A Tool Path B-spline Fitting Method With Arc-length Parameterization,G2-continuous Blending,and Quality Evaluation

During CNC machining,G01-based tool paths generated by CAM systems lack G1 continuity and cause large storage.The discontinuity leads to fluctuation of feed rate and acceleration,which brings about vibration and unexpected slow-downs.To improve the machining efficiency and quality,smooth tool paths are preferred.B-spline fitting methods have been developed for tool path smoothing.Due to the nonlinear relationship between the arc length and the parameter,it is hard to obtain the exact next interpolating point,resulting in feed rate fluctuation.A large number of data points of G01-based tool paths lead to large computation and low efficiency in tool path B-spline fitting.In general,discrete G01 points are divided into several subsections and tool path B-spline fitting is applied in every subsection.The junction point of two adjacent B-splines has less G2-continuity.Besides,exisiting tool path B-spline fitting methods lack of a solution to evaluate the tool path quality.This paper presents the arc length parameterization algorithm based on twice-fitting to avoid the feed rate fluctuation.An interpolating initial spline curve satisfied chord error and shape preserving constraints is constructed in the pre-fitting stage.Then the initial spline curve is sampled and arc length parameters of sample points are calculated.Finally,the sample points are fitted to B-spline tool paths with arc-length parameters.Besides,an algorithm to blend two adjacent B-splines is proposed.A blending curve is inserted between two successive B-splines to ensure the joints of the blending curve and the original B-splines G2 continous and satisfy the chord error and shape preserving constraints.Furthermore,a method to evaluate the B-spline quality is provided.The quality evaluation includes computing the maximum chord error between the B-spline and the polyline composed by the data points and the smoothness assessment.To verify the effectiveness of the algorithms mentioned above,workpieces are machined using: the existing B-spline fitting method,the fitting method with arc length parameterization algorithm,and the fitting method with G2 blending algorithm.The simulation demonstrates that the quality assessment can detect the deficiencies of tool paths.The experiment shows that the arc length parameterization algorithm can improve the machining efficiency but have little effect on the surface quality.Besides,the G2 blending algorithm can not improve the machining quality.