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.

Circular Interpolation Algorithms of 5-Axis Simultaneous CNC System

Spatial circular arc can be machined conveniently by a 5-axis NC machine tool.Based on the data sampling method,circular interpolation in two-dimensional plane is discussed briefly.The key is to solve the problem of circular center ex- pressed in the workpiece coordinate system by means of the transformation matrix.Circular interpolation in three-dimensional space is analyzed in detail.The method of undetermined coefficient is used to solve the center of the spatial circle and the method of coor- dinate transformation is used to transform the spatial circle into the XY-plane.Circular arc in three-dimensional space can be ma- chined by the positional 5-axis machining and the conical surface can be machined by the continuous 5-axis machining.The velocity control is presented to avoid the feedrate fluctuation.The interpolation algorithms are tested by a simulation example and the inter- polation algorithms are proved feasible.The algorithms are applied to the 5-axis CNC system software.

MOTION ERROR ESTIMATION OF 5-AXIS MACHINING CENTER USING DBB METHOD

In order to estimate the motion errors of 5-axis machine center, the double ball bar （DBB） method is adopted to realize the diagnosis procedure. The motion error sources of rotary axes in 5-axis machining center comprise of the alignment error of rotary axes and the angular error due to various factors, e.g. the inclination of rotary axes. From sensitive viewpoints, each motion error is possible to have a particular sensitive direction in which deviation of DBB error trace arises from only some specific error sources. The model of the DBB error trace is established according to the spatial geometry theory. Accordingly, the sensitive direction of each motion error source is made clear through numerical simulation, which is used as the reference patterns for rotational error estimation. The estimation method is proposed to easily estimate the motion error sources of rotary axes in quantitative manner. To verify the proposed DBB method for rotational error estimation, the experimental tests are carried out on a 5-axis machining center M-400 （MORISEIKI）. The effect of the mismatch of the DBB is also studied to guarantee the estimation accuracy. From the experimental data, it is noted that the proposed estimation method for 5-axis machining center is feasible and effective.

Systematic Geometric Error Modeling for Workspace Volumetric Calibration of a 5-axis Turbine Blade Grinding Machine

A systematic geometric model has been presented for calibration of a newly designed 5-axis turbine blade grinding machine. This machine is designed to serve a specific purpose to attain high accuracy and high efficiency grinding of turbine blades by eliminating the hand grinding process. Although its topology is RPPPR （P： prismatic; R： rotary）, its design is quite distinct from the competitive machine tools. As error quantification is the only way to investigate, maintain and improve its accuracy, calibra- tion is recommended for its performance assessment and acceptance testing. Systematic geometric error modeling technique is implemented and 52 position dependent and position independent errors are identified while considering the machine as five rigid bodies by eliminating the set-up errors of workpiece and cutting tool. 39 of them are found to have influential errors and are accommodated for finding the resultant effect between the cutting tool and the workpiece in workspace volume. Rigid body kinematics techniques and homogenous transformation matrices are used for error synthesis.

Tool Orientation Optimization and Path Planning for 5-Axis Machining

Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact(CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately;while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.

Fundamental Investigations in the Design of Five-Axis Nanopositioning Machines for Measurement and Fabrication Purposes

The majority of nanopositioning and nanomeasuring machines(NPMMs)are based on three independent linear movements in a Cartesian coordinate system.This in combination with the specific nature of sensors and tools limits the addressable part geometries.An enhancement of an NPMM is introduced by the implementation of rotational movements while keeping the precision in the nanometer range.For this purpose,a parameter-based dynamic evaluation system with quantifiable technological parameters has been set up and employed to identify and assess general solution concepts and adequate substructures.Evaluations taken show high potential for three linear movements of the object in combination with two angular movements of the tool.The influence of the additional rotation systems on the existing structure of NPMMs has been investigated further on.Test series on the repeatability of an NPMM enhanced by a chosen combination of a rotary stage and a goniometer setup are realized.As a result of these test series,the necessity of in situ position determination of the tool became very clear.The tool position is measured in situ in relation to a hemispherical reference mirror by three Fabry-Perot interferometers.FEA optimization has been used to enhance the overall system structure with regard to reproducibility and long-term stability.Results have been experimentally investigated by use of a retroreflector as a tool and the various laser interferometers of the NPMM.The knowledge gained has been formed into general rules for the verification and optimization of design solutions for multiaxial nanopositioning machines.

A novel method for sculptured surface subdivision

In this work, a novel method for sculptured surface subdivision to improve the machinery＇s ability and efficiency in 5-axis CNC machining complex surface is introduced. The method subdivides automatically a monolithic convex or concave or simultaneously complex sculptured surface into a number of surface patches and achieves the goal of similar normal directions and small difference between the curvatures in every patch by using weight fuzzy cluster algorithm which takes the curvatures and normal vectors of the sculptured surface into account simultaneously. The inclination angle variation between every two Cutter Contact Points （CC Points） is decreased in every patch to avoid large-angle rotation of tool to save machining time when a flat-end mill is used. This work contributes to automating 5-axis CNC tool path generation for sculptured part machining and forming a foundation for further research.

Smoothing strategy for corner of small curvature radius by abrasive waterjet machining

Abrasive waterjet(AWJ)is widely applied in 2D machining as it offers high machining efficiency and low machining cost.However,machining a 3D surface,especially for a small curvature radius freeform surface(SCRFS),results in over-erosion of the corner,and has been one of the greatest issues of AWJ.To solve this problem,a local smoothing algorithm for SCRFS is developed by the junction of two linear segments at the corner by inserting cubic second-order B-spline to smooth the nozzle path and posture under the setting tolerance error,which is aimed to avoid over-erosion due to the change in dwell time.Analytical solutions of the smooth corner position and orientation of the nozzle path are obtained by evaluating a synchronization algorithm.According to the set tolerance error of the nozzle position and orientation,the interpolation of the smooth path of the corner meets the constraint conditions of the linear feed drive.Path simulation and experimental results show that the proposed method is validated by the experimental results and has been applied to the integral blisk machining of an aero-engine.