Direct interpolation algorithm for pen-cutting of sculptured surfaces

A direct interpolation algorithm for spatial curves on a surface is proposed for pen-cutting of sculptured surfaces. The algorithm can carry out the direct interpolation for projective curves lying on the sculptured surface. It is based on the geometric and kinetic relationships between drive curves and cutter-contact （C-C） curves. It evaluates the parameter of drive curves corresponding to interpolation points by the Taylor formula. Then it gains coordinates of interpolation points indirectly by inverse calculation. Finally, it generates the motion commands for machine tool controller. This method extends the locus-controlled function in the computer numerical control （CNC） system effectively and improves the efficiency for the numerical control （NC） machining of sculptured surfaces. The simulation shows that the proposed algorithm is feasible and practical. This algorithm can also be applied to the machining of the whole surface.

A NEW ALGORITHM BASED ON TRIANGULATION FOR 5 AXIS MACHINING OF SCULPTURED SURFACES

NC machining path of sculptured surfaces in CAD/CAM system plays an important role on manufacture. This paper describes a new algorithm for 5 axis machining of sculptured surfaces and the algorithm is interference free. The approach includes: (1) the tesselation of the parametric surfaces into triangles; (2) building topological relations among triangles;(3) 5 axis tool path generation; (4) interference detection and tool position correction.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact（CC） point,while not considering the smoothness and continuity of a whole tool path.When the surface curvature varies significantly,a local abrupt change of tool paths will happen.The abrupt change has a great influence on surface machining quality.In order to keep generated tool paths smooth and continuous,a five-axis tool positioning algorithm based on smooth tool paths is presented.Firstly,the inclination angle,the tilt angle and offset distance of the tool at a CC point are used as design variables,and the machining strip width is used as an objective function,an optimization model of a local tool positioning algorithm is thus established.Then,a vector equation of tool path is derived by using the above optimization model.By analyzing the equation,the main factors affecting the tool path quality are obtained.Finally,a new tool position optimization model is established,and the detailed process of tool position optimization is also given.An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine,and the machined blade surface is measured with a coordinate measuring machine（CMM）.Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous,improve the tool path quality,avoid the local abrupt change of tool paths,and enhance machining quality and machining efficiency of sculptured surfaces.

NON-CONTACT MEASUREMENT OF SCULPTURED SURFACE OF ROTATION

A method for measuring the sculptured surface of rotation by using coordinatemeasuring machine (CMM) and rotary table is proposed. The measurement is realized during thecontinuous rotation of the workpiece mounted on the rotary table while the probe moves along thegeneratrix of the surface step by step. This method possesses lots of advantages such as simplicityof probe motion, high reliability and efficiency. Some key techniques including calibration of theeffective radius of the probing system, determination of the position of axis of rotation,auto-centering of the workpiece, data processing algorithm, are discussed. Approaches fordetermining the coordinates on measured surface, establishing workpiece coordinate system andsurface fitting are presented in detail. The method can be used with contact or non-contact probes.Some fragile ceramic and plaster parts are measured by using the system consisting of a CMM, rotarytable, motorized head and non-contact laser triangulation probe. The measuring uncertainty is about0.02 mm which meets the general requirement in most cases.

NC Rough Machining of Sculptured Surface Based on Measured Data

A new method for generating tool paths for rough machining of sculpturedsurface is presented in this paper. The sculptured surface is approximated by a regular mesh ofquadrangular facets. A set of equidistant horizontal planes are assigned to intersect the blank ofmachined part and surface model , resulting in a series of contours, which demarcate the feasiblecutting regions of each layer of material removal. The desired cutter path is computed through NCprogramming and any gouging between the cutter and the part being machined is detected and correctedautomatically. The proposed algorithm successfully solves the problem of layered milling forsculptured surface with nested islands.

Adaptive compensation of sculptured surface machining errors by open architecture manufacturing system

Presents the adaptive compensation of sculptured surface machining errors by using the open architecture intelligent manufacturing system to ensure real time high precision machining of sculptured surface, and the tool deflection model constructed for prediction of machining errors to be compensated and analysis of the effect of tool deflection on machining errors, and concludes from experimental results that the open architecture intelligent manufacturing system can effectively improve the machining precision and reduce the machining errors by 30%.

A Tool Path Generation Strategy for Sculptured Surfaces Machining

This paper presents a strategy to generate interference-free tool paths for machining sculptured surfaces. The strategy proposed here is first to determine the tool path topology. The values of the step length and the path interval are then calculated based on the machining tolerance requirements. After detecting and eliminating the tool interference, the interference-free tool path is generated. The effectiveness of the developed algorithm is demonstrated through simulation and actual cutting tests.

A Gradient-Simulated Annealing Algorithm of Pre-location-Based Best Fitting of Blank to Complex Surfaces Machining

The algorithm is divided into two steps. The first step pre-locates the blank by aligning its centre of gravity and approximate normal vector with those of destination surfaces, with largest overlap of projections of two objects on a plane perpendicular to the normal vector. The second step is optimizing an objective function by means of gradient-simulated annealing algorithm to get the best matching of a set of distributed points on the blank and destination surfaces. An example for machining hydroelectric turbine blades is given to verify the effectiveness of algorithm.

