Prediction model for profile errors in thin-walled blade milling based on dynamic-static decoupling and spatio-temporal mapping

Five-axis milling of thin-walled blades is highly sensitive to tool path deviations as well as quasi-static and dynamic workpiece deflections, leading to excessive profile errors. Constrained by the highly coupled nature of multiple error sources in the spatio-temporal domain, traditional theoretical predictions often fail to accurately capture the true profile errors. To address this gap, this study proposes a novel spatio-temporal mapping error prediction model that integrates machine tool kinematic deviations with the workpiece system's quasi-static and dynamic responses. Specifically, an enhanced cutter-workpiece engagement (CWE) extraction method is developed to construct a transient milling force model capable of adapting to the complex geometry and time-varying tool axes of thin-walled blades. Driven by these transient cutting loads, a dynamic-static decoupling framework is formulated to explicitly evaluate the quasi-static and high-frequency dynamic deflections of the workpiece. The instantaneous normal relative deviations between the tool and the workpiece are then derived by incorporating machine tool kinematic deviations. As a key innovation, an entry-phase-based spatio-temporal mapping algorithm is proposed. Through the discrete sampling of relative deviations and the superposition of three-dimensional residual heights, blade profile errors are accurately predicted. The results indicate that the model possesses high prediction accuracy and robustness, providing reliable theoretical support for elucidating error mechanisms in multi-axis milling of complex thin-walled parts and facilitating its engineering applications.