Tool path planning for 5-axis flank milling of ruled surfaces considering CNC linear interpolation

This paper investigates tool path planning for 5-axis flank milling of ruled surfaces in consideration of CNC linear interpolation. Simulation analyses for machining error show insights into the tool motion that generates a precision machined surface. Contradicting to previous thoughts, the resultant tool path does not necessarily produce minimal machining error when the cutter contacts the rulings of a developable surface. This effect becomes more significant as the distance between two cutter locations is increased. An optimizing approach that adjusts the tool position locally may not produce minimal error as far as the entire surface is concerned. The optimal tool path computed by a global search scheme based on dynamic programming supports this argument. A flank milling experiment and CMM measurement further validate the findings of this work.     

Improving optimization of tool path planning in 5-axis flank milling using advanced PSO algorithms

This paper studies optimization of tool path planning in 5-axis flank milling of ruled surfaces using advanced Particle Swarm Optimization (PSO) methods with machining error as an objective. We enlarge the solution space in the optimization by relaxing the constraint imposed by previous studies that the cutter must make contact with the boundary curves. Advanced Particle Swarm Optimization (APSO) and Fully Informed Particle Swarm Optimization (FIPS) algorithms are applied to improve the quality of optimal solutions and search efficiency. Test surfaces are constructed by systematic variations of three surface properties, cutter radius, and the number of cutter locations comprising a tool path. Test results show that FIPS is most effective in reducing the error in all the trials, while PSO performs best when the number of cutter locations is very low. This research improves tool path planning in 5-axis flank milling by producing smaller machining errors compared to past works. It also provides insightful findings in PSO based optimization of the tool path planning.     

Generation of reciprocating tool motion in 5-axis flank milling based on particle swarm optimization

This paper proposes a novel method for generation of optimized tool path in 5-axis flank milling of ruled surfaces based on Particle Swarm Optimization (PSO). The 3D geometric problem, tool path generation, is transformed into a mathematical programming task with the machined surface error as the objective function in the optimization. This approach overcomes the limitation of greedy planning methods employed by most previous studies. By allowing the cutter to move backforward, reciprocating tool path produces smaller machining error compared with the traditional one consisting of only forward cutter movement. A cutting experiment is conducted with different tool paths and the CMM measurement verifies the effectiveness of the proposed method.     

An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears

To transfer power, a pair of spiral bevel or hypoid gears engages. From beginning to end of two tooth surfaces engaging with each other: for their rigid property, they contact at different points; and for their plastic property, they contact at small ellipses around the points. On each surface, the contact line (or called as contact path) by connecting these points and the contact area by joining these ellipses are critical to driving performance. Therefore, to machine these surfaces, it is important to machine the contact line and area with higher accuracy than other areas. Five-axis flank milling is efficient and is widely used in industry. However, tool paths for flank milling the gears, which are generated with the existing methods, can cause overcuts on the contact area with large machining errors. To overcome this problem, an innovative approach to NC programming for accurate and efficient five-axis flank milling of spiral bevel or hypoid gears is proposed. First, the necessary conditions of the cutter envelope surface tangent with the designed surface along a designed line are derived to address the overcut problem of five-axis milling. Second, the tooth surface including the contact line and area are represented using their machining and meshing models. Third, according to the tooth surface model, an optimization method based on the necessary conditions is proposed to plan the cutter location and orientation for flank milling the tooth surface. By using these planned tool paths, the overcut problem is eliminated and the machining errors of contact area are reduced. The proposed approach can significantly promote flank milling in the gear manufacturing industry.     

On the effective tool path planning algorithms for sculptured surface manufacture

This paper describes the cutter path planning and cutter interference (gouging) analysis algorithms developed to generate optimal tool path for manufacturing sculptured surfaces on three axes CNC machine tools. Cutter path planning algorithm approximates the parametric curves on three dimensional surfaces by a sequence of straight line segments and generates optimal tool paths by minimizing the number of interpolation points while keeping the path deviations within the specified tolerances. Cutter interference analysis algorithm checks for the self intersection of an offset surface and determines the self-intersection curve. The tool path is then planned over the cutter contact (CC) surface after removing the CC data that lies inside the self-intersection curve. Finally, the effectiveness of these algorithms is demonstrated by implementing them in CAD/CAM system.     

