Research On Real-Time Toolpath Smoothing And Feedrate Scheduling For Five-Axis Machining

Advanced five-axis CNC systems are the key equipment for machining complex parts used in defence and transportation industries,and directly influence the machining accuracy and efficiency.To realize high-precision and high-efficiency machining,the primary task of the CNC systems is to generate smooth and efficient tool trajectories in real time.In commercial CNC systems,the most widely adopted format of toolpaths is still linear blocks,and the used feedrate is increasing.The tangent at the corners of the linear toolpath is discontinuous.To reduce feedrate fluctuation and maintain machining precision,CNC systems usually traverse the corners with a much lower feedrate than the commanded value.This will bring about frequent acceleration and deceleration of axial movements,and significantly reduce machining efficiency and quality in high-speed machining.To improve machining precision and efficiency,researches on how to generate smooth and efficient trajectories should be carried out from the following two aspects:toolpath smoothing and feedrate scheduling.Existing works mainly concerned three-axis machining,and still have several drawbacks.For toolpath smoothing,the smoothing error of the tool orientation cannot be directly controlled;and the curve parameters of the tool position and tool orientation paths are difficult to analytically synchronized.For feedrate scheduling,the low-order trajectories will introduce impacts to the machine tool structure in high-speed machining;the lookahead technique scans the path blocks serially,and thus inefficiently;and there still lacks a real-time feedrate scheduling method which can consider the kinematic constraints for the tool position as well as for the tool orientation.To address the above problems,this dissertation conducts researches from four aspects:trajectory generation for parametric curves,look-ahead feedrate scheduling,analytical five-axis toolpath transition,and real-time five-axis feedrate scheduling.It is organized from three-axis to five-axis machining,and from toolpath smoothing to feedrate scheduling.A high-order time law is proposed to make the feedrate continuous within each path block.A tweaked lookhead method as well as a parallel scanning method is introduced,which can ensure the feedrate continuity at block junctions.An analytical five-axis toolpath transition method is proposed to obtain G~2 continuous parametric toolpath.A real-time five-axis feedrate scheduling method is proposed,which can consider the kinematic constraints for the tool position and for the tool orientation.The main contents and new developments are summarized as follows:1.A time law with sine series representation of jerk function is proposed.By using geometric sequence as the coefficients of the sine series,all the velocity,acceleration and jerk functions of the time law obtain closed-form expressions.These expressions are more concise than those of the piecewise polynomial time law.By optimizing the common ratio of the geometric sequence,the time law improves the movement efficiency.Its resultant movement efficiency is improved by 10.9%compared with the trigonometric time law,and reaches 95.4% of the efficiency of the polynomial time law.Meanwhile,an integral interpolation method is proposed for parametric curves.By sampling on the whole velocity,acceleration and jerk functions,the integral interpolation method avoids the compensations for the arc length errors within each path block.Therefore,it can generate overall continuous axial velocities and axial accelerations.Path tracking experiments demonstrate that the proposed time law can significantly improve the movement efficiency while keeping comparative contouring errors.2.Two properties of the acceleration time law are revealed:(1)If the kinematic constraints are symmetric,the acceleration displacement is the product of the duration and the average value of the two boundary velocities;(2)If there is an acceleration time law and its end velocity is decreased,there always exists another time law.On this basis,a tweaked look-ahead feedrate scheduling method and a parallel bi-directional scanning method are proposed.The tweaked method can adopt high-order time laws,and the bi-directional method can improve the scanning efficiency.Since the displacement is not decreasing with respect to the start velocity of an acceleration time law,the traditional look-ahead method cannot guarantee an overall continuous feedrate profile if the size of the look-ahead buffer is insufficient.The tweaked method can achieve overall continuous feedrate profile,regardless of the buffer size.In the look-ahead method,the bi-directional scanning algorithm scans the path blocks serially,which is inefficient.The proposed parallel method divides the path blocks into two kinds of groups,and scans the path blocks in each group parallel.Compared with the serial method,it can improve the scanning efficiency by 370% on a quad-core CPU.3.An analytical transition method for linear five-axis toolpaths is proposed.It can directly control the tool orientation smoothing error,and analytically synchronize the curve parameters of the tool position path and tool orientation path.The tool orientation error is controlled via two steps:(1)replace the corner of the linear toolpath with a cubic B-spline in the workpiece coordinate system;(2)project the smoothed path onto the unit sphere.The curve parameters of the two smoothed paths are synchronized by converting the remaining linear segments into cubic B-splines.Compared with the transition methods in the machine coordinate system,the proposed method does not involve kinematic transformation.It improves the computation efficiency by 34.0%,and can strictly constrain the tool orientation error.Experiments on a self-developed machine tool show that the axial accelerations can be decreased by up to 28.0% after using the proposed method.4.A simultaneous linear and angular feedrate scheduling method is proposed.The proposed method can strictly respect the kinematic constraints for the tool position and tool ori-entation in the workpiece coordinate system.It can also consider the axial kinematic constraints by mapping these values into the workpiece coordinate system.For a five-axis toolpath compris-ing 16 cutter locations,the proposed method completes the feedrate scheduling in 0.5ms,which suffices to meet the real-time requirement of CNC systems.It consists of two steps:(1)plan the movements for the tool position and tool orientation separately;(2)synchronize the durations of the two movements.Compared with the traditional parameter synchronization method,the proposed method can guarantee that all the axial velocities are nearly under the limits,and can decrease the axial accelerations for the inserted parametric curves by up to 97.2%.After using the proposed analytical toolpath transition and the proposed feedrate scheduling methods,compared with the linear toolpath,the machining efficiencies for two case studies are increased by 38.4% and 84.2%,respectively.Finally,integrating the proposed algorithms,an platform which can generate smooth and efficient trajectories for five-axis CNC machining is provided.Experiments on the self-developed machine tool show that the platform can be used for open-architecture CNC systems to schedule the feedrate in real time,and cutting experiments with a commercial CNC system show that the platform can be used for the commercial CNC systems to optimize the feedrate offline.