开式整体叶盘四坐标侧铣开槽粗加工轨迹规划

为了提高开式整体叶盘的粗加工稳定性，在粗加工阶段，提出采用将自由曲面蜕变为直纹面的方式简化开式整体叶盘通道开槽加工的难度，实现稳定切削。讨论了直纹面逼近自由曲面的算法，提出了一种新的刀轴矢量计算方法，并基于直纹面给出了开式整体叶片通道四坐标侧铣粗加工数控编程方法，规划出了无干涉的刀位轨迹。实例验证表明，采用该方法可快速有效地实现开式整体叶盘的开槽粗加工，并可提高开式整体叶盘加工中的稳定性。     

Space cutter radius compensation method for free form surface end milling

The numerical control (NC) program for multi-axis end milling depends on the parameters of the tool, in particular, the radius of the tool. When there is any tool dimensional change due to various reasons, the user needs to re-generate the NC program, which is a time-consuming procedure. In this article, a cutter radius compensation method for multi-axis end milling is proposed. It takes a general NC program as the input, recovers the normal vectors of the machined surface from the NC program via surface reconstruction, and uses these vectors as compensation vectors to realize space cutter radius compensation. The proposed algorithm of shape reconstruction and normal vector computation has a linear complexity in terms of the number of cutter center location points in the NC program. Thus, real-time computation and compensation is possible. Our method also provides a way to restore the machined surface if the CAD model of the machines surface is not accessible. This has other applications, such as interference detection and manufacturing simulation. The compensation algorithm is shown to be very effective in reducing the number of undercut points through simulation with the software VERICUT and with real milling for real-world NC programs.     

Tool orientation optimization and location determination for four-axis plunge milling of open blisks

Plunge milling has been widely adopted in the manufacturing industry to rough machine open blisks, and its objective is to remove stock material with high efficiency and machining stability. A current technique challenge is to calculate the tool orientation and locations (called plunger paths) in four-axis rough plunging of open blisks, so that the residual raw material left on the blades after roughing is close to the specified value. To address this challenge, a novel approach is proposed to optimize tool orientation and determine tool locations for four-axis plunge milling of open blisks. First, tool locations are determined with two principles without interfering the blades and hub. Second, tool orientation is optimized according to a new evaluation criterion. Then, considering the impact of previous tool paths, an in-process model of a blisk is used to calculate residual material. Finally, an experiment is conducted to verify this new approach. This approach can promote four-axis plunge milling in the open blisk manufacturing.     

Feedrate planning for synchronized movements involving rotary axes in multi-axis EDM for shrouded blisks

As compared to traditional machining approaches, multi-axis electrical discharge machining (EDM) has its unique advantages in machining components which are made of difficult-to-cut materials and have complex structures, such as shrouded blisks. Manufacturing processes of such complex parts involve synchronized movements of both linear and rotary axes. Due to different dimensions of angular and linear velocities, there is a discrepancy between demanded and actual feedrates. This feedrate discrepancy, on the one hand, can cause feedrate fluctuations leading to a machining instability, and on the other hand, can cause inaccurate heights of electrode jumps. In order to ensure the machining stability, this paper proposes a feedrate planning method for multi-axis EDM of shrouded blisks. In this method, CAD models of both an electrode and an shrouded blisk are utilized to extract characteristic radii for feedrate planning in G-code generations. A feedrate post-processing algorithm for multi-axis EDM for shrouded blisks is proposed to reduce feedrate fluctuations and achieve a proper electrode jump height. Data analysis demonstrates the resultant feedrate can be kept in a proper range. In comparative multi-axis EDM for shrouded blisks, the machining time has been reduced by up to 21.43 % by using the proposed feedrate planning method.     

