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.     

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.     

An efficient memory-based electromagnetism-like mechanism for the redundancy allocation problem

Meta-heuristic algorithms have been successfully applied to solve the redundancy allocation problem in recent years. Among these algorithms, the electromagnetism-like mechanism (EM) is a powerful population-based algorithm designed for continuous decision spaces. This paper presents an efficient memory-based electromagnetism-like mechanism called MBEM to solve the redundancy allocation problem. The proposed algorithm employs a memory matrix in local search to save the features of good solutions and feed it back to the algorithm. This would make the search process more efficient. To verify the good performance of MBEM, various test problems, especially the 33 well-known benchmark instances in the literature, are examined. The experimental results show that not only optimal solutions of all benchmark instances are obtained within a reasonable computer execution time, but also MBEM outperforms EM in terms of the quality of the solutions obtained, even for large-size problems.     

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.     

Algorithms for selecting cutters in multi-part milling problems

This paper describes geometric algorithms for automatically selecting an optimal sequence of cutters for machining a set of 2.5-D parts. In milling operations, cutter size affects the machining time significantly. Meanwhile, if the batch size is small, it is also important to shorten the time spent on loading tools into the tool magazine and establishing z-length compensation values. Therefore, in small-batch manufacturing, if we can select a set of milling tools that will produce good machining time on more than one type of parts, then several unnecessary machine-tool reconfiguration operations can be eliminated. In selecting milling cutters we consider both the tool loading time and the machining time and generate solutions that allow us to minimize the total machining time. In this paper we first present algorithms for finding the area that can be cut by a given cutter. Then we describe a graph search formulation for the tool selection problem. Finally, the optimal sequence of cutters is selected by using Dijkstra's shortest path planning algorithm.     

Time-optimal tool motion planning with tool-tip kinematic constraints for robotic machining of sculptured surfaces

A time-optimal motion planning method for robotic machining of sculptured surfaces is reported in this paper. Compared with the general time-optimal robot motion planning, a surface machining process provides extra constraints such as tool-tip kinematic limits and complexity of the curved tool path that also need to be taken into account. In the proposed method, joint space and tool-tip kinematic constraints are considered. As there are high requirements for tool path following accuracy, an efficient numerical integration method based on the Pontryagin maximum principle is adopted as the solver for the time-optimal tool motion planning problem in robotic machining. Nonetheless, coupled and multi-dimensional constraints make it difficult to solve the problem by numerical integration directly. Therefore, a new method is provided to simplify the constraints in this work. The algorithm is implemented on the ROS (robot operating system) platform. The geometry tool path is generated by the CAM software firstly. And then the whole machine moving process, i.e. the feedrate of machining process, is scheduled by the proposed method. As a case study, a sculptured surface is machined by the developed method with a 6-DOF robot driven by the ROS controller. The experimental results validate the developed algorithm and reveal its advantages over other conventional motion planning algorithms for robotic machining.     

Optimal tool selection for pocket machining in process planning

In process planning for pocket machining, selection of tool size, tool path, cutting width at each tool path, and calculation of machining time are very important factors for optimal process planning. The tool size is the most important factor because the other factors depend on tool size. Therefore, the optimal selection of tool size is the most essential task in pocket machining process planning. This paper presents a method for selecting optimal tools for pocket machining for the components of injection mold. The branch and bound method is applied to select the optimal tools which minimize the machining time by using the range of feasible tools and the breadth-first search.     

