Envelope surface formed by cutting edge under runout error in five-axis flank milling

This paper investigates the analytical envelope surface model formed by specially designed cutting edge under cutter runout error, including axis offset error and tilt error, in five-axis flank milling. This model, which is independent of the machine tool type, is determined by the tangency condition in envelope theory. First, the cutter runout is defined by four parameters, namely offset distance, offset direction angle, locating angle, and tilt angle. Then, the cutting edge represented by cubic B-spline curve is used as the generator of cutter rotation surface to formulate the closed-form envelope surface model. In particular, the runout error and feedrate are both integrated into the model. In addition, we study special cases of the analytical model and the runout effect on envelope surface. Finally, computer example validates the feasibility of the proposed model with runout. We find that envelope surface formed by cutter edge is different from each other at the existence of runout, and envelope surface dedicated to final machined surface is generated by the composition of some segments of cutter edges. The results can be applied to tool path optimization in five-axis flank milling and NC simulation with cutter runout.     

Tool path optimization in postprocessor of five-axis machine tools

Generally, tool path is generated in a computer-aided manufacturing software considering only the geometry of machining parts. It is converted into numerical control (NC) codes in the postprocessor based on the particular machine kinematics. For some special types of five-axis machine tools, e.g., non-orthogonal five-axis machine tools, the generated NC codes may produce unqualified parts because of the existence of the non-linear error. Conventional commercialized postprocessors usually do not have the function of non-linear error checking. Observing that the tool path is a non-smooth trajectory full of corners and a series of connected line segments, cubic spline interpolation is applied to smooth the tool path at regular points in this study. The cutter tip center points are computed by the cubic spine interpolation, while the cutter posture vectors are obtained via linear interpolation. At the splines (for regular points) and the line segments (feature points), more points are chosen to be converted into NC codes to reduce the non-linear error, which is called data densification. Using the cubic spline to smooth the tool path and the data densification to reduce the non-linear error, a novel tool path optimization algorithm in postprocessor is proposed. Experiments were carried out on an inclined rotary spindle axis non-orthogonal five-axis machine tool. It shows that the proposed tool path optimization provides improved accuracy and surface quality.     

复杂参数曲面高精度刀具轨迹规划算法

在对等残余高度刀具轨迹规划算法加工参数曲面研究的基础上,提出带有误差补偿值的复杂参数曲面高精度刀具轨迹规划算法——高精度刀轨误差补偿算法。通过分析刀触点及与之相应的相邻路径上的粗、精刀位对应点间的关系,引入误差补偿值以提高精对应刀位点的求解精度,得到经过合理简化的误差补偿值表达式,并得出粗、精对应刀位点与理论刀位点的距离误差表达式。高精度刀轨误差补偿算法可以在满足插补运算实时性要求的前提下,使相邻轨迹上与刀触点相对应的刀位点的参数值计算精度得到极大提高,进而提高复杂参数曲面的加工刀具轨迹精度。以使用平底铣刀为例进行仿真加工,结果表明高精度刀轨误差补偿算法适合进行对复杂参数曲面的高精度加工。     

Tool-path generation from densely scattered measure points based on CQEM

An algorithm of tool-path generation from densely scattered measure points is presented in this paper based on constraint quadratic error metrics (CQEM). In the algorithm where the surface to be machined is represented directly with measured points, first, a mesh interpolating the points is dynamically constructed according to cutter sizes and slicing plane locations. Second, the initial C-C points are generated from the intersection points between the mesh and the slicing planes. Finally, the initial C-C points are optimized with CQEM. The algorithm shows capability to save memory usages and to achieve a higher precision in path location calculation.     

Non-singular tool path planning by translating tool orientations in C-space

This paper discusses the singular problem in five-axis machining of freeform surfaces. At first, the generating mechanism of the singularities is studied on the unit sphere in the P-system. Then a new method is developed to avoid the singularities by translating the tool orientations in the configuration-space (C-space) at the time just after the initial cutter locations have been generated for a cutter contact (CC) trajectory on the surface. The tool orientation vectors of the initial cutter locations are projected onto the C-space, forming the orientation polyline. In the C-space, a taper circle is defined. The singularities are detected by contact checking between the orientation polyline and the taper circle. Once they contact, the orientation polyline is translated by a minimum translating vector to avoid the contact. The minimum translating vector is picked on the offset polyline of the original orientation polyline. After that, the translated orientation polyline is inversed to calculate the optimized cutter locations in the P-system. The benefit of avoiding singularities at the tool path planning stage is that the original CC points on the CC trajectory are respected. The developed method is programed and tested through contrastive experiments. Results show that the optimized cutter locations can effectively avoid the singularities.     

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.     

复杂曲面投影法精加工刀轨生成

针对复杂曲面投影法精加工问题,提出一种简捷而有效的计算投影轨迹的方法。该算法以减少计算量,提高干涉调整效率为目的。为了避免传统方法中的复杂的曲面偏置问题,提出了一种新的思路,该方法摒弃了先求偏置面再计算投影轨迹并使用对分法处理干涉问题的思路。首先规划导动轨迹,然后将刀触点轨迹沿曲面法向偏置,再利用刀位点到曲面的最短距离进行干涉检测与调整,最后生成了无干涉的投影法轨迹。仿真实验证明,该方法计算量小,可以消除干涉,加工效果好。     

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.     

