平底刀底面加工叶片进排气边

平底刀加工叶片进排气边的传统方法以刀具侧刃切削工件,由于叶片进排气边处曲 面沿着截型线切线方向曲率半径较小,当走刀方向沿着截型线切向时,加工带宽较小。对影响凸 曲面加工带宽的因素进行研究发现,使用平底刀底面进行切削可以提高叶片进排气边处加工带 宽,由此提出了用平底刀底面加工进排气边的刀具定位方法,通过优化两个刀具定位参数使加工 带宽达到最大。以某航空发动机叶片进排气边为例进行仿真加工,结果表明该方法可有效增大叶 片进排气边处的加工带宽。     

Automated tool sequence selection for 3-axis machining of free-form pockets

This paper describes an efficient method to find the lowest cost tool sequence for rough machining free-form pockets on a 3-axis milling machine. The free-form pocket is approximated to within a predefined tolerance of the desired surface using series of 2.5-D layers of varying thicknesses that can be efficiently removed with flat-end milling cutters. A graph-based method finds an optimal sequence of tools for rough machining the approximated pocket. The algorithm used here can be tuned to suit any available tool set and preferred cost models. The tool sequence that is obtained is near optimal, and may take into account tool wear, as well as various overhead costs of the machine shop.     

A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width

Due to the complexity of geometry, the feed direction with maximal machining strip width usually varies among different regions over a freeform surface or a shell of surfaces. However, in most traditional tool path generation methods, the surface is treated as one machining region thus only local optimisation might be achieved. This paper presents a new region-based tool path generation method. To achieve the full effect of the optimal feed direction, a surface is divided into several sub-surface regions before tool path computation. Different from the scalar field representation of the machining strip width, a rank-two tensor field is derived to evaluate the machining strip width using ball end mill. The continuous tensor field is able to represent the machining strip widths in all feed directions at each cutter contact point, except at the boundaries between sub-regions. Critical points where the tensor field is discontinuous are defined and classified. By applying critical points in the freeform surface as the start for constructing inside boundaries, the surface could be accurately divided to such that each region contain continuous distribution of feed directions with maximal machining strip width. As a result, tool paths are generated in each sub-surface separately to achieve better machining efficiency. The proposed method was tested using two freeform surfaces and the comparison to several leading existing tool path generation methods is also provided.     

Tool path regeneration for mold design modification

This paper proposes a novel mold modification tool path regeneration algorithm for three-axis CNC machining based on ball end-mills. It utilizes the existing tool path points that have been generated for the original mold design prior to modification. With the proposed algorithm, a closed profile of the tool path points for the boundary of the modified region is first calculated. It is proven that if the boundary of the mold modification is interference-free, only the tool path points inside this boundary are affected by the mold modification. The tool path points that are outside the boundary can be reused to machine the modified mold. When the affected tool path points are detected, they are removed and replaced by the new tool path points. The scallop height values for the modified region are then checked. If the scallop height is greater than the given value, more CL points are added to this region to maintain the required surface finish. The algorithm has been tested on several industrial parts, and it is proven to be efficient and robust. The generated new tool path is interference-free and meets the required surface finish.     

Accurate tool position for five-axis ruled surface machining by swept envelope approach

This paper presents a swept envelope approach to determining tool position for five-axis ruled surface machining. The initial tool position is traditionally located to contact with two directrices of a ruled surface. The swept profile of the tool is then determined based on the tool motion. By comparing the swept profile with the ruled surface, the tool position is corrected to avoid machining errors. The cutter's swept envelope is further constructed by integrating the intermediate swept profiles, and applied to NC simulation and verification. This paper presents the explicit solution for the swept profile of a taper-end cutter in five-axis ruled surface machining. The relation of the ruled surface geometry, the tool motion and the machining errors is developed. Therefore, the error sources can be detected early and prevented during tool path planning. The explicit swept envelope indicates that the machined surface is not a ruled surface in five-axis ruled surface machining. Manufacturing industries should take extra care in high precision ruled surface machining. Computer illustrations and example demonstrations are shown in this paper. The results reveal that the developed method can accurately position tool location and reduce machining errors for five-axis ruled surface machining.     