基于自适应Tent混沌搜索的粒子群优化算法

为解决粒子群优化算法易于陷入局部最优问题,提出基于自适应Tent混沌搜索的粒子群优化算法。应用Tent 映射初始化均匀分布的粒群,并以当前整个粒子群迄今为止搜索到的最优位置为基础产生Tent混沌序列,混沌序列的搜索范围采用自适应调整方法。该方法可以有效避免计算的盲目性,还能够快速搜寻到最优解。实验表明该算法在多个标准测试函数下都超越了同类改进算法。     

Iso-scallop tool path planning for triangular mesh surfaces in multi-axis machining

Triangular mesh enables the flexible construction of complex surface geometry and has become a general representation of 3D objects in computer graphics. However, the creation of a tool path with constant residual scallop height on triangular mesh surfaces in multi-axis machining is not a convenient task for current algorithms. In this study, an isoscallop tool path planning method for triangular mesh surfaces, in which the tool path is derived directly from the contours of a normalized geodesic distance field (GDF), without any post-processing is proposed. First, the GDF is built to determine the shortest geodesic distance from each vertex to the mesh boundary. Then, the normalizing process is performed on the GDF to ensure that its first contour meets the isoscallop height requirement considering the mesh curvature and effective cutter radius. To improve the computational efficiency, the GDF is only built in the mesh area related to the first contour by specifying a stop distance. Moreover, an adaptive refinement process is conducted on the mesh to improve the smoothness and accuracy of the tool path. Finally, the triangular mesh is trimmed along this first contour for a new round of tool path planning. The proposed method is organized recursively and terminated when no new paths are generated. Simulations and experiments are conducted to verify the effectiveness and superiority of the proposed tool path planning method.     

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.     

基于改进粒子群算法的UAV航迹规划方法

结合当前无人机集群发展趋势,针对航迹规划算法和策略问题开展研究,在分析经典粒子群算法和传统航迹规划方法基础上,提出了一种基于改进粒子群算法的航迹规划方法,将无人机航迹规划分为整体航迹规划和节点间航迹规划两部分,针对两部分对于搜索速度和解的精度的不同需求,结合环境模型及约束条件,分别设计粒子群航迹规划算法的评价函数;对于节点间粒子群航迹规划,通过设计分段式惯性权重调整公式改进粒子群算法,在保证了算法的搜索速度的同时,提高了航迹规划解的精度。通过仿真验证了该方法的正确性和可行性,横向对比其他算法策略分析了该方法的优越性。最后在算法自主实时性方向上对于后续的工作开展提出了期望。     

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.     

Optimizing tool orientations for 5-axis machining by configuration-space search method

This paper presents a methodology and algorithms of optimizing and smoothing the tool orientation control for 5-axis sculptured surface machining. A searching method in the machining configuration space (C-space) is proposed to find the optimal tool orientation by considering the local gouging, rear gouging and global tool collision in machining. Based on the machined surface error analysis, a boundary search method is developed first to find a set of feasible tool orientations in the C-space to eliminate gouging and collision. By using the minimum cusp height as the objective function, we first determine the locally optimal tool orientation in the C-space to minimize the machined surface error. Considering the adjacent part geometry and the alternative feasible tool orientations in the C-space, tool orientations are then globally optimized and smoothed to minimize the dramatic change of tool orientation during machining. The developed method can be used to automate the planning and programming of tool path generation for high performance 5-axis sculptured surface machining. Computer implementation and examples are also provided in the paper.     

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.     

一种新的变维粒子群路径规划算法

针对传统粒子群路径规划不能根据不同环境调节路径节点数、搜索效率低、甚至在一些地形下得不到可行解的不足,提出一种基于变维粒子群的路径规划算法.通过动态改变粒子的维度,控制路径节点数目并调整节点分布,加快了算法收敛速度.在需要沿障碍物迂回才能通过的复杂障碍物的情况下,采用一次位置记忆的避障算法得到无障碍路径.仿真结果表明,该算法可获得较优的路径且收敛速度较快.     