基于正向杜邦指标线的五坐标侧铣加工

为实现叶轮类零件的多坐标侧铣加工,通过引入正向杜邦指标线,利用鼓锥形刀对自由曲面的五坐标侧铣加工进行研究。针对具有严格凸切削刃的侧铣加工刀具,提出不发生局部干涉的充要条件是切触点处刀具曲面的正向杜邦指标线位于被加工曲面的正向杜邦指标线之内。给出利用鼓锥形刀侧铣加工自由曲面时实施干涉检查的判断准则以及消除干涉的修正方法,推导出具有严格凸切削刃的刀具在给定的残留高度下侧铣加工带宽的计算方法。在此基础上,利用等残留高度法实现鼓锥形刀侧铣加工自由曲面无干涉刀具轨迹的生成。算例表明,在相同残留高度下,鼓锥形刀侧铣较之球头刀加工效率提高37.44%,说明侧铣加工是提高切削效率和加工质量的一种有效途径。     

An Operation Planning System for Multi-Axis Milling of Sculptured Surfaces

Multi-axis milling of sculptured surfaces with cylindrical or toroidal cutters has many advantages compared to the use of three-axis milling with ball nose cutters. Surfaces to be machined are often of complex shape and characterised by convex, concave and saddle areas. Today, CAM-systems do not support the user in the selection of the different operations in order to finish the workpiece. This paper describes an operation planning system, which facilitates process planning for the multi-axis machining of sculptured surfaces. The core of the system is surface analysis, which divides the surfaces into regions, each characterised by a preferred milling direction and tool diameter. Further, for each region or set of regions, a drive surface is constructed that is used as the basis for the tool-path calculation. The drive surface approximates to the original workpiece as closely as possible, and the isoparametric lines which will be the tool-path feed direction lie in the preferred milling direction.     

Adaptive tool-path generation on point-sampled surfaces

In this paper, we present a new approach to generate tool paths for machining point sampled surfaces using a direct projection algorithm, which is based on generating tool paths along planar intersection curves. In our implementation, a guide surface, with simple geometry like planes or cylinder surfaces, is first created according to the bound volume of the point cloud and initial tool paths are planned on it in terms of the motion pattern of the cutters. For each point of the initial tool paths, then, the corresponding cutter contact point (CC) of the point set surface is located by projecting the point onto the point cloud using the direct projection algorithm. In order to obtain adaptive cutter location points (CL), a least squares-based curve fitting method is applied to approximate the CC points using piecewise cubic Bezier, and a numerical method derived to estimate the length of the curve is used to adjust the position of the points along the curve, and make them evenly spaced on the curve with equal arc lengths. In addition, considering that offset curves or surfaces are necessary for locating CL points in many applications, such as machining using ball end milling cutter, torus ended milling cutters, an offset strategy for cubic Bezier curves is also studied. By testing the proposed method on several point clouds, it has been demonstrated to be promising.     

复杂曲面的数控加工误差分析

针对复杂曲面的多轴数控加工,应用数学知识建模,从理论上分析了平底铣刀刀具加工复杂曲面时的误差,得出了影响数控加工精度的主要因素并提出了误差补偿方法,为控制多轴数控加工的误差提供了理论依据与补偿算法,对高精度复杂曲面的数控加工具有借鉴意义。     

An improved calculation method for cutting contact point and tool orientation analysis according to the CC points

Tool path generation is an important step of five-axis NC milling which plays an important role in parametric surfaces and free-form surfaces manufacturing. Cutter contacting (CC) point calculation is considered as a basic procedure of tool path generation. The step lengths formed by cutter contacting points have an effect on the chord error along feed direction. In traditional calculation method for CC point discretization, the segments connected by adjacent CC points distribute on both sides of the theoretical tool path curve. This situation magnifies the cutting error to some extent and enlarges the expected margin if the surface demands polishing or grinding. Aiming at this issue, this paper proposes an improved constant chord error method for CC point calculation. In the proposed method, the CC points lay on the theoretical tool path curve when the tool path curve is concave and lay on the chord error offset curve when is convex, which ensures the segments connected by the adjacent CC points distribute on one side of design surface, the side of the scallop height between tool paths. Therefore, the actual margin of polishing or grinding can be reduced. The influence of inflection points is also considered in this method to avoid accuracy deterioration caused by the long steps occurring near the inflection points. In part processing, local gouging and global collision must be avoided in tool orientation determination. This paper analyzes tool orientations with no rear gouging and no collision based on the calculated CC points. The novel discretization method for CC points is calculated on a single blade model, and the tool orientations are generated on an open integral impeller. A DMG DMU50 machine tool and a Hexagon three coordinates measuring machine are applied for experiments and measurements. The results show that, the CC point discretization method proposed in this paper offers many advantages over the traditional constant chord error method and commercial software, such as quantity of points, curve fitting, no overcut, and residual margin distributing. At last, blade and tunnel of the open integral impeller with safety tool orientation is machined and verified on the DMG DMU50 machine tool.     

