Multi-Axis NURBS-Trajectory Interpolation Algorithm And Its Controuring-Error Control Technique

Parts with varied-curvature geometric features are widely utilized in the high-end equipment in aerospace,energy,and power fields.These parts are often served in important environments and are in high demand.However,due to the existence of complex varied curvature machining paths,their machining quality,precision,and efficiency can hardly be simultaneously guaranteed.Improvement of the high-quality and high-efficiency machining capability of the parts with varied curvature features is thus a permanent task in industrial fields.Three-axis and five-axis CNC(Computer-Numerical-Control)machining is one of the key means for production of the parts with varied curvature features.However,when using traditional linear/circular interpolator of the CNC system for machining of the parts with varied curvature features,the varied-curvature curve paths should be expressed as short line/circular segments,which results in frequent acceleration/deceleration in transition stops between small path segments where is first-order discontinuous,and this is adverse to the machining efficiency and surface quality.Additionally,due to the existence of servo lag of the CNC feed drive systems who increases with the rising of feedrate,the contouring error between the actual motion position and the desired motion contour will be formed during multi-axis high-speed following of the varied curvature paths,and this is bad to the machining precision.Above problems result in the facts that traditional NC machining techniques can hardly realize the direct high-quality and high-efficiency machining of the parts with varied curvature features,so that the additional processes such as multiple finish machining and repeated grinding should be applied,which not only increases the machining costs,but also seriously restricts the development process of high-end equipment.Therefore,the high-efficiency and high-quality machining requirement of the parts with curvature-varied features poses great challenges for multi-axis NC techniques.As a result,aiming at the high-efficiency and high-quality machining requirement of the parts with varied curvature features and the deficiency of existing CNC systems and machining techniques for such parts,this thesis conducts the following studies.Due to the facts that conventional linear/circular-interpolation trajectory is not suitable for curvature-varied machining paths,and the NURBS(Non-Uniform Rational B-Spline)has advantages in curved surface modeling,three-axis and five-axis NURBS-trajectory interpolation algorithms are studied.Meanwhile,to solve the servo-lag induced contouring-error problem during multi-axis following of varied curvature curve paths,three-axis and five-axis contouring-error control techniques are researched.The detail research contents are as follows.(1)The three-axis NURBS-trajectory interpolation algorithm.In order to balance both of the curvature-varied toolpath feed-motion stability and efficiency,a feedrate-scheduling method with constant speed at feedrate-sensitive regions is proposed for the NURBS paths.In this method,feedrate-sensitive regions and feedrate-non-sensitive regions are determined according to the geometry and drive constraints,and safety low constant speed is scheduled in sensitive regions,then high constant speed is scheduled in partial of non-sensitive regions and smooth transaction speed is planned in the other partial of non-sensitive regions.Thus the motion stationarity and time optimality can be equilibrated.Further,a parameter-compensation based second-order Runge-Kutta algorithm with speed correction at transaction points between constant and variable speed stages is proposed,so that the interpolation-point coordinates can be calculated with a high precision according to the scheduled feedrate.(2)The three-axis contouring-error control technique.Aiming at the contouring error in high-speed following of curvature-varied machining paths,the contouring-error control techniques for NURBS paths are studied.Although the CCC(Cross-Coupled Controller)can effectively constrain the contouring error,the three-axis CCCs are lacking comparing with two-axis CCCs.Therefore,a three-axis contouring-error online equivalent-plane cross-coupling control technique is proposed.An initial-value regeneration based Newton method for solution of the foot point from the actual motion position to the desired curved contour,is provided.Through construction of the equivalent plane containing the space contouring-error vector using the proposed initial-value regeneration based Newton method,the well-researched two-axis cross-coupling controller can thus be used in the equivalent plane to constrain the three-axis toolpath contouring errors.(3)The five-axis dual-NURBS-trajectory interpolation algorithm.The dual-NURBS curves can intuitively express the five-axis toolpath,therefore the proposed three-axis NURBS trajectory-calculation method is generalized to five-axis dual-NURBS toolpath.By modeling the relation between tool tip and axial motions,the tool-tip regional-constant feedrate is scheduled according to the axial drive constraints.Furthermore,to solve the five axial succession and unique positions according to the obtained tool-tip and tool-orientation vectors of the interpolation algorithm,an Adams prediction-correction five-axis trajectory generation method based on the generalized inverse Jacobi matrix is proposed.Thus,the five-axis dual-NURBS interpolation with constant speed at feedrate-sensitive regions under axial drive constraints is obtained.(4)The five-axis contouring-error control technique.The five-axis curvature-varied toolpath contouring error consists not only tool-tip error,but also the coupled tool-orientation error.To realize their high-accuracy estimation for dual-NURBS toolpath,the initial-value-regeneration based Newton method is generalized to compute the foot point from the actual tool tip to the desired tool-tip contour,thus a five-axis tool-tip and tool-orientation contouring-error synergistic estimation method is presented.Based on above error estimation,a five-axis contouring-error double-loop compensation method with inner-loop predictive compensation based on a feedback correction and outer-loop feedback compensation is provided.By compensate the next-period error predictively and the current-period error simultaneously,the five-axis contouring error can be constrained fast and steadily.At last,an open five-axis motion-control experimental system is established in house,so as to verify the NURBS trajectory interpolation and contouring-error constrain methods proposed in this thesis.Furthermore,real machining tests are also conducted by cooperation with a CNC system Corporation.From the testing results it can be seen that the proposed three-axis and five-axis NURBS-trajectory interpolation methods can give feedrate profile with balanced motion stationarity and efficiency under the considered constraints,and can generate precise axial motion trajectories.When comparing with conventional linear interpolator,the obtained NURBS paths by the proposed algorithms can improve the machining efficiency and quality of parts with varied curvature features significantly.When comparing with existing time-varying feedrate NURBS interpolation method,although the machining efficiency is decreased,the contouring accuracy and surface quality are simultaneously improved.In addition,the proposed contouring-error estimation methods possess the micron-level estimation accuracy for tool-tip error,and milliradian-level estimation accuracy for tool-orientation error,and through the three-axis and five-axis contouring-error control,the maximum error can be decreased by more than 60%.When comparing with conventional contouring-error estimation and control methods,the proposed method has better adaptability to the curvature-varied curved machining paths.To sum up,contributions of this thesis is significant for enriching the fundamental theory and techniques in the field of digital manufacturing,and are of great value for high-quality and high-efficiency machining of parts with varied curvature features and the high-end CNC system development.