Selection of optimal machining parameters for hexapod machine tool

Parallel kinematic machine tools (PKM) have the advantages of higher stiffness, higher payload capacity and lower inertia. Still their penetration into the machine tool industry is very less. One of the difficulties in using PKMs such as hexapod machine tools is that the stiffness continuously varies with configuration change at every instant. This makes location of work piece and selection of machining parameters difficult and complicated. A methodology is presented in this article to select optimal machining parameters for hexapod machine tools. Particle swarm optimization is used as a tool in the optimization process. A profile-milling example is also presented to demonstrate the selection of machining parameters.     

A near-optimal part setup algorithm for 5-axis machining using a parallel kinematic machine

A near-optimal part setup model (NOPSM) is developed. The purpose of this model is to find the near-optimal part setup position and orientation based on the workspace, stiffness and accuracy capability of a parallel kinematic machine that can be used for 5-axis machining. To build the proposed NOPSM, the knowledge on the hexapod kinematics, workspace, stiffness, structural imperfection, nonuniform thermal gradient and accuracy is required. Thus, it is a comprehensive performance capability study for a parallel kinematic machine. The proposed model is a software solution concept to improve the machines performance. It is very cost effective and can also be modified for other 5-axis machine tool applications.     

Surface location error of a parallel robot for routing processes

This paper deals with the static characterisation of a parallel manipulator for routing processes. Since accuracy and surface finishing are critical in all machining processes, the performance of a parallel machine is analysed in this paper in terms of these parameters. Using a previously developed static analysis methodology, the stiffness of the machine structure is obtained and used as an input for a process model. This approach allows the static behaviour of the machine to be evaluated in terms of the surface location error for a given routing operation in the manipulator workspace. The study focusses on certain discrete points in the operational workspace for each direction of the tool feed. Then, the global behaviour of the machine is presented using surface location maps. Furthermore, some static constraints are imposed to obtain the static workspace of the manipulator for the routing process.     

基于工作空间和灵活性的并联机床结构参数优化设计

分析了 6SPS型并联机床仿五坐标机床加工工作空间的要求,将满足工作空间要求的机床参数设计问题归结为五变量优化问题.以并联机床工作空间的灵活性为指标,采用遗传算法进行求解。运用该法可确定主要的机床参数,为机床的总体设计提供依据     

Optimal design and development of a 2-DOF PKM-based machine tool

This paper presents multiobjective optimization of a typical 2-degree-of-freedom (DOF) parallel kinematic machine (PKM) tool that has only single DOF joints. Nondimensional indices, namely global stiffness index (GSI), global conditioning index (GCI), and workspace index, are considered as the objectives for optimization. The indices GSI and GCI depict the variation of stiffness and dexterity of PKM within the workspace. The leg length and distance between two rails on which actuators slide are treated as design variables as these greatly influence the characteristics of PKM. A multiobjective genetic algorithm (MOGA) approach is implemented in MATLAB to find an efficient solution to this complex optimization problem. Fitness function includes inverse kinematics equations, Jacobian and stiffness matrices to compute and optimize the nondimensional indices. First, the optimal value of each index is obtained by single-objective GA. To further improve the results, a hybrid function PATTERNSEARCH is used. This helps to select appropriate boundary conditions for MOGA. To obtain the optimal values of all the three indices, a multiobjective GA is carried out. The results are compared with a conventional exhaustive search method of optimization. The obtained results show that the use of MOGA enhances the quality of the optimization outcome. Secondly, a prototype has been designed and developed with the optimal dimensions. The actual workspace of the PKM and influence of leg collision on the workspace are studied. Finally, a preliminary experimentation was carried out. A comparison between PKM and the three-axis serial kinematic machine tool is presented.     

多轴数控加工刀具姿态优化及其刚度性能指标分析

在变形叠加基本原理的基础上,对多轴数控机床刚度模型进行了研究,得到了多轴数控加工刀具姿态优化的物理约束条件。在被加工复杂曲面刀具轨迹上,根据多轴机床综合刚度模型计算机床刚度性能指标,并在刀具可达工作空间中优化多轴机床刚度性能指标,以确定对应的刀具姿态。对基于多轴机床刚度模型的刀具姿态优化作了详细的讨论,分析了任务空间的力椭球特性,提出了面向切削加工的多轴机床刚度性能指标,并将其用于指导刀具姿态规划。

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multi-axis NC machine tool;stiffness;tool posture;force ellipsoid     

A hybrid 5-axis CNC milling machine

5-Axis CNC milling machines are important in a number of industries ranging from aerospace to consumer-die-mold machining because they can deliver high machining accuracy with a spindle tilting capacity. Most of these machines have serial mechanisms so that modest static and dynamic stiffness become very critical design issues when high speed machining capability is required. Parallel mechanisms have recently received attention from machine tool designers because of their inherent potential for stiffness and because of their compactness. However, much of the promised advantages of parallel machines only occur within a very small region of their workspace. We discuss some of the kinematic and structural challenges to extract machining performance from serial and parallel machines. We compare a hybrid machine, which combines serial and parallel mechanisms, with typical serial and parallel machines such as Euler angle machines and a hexapod. In particular, we consider singularities, reversal characteristics, and manufacturability. We show that hybrid machines can benefit from the advantages of serial and parallel mechanisms while avoiding most potential pitfalls. However, hybrid structures can suffer from the manufacturing problem of over-constraint. We show that the degree of over-constraint depends on machine size. We have designed a small hybrid 5-axis motion platform, the MIT-SS-1, which can tolerate this over-constraint through a novel layout of axes. We show that this structure has potential as a small 5-axis CNC milling machine.     