Flat-end cutter orientation on a quadric in five-axis machining

The authors have recently developed methods for cutter orientation and tool path generation in 5-axis sculptured surface machining, where the design surface is approximated locally by a quadric. This paper presents, from a purely geometric perspective, the fundamental theory for optimising the cutter orientation on a quadric, which maximises the machined strip width whilst avoiding local and rear gouging. The analysis focuses on the flat-end cutter which is modelled by a circular cylinder but can be generalised for any fillet-end cutter using an appropriate offset of the design surface and the concept of geometric equivalency. The theory is illustrated by three examples.     

Minimization of the kinematics error for five-axis machining

Kinematics of a particular five-axis milling machine can drastically change the machining accuracy. Therefore, the reduction of the kinematics error is an important problem associated with the tool path planning.Our new optimization method employs a closed form of the kinematics error represented as a function of the positions of the cutter contact points. The closed form is derived from the inverse kinematics associated with a particular five-axis machine and obtained through automatic symbolic calculations.The second component of the algorithm is the optimal setup of the part surface on the mounting table employed in an iterative loop with the generation of the cutter contact points.For a prescribed tolerance the proposed optimization allows for substantial reduction in the number of required cutter contact points. The reduction can be significant and may amount to long hours of machining if the machining time at the programmed feed is less than the sampling time of the controller.In turn, when the number of cutter location points is fixed, the error can be substantially reduced. However, this refers to commanded error wherein the dynamics of machine tool are not taken into account.We present an analysis, systematic numerical experiments and results of real cutting (ball nose and flat-end cutters) as an evidence of the efficiency and the accuracy increase produced by the proposed method. We also evaluate the relative contributions of the setup and the point optimization.The method is shown to work with advanced tool path generation techniques proposed earlier such as the adaptive space filling curves.The numerical and machining experiments demonstrate that the proposed procedure outperforms tool paths based on the equi-arclength principle and paths generated by MasterCam 9.     

Performance evaluation of CUDA programming for 5-axis machining multi-scale simulation

5-Axis milling simulations in CAM software are mainly used to detect collisions between the tool and the part. They are very limited in terms of surface topography investigations to validate machining strategies as well as machining parameters such as chordal deviation, scallop height and tool feed. Z-buffer or N-buffer machining simulations provide more precise simulations but require long computation time, especially when using realistic cutting tools models including cutting edges geometry. Thus, the aim of this paper is to evaluate Nvidia CUDA architecture to speed-up Z-buffer or N-buffer machining simulations. Several strategies for parallel computing are investigated and compared to single-threaded and multi-threaded CPU, relatively to the complexity of the simulation. Simulations are conducted with two different configurations including Nvidia Quadro 4000 and Geforce GTX 560 graphic cards.     

Constant scallop-height tool path generation for three-axis sculptured surface machining

This paper presents a new approach for the determination of efficient tool paths in the machining of sculptured surfaces using 3-axis ball-end milling. The objective is to keep the scallop height constant across the machined surface such that redundant tool paths are minimized. Unlike most previous studies on constant scallop-height machining, the present work determines the tool paths without resorting to the approximated 2D representations of the 3D cutting geometry. Two offset surfaces of the design surface, the scallop surface and the tool center surface, are employed to successively establish scallop curves on the scallop surface and cutter location tool paths for the design surface. The effectiveness of the present approach is demonstrated through the machining of a typical sculptured surface. The results indicate that constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches.     

Iso-planar piecewise linear NC tool path generation from discrete measured data points

This article presents a method of generating iso-planar piecewise linear NC tool paths for three-axis surface machining using ball-end milling directly from discrete measured data points. Unlike the existing tool path generation methods for discrete points, both the machining error and the machined surface finish are explicitly considered and evaluated in the present work. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. The machining error of an individual data point is evaluated within its bounding CL-net cell from the adjacent tool swept surfaces of the ball-end mill. The positions of the CL-net nodes can thus be optimized and established sequentially by minimizing the machining error of each CL-net cell. Since the linear edges of adjacent CL-net cells are in general not perfectly aligned, weighted averages of the associated CL-net nodes are employed as the CL points for machining. As a final step, the redundant segments on the CL paths are trimmed to reduce machining time. The validity of the tool path generation method has been examined by using both simulated and experimentally measured data points.     

