driven stochastic subspace identification (SSI-cov) method integrated with a simulated annealing (SA) strategy and fuzzy C-means (FCM) clustering algorithm to achieve the automated identification of modal parameters for electric spindles. Using both finite element simulations and experimental tests conducted at 22 °C, the first five natural frequencies of the electric spindle under free, constrained, and dynamic conditions were extracted. The experimental results demonstrated experiment errors of 0.17% to 0.33%, 1.05% to 3.27%, and 1.29% to 3.31% for the free, constrained, and dynamic states, respectively. Compared to the traditional SSI-cov method, the proposed SA-FCM method improved accuracy by 12.05% to 27.32% in the free state, 17.45% to 47.83% in the constrained state, and 25.45% to 49.12% in the dynamic state. The frequency identification errors were reduced to a range of 2.25 Hz to 20.81 Hz, significantly decreasing errors in higher-order modes and demonstrating the robustness of the algorithm. The proposed method required no manual intervention, and it could be utilized to accurately analyze the modal parameters of electric spindles under free, constrained, and dynamic conditions, providing a precise and reliable solution for the modal analysis of electric spindles in various dynamic states.