Computer-aided geometric machining of a 3D free surface using a 3-UPU spatial parallel machine tool

A novel computer-aided geometric approach for machining a 3D free surface by adopting a 3-UPU spatial parallel machine tool is proposed. Based on the geometry constraint and dimension-driving technique, first, a spatial 3-UPU parallel simulation mechanism is created. Next, a 3D free surface and a guiding plane of tool path are constituted. Finally, the 3-UPU spatial parallel simulation mechanism, the 3D free surface, and the guiding plane of tool path are combined together, and a novel spatial parallel 3-UPU simulation machine tool is created for machining a 3D free surface. In the light of two specified tool paths, the extensions of three driving limbs and the position of the moving platform are solved dynamically by adopting the dimension-driving technique. The results of computer simulation prove that the computer-aided geometric approach is not only fairly quick and straightforward in developing or designing, but is also advantageous from the viewpoint of accuracy and repeatability .     

Simulation of machining 3D free-form surface in normal direction using 6-SSP and 4SPS+UPU parallel machine tools

A novel 6-SSP parallel machine tool and a novel 4SPS+UPU parallel machine tool are presented, and a novel CAD approach is proposed to machine a 3D free-form surface in its normal direction by using the two parallel machine tools. First, by adopting the CAD geometry constraint and dimension-driving technique, the simulation mechanisms of a 6-SSP parallel manipulator with 6-DOF and a 4SPS+UPU parallel manipulator with 5-DOF are created. Second, a 3D free-form surface and a guiding plane of tool path are constructed above the moving platform of the two simulation mechanisms. Third, the tool axis of simulation parallel machine tool is retained perpendicular to the 3D free-form surface. In the light of two prescribed tool paths, the driving limbs and the pose of the moving platform of parallel machine tools are solved automatically and visualized dynamically.     

基于变量几何法的两种并联机床法向加工自由曲面仿真

采用CAD变量几何法,用两种新型5自由度3SPS+RRPU和2SPS+RRPRR并联机床对任意3D自由曲面进行法向加工。通过CAD几何约束和尺寸驱动技术,首先建立两种并联机床的模拟机构,再在并联机构动平台上构造任意3D自由曲面和刀具轨迹的引导平面,与并联机构合成,得到模拟并联机床。保持刀具与自由曲面垂直关系,给定加工路径,各驱动杆长和动平台的位置能自动求解和动态显示。结果表明:CAD变量几何法不仅简单直观,而且省去了大量的编程计算。     

4SPS+UPU并联机床法向加工自由曲面的研究与仿真

采用CAD变量几何法,用一种新型5自由度4SPS+ UPU并联机床对任意3D自由曲面进行法向加工.通过CAD几何约束和尺寸驱动技术,首先建立4SPS+ UPU并联模拟机构,再在并联机构动平台上构造任意3D自由曲面和刀具轨迹的引导平面,与4SPS+UPU并联机构合成,得到模拟并联机床.保持刀具与自由曲面垂直关系,给定加工...     

Simulation solving/modifying velocity and acceleration of a 4UPS+SPR type parallel machine tool during normal machining of a 3D free-form surface

A CAD variation geometry approach is proposed for solving/modifying the inverse velocity/acceleration of the active legs and the forward velocity/acceleration of a 5-dof 4UPS + SPR parallel machine tool (PMT) during its simulation normal machining of a 3D free-form surface. First, the twin simulation mechanisms of this PMT with the same base are created for normal machining the same 3D free-form surface. Second, a velocity simulation mechanism of this PMT is created from the twin simulation mechanisms. Third, an acceleration simulation mechanism of this PMT is created from the three similar simulation mechanisms with the same base. Finally, the extension, the velocity and acceleration of the active legs, and the velocity and acceleration of the PMT are solved and modified during the simulation normal machining of the 3D free-form surface. The simulation solutions are verified by an analytic approach.     

