A geometry-constraint-driven high-precision cutter contact point determination method for toroidal end mills in five-axis machining of compressor blades

To ensure the in-service performance of aero-engines, compressor blades are typically fabricated from difficult-to-cut materials and are subject to exceptionally stringent dimensional accuracy requirements. The in-service performance of blades must be underpinned by advanced manufacturing processes. Owing to the ability to accommodate complex cutter orientations when machining free-form surfaces, five-axis CNC machining technology has been widely adopted in the manufacturing of high-value components such as blades and blisks. In five-axis CNC milling, accurate determination of the cutter contact point is a fundamental prerequisite for constructing a position-oriented process monitoring framework in blade milling, achieving precise prediction of machining errors, and ultimately realizing high-performance manufacturing. This paper presents a geometry-constraint-driven cutter contact point determination method for toroidal end mills in five-axis machining of compressor blades. The proposed method is applicable to arbitrary machining stages throughout the blade manufacturing process. A notable characteristic of this method is that it operates independently of separately provided in-process workpiece models and tool-axis vectors. Specifically, the kinematic chain structure of an A/B dual-rotary-table five-axis machining center is first analyzed, upon which a forward kinematic model is established for deriving the tool-axis vector from the A- and B-axis rotation angles of the machine tool. By exploiting the fundamental geometric property that the surface normal vector at any true cutter contact point must pass through the center of the corresponding corner radius circle, two necessary geometric constraints governing the contact between a toroidal end mill and the workpiece surface are subsequently established, namely the center-circle plane constraint and the center-circle radius constraint. On this basis, the residuals associated with both constraints are formulated, and the original cutter contact point determination problem is reformulated as a least-squares optimization problem defined over the parametric surface domain, wherein the objective is to identify the parameter pair that minimizes the combined constraint residuals. A Gauss–Newton iterative algorithm is subsequently developed to efficiently solve this optimization problem. Finally, statistical analysis of three categories of quantitative data, comprising the deviations between the calculated and theoretical cutter contact points, the spatial errors between the reconstructed and actual cutter location points, and the residuals of both geometric constraints, collectively demonstrates the high precision and stability of the proposed methodology in cutter contact point determination. The present study holds considerable engineering significance for the precise control of machining errors in blade manufacturing, the assurance of aerodynamic in-service performance, and the improvement of both qualification rate and production efficiency in batch blade fabrication.