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.     

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.     

Electromagnetism-like algorithms for optimized tool path planning in 5-axis flank machining

Optimization of tool path planning using metaheuristic algorithms such as ant colony systems (ACS) and particle swarm optimization (PSO) provides a feasible approach to reduce geometrical machining errors in 5-axis flank machining of ruled surfaces. The optimal solutions of these algorithms exhibit an unsatisfactory quality in a high-dimensional search space. In this study, various algorithms derived from the electromagnetism-like mechanism (EM) were applied. The test results of representative surfaces showed that all EM-based methods yield more effective optimal solutions than does PSO, despite a longer search time. A new EM-MSS (electromagnetism-like mechanism with move solution screening) algorithm produces the most favorable results by ensuring the continuous improvement of new searches. Incorporating an SPSA (simultaneous perturbation stochastic approximation) technique further improves the search results with effective initial solutions. This work enhances the practical values of tool path planning by providing a satisfactory machining quality.     

Continuity-preserving tool path generation for minimizing machining errors in five-axis CNC flank milling of ruled surfaces

Five-axis CNC flank machining has been commonly used in the industry for shaping complex geometries. Geometrical errors typically occur in five-axis flank finishing of non-developable surfaces using a cylindrical cutter. Most existing tool path planning methods adjust discrete cutter locations to reduce these errors. An excessive change in the cutter center or axis between consecutive cutter locations may deteriorate the machined surface quality. This study developed a tool path generation method for minimizing geometrical errors on finished surfaces while preserving high-order continuity in the cutter motion. A tool path is described using the moving trajectory of the cutter center and changes in two rotational angles in compact curve representations. An optimization scheme is proposed to search for optimal curve control points and the resulting tool path. A curve subdivision mechanism progressively increases the control points during the search process. Simulation results confirm that the proposed method not only enhances the computational efficiency of tool path generation but also improves the machined surface finish. This study provides a computational approach for precision tool path planning in five-axis CNC flank finishing of ruled surfaces.     

具有反向学习和自适应逃逸功能的粒子群优化算法

为克服粒子群优化算法进化后期收敛速度慢、易陷入局部最优等缺点,提出一种具有反向学习和自适应逃逸功能的粒子群优化算法.通过设定的阈值,算法将种群进化状态划分为正常状态和"早熟"状态: 若算法处于正常的进化状态,采用标准粒子群优化算法的进化模式;当粒子陷入"早熟"状态,运用反向学习和自适应逃逸功能,对个体最优位置进行反向学习,产生粒子的反向解,增加粒子的反向学习能力,增强算法逃离局部最优的能力,提高算法寻优率.在固定评估次数的情况下,对8个基准测试函数进行仿真,实验结果表明:所提算法在收敛速度、寻优精度和逃离局部最优的能力上明显优于多种经典粒子群优化算法,如充分联系的粒子群优化算法(FIPS)、基于时变加速度系数的自组织分层粒子群优化算法(HPSO-TVAC)、综合学习的粒子群优化算法(CLPSO)、自适应粒子群优化算法(APSO)、双中心粒子群优化算法(DCPSO)和具有快速收敛和自适应逃逸功能的粒子群优化算法(FAPSO)等.     

Correlation between machining direction,cutter geometry and step-over distance in 3-axis milling: Application to milling by zones

Computer-Aided Manufacturing (CAM) occupies an increasingly important role in engineering with all it has to offer in terms of new possibilities and improving designer/manufacturer productivity. The present study addresses machining of free-form surfaces on a 3-axis NC machine tool. There have recently been a large number of studies devoted to planning tool paths on free-form surfaces with various strategies being adopted. These strategies are intended to increase efficiency by reducing the overall length of machining. Often, the choice of the cutter is arbitrary and the work focuses on planning. In order to boost productivity, the present work offers assistance in choosing the cutting tool, the machining direction and cutting by surface zones, adopting a milling strategy by parallel planes. To do so, a comparison is made between milling using a spherical end milling cutter and a torus end milling cutter with the same outer radius. This comparison relates to the radius of curvature of the trace left by the cutter at the point of contact between the tool and the workpiece in relation to the direction of feed motion.     