Optimising positioning of the axis of a milling cutter on an offset surface by geometric error minimisation

This article covers side milling of ruled surfaces using a milling cutter. Flank milling is useful for machining objects such as impellers, turbine blades, fan vanes and all workpieces defined by nondevelopable ruled surfaces. In the present article, we first introduce a new approach to positioning for side milling of ruled surfaces. The reasoning adopted is based on improved positioning as developed within the Toulouse Mechanical Engineering Laboratory. Having defined the offset surface of a ruled surface, we shall study various positionings of the milling cutter’s axis on this offset surface. We shall then perform a comparative study into geometrics errors caused by these different positionings, before going on to propose error processing by adopting various criteria for minimisation that will then be subjected to comparison.     

Geometric error compensation for five-axis ball-end milling by considering machined surface textures

Arbitrarily adjusting tool poses during error compensation may affect the quality of surface textures. This paper presents one tool center limitation-based geometric error compensation for five-axis ball-end milling to avoid the unexpected machined textures. Firstly, the mechanism of cutter location generation with cuter contact (CC) trajectory is analyzed. Due to zero bottom radius of ball-end cutter, CC points of the surface are only related to the tool center of the cutter. Realizing that, tool center limitation method of ball-end milling is established based on the generation of movements of all axes in order to ensure the machined textures. Then, geometric error compensation of ball-end milling is expressed as optimizing rotation angles of rotary axes by limiting tool centers of cutter locations. Next, particle swarm optimization (PSO) is intergraded into the geometric error compensation to obtain the compensated numerical control (NC) code. The limited region for particles of rotation angles is established, and moving criterion with a mutation operation is presented. With the help of the tool center limitation method, fitnesses of all particles are calculated with the integrated geometric error model. In this way, surface textures are considered and geometric errors of the machine tool are reduced. At last, cutting experiments on five-axis ball-end milling are carried out to testify the effectiveness of the proposed geometric error compensation.     

基于散乱测量数据点的三轴数控粗加工刀位轨迹生成算法

提出了一种直接利用三维散乱测量数据点的三轴数控粗加工刀位轨迹生成算法。首先根据切层深度作一组垂直于Z轴的平面,去截取测量点云,得到一系列切层截面点集,再在每个切层面上组环并判断加工区域,规划出刀位轨迹,将每一分层平面上的刀位轨迹按适当的方式连接起来,就可构成零件的整体加工轨迹。该算法避免了由测量点构造曲面且由曲面来进行刀位轨迹生成的这一复杂过程。     

叶轮数控加工中的干涉检查

针对自由曲面离心叶轮多坐标数控加工中可能出现刀具与叶片干涉的问题,提出了一种干涉检查方法。首先计算出叶片曲面的等距面,等距面的偏移距离为刀具半径,再根据所给定的刀位数据得出刀轴的表达式,然后计算该等距面与刀轴是否有交点,如果有交点则存在干涉,否则计算叶片边界线到刀轴的最小距离,若此距离大于刀具半径则无干涉,否则存在干涉。该方法计算量小,对于叶轮数控加工编程中大量刀位数据的干涉检查,可以显著地节省计算机运算时间。     

NURBS approximation to the flank-milled surface swept by a cylindrical NC tool

In this paper, a method to approximate the flank-milled surface swept by a cylindrical cutter with a non-uniform rational basis spline (NURBS) surface is presented. The swept surface produced by the moving tool can be calculated as a collection of points organized as a series of grazing curves along the surface. The generated NURBS surface closely matches the grazing surface. The deviation between this surface and the grazing surface is calculated and is controlled by increasing the number of control points used to represent the surface.     

Effect of electropulsing on springback during V-bending of Ti-6Al-4V titanium alloy sheet

Because the intermediate-stage forming surface and the intermediate-stage forming tool path of the complex shape model are difficult to generate, the existing multi-stage CNC incremental forming takes the regular rotary body model or the square model as the research objects, and all adopt the three-axis CNC incremental forming mode. In this paper, a method for generating the intermediate-stage surface by using a longitude line that can reflect the personality of the surface and the five-axis CNC multi-stage incremental forming tool path was proposed. Firstly, the vertexes of the triangular facets of the STL model are used to generate the longitude lines which can reflect the characteristic of the surface, then the longitude lines are offset according to the multi-stage forming strategy and the characteristics of each surface associated with the longitude lines so that the intermediate-stage longitude lines could be generated, and then the intermediate-stage surfaces are built using the intermediate-stage longitude lines. Finally, the cutter location points of each intermediate stage are obtained by cutting the intermediate-stage surfaces, and the postures of the five-axis CNC pressing tool are determined according to the normal vector of the cutter location points. The case studies show that the proposed method can well generate the five-axis CNC multi-stage incremental forming path for the complex shape sheet metal part. The results of the numerical simulation analysis and forming experiments show that the proposed method is applicable.     