Multi-objective optimisation of surface grinding operations using scatter search approach

A scatter search based optimisation approach is developed to optimise the grinding parameters of wheel speed, work piece speed, depth of dressing and lead of dressing using a multi-objective function model with a weighted approach for the surface grinding process. The production cost and production rate are evaluated for the optimal grinding conditions, subject to the constraints such as thermal damage, machine tool stiffness, wheel wear parameters and surface finish. The results are compared with the results obtained by the ants-colony algorithm, genetic algorithm and quadratic programming techniques.     

Multi-objective optimisation of surface grinding operations using scatter search approach

A scatter search based optimisation approach is developed to optimise the grinding parameters of wheel speed, work piece speed, depth of dressing and lead of dressing using a multi-objective function model with a weighted approach for the surface grinding process. The production cost and production rate are evaluated for the optimal grinding conditions, subject to the constraints such as thermal damage, machine tool stiffness, wheel wear parameters and surface finish. The results are compared with the results obtained by the ants-colony algorithm, genetic algorithm and quadratic programming techniques.     

Multi-objective optimization of a 3-DOF translational parallel kinematic machine

In this paper, stiffness modelling and analysis of a typical 3-DOF parallel kinematic machine (PKM) that provides translational motion along X, Y and Z axes is presented. The mechanism consists of three limbs each having an arm and a forearm with prismatic-revoluterevolute-revolute joints (PRRR). The joint arrangement is in such a way that the moving or tool platform maintains same orientation in the entire workspace. Through inverse kinematics, the joint angles for a given position of tool platform necessary for the stiffness modelling and analysis are obtained. The stiffness modelling is based on the compliance matrices of arm and forearm of each limb. Typical non-dimensional performance indices, namely, workspace volume index (WVI), global translational stiffness index (GTSI), and global rotational stiffness index (GRSI), are introduced and used to study the influence of dimensions. Attempts are also made to find the optimal dimensions of the translational PKM using multi-objective optimization based on the genetic algorithms (MOGA) in MATLAB. The methodology presented and the results obtained are useful for predicting the performance capability of the PKM under study.     

混联机床的静刚度实验测量

机床的静刚度是保证其工作性能的重要指标,用理论模型对机床静刚度进行研究难免产生偏差,因此有必要对其进行实验研究.文中针对一台近期研发成功的混联机床,利用力传感器和千分表对其进行静刚度的实验研究.对实验数据进行最小二乘直线拟合,得到该机床在工作空间内9个位姿的各方向静刚度.为了研究该机床静刚度的变化情况,计算同一水平面或竖直面内的静刚度变化率.文中方法和结论为该类型机床的静刚度理论研究和仿真提供实验依据.     

准双曲面齿轮数控加工的坐标变换

分析了机械摇台式机床和数控铣齿机床的结构模型并建立相应机床坐标系。在保证摇台式机床刀具和工件的相对运动和相对位置关系不变的前提下,利用坐标变换原理,推导出数控铣齿机床加工瞬时的运动位置函数,便于数控机床的编程加工。     

基于RGRR-Ⅰ并联双自由度转动机构的混联五轴机床研究

传统的串联式数控机床存在刚度低的缺点.并联双自由度转动机构RGRR-Ⅰ刚度高,且有着工作空间/机构尺寸比大、耦合为零、制造容易等一系列的优点.运用RGRR-Ⅰ构造的并联双自由度转动刀头摆动精度高、工作空间大.基于混联五轴联动车床的工作要求,研究能实现绕xyz三个直线运动坐标移动,两个运动轴坐标回转的混联五轴联动机床,分析其工作机理,建立有关模型.该研究也可为其他混联机床的设计与制造提供借鉴.     