基于多目标蝗虫优化算法的移动机器人路径规划

在静态多障碍物环境下的移动机器人路径规划问题中，粒子群算法存在容易产生早熟收敛和局部寻优能力较差等缺点，导致机器人路径规划精度低。为此，提出一种多目标蝗虫优化算法（MOGOA）来解决这一问题。根据移动机器人路径规划要求将路径长度、平滑度和安全性作为路径优化的目标，建立相应的多目标优化问题的数学模型。在种群的搜索过程中，引入曲线自适应策略以提高算法收敛速度，并使用Pareto最优准则来解决三个目标之间的共存问题。实验结果表明：所提出的算法在解决上述问题中寻找到的路径更短，表现出更好的收敛性。该算法与多目标粒子群（MOPSO）算法相比路径长度减少了约2.01%，搜索到最小路径的迭代次数减少了约19.34%。     

基于改进粒子群优化算法的AGV全局路径规划

分析了用人工神经网络模型描述环境时,采用Sigmoid函数作为神经网络作用函数的不足之处,提出采用双曲正切函数作为神经网络的作用函数,使网络更有利于路径优化算法的寻优计算。粒子群优化（Particle Swarm Optimization,PSO）算法具有收敛速度快,需要调节的参数少等优点,但优化过程中容易发生“早熟”收敛,使优化陷入局部极小值。通过引入模拟退火算法、“交叉算子”和“变异算子”,提出了一种新的改进粒子群优化算法（Improved Particle Swarm Optimization,IPSO）来解决AGV全局路径规划问题。仿真结果表明,IPSO具有很强的全局寻优能力,并且收敛速度比PSO快,能够为AGV规划出理想的路径。     

An integrated framework of tool path planning in 5-axis machining of centrifugal impeller with split blades

Centrifugal impeller is a complex part commonly used in aerospace, energy, and air-conditioning industries. Its manufacture involves multi-axis free form machining, a time consuming and error-prone process. Tool path planning is considered a critical issue in the process but still lacking of systematic solutions. This paper proposes a tool path planning framework for 5-axis machining of centrifugal impeller with split blades. It provides several CAM functions that assist the users to generate collision-free cutter motions with smooth tool orientations. First, the machining process is divided into four operations and the planning tasks of each operation are standardized. Second, the hub surfaces are properly decomposed, re-grouped, and re-parameterized to facilitate calculation of quality tool path with reduced cutter retraction and plunging. Finally, geometric algorithms are developed to automatically detect tool collisions and then correct the erroneous tool orientations. An optimization scheme is applied to minimize the total amount of tool posture changes after the correction. An impeller is machined with the NC codes generated from the framework. The result shows the effectiveness of this work in automating the tool path planning in 5-axis machining of highly intricate impeller.     

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.     

基于改进粒子群优化算法的牙齿正畸路径规划方法

针对虚拟口腔正畸治疗系统中牙齿移动路径规划问题,提出了一种基于正态分布的简化均值粒子群的牙齿正畸路径规划方法。首先建立了单颗牙齿及整体牙齿的数学模型,并根据牙齿运动的特性,将牙齿正畸路径规划问题转化为带约束的优化问题;其次,在简化粒子群算法的基础上,引入正态分布及均值粒子群的思想,提出了一种基于正态分布的简化均值粒子群优化（NSMPSO）算法;最后,从平移路径长度、旋转角度、碰撞检测以及牙齿在单阶段的移动量、旋转量这五个方面构造了高安全性的适应度函数,实现了牙齿正畸移动路径的规划。将NSMPSO与基本粒子群优化（PSO）算法、均值粒子群优化（MPSO）算法和动态调整惯性权重的简化均值粒子群优化（DSMPSO）算法进行对比,结果表明,改进的算法在Sphere、Griewank和Ackley这三大基准测试函数上均在50次迭代内趋于稳定收敛,且均具有最快的收敛速度和最高的收敛精度。通过Matlab中的仿真实验,验证了利用该数学模型和改进算法求得的最优路径安全可靠,可以为医生提供辅助诊断。     