Optimal grids for five-axis machining

This paper presents a new grid generation method for tool path planning for five-axis machining based on minimization of the kinematics error. First, the procedure constructs a space-filling curve so that the scallops between the resulting tracks of the tool do not exceed a prescribed tolerance. At the second stage (which is the subject of this paper) a one-dimensional grid along the space-filling curve is generated using direct minimization of the kinematics error. A closed form representation of the kinematics error as a function of locations cutter contact points is derived from the inverse kinematics transformations associated with a particular five-axis machine and obtained through automatic symbolic calculations. The grid of cutter location points is generated so that it minimizes the kinematics error. Numerical and cutting experiments demonstrate that the proposed procedure outperforms distribution of points based on the equi-arc-length principle. Finally, we show that our optimization routine requires less points than that based on sequential point insertion and numerical evaluation of the cost function, such as bisection.     

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.     

Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres

This paper presents an efficient parametric approach of determining the shape of the envelope surface by a generalized cutter that follows five-axis tool path during NC machining. In this approach the cutter is modeled as a canal surface. By considering the tool motions the cutter is decomposed into a set of characteristic and great circles which are generated by two-parameter families of spheres. The center of a sphere from these families is described by two parameters which represent the spine curve and the tool path, and the radius of the sphere is described by one parameter representing the spine curve. Considering the relationship between characteristic and great circles the grazing points on the tool surface are identified. Analytically it is proven for the NC cutter geometries that any point on the envelope surface is located at the intersection of the characteristic and great circles. Then based on the proofs a closed-form solution for computing the grazing points generated by a surface of revolution is presented. The presented methodology is reduced to a simpler parametric form when the NC cutters are described by pipe surfaces.     

A computerised minimum distance algorithm for machining of sculptured surfaces

This paper presents a unique minimum distance algorithm for machining of sculptured surfaces on computer numerical control (CNC) machines. The algorithm has been used to develop a system that graphically simulates the cutter path of the defined surfaces and generates the required CNC programs. The paper presents the experimental results of the surface roughness, tool size, and computed numerical control (NC) points for various tolerance values used on several sculptured surfaces designed by the system and actually machined on a CNC machining centre using the generated NC program from the system.     

Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface

This paper presents a global optimization method to generate a tool path for flank milling free-form surfaces with a generic cutter based on approximation using the tool envelope surface. It is an extension of our previous work [Gong Hu, Cao Li-Xin, Liu Jian. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Computer Aided Design 2005; 37:1205–13]. First, given initial tool path or tool axis trajectory surface, the grazing points of the tool envelope surface can be calculated. Second, the errors between the tool envelope surface and the designed surface along the normal direction of the tool envelope surface are calculated. Based on this new definition of error, an optimization model is established to get the global optimized tool axis trajectory surface. In order to simplify the calculation, two variants of this method based on the least square criterion are proposed to solve this model. Since this method is really based on the tool envelope surface, it can reduce the initial machining errors effectively. The proposed method can be used not only for cylindrical cutters and conical cutters, but also for generic cutters with a surface of revolution. In addition to ruled surfaces, it also can be used for machining non-ruled surfaces. Finally, several examples are given to prove its effectiveness and accuracy. The generated tool paths and calculated grazing points for test are available in supplementary files for the readers’ convenience in verifying this work in different CAD/CAM systems.     

基于四点偏置法的非可展直纹面侧铣刀位计算

针对非可展直纹面五轴侧铣加工的问题,分析了非可展直纹面几何特点,根据等距 映射下的极差不变性,提出了一种计算非可展直纹面叶片五轴侧铣刀位数据的新方法。以刀具包 络面与设计曲面之间的整体误差为优化目标,建立了圆柱铣刀侧铣非可展直纹面的刀位计算方 法,运用四点偏置法确定初始刀位,采用最小二乘法对初始刀位进行优化,建立刀轴矢量偏转模 型进一步修正刀位以减小过切误差。通过实例计算分析,表明该方法可以在一定程度上减小加工 误差。     

Tool path generation for free form surfaces using Bézier curves/surfaces

Presented in this paper is a tool path generation method for multi-axis machining of free-form surfaces using Bézier curves and surfaces. The tool path generation includes two core steps. First is the forward-step function that determines the maximum distance, called forward step, between two cutter contact (CC) points with a given tolerance. The second component is the side step function which determines the maximum distance, called side step, between two adjacent tool paths with a given scallop height. Using the Bézier curves and surfaces, we generate cutter contact (CC) points for free-form surfaces and cutter location (CL) data files for post processing. Several parts are machined using a multi-axis milling machine. As part of the validation process, the tool paths generated from Bézier curves and surfaces are analyzed to compare the machined part and the desired part.     