Simulation of pre-solving active forces of a 4SPS+SPR parallel machine tool in normal machining a 3D free-form surface

A CAD variation geometry approach is proposed for simulation of pre-solving and pre-modifying the accurate active forces of a 5-DOF 4SPS+SPR parallel machine tool (PMT) in normal machining of a three-dimension (3D) free-form surface s. First, an initial simulation mechanism of the 4SPS+SPR PMT is created. Second, a variable workload which is composed of a tangent force, a normal force, and a rotational torque of the tool is constructed and applied to the center of the platform in the simulation of machining s. Third, the whole simulation mechanism of the 4SPS+SPR PMT with Euler angles and a variable workload is created, and the displacement and the accurate active forces of this simulation PMT are solved in normal machining of s. The solutions of the simulation coincide with the analytic ones.     

Experimental investigation on various tool path strategies influencing surface quality and form accuracy of CNC milled complex freeform surface

Four tool path strategies such as equal-interval tool paths, parallel tool paths, parallel–tangency tool paths, and freeform tool paths are proposed in computer numerical control milling of a complex freeform surface. The objective is to understand how 3D tool paths influence their machining efficiency, surface quality, and form accuracy. In this study, their scallop heights were less than or equal to 15 μm. First, their scallop heights distributions and 3D tool path distances were theoretically analyzed; then, four tool path strategies were investigated with reference to machining efficiency, surface texture height, surface roughness, and form errors. It is shown that scallop heights distribution can be used to display the surface texture state and predict tool path distance. Experimental results indicate that the surface texture height, the surface roughness, and the form errors were nearly identical on the machined flat location and surface for various tool path strategies, whereas their surface quality and form accuracy are easily destroyed on the abrupt ones except for the parallel tool paths. Although the freeform tool paths produce the shortest tool path distance through 3-axes driving mode, the parallel tool paths offer the best surface quality and form accuracy through 2-axes driving mode. This is because the 3-axes driving and its vector changes on abrupt location easily lead to large machine vibration and movement errors. It is confirmed that the parallel tool path strategy with 2-axes driving mode can improve the surface quality and form accuracy in actual milling of a complex freeform surface.     

面向并联机床的后置处理方法

为了解决并联机床的后置处理问题,克服现有方法开发的难度和工作量大的缺点,提出了直接转化传统数控机床数控代码,得到并联机床数控代码的方法。对5-虎克铰-移动副-球铰／移动副-转动副-移动副-虎克铰并联机床和刀具双摆动5轴数控机床进行运动学分析,得出并联机床动平台的两个可变化的姿态角具有与刀具双摆动5轴数控机床中两个摆动转角相同的性质;然后直接利用智能制造后置处理软件进行后置处理得到刀具双摆动5轴数控机床的数控程序;再经过适当的变换,得到并联机床的数控程序。曲面加工的计算机模拟结果表明,该方法正确、有效。     

Kinematics analysis and solution of the active/passive forces of a 4SPS+SPR parallel machine tool

A 5-dof 4SPS+SPR parallel machine tool with four SPS-type active legs and one SPR-type active leg is proposed. Its inverse kinematics is analysed by using an analytic approach and a CAD variation geometry approach. Some analytic formulae for solving the active/passive forces are derived by adopting a vector approach. First, a simulation mechanism of the 4SPS+SPR parallel machine tool is created and some kinematic characteristics are analysed. Second, the formulae for solving its inverse kinematics and the Jacobian matrix are derived and a reachable workspace is constructed. Third, the poses of the active/passive forces are analysed and an active/passive force transformation matrix and the analytic formulae for solving the active/passive forces of the 4SPS+SPR parallel machine tool are derived. The analytic results are verified by the simulation mechanism.     