计及设备因素的成形制件精度驱动的模具结构分析

依据某厂万吨液压机尺寸,应用有限元软件建立了液压机的分析模型。在液压机系统中提出并定义了耦合刚度的概念。应用实验数据得到了锻件平面度误差与垫板、滑块高度变化关系规律,即:模具高度越大,锻件精度越高;垫板越高,同样也是精度越大,但是精度变化的范围越来越小;并建立了垫板高度和模具高度的2阶响应面数学模型并对其验证。运用这些规律和数学模型,可以更好地以产品的精度作为驱动性能,控制模具、垫板尺寸,进一步提高液压机装备的耦合刚度。     

六足仿生步行机器人足端工作空间和灵活度研究

基于六足仿生步行机器人机构学特性的研究，采用数值分析法求解了机器人步行足的足端工作空间，利用虚拟样机技术计算了机器人的灵活度，从两方面综合衡量六足仿生步行机器人的工作能力。并以六足步行机器人各腿节比例关系的确定为例，介绍了六足步行机器人结构优化的具体方案。所用方法同样适用于六足仿生步行机器人其他结构参数的优化，也为六足仿生步行机器人的合理驱动和精确控制提供了理论依据。     

基于运动相对性的六足机器人机体运动规划

将处于支撑相的六足机器人视为时变的并联机构进行运动学分析,给出了姿态给定情况下机体工作空间的确定方法及边界方程。在此基础上基于运动相对性原理,提出将机体的运动规划转化为足端轨迹规划的方法,从而简化机体运动规划中逆解的求取问题,并通过仿真与实验进行了验证。结果表明：六足机器人在支撑相内机体的工作空间为至多是支撑腿条数个空心球体的交集,利用运动相对性原理对支撑相内机体的运动规划问题进行转化简便、可行。     

Optimal design of 3-DOF PKM module for friction stir welding

Friction stir welding (FSW) has recently emerged as a solid-joining technology for high-strength aluminum alloys and light metal welding. The large axial force to be maintained between the welding tool and workpiece is the primary requirement of FSW process, which has also been a great obstacle to the design and application of FSW in manufacturing. Further complicating the issue is the need to perform FSW over three-dimensional contours, which requires a mechanism dexterous enough to set the stir pin used in welding to track a predefined trajectory with prescribed poses. Apart from the position specification, the design of a dexterous mechanism to pose the orientation of stir pin is a great challenge. This paper proposed the application of 3-PRS (P, R, and S standing for prismatic, revolute, and spherical joint, respectively) parallel mechanism as a welding tool head and employed it to form a five-axis welding machine tool for FSW. In order to accommodate the orientation capability requirements, the kinematic feature has been analyzed. With the dimensionless treatment of the Jacobian matrix of 3-PRS manipulator, a global condition index is proposed to estimate the kinematic dexterity in the whole orientation workspace. Finally, by means of an optimal design method and performance atlas, optimal designs of the 3-PRS parallel mechanism is carried out. A preferable set of optimized geometric parameters are obtained to achieve a compact and dexterous design, and the optimization results are used in development of a prototype machine for FSW.     

Anisotropic force ellipsoid based multi-axis motion optimization of machine tools

The existing research of the motion optimization of multi-axis machine tools is mainly based on geometric and kinematic constraints, which aim at obtaining minimum-time trajectories and finding obstacle-free paths. In motion optimization, the stiffness characteristics of the whole machining system, including machine tool and cutter, are not considered. The paper presents a new method to establish a general stiffness model of multi-axis machining system. An analytical stiffness model is established by Jacobi and point transformation matrix method. Based on the stiffness model, feed-direction stiffness index is calculated by the intersection of force ellipsoid and the cutting feed direction at the cutter tip. The stiffness index can help analyze the stiffness performance of the whole machining system in the available workspace. Based on the analysis of the stiffness performance, multi-axis motion optimization along tool paths is accomplished by mixed programming using Matlab and Visual C++. The effectiveness of the motion optimization method is verified by the experimental research about the machining performance of a 7-axis 5-linkage machine tool. The proposed research showed that machining stability and production efficiency can be improved by multi-axis motion optimization based on the anisotropic force ellipsoid of the whole machining system.     

基于正交试验的机床结合部动刚度优化配置

机床中结合部分布众多且不同接触条件下其动刚度值不同,优化分析时很难研究每个动刚度值对机床动态性能的影响。针对此类问题,提出一种基于正交试验的机床结合部动刚度优化配置方法。该方法通过模态柔度与弹性能分布理论判定机床的薄弱模态和薄弱结合部,建立以薄弱结合部的动刚度为设计变量,各阶薄弱模态的最小模态柔度为目标的多目标优化模型。为提高优化效率,采用正交试验方法规划试验方案,并在试验结果分析中引入相似优先比法对结合部动刚度进行协同优化配置。以某型立式加工中心为例,采用优化配置方法确定其结合部动刚度的最优配置方案。仿真结果显示该方案下薄弱模态的模态柔度明显降低,整机动态性能提高,验证了该方法的可行性。     

新型并联机床静刚度特性的有限元分析及优化设计

静刚度分析是机床设计的重要内容之一,对一种新型龙门式并联机床的平面并联机构进行了研究,通过位置逆解求出了广义全工作空间;建立了整机静刚度的有限元模型,得到动平台在广义工作空间下的刚度分布规律;找出影响Z向位置精度的关键因素并进行了优化设计,为进一步改进并联机床提供重要的依据。