基于混合粒子群算法的移动机器人路径规划

为了确定复杂环境中移动机器人最优轨迹,提出了一种混合粒子群优化算法(IPSO-GOP).首先对粒子群优化算法进行改进,在算法运行的各个阶段对惯性权重进行自适应调整来增强粒子的搜索能力,并采用混沌变量对粒子进行扰动以提高收敛速度;其次,为了提高算法寻优能力,摆脱局部极小值并增加种群的多样性,引入遗传算法继承的多重交叉和变异两个进化算子(GOP)优化改进版本的粒子群算法(IPSO);最后,使用三次样条插值对该混合算法生成的路径进行平滑处理,得到无碰撞最短的几何连续路径.实验结果表明,多障碍物环境下IPSO-GOP算法减少了陷入局部最优的发生,加快了收敛速度;同时,与原粒子群优化算法(PSO)相比,该算法寻优能力显著,在路径规划问题上有明显的优势.     

基于改进粒子群算法的智能机器人路径规划

针对粒子群算法局部寻优能力差的缺点,提出一种非线性动态调整惯性权重的改进粒子群路径规划算法。该算法将栅格法与粒子群算法进行有效结合,在路径长度的基础上引入安全度和平滑度概念,建立动态调整路径长度的适应度函数。与传统的粒子群算法相比,实验结果表明,改进算法具有较强的安全性、实时性及寻优能力。     

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.     

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.     

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.     

动态扩散粒子群算法及其应用

针对粒子群算法搜索精度不高特别是对高维函数优化性能不佳问题,提出了一种动态扩散粒子群算法,并将其应用于移动机器人路径规划中。该算法通过引进动态调节数,动态地选择粒子的运行轨迹,阻止种群在演化过程中搜索效率降低的缺陷,提高算法的寻优性能。实验结果表明,该算法在处理高维函数优化及移动机器人路径规划方面具有更强的寻优能力及更高的搜索精度。     

基于“Stretching”技术的QPSO算法

基于量子行为的粒子群优化算法(QPSO)是一种随机的全局优化搜索新方法。文章系统的介绍了PSO算法、QPSO算法和“Stretching”技术。在对QPSO算法和基于“Stretching”技术的PSO算法分析的基础上,提出了基于“Stretch-ing”技术的QPSO算法。然后用标准测试函数对新算法进行了实验。实验结果表明,新算法在解的收敛性和稳定性等方面优于基于“Stretching”技术的PSO算法。     

改进的二阶振荡粒子群算法

针对粒子群算法易陷入局部最优等问题,分析了粒子群算法的进化方程,提出了一种改进的粒子群优化算法。算法在振荡环节采用互不相同的参数取值来调节粒子群算法的全局和局部搜索能力,并通过对测试函数和机器人路径规划问题仿真模拟,与标准PSO、标准二阶PSO、二阶振荡PSO算法的实验结果进行对比分析,验证了所提出算法的有效性和可行性。     

Automated path planning for face milling of N-sided convex polygonal surfaces using staircasing strategy

In a manufacturing environment, many times, it is difficult to have NC physical effort with actual machining. This effort can be considerably minimized by analytical modeling of tool path. The path selected for face milling of flat convex polygonal surfaces can significantly affect the cutter travelling distance. Past studies have identified that efforts were made to minimize the path selected for maching these surfaces. However, not much information is available on machining convex polygonal parts for N-sides. An object oriented software package was developed in Turbo C++ to graphically simulate the tool path while face milling different N-sided polygonal surfaces following staircasing path. The staircasing strategy was adopted since the shortest length of cut generated is better than that generated by window frame milling. Pop Up menus were created so that the software developed is interactive, user friendly and completed with error handling.