新型3T2R龙门式混联机床动力学模型

提出了一种以能实现沿X、Z轴平移和绕X、Y轴转动的新型并联机构2-RPU2-UPS作为主体,辅以能实现主体Y轴滑动的直线导轨来共同实现五坐标联动加工的一种新型龙门式混联机床的机构设计方案。运用螺旋理论分析了该机床实现3T2R运动原理,计算出该机床的自由度,进行输入选取与论证,并进行机床机构奇异分析,提出减少奇异的参数设计条件。建立该机床的位置反解数学模型,推导出了该机床的速度雅可比矩阵和加速度分析表达式,求解了该机床的位置反解、速度和加速度。基于虚功原理和该机床的运动学模型建立该机床的动力学模型,并采用Adams软件对该机床动力学进行模拟仿真,模拟结果表明理论结果完全正确。     

一种三杆并联机床的静力分析

推导了在重力和切削力作用下并联机床驱动力的计算方程，并对一种三杆并联机床进行了仿真计算。结果表明，该种并联机床进行切削加工时，各杆输出的驱动力比较均匀，没有突变，各杆驱动力最大不超过切削力的1．4倍；机床自重产生的驱动力在工作空间中无突变，并且在工作空间边缘处较大；为了克服机床自重，需要各杆输出较大的驱动力，因此需要对机床进行平衡。     

新型三维平台机床全域承载能力及其在几何空间模型内的分布

应用并联机器人机构学理论，定义新型6自由度三维平台并联机床的全域承载能力指标，并基于空间模型理论，研究了全域承载能力指标在并联机床几何空间模型内的分布，为该并联机床的结构参数的计算机辅助优化设计提供了一条新途径。     

计算机辅助几何法分析4-DOF并联机器人

提出运用计算机辅助几何法来研究新型四自由度并联机器人的型综合问题,利用在CAD软件草图环境下建立的并联机器人模拟机构,基于并联机器人的模拟机构,综合出多种新型四自由度机构,并用计算机模拟法,分析了动平台的运动特性。模拟结果表明,计算机辅助几何法的应用不但大大简化了并联机器人机构型综合的难度,而且快捷直观,值得推广。     

空间自由曲面五轴联动数控加工

介绍了五轴数控机床的运动方式,阐述了空间自由曲面五轴联动数控加工中刀具路径规划的基本方法:参数线法、CC路径截面线法、CL路径截面线法、导动面法等。之后对五轴加工中刀具轴向规划进行了论述:垂直于表面方式、平行于表面方式、倾斜于表面方式。最后归纳总结了刀具干涉的检测与处理的方法,并分别说明了其优缺点和适应范围。     

计算机辅助几何技术用于并联机器人机构学研究方法论

提出将计算机辅助几何技术用于并联机器人机构学研究的基本理论和方法。基于CAD几何约束和尺寸驱动技术原理,建立并联机器人模拟机构,该模拟机构的运动特性与装配成的三维机构实体完全等效。研究表明,计算机辅助几何技术用于并联机器人机构学的研究不仅具有简捷直观、求解精度高和重复性好的优点,而且无需解析求解和辅助编程就可完成并联机构的型综合和运动特性分析,为研制更多实用的新型并联机器人提供有效的工具。     

Three-dimensional tool radius compensation for multi-axis peripheral milling

Few function about 3D tool radius compensation is applied to generating executable motion control commands in the existing computer numerical control (CNC) systems. Once the tool radius is changed, especially in the case of tool size changing with tool wear in machining, a new NC program has to be recreated. A generic 3D tool radius compensation method for multi-axis peripheral milling in CNC systems is presented. The offset path is calculated by offsetting the tool path along the direction of the offset vector with a given distance. The offset vector is perpendicular to both the tangent vector of the tool path and the orientation vector of the tool axis relative to the workpiece. The orientation vector equations of the tool axis relative to the workpiece are obtained through homogeneous coordinate transformation matrix and forward kinematics of generalized kinematics model of multi-axis machine tools. To avoid cutting into the corner formed by the two adjacent tool paths, the coordinates of offset path at the intersection point have been calculated according to the transition type that is determined by the angle between the two tool path tangent vectors at the corner. Through the verification by the solid cutting simulation software VERICUTwith different tool radiuses on a table-tilting type five-axis machine tool, and by the real machining experiment of machining a soup spoon on a five-axis machine tool with the developed CNC system, the effectiveness of the proposed 3D tool radius compensation method is confirmed. The proposed compensation method can be suitable for all kinds of threeto five-axis machine tools as a general form.     

