Six-dimensional B-spline Fitting Method For Five-axis Tool Paths

In computer numerical control(CNC)machining,tool paths are typically represented with piecewise linear segments(GO1s),which lack~1 and~2 continuity and cause fluctuation of feed rate and acceleration,as well as vibration and unexpected slow-downs.To improve the machining efficiency and quality,smooth tool paths are preferred and B-spline fitting methods have been developed for tool path smoothing.The energy-incorporating progressive and iterative approximation for least squares fitting(ELSPIA)method was shown to effectively and reliably accomplish B-spline fitting of piecewise linear tool paths and thus suitable for industrial applications.However,it has several shortages:(1)exclusively utilized in three-axis B-spline fitting,(2)lack of a solution to deal with the nonlinear relationship between the arc-length and the parameter of B-spline,(3)lack of a systematical solution to evaluate and improve the tool path quality.To slove the issues in 5xNurbs interpolation and ELSPIA method,this paper makes several improvements,including:(1)The relationship between cutter contact(CC)error,and cutter location(CL)error and tool-axis error is established to ensure that CL error and tool-axis error can be translated into CC error(machining errror),so as to ensure the machining error of five-axis B-spline can be accurately calculated.(2)The ELSPIA method is extended in six-dimensional space to ensure that the ELSPIA method is suitable for five-axis tool paths.(3)An algorithm based on tool-axis smoothness is presented to generate the tool paths with arc-length parameter to ensure precise and stable speed-scheduling inside CNC interpolation,which can guarantee tool paths satisfy minimal tool-axis change rate.(4)A method is used to evaluate the fitting quality,and an additional refinement procedure is employed when the evaluation finds any disqualification.(5)Offline intelligent B-spline tool path optimization software which supports the output of five-axis B-spline tool paths is developed.Our developed CNC intelligent software which supports the output of five-axis B-spline tool paths is introduced.Simulation is conducted in our developed CNC intelligent software.Simulation result proves that the proposed methods are effective and suitable for five-axis blade machining.Experiments and Roughness tests are presented for verification of machining quality and machining efficiency.The experiment results show that the proposed algorithm can improve the machining quality and machining efficiency,and thus suitable for industrial applications.