Particle Swarm Optimization inspired by starling flock behavior

Swarm intelligence is a meta-heuristic algorithm which is widely used nowadays for efficient solution of optimization problems. Particle Swarm Optimization (PSO) is one of the most popular types of swarm intelligence algorithm. This paper proposes a new Particle Swarm Optimization algorithm called Starling PSO based on the collective response of starlings. Although PSO performs well in many problems, algorithms in this category lack mechanisms which add diversity to exploration in the search process. Our proposed algorithm introduces a new mechanism into PSO to add diversity, a mechanism which is inspired by the collective response behavior of starlings. This mechanism consists of three major steps: initialization, which prepares alternative populations for the next steps; identifying seven nearest neighbors; and orientation change which adjusts velocity and position of particles based on those neighbors and selects the best alternative. Because of this collective response mechanism, the Starling PSO explores a wider area of the search space and thus avoids suboptimal solutions. We tested the algorithm with commonly used numerical benchmarking functions as well as applying it to a real world application involving data clustering. In these evaluations, we compared Starling PSO with a variety of state of the art algorithms. The results show that Starling PSO improves the performance of the original PSO and yields the optimal solution in many numerical benchmarking experiments. It also gives the best results in almost all clustering experiments.     

受限空间自适应区域栅格化的优化路径规划

针对障碍物分布复杂、存在封闭边界的受限空间,提出一种环境自适应区域栅格化的优化路径规划算法.该算法首先将环境自适应划分为区域栅格,并提出阻碍度指标降低搜索空间的维度以优化区域栅格的划分;然后结合随机变异和定向变异,给出一种可有效平衡搜索效率与精度矛盾的多维变异粒子群优化算法;最后使用最小二乘曲线拟合方法对优化路径予以平滑处理.与非线性递减惯性权值粒子群算法（NDW-PSO）及组合粒子群算法（C-PSO）对比的仿真结果验证了所提出算法的先进性.     

改进粒子群算法的潜器导航规划

针对粒子群算法的寻优搜索能力强和已有的一些导航算法存在收敛速度慢、迭代时间长的缺点,提出一种基于粒子群算法的潜器导航算法.利用群智能理论,对基本粒子群算法进行改进:提出一个含突变因子的可变调的惯性权值策略,从而达到增强粒子群算法局部和全局寻优的调度能力.通过实验仿真验证,证明了改进粒子群算法具有更优的性能.在此基础上,将该算法应用到水下潜器的路径规划中,通过对环境的建模分析进行条件约束,最终将路径规划问题转化为路径点求解的优化问题.实验仿真结果获得了从起点到终点的无碰撞路径,收敛速度也较快,验证了该方法的有效性和可行性.     

一种改进PSO的室内机器人路径规划方法

针对室内空间局限性造成的移动机器人路径规划难度提升问题,文章分析了机器人室内移动中转弯、启停等运动特征,为获得最优规划路径引入了粒子群算法(particle swarm optimization, PSO),同时为改善经典算法中收敛度低,易早熟等问题,首先使用收敛因子、线性递减、非线性凹函数、随机分布方式等对PSO惯性权重的选取进行了讨论,并结合三次样条插值方法、选取罚函数作为适应度函数等对PSO进行了算法改进,最后,以实验室作为室内环境背景进行了仿真实验,并与经典的PSO路径规划方法进行了对比,实验结果表明,文章中改进的PSO路径规划方法精度高于经典PSO方法5%,平均寻优时间比经典PSO的少5s左右,能够有效的提高规划路径的平滑度,对于室内环境中机器人路径规划具有良好的实时性和有效性。     

Cryptanalysis of Vigenere cipher using Cuckoo Search

Evolutionary techniques such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Cuckoo Search (CS) are promising nature-inspired meta-heuristic optimization algorithms. Cuckoo Search combined with Lévy flights behavior and Markov chain random walk can search global optimal solution very quickly. The aim of this paper is to investigate the applicability of Cuckoo Search algorithm in cryptanalysis of Vigenere cipher. It is shown that optimal solutions obtained by CS are better than the best solutions obtained by GA or PSO for the analysis of the Vigenere cipher. The results show that a Cuckoo Search based attack is very effective on the Vigenere cryptosystem.