Tool Orientation Optimization Based on Spatial Tractrix Method for Five-Axis CNC Machining with Ball End Cutters

When milling part surfaces with a ball-end tool in 5-axis CNC machining,maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface.Under this constraint,the variation of tool orientation is expected to be“smoothest possible”to reduce the angular speed of the rotary axes for the efficient and robust machining.To address this issue,the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system.The proposed model describes the relations between the tilt angle and the variation of ball-end tool orientation.Two spatial tractrix-based methods,synchronizing tractrix-based method and equilibrating tractrix-based method,are developed to minimize the variation of tool orientation by controlling the variation of tilt angle.These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface.The performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport method.The synchronizing tractrix-based method works well in some special cases.

Collisionless tool orientation smoothing above blade stream surface using NURBS envelope

In five-axis machining,tool orientation above a blade stream surface may lead to tool collision and a decrease in workpiece rigidity.Hence,collisionless tool orientation smoothing(TOS)becomes an important issue.On the basis of a constant scallop height tool path,the triangular facets in the faces,vertices format are constructed from cutter contact(CC)using the Voronoi incremental algorithm.The cutter location(CL)points candidate set is represented by an oblique elliptic cone whose vertex lies at CC using NURBS envelope.Whether the CL point is above its CC is judged by the dot product between the normal vector and the point on triangulation nearest to the CL point.The curvatures at CC are obtained by fitting a moving least square(MLS) quadratic patch to the local neighborhood of a vertex and calculating eigenvectors and eigenvalues of the Hessian matrix.Triangular surface elastic energy is employed as the weight in selection from the NURBS envelope.The collision is judged by NURBS surface intersection.TOS can then be expressed by selecting a CL point for each CC point and converted into a numerical control(NC)code automatically according to the postprocessor type of the machine center.The proposed method is verified by finishing of a cryogenic turboexpander impeller of air separation equipment.

Flat-end tool orientation based on rotation-minimizing frame

Well-designed tool orientation is crucial for the quality execution of five-axis machining with flat-end tools.Tool orientation can be specified in terms of tool inclination and tool tilt angles.For a given surface path,these aspects need to be specified for each cutter contact point along the path,because poor tool orientation choice can cause large axial acceleration of the machine tool,leading to inferior quality of the machined surface.The rotation-minimizing frame aims to reduce unnecessary frame rotation during movement.This concept has been adopted to develop tool orientation methods that allow variation in the inclination angle,the tilt angle,and both the inclination and tilt angles.The intention is to reduce unnecessary rotation of the tool frame as the tool follows a specified path.Evaluation was conducted in the context of five-axis flat-end tool machining.Based on these methods,tool orientation was planned along surface paths of a torus,sphere,and dome.Changes in tool orientation were always smooth.From the perspective of reducing tool orientation changes and axial acceleration,it was demonstrated that simultaneous variation of the inclination and tilt angles based on rotation minimization provided the best results.

Tool path generation for 5-axis flank milling of ruled surfaces with optimal cutter locations considering multiple geometric constraints

Ruled surfaces found in engineering parts are often blended with a constraint surface,like the blade surface and hub surface of a centrifugal impeller.It is significant to accurately machine these ruled surfaces in flank milling with interference-free and fairing tool path,while current models in fulfilling these goals are complex and rare.In this paper,a tool path planning method with optimal cutter locations(CLs)is proposed for 5-axis flank milling of ruled surfaces under multiple geometric constraints.To be specific,a concise three-point contact tool positioning model is firstly developed for a cylindrical cutter.Different tool orientations arise when varying the three contact positions and a tool orientation pool with acceptable cutter-surface deviation is constructed using a meta-heuristic algorithm.Fairing angular curves are derived from candidates in this pool,and then curve registration for cutter tip point on each determined tool axis is performed in respect of interference avoidance and geometric smoothness.On this basis,an adaptive interval determination model is developed for deviation control of interpolated cutter locations.This model is designed to be independent of the CL optimization process so that multiple CLs can be planned simultaneously with parallel computing technique.Finally,tests are performed on representative surfaces and the results show the method has advantages over previous meta-heuristic tool path planning approaches in both machining accuracy and computation time,and receives the best comprehensive performance compared to other multi-constrained methods when machining an impeller.

A TOOL PATH CORRECTION AND COMPRESSION ALGORITHM FOR FIVE-AXIS CNC MACHINING

A novel approach is proposed for correcting command points and compressing discrete axis commands into a C2 continuous curve.The relationship between values of rotation angles and tool posture errors is firstly analyzed.A segmentation method based on values of rotation angles and lengths of adjacent points is then used to subdivide these command points into accuracy regions and smoothness regions.Since tool center points generated by CAD/CAM system are usually lying in the space that is apart from the desired curve within a tolerance distance,and the corresponding tool orientation vector may change a lot while the trajectory length of the tool center point is quite small,directly machining with such points will lead to problems of coarse working shape and long machining time.A correction method for command points is implemented so that good processing effectiveness can be achieved.Also,the quintic spline is used for compressing discrete command points into a C2 continuous smooth curve.The machining experiment is finally conducted to demonstrate the effectiveness of the proposed algorithm.