Cutting errors analysis for spindle-tilting type 5-axis NC machines

Current computer-aided manufacturing (CAM) systems generate cutter contact points (CC points), cutter location points (CL points) and cutter orientation angles (CO angles) based only on the sculptured surface geometry. However, under certain situations, the cutting errors of 5-axis NC machines are larger than expected using these CC, CL and CO data. It is shown in this paper that the cutting error depends on the structures of 5-axis NC machines as well as the surface geometry. A new algorithm has been developed to estimate the cutting error and calculate the maximum allowable step length for spindle-tilting type 5-axis NC machines. Simulation results show that the new algorithm provides better estimation on the cutting errors for spindle-tilting type 5-axis NC machines.     

Optimising tool positioning for achieving multi-point contact based on symmetrical error distribution curve in sculptured surface machining

The multi-point tool positioning algorithms produce much larger machining strip width than the single-point algorithms and apparently reduce the actual machining time. This paper presents a tool positioning algorithm for multi-point machining of sculptured surface, which is excellent at dealing with both of concave and convex surfaces. The proposed method is based on the middle-point error control (MPEC) method, which means the connection point between cutter and surface corresponds to the middle point of error distribution curve. Usually, only one cut contact (CC) point can be obtained with this method. Thus, the proposed method improved the MPEC method for achieving two CC points. At first, the shape of error distribution curve is investigated, and its asymmetry is evaluated. Secondly, the error distribution curve becomes symmetrical after the cutter is rotated with a roll angle, and the cutter is separated with surface at the same time. Finally, the minimum tilt angle is found, and two CC points are obtained without gouging. Machining experiment is conducted to verify the proposed method, and the result reveals that the machining strip width is increased apparently and the tool position is almost unchanged after the adjustment with proposed method. Simulation, measurement, and analysis are also given in the part of the experiment.     

Generating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter’s accessibility map

In five-axis high speed milling, one of the key requirements to ensure the quality of the machined surface is that the tool-path must be smooth, i.e., the cutter posture change from one cutter contact point to the next needs to be minimized. This paper presents a new method for generating five-axis tool-paths with smooth tool motion and high efficiency based on the accessibility map (A-map) of the cutter at a point on the part surface. The cutter’s A-map at a point refers to its posture range in terms of the two rotational angles, within which the cutter does not have any interference with the part and the surrounding objects. By using the A-map at a point, the posture change rates along the possible cutting directions (called the smoothness map or S-map) at the point are estimated. Based on the A-maps and S-maps of all the sampled points of the part surface, the initial tool-path with the smoothest posture change is generated first. Subsequently, the adjacent tool-paths are generated one at a time by considering both path smoothness and machining efficiency. Compared with traditional tool-path generation methods, e.g., iso-planar, the proposed method can generate tool-paths with smaller posture change rate and yet shorter overall path length. The developed techniques can be used to automate five-axis tool-path generation, in particular for high speed machining (finish cut).     

A CL surface deformation approach for constant scallop height tool path generation from triangular mesh

In this paper, we present a cutter location (CL) surface deformation approach for constant scallop height tool path generation from triangular mesh. The triangular mesh model of the stereo lithography (STL) format is offset to the CL surface and then deformed in accordance with the deformation vectors, which are computed by the slope and the curvature of the CL surface. In addition, the tool path, which is computed by slicing the deformed CL surface, is inversely deformed by those same deformation vectors to a tool path with a constant scallop height. The proposed method is implemented, and a tool path is generated and tested by simulation and by numerical control (NC) machining. The scallop height was found to be constant over the entire machined surface, demonstrating much better quality than that of mesh slicing, under the same constraints for machining time.     

Loop细分曲面的自适应等距面生成算法与实现

提出一种精确快速生成有边界等距 L oop细分曲面的新算法 ,其核心思想是 :从控制网格顶点在 L oop细分曲面上的位置 ,按照给定的等距值 ,沿其法矢正 (反 )向等距 ,通过解线性方程组求出等距后的控制网格 ,然后检测等距误差 ,对部分超过给定等距精度的控制网格进行局部自适应细分 ,重新生成等距面并检测误差 ,直至整个细分等距曲面满足精度要求 ,所生成的等距细分曲面除局部 C1 外其余 C2 连续。实例表明 :本算法高效稳定 ,生成的等距细分曲面已完全满足实际工程需要。     

基于解析法的整体式叶轮侧铣高精加工技术

提出了加工非可展直纹面刀轴矢量的解析解法,给出了解析解法的加工误差,并将其与“R偏置法”的侧铣加工方法的误差进行了比较。计算结果证明,该方法减小了理论误差。应用MATLAB绘制了依据该方法计算出的叶片刀轴轨迹。最后,通过数控加工试验验证了所提出方法的正确性。加工结果表明,加工误差在允许加工误差范围内,叶轮加工表面质量好。