Simultaneous optimization of tool path and shape for five-axis flank milling

By representing the swept envelope of a generic rotary cutter as a sphere-swept surface, our previous work on distance function based tool path optimization is extended to develop the model and algorithm for simultaneous optimization of the tool path and shape for five-axis flank milling. If the tool path is fixed, a novel tool shape optimization method is obtained. If the tool shape is fixed, a tool path optimization method applicable to any rotary cutter is obtained. The approach applies to non-ruled surfaces, and also finds applications in cutter dimension optimization and flank millable surface design. Numerical examples are given to confirm its validity.     

曲面数控加工中面向NURBS刀具路径生成的刀位点分段算法

曲面数控加工中,NURBS刀具路径生成技术需要在大量有序刀位点中提取适合于NURBS刀具路径表示的刀位点段,刀位点的分段质量是决定NURBS刀具路径生成的前提.通过分析NURBS刀具路径的特点,对由刀位点表示的刀具路径之间的连接方式和边界点进行分类,提出通过层次聚类法将刀具路径进行分段的算法.在此基础上,通过判断连接点的类型来提取合适的刀位点段以进行NURBS刀具路径的生成.实例结果表明,该算法分段可靠、快捷,对不同曲线曲面轮廓刀具轨迹点进行分段的适应性强,分段结果可以满足NURBS刀具路径的生成.     

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.     

Tool path generation for multi-axis freeform surface finishing with the LKH TSP solver

In freeform surface finishing, there are three major types of tool path topologies: the direction-parallel type, the contour–parallel type and the space-filling curve (SFC) type. The SFC topology is capable of covering the whole surface with only one path. In this paper, we present a new way of planning the SFC type tool path by formulating the planning task as a traveling salesman problem (TSP). The optimal path is generated in two steps. Firstly, a set of regular cutter contact (CC) points is generated on the input surface. A cutting simulation method is developed to evaluate the scallop error and determine the position of the next CC point in cross-feed direction. This method is free of local surface curvature assumptions and is therefore accurate for big cutters. Secondly, the obtained CC points are input into an efficient TSP solver LHK for the optimal CC point linking sequences. To stop the CC points from diagonal linking or penetrating linking, the Euclidean distance evaluation function for two CC points is redefined in LHK. The proposed tool path generation method is verified with several freeform surface examples; the results show that the method can automatically find the optimal feed direction and it can generate shorter tool path than the traditional SFC method. The feasibility of the proposed method is also verified by a cutting experiment.     

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.     

三角网格表面等残留高度刀轨生成算法

针对截平面法规划的三角网格表面的刀轨长度较长、加工表面残留高度不均匀的问题,提出一种基于改进截平面法的等残留高度刀轨生成算法.首先在估算刀触点轨迹线垂直方向曲率半径的基础上,计算刀触点轨迹投影线并对其进行修正,去除其中冗余的投影点;然后由修正后的刀触点轨迹投影线构造驱动表面,利用驱动表面和网格表面迭代计算刀触点轨迹线;最后由刀触点轨迹线计算无干涉刀轨.与截平面法生成的刀轨进行比较分析的结果表明,文中算法生成的刀轨长度较小且获得的残留高度保持均匀,适合于三角网格表面表示的复杂表面的精加工.     

Optimization of rotations of a five-axis milling machine near stationary points

We consider a new algorithm designed for five-axis milling to minimize the kinematics error near the stationary points of the machined surface. Given the tool orientations, the algorithm optimizes the required rotations on the set of the solutions of the corresponding inverse kinematics equations. We solve the problem by means of the shortest path scheme based on minimization of the kinematics error.We present an application of the proposed algorithm to tool-path planning and demonstrate the efficiency of the proposed scheme verified by practical machining.     

Error compensation and accuracy improvements in 5-axis machine tools using the global offset method

To enhance the machine tool accuracy, the Global offset method is developed for compensating the five-axis machine tool errors based on the measurement results of one or more identical machined parts. The machined features of a part are measured in a CMM and evaluated by a compensation processor, based on which the Global offset parameters, representing the machine tool errors, are estimated. The methodology is capable of compensating the overall effect of all position-dependent and position-independent systematic errors which contribute to particular workpiece accuracy. The developed technique and software are based on the Global offset method which interprets the computed deviations between the measured and nominal dimensions of the part through the analysis, synthesis and modeling of a fixture and rotary tables errors. The proposed model-based error compensation method is simple enough to be implemented in five-axis CNC machine tools. Production results exhibit effective compensation and remarkable improvement in the workpiece accuracy of the five-axis machine tools.