Research On Compression Of Small Line Segments Based On Archimedes Spiral And Its Interpolation Algorithm

Under the background of promoting the high-end CNC system development and improving the processing efficiency and quality,it is difficult to achieve high speed machining process using the small line processing program in the face of complex curve and surface.And too many turning points between lines may cause overcut or undercut,which will affect the processing quality.In order to solve the above problem and improve the ability of high speed and high precision machining of CNC system,this thesis based on Archimedes spiral made a related study on the optimization and interpolation of small line segments NC program.In order to solve the problem of large amount of small line segments tool path data in numerical control machining process,a compression processing algorithm based on Archimedes spiral for small line segments was proposed.The relationship between parameters of Archimedes spiral and angle between tangent vector and radius vector was analyzed.Based on this,the approximate method for calculating the center of spiral was given.The calculation formula of spiral parameters based on least square principle was derived,which took the sum of squared error of intermediate data points as the objective function.The forward and backward searching strategy was applied to traverse all the data points.Finally,the small line segments tool path was compressed as a set of trajectories composed of spirals and small line segments.Aiming at spiral direct interpolation,this thesis proposed hybrid T-type and hybrid S-type ACC/DEC algorithm.The two speed planning methods constructed the constraint relationship between chord error and running speed based on curvature characteristic during adaptive interpolation.So the speed planning result was got under the constraints of the ACC/DEC mode,the performance of machine tool and chord error.A look-ahead algorithm and transition speed processing strategy were designed for multi spiral segments and small line segments.And the correctness of the above speed planning algorithm were verified by simulation experiment.For reducing velocity fluctuation,a predictor-corrector method based on improved Newton iteration was designed to calculate the interpolation parameter.The estimated initial value was solved by the first order Taylor expansion,and the improved Newton iteration was used to correct the calculation.The simulation results showed that the predictor-corrector method had good comprehensive performance in both calculation accuracy and calculation efficiency.The algorithm proposed in this thesis was embedded in the reconfigurable CNC system of the research group.And the small line segments track of four leaf clover was processed on three-axis milling machine.The experimental results showed that the proposed algorithm's data was compressed by 42.96% when the fitting precision was 0.02 mm.And it increased machining efficiency by 26.69% while reducing the following error of machine tool.