Adaptive Gregory Patch Approximation to Z-Map Data

A method is proposed for Gregory surface approximation to 3D array data points. Surface approximation is the process of constructing a compact representation to model an object surface based on a fairly large number of measured 3D data points. Based on an adaptive subdivision technique, the proposed method begins with a rough initialisation of the surface and progressively refines it in successive steps in the regions where the data is poorly approximated. The method has been implemented using piecewise bicubic Gregory patches with G 1 continuity. An advantage of this approach is that the refinement is essentially local, reducing the computational requirements that permit the processing of a large number of data points This method, combined with the inverse offsetting method, can be used to obtain an offset surface without self-interference. The offset surface can be used to generate gouging-free CL tool paths for machining compound surfaces on milling machines.     

Local interference detection and avoidance in five-axis NC machining of sculptured surfaces

The tool interference problem is the most critical problem faced in sculptured surface machining. This paper presents a methodology for interference detection and avoidance in five-axis NC machining of sculptured surfaces with a filleted-end cutter. The surfaces to be machined are divided into convex and non-convex regions. There is no local interference inside the convex regions. For the non-convex regions, based on the analysis of the different local interference, local gouging is first detected and avoided by determining optimal cutter orientations. Rear gouging detection and avoidance algorithms are then proposed for simple smooth surfaces and complex shaped surfaces, respectively. The techniques presented in this paper can be used to generate interference-free tool paths. The realistic results indicate that the proposed method is feasible and reliable .     

The avoidance of cutter gouging in five-axis machining with a fillet-end milling cutter

This paper proposes a new method of automatic detection and elimination of cutter gouging when using the fillet-end milling cutter to produce a complex surface on the five-axis computer numerical control machine tool. To avoid local cutter gouging at the point where the cutter and part surface make contact with each other, the method of exact curvature matching between the cutter and part surface is presented. The size of cutter radii is more easily determined by this method. To detect if a rear cutter gouging occurs near the contact point, a square grid with horizontal and vertical points is used for illustrating the checking area and checking points. The technique of automatic generation of the square grid points and the method of detection and avoidance of rear cutter gouging are investigated throughout this article. In the end, the studied methodology and algorithms are inspected and verified by using an example of nonuniform rational B spline surface.     

Accuracy improvement method for flank milling surface design

In this paper, a variation of the method of designing surfaces for flank milling proposed by Li et al. 2006 (Surface design for flank milling. Submitted to CAD, July) is presented. Li’s method is based on the premise that the surface flank milled by a cylindrical tool can be represented by a NURBS surface and can be used by designers to build efficient impellers, blades and other engineering parts. In the proposed method, a four control point curve is used to approximate the grazing curves and for subsequent generation of a polynomial surface. This eliminates the need of weights for the interior control points and still results in a good surface. The accuracy of the surface can be controlled by adding control points. Examples are given to demonstrate the proposed surface design method.     

A solid trimming method to extract cutter–workpiece engagement maps for multi-axis milling

A solid trimming method is proposed to determine cutter–workpiece engagement (CWE) maps, which are essential to investigate cutting forces, machining errors, and chatter stability in multi-axis milling. In this method, CWE maps, defined as the instantaneous contact area from the cutting flutes’ entrance to exit, are extracted by trimming the removal volume (RV) with the feasible contact surfaces. Compared to the traditional Boolean operation approach, the trimming method extracts CWE maps without the requirement of abundant surface/surface intersection operations. Moreover, instead of using the union solid model associated with all cutter locations, RV is calculated for the first time by introducing the existing concept of analytical tool swept volume, which is previously limited to tool path planning. Verification tests show that the proposed method has the advantages of high accuracy and efficiency.     

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.     