实体模型的三轴数控粗加工刀轨生成算法

提出一种适合实体模型的三轴数控粗加工刀位轨迹生成算法。首先根据加工行距作一组平行于刀轴的平面，与模型的待加工表面求交，得到一系列交线；再根据精度规划一组垂直于刀轴的分层平面，与上述交线求交，在每一分层平面上判断加工区域，规划出加工刀位轨迹，将每一分层平面上的刀位轨迹较适当的方式连接起来，就构成零件的整体加工轨迹。该算法避免了轮廓环等距、自交处理和布尔运算等复杂的计算过程；同时，对生成开型腔的加工刀位轨迹也是有效的。     

Complete swept volume generation, Part I: Swept volume of a piecewise C-continuous cutter at five-axis milling via Gauss map

In this paper, we present a methodology to generate swept volume of prevailing cutting tools undergoing multi-axis motion and it is proved to be robust and amenable for practical purposes with the help of a series of tests. The exact and complete SV, which is closed from the tool bottom to the top of the shaft, is generated by stitching up envelope profiles calculated by Gauss map.The novel approach finds the swept volume boundary for five-axis milling by extending the basic idea behind Gauss map. It takes piecewise C¹-continuous tool shape into account. At first, the tool shape is transformed from Euclidean space into Tool map (T-Map) on the unit sphere and the velocity vector of a cutter is transformed into Contact map (C-Map) using Gauss map. Then, closed intersection curve is found between T-Map and C-Map on the Gaussian sphere. At last, the inverse Gauss map is exploited to get envelope profile in Euclidean space from the closed curve in the range. To demonstrate its validity, a cutting simulation kernel for five-axis machining has been implemented and applied to mold and die machining.     

复杂曲面加工精度检验中曲面法矢与刀具扫描体求交算法的研究

提出了一种用于实现矢量与扫描体（代表五轴数控加工铣刀的运动）求交的有效算法,该算法首先对曲面法矢和刀具扫描体进行预处理,将曲面法矢与刀具扫描体之间的求交问题转化为有向线段与三角网格之间的求交计算,然后建立有向线段和三角网格的求交子集,减少了不必要的求交计算,提高了乍法的效率。文中举例说明了该算法在复杂曲面NC精度检验中的应用。     

A corner-looping based tool path for pocket milling

In milling around corners, cutting resistance rises momentarily due to an increase of cutter contact length. NC tool path generation in dealing with sharp corners thus requires special consideration. This paper describes an improved NC tool path pattern for pocket milling. The basic pattern of the improved tool path is a conventional contour-parallel tool path. Bow-like tool path segments are appended to the basic tool path at the corner positions. When reaching a corner, the cutter loops around the appended tool path segments so that corner material is removed progressively in several passes. By using the corner-looping based tool path, cutter contact length can be controlled by adjusting the number of appended tool path loops. The procedures of creating the improved tool path for different corner shapes are explained. The proposed tool path generation was implemented as an add-on user function in a CAD/CAM system. Cutting tests were conducted to demonstrate and verify the significance of the proposed method.     

The stencil buffer sweep plane algorithm for 5-axis CNC tool path verification

A new algorithm based on the sweep plane approach to determine the machined part geometry in 5-axis machining with general APT tools is presented. Undercut and overcut can be determined. Collision detection between the toolholder, workpiece and workpiece fixture can also be detected. The subtraction of the removed material is obtained for each sweep plane by using a stencil buffer. A flat plane is swept through the blank part, fixture and tool swept volume geometry. The intersections of sweep planes and the swept tool volume are computed based on the canonical representation of a cone, torus and sphere. The necessary data to compute all the intersections is stored in a text file, here called the M-Plane file (Memory Plane). The equations of the intersections are approximated by a polygon with variable accuracy. The resulting APT tool intersection in each sweep plane is then clipped against the blank workpiece intersection with the current sweep plane. The stencil buffer provides automatically the union of all tool intersections and the subtraction from the blank workpiece. This algorithm provides a 3D geometric model of the tool swept volume. The display algorithm is based on the Painter's algorithm, but there is no time consuming sorting from back to front required, as the sweep proceeds from back to front. The accuracy of the algorithm can be varied as a function of the requirements by changing the polygon approximation and the distance between the sweep planes.     