Dual Drive Curve Tool Path Planning Method for 5-axis NC Machining of Sculptured Surfaces

The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters. To solve this problem, a dual drive curve tool path planning method is proposed in this article. First, the maximum machining strip width of a whole tool path can be obtained through optimizing each tool position with multi-point machining （MPM） method. Second, two drive curves are then determined according to the obtained maximum machining strip width. Finally, the tool is positioned once more along the dual drive curve under the condition of tool path smoothness. A computer simulation and cutting experiments are carried out to testify the performance of the new method. The machined surface is measured with a coordinate measuring machine （CMM） to examine the machining quality. The results obtained show that this method can effectively eliminate sharp scallops between adjacent tool paths, keep tool paths smooth, and improve the surface machining quality as well as machining efficiency.

Realization Methodology of a 5-axis Spline Interpolator in an Open CNC System

By making use of the advantages of non-uniform rational B-spline （NURBS） curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control （NC） files in sculptured surface machining. A generation procedure of the NC files with the presented format is introduced and the method to realize the interpolation in an open computer numerical control （CNC） system is developed by ourselves. These illustrated the feasibility of the proposed method and its capability of avoiding all the shortages of 5-axis linear interpolation method.

A new iso-scallop height tool path planning method in three-dimensional space

This paper presents a new approach for designing the tool paths in the machining of sculptured surfaces for computer nu- merical controlled end milling. In the proposed method, the tool paths are determined so that the scallop height formed by two adja- cent machining paths is maintained constant across the machined surface. Unlike previous work on iso-scallop height milling, the present work considers the true 3D configuration of the milling procedure and can be used to generate better results, which is shown by examoles.

A Generic Kinematic Model for Three Main Types of Five-axis Machine Tools

Material removal is one of the most used processes in manufacturing. Five-axis CNC machines are believed to be the best tools in sculptured surface machining. In this study, a generic and unified kinematic model was developed as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of a five-axis machine-tool. This versatile model is very useful applied to the design of five-axis machine tools.

Achene Wall Anatomy and Surface Sculpturing of Lactuca L. and Related Genera （Compositae： Lactuceae） with Notes on Their Systematic Significance

The achene wail anatomy and surface sculpturing of 14 species representing Lactuca L. and related genera were Investigated to evaluate inter-and Intrageneric relationships. The achene wall anatomy of the studied species can be divided Into two types： winged and ribbed. The winged type is present in Lactuca L., Pterocypsela Shlh, Clcerblta Wallr., Chaetoserls Shlh and Stenoseris Shlh, and is characterized by protruding wings and costae in transverse section. Winged type achene mesocarps are composed of parenchymatous cells and fiber ceils, and the distinct fibrous strands are confined to the costae or wings of the achenes. The ribbed type is present in Notoseris Shih and Paraprenanthes Chang ex Shih, and Is characterized by only having costae In transverse section. Fiber cells are continuous in the costae and intercostae, in surface sculpturing, the ornamentation and the shape of epidermal cells are different among these genera. The results Indicate that L. altalca and L. serrlola should be conspeclfic, and that L. dollchophylla is probably an Intermediate taxon between Lactuca and Chaetoserls. The results also support the separation of Pterocypseia, Paraprenanthes, Notoseris, Chaetoseris and Stenoserls from Lactuca and Clcerblta as independent entitles. Close affinities between Pterocypsela and Lactuca, Paraprenanthes and Notoserls, and Chaetoserls and Stenoserls are also proposed.

Integration of a 5-axis Spline Interpolation Controller in an Open CNC System

A 5-axis controller with curve interpolation function is developed to satisfy high-speed and high-precision computer numerical control (CNC) machining of machine parts with complex shapes in the authors-devised open CNC system. The instruction for- mat of this interpolation method and the generation procedure of the numerical control (NC) files are introduced. The interpola- tion curves of both position vectors and orientation vectors constructed by the controller are C2 continuous and independent of machin...

Realization of a 5-axis NURBS Interpolation with Controlled Angular Velocity

5-axis machine tool plays an important role in high-speed and high-precision computer numerical control （CNC） machining of workpieces with complex shapes. A non-uniform rational B-spline （NURBS） interpolation format for 5-axis machining is pro- posed to adapt to the high speed machining （HSM）. With this interpolation format, angles between orientation vectors are chosen as parameters of orientation B-spline constructed by an open controller to achieve reasonable orientation vectors in real-time interpolation process. Coordinated motion between linear axes and rotary axes is achieved by building a polynomial spline which relates interpolation arc lengths of position spline to angles of orientation spline. Algorithm routine of this interpolation format and its realization methods in the supported controller are discussed in detail. Finally, performance of the proposed NURBS in- terpolation format is demonstrated by a practical example.