Vector model-based workpiece update in multi-axis milling by moving surface of revolution

This paper presents a parametric approach to updating workpiece surfaces in a virtual environment. The workpiece surfaces are represented by a series of discrete vectors, which may be orientated in different directions. The methodology is developed for multi-axis machining in which a tool can be arbitrarily oriented in space. The cutter is modeled as a surface of revolution, which is a canal surface formed by sweeping a sphere with varying radius along a spine curve. To define the tool swept envelope, the cutter surfaces are decomposed into a set of characteristic circles which are generated by a two-parameter family of spheres. Then, the grazing points, at which the discrete vectors can intersect the tool envelope, are obtained by considering the relationships between these circles and feed vector of the cutter. From this, the envelope-vector intersections are transformed into a single-variable function. Examples of this technique are generated for typical milling tools with both linear and circular spine curves. The vector/tool envelope intersection calculations for cutters with linear spine curves can be performed analytically. However, the intersection calculations for cutters having circular spine curves require solving a system of nonlinear equations. For this purpose, a root-finding analysis is developed for guaranteeing the root(s) in the given interval. Finally, to improve the efficiency when updating the workpiece, a vector localization scheme is developed based on the Axis-aligned Bounding Box method.     

Price, delivery time, and capacity decisions in an M/M/1 make-to-order/service system with segmented market

In this paper, a method to determine the optimal tool orientation to make a more perfect impeller blade surface using a five-axis flank milling machine is presented. Verification of surface geometric accuracy using a 3D coordinate measuring machine is also shown. A mathematical formula is derived which includes the parameters of tool and curved surface to calculate the appropriate tool orientation, whose direction is named the optimal tool orientation. The 3D CAD software Unigraphics (UG) is used to plot models which include the curved surface and the tools of optimal tool orientation and other orientations. The reasonable overlap between curved surface and tool is obtained (overcutting) by checking the interference from the UG, its tool orientation is the optimal tool orientation. According to the optimal tool orientation and position at all cutting points on curved surface, a cutting location source file is derived, which can transform into the NC code for the five-axis tool machine to make the centrifugal impellers of various types. These impellers are measured by using the 3D Coordinate Measuring Machine to verify blade to be free of flaws, and with accurate geometry and the tool, marks are removed from its surfaces.     

Surface topography analysis in high speed finish milling inclined hardened steel

The surface texture of a milled surface is an inherently important process response in finish milling. It is one of the most commonly used criteria to determine the machinability of a particular workpiece material. However, literature survey on the study of the surface topography analysis relating to the cutter path orientations when high speed finish inclined milling is scant. Previous works were either involved in conventional milling of easy-to-cut workpiece materials or machining at different workpiece inclination angles. Furthermore, none of the previous work has detailed the true surface topography of the machined surface with regards to the cutter condition. Instead, the works provided quantitative values in terms of the Ra value. This article is concerned with evaluating cutter path orientations on an inclined workpiece angle of 75° to simulate finish milling of free form moulds and dies. Surface topography effects are assessed with regards to different cutter path orientations on its surface. The aims of this study are to provide an in-depth understanding on the surface texture produced by various cutter path orientations when high speed finish inclined milling hardened steel at a workpiece inclination angle of 75° using surface topography analysis and determine the best cutter path orientation with respect to the best surface texture achieved. 3D topography maps together with 2D surface profiles are used to assess the experimental results. The conclusion is that milling in a single direction vertical upward orientation gave the best workpiece surface texture.     

球头铣刀曲面加工的刀具切触区域解析建模

针对球头铣刀三维曲面加工,提出一种刀具切触区域仿真的通用解析模型。采用微分方法,将曲面加工过程离散为一系列连续的微小斜平面稳态加工。以每一小斜面切削过程为研究对象,建立描述刀具进给方向变化的数学模型,针对不同的进给方向并基于空间坐标系旋转变换,提出一组确定刀具切触边界曲线及各边界交点的解析公式,以精确界定刀具切触区域的封闭几何。通过与Z-Map模型的切触区域仿真对比,验证了本文模型的有效性及其精确高效的特点。     

刀具空间运动扫掠体包络面建模的双参数球族包络方法

将锥刀、鼓刀和环刀的切削刃回转面表示为单参数可变半径球族的包络面,利用双参数球族包络理论推导出这三种刀具在一般空间运动下的扫掠体包络面的解析表达式,对于环刀还给出两种边界线的计算方法,所提出的原理也适用于其他类型的回转刀具。该方法可用于多轴(包括并联机床)数控加工干涉检验、精度评估、行距优化、路径生成等的全面数字化描述和并行计算处理,锥刀五轴侧铣加工精度校验的结果表明该方法具有很高的精度和稳定性。