并联机床工作空间快速校验与仿真

根据并联机床工作空间的定义及几何约束条件 ,提出了工作空间快速定位校验算法和许用平台倾角[β]x ,y ,z 的概念 ,论述了用许用平台倾角 [β]x ,y,z 组成的工作空间文件描述并联机床不发生干涉的工作空间的思想。在此理论基础上 ,利用VC6 .0开发了并联机床刀具轨迹干涉校验模块 ,该模块实现了对UG的CAM模块产生的刀具路径进行快速校验的功能。同时 ,应用OpenGL ,实现了对并联机床工作空间和机床加工运动过程的三维仿真     

Accurate spiral tool path generation of ultraprecision three-axis turning for non-zero rake angle using symbolic computation

An accurate spiral tool path generation method of ultraprecision three-axis turning free form surface is proposed based on symbolic computation in this paper. Many analytic optical free form surfaces often need to be machined to submicron in form error, such as optical nonaxisymmetric aspheric surfaces, but current mainstream CAM systems usually use nonuniform rational basis spline (NURBS) to describe the designed surface and generate tool path. If we want to use these systems, the analytical optical surfaces must be approximated using NURBS surfaces, but it will introduce approximation error and may be difficult to achieve the approximation error less than submicron. More importantly, there is no effective tool path generation method for the special three-axis turning machine tool in current mainstream CAM systems. In this context, we propose to calculate the tool path directly from these analytic surfaces by using symbolic math. The proposed method can be used to generate accurate spiral tool paths for zero/negative/positive rake angle in a unified way. Finally, several examples are given to prove its effectiveness.     

Error analysis and auto-calibration for a Cartesian-guided tripod machine tool

This paper focuses on the error analysis and calibration methodologies for a parallel kinematic machine (PKM) called a Cartesian-guided tripod (CGT). The CGT volumetric error due to the geometric error, kinematic parameter error and nonlinear machine stiffness were studied. It is well known that the PKM nonlinear machine stiffness can produce significant volumetric errors from several tens to several hundreds of micrometres depending on the averaged value and deviation range for the machine stiffness. For most PKMs, joint level sensors are used to estimate the virtual Cartesian movements of the cutting tool. The nonlinear stiffness effect is not detected by this indirect metrology method and must be compensated for by a calibration methodology. A solution for the nonlinear stiffness effect implemented on the CGT involves using a passive Cartesian guiding/metrology leg that is independent of the driving legs to directly measure the Cartesian movement of the motion platform. Because the metrology loop of the Cartesian guiding/metrology leg is separated from the kinematic loops of the driving legs, the volumetric accuracy of the CGT is immunised against thermal errors and load deformations on the drive mechanisms. The passive Cartesian guiding/metrology leg is also used for the auto-calibration of the CGT kinematic parameters. The auto-calibration methodology and simulation results were studied and reported.     

Reduction of geometry-based errors in five-axis machining through enhanced 5D interpolation

Geometry-based errors constitute a special category of CAM-originated machining inaccuracies that significantly influence the precision of five-axis surface machining operations. Geometry-based errors reflect the inability of the cutter to accurately trace a prescribed 3D tool path in five-axis machining. Their magnitude constitutes an overlapped effect of the adopted interpolation scheme, cutter, and surface geometries, as well as kinematics of the five-axis machine tool, assumed free of errors by the CAM software. Although the presence of these errors is inherent in the current configuration of five-axis computer numerically controlled machining systems, little efforts were made so far towards their reduction. In this regard, the present study has investigated the magnitude of geometry-based errors as generated by various 5D interpolation schemes. These enhanced interpolation functions were determined by enforcing better approximations of the ideal machine control coordinate (MCC) trajectory as calculated in five-axis machine tool’s joint space. By comparing the geometry-based errors generated by the enhanced 5D interpolation schemes with linear interpolation baseline, it was found that significant error reductions will be obtained when synchronized 5D quadratic functions are used to approximate the ideal MCC curve in joint space. Moreover, the parametric synchronization between rotational and translational machine tool motions represents an essential requirement for limitation of the amount of geometry-based errors.