To enhance the accuracy of CNC machines for the request of modern industry, an effective static/quasi-static error compensation system composing of an element-free interpolation algorithm based on the Galerkin method for error prediction, a recursive software compensation procedure, and an NC-code converting software, is developed. Through automatically analyzing the machining path, the new error prediction method taking into the consideration of the fact that machine structure is non-rigid, can efficiently on-line determine the position errors of the cutter for compensation without computing a complex error model. The predicted errors are then compensated based on a recursive compensation algorithm. Finally, a compensated NC program will be automatically generated by the NC-code converting software for the precision machining process. Because of the advantage of element-free theory, the error prediction method can flexibly and irregularly distributing nodal points for accurate error prediction for a machine with complex error distribution characteristics throughout the workspace. To verify the algorithm and the developed system, cutting experiments were conducted in this study, and the results have shown the success of the proposed error compensation system.

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