Complete swept volume generation — Part II: NC simulation of self-penetration via comprehensive analysis of envelope profiles

In this paper the swept volume with self-penetration (or self-intersection) of the cutter is presented. The complete swept volume (SV), which describes the side and bottom shape of a milling cutter undergoing self-penetration, is generated by using the Gauss map method proposed in the authors’ previous paper [Lee SW, Nestler A. Complete swept volume generation—part I: swept volume of a piecewise C¹-continuous cutter at five-axis milling via Gauss map. Computer-Aided Design 2011; 43(4): 427–41]. Based on the Gauss map method, the comprehensive analysis of envelope profiles of the tool is accomplished. Through the analysis the necessary condition of the self-penetration of the cutter at five-axis movement is identified. After having classified movement types of the milling cutter in an in-depth manner, the topologically consistent boundary of SV is generated by trimming the invalid facets interior to the SV. To demonstrate the validity of the proposed method, a cutting simulation kernel for five-axis machining has been implemented and applied to cavity machining examples such as intake ports of automobile engines and so forth where the self-penetration occurs. The proposed method is proved to be robust and amenable for the practical purpose of the NC simulation.     

Five-axis NC cylindrical milling of sculptured surfaces

In theory, the five-axis numerical control (NC) machining of sculptured surfaces can be classified into facing milling and cylindrical milling (or side milling). In general, the first one, using flat-end cutter, is suitable for the machining of large sculptured surfaces, e.g. the blade of hydraulic turbine, whose binding relations with drive surface (DS) and check surface (CS) are simple, and the second one, using cylindrical cutter, has wide applications for the milling of small and middle dimensional surfaces whose binding relations with DS and CS are more complex, such as the milling of integral turbine wheels. In practice, the second one suffers more difficulties than the first one, which are mostly related to gouge avoidance, interference avoidance and tool strength. This paper, on the basis of the theories of differential geometry and analytical geometry, describes research on algorithms for the toolpath generation of five-axis cylindrical milling of sculptured surfaces with cylindrical cutter. The approach includes (a) single point offset (SPO) algorithm, and (b) double point offset (DPO) algorithm for the cutter location data (CLDATA) calculation of five-axis cylindrical milling.     

A machining potential field approach to tool path generation for multi-axis sculptured surface machining

This paper presents a machining potential field (MPF) method to generate tool paths for multi-axis sculptured surface machining. A machining potential field is constructed by considering both the part geometry and the cutter geometry to represent the machining-oriented information on the part surface for machining planning. The largest feasible machining strip width and the optimal cutting direction at a surface point can be found on the constructed machining potential field. The tool paths can be generated by following the optimal cutting direction. Compared to the traditional iso-parametric and iso-planar path generation methods, the generated MPF multi-axis tool paths can achieve better surface finish with shorter machining time. Feasible cutter sizes and cutter orientations can also be determined by using the MPF method. The developed techniques can be used to automate the multi-axis tool path generation and to improve the machining efficiency of sculptured surface machining.     

汽轮机叶片五轴数控加工的一种实用方法

提出了一种汽轮机叶片五轴数控加工的实用方法 ,对于叶背和叶盆采用中凹盘形铣刀 ,基于密切曲率法给出优化刀位轨迹的计算方法 ;而对于进、排汽边圆弧采用无干涉侧铣加工方法 ,根据误差估算自动进行刀位排布 .通过这两种加工方法的有机结合 ,在保证精度的前提下 ,大大提高了加工效率 ,对于汽轮机叶片多轴数控加工具有实用价值 .