五坐标数控加工的理论误差分析与控制

对五坐标曲面加工中由离散线性运动逼近理想刀具轨迹所引起的理论加工误差进行了较严格的分析。基于五维线性包络运动分析,得出了适用于多种类型刀具的加工误差估计的通能表达式。该误差是三维意义下较严格的刀具包络成型误差,综合考虑了零件表面的局部几何形状、刀具的形状尺寸与刀轴控制参数、走刀进给方向、机床旋转/摆动机构参数以及走刀步长的影响。在此基础上,分析了减小加工误差的措施,给出了能较严格满足给定精度要求的走刀步长估计算法,有效控制加工误差并提高刀具轨迹质量。     

五坐标数控加工曲面的加工步长计算

讨论了在五坐标数控机床上加工曲面时刀具走刀步长和切削带步长与加工误差的关系并推导了计算公式。     

自由曲面五轴加工刀具轨迹规划技术的研究进展

利用五坐标设备进行自由曲面的数控加工是提高加工质量和加工效率的有效途径,自由曲面形状和五坐标机床运动的复杂性导致其刀具轨迹规划技术十分困难。针对自由曲面五坐标端铣加工、侧铣加工以及碰撞干涉分析中的关键技术,综述了近年来自由曲面五坐标数控加工领域刀具轨迹规划技术的研究进展和现状。结合自由曲面数控加工的工程实用性要求,分析了当前研究中存在的不足,指出目前的研究成果在通用性、稳定性和有效性方面尚不能完全满足工程应用,认为自由曲面五坐标数控加工刀具轨迹规划技术的研究应从三维的角度出发,在更为广域的刀具影响空间研究刀具同自由曲面之间的几何啮合关系,同时需要考虑机床的运动学和动力学特性以实现五坐标机床的高速和高效运行。     

自由曲面的五坐标端铣加工研究

针对自由曲面的五坐标端铣加工，建立了平底刀有效切削轮廓的数学模型，分析了刀具姿态对有效切削轮廓及加工效率的影响。沿行距方向，通过对被加工曲面法截线的偏置曲线与有效切削轮廓求交，得到一种走刀行距的计算方法。探讨了影响走刀行距的因素，在不发生干涉的前提下，小的后跟角和侧偏角有利于加工行距的提高。结合平底刀加工不发生过切的充要条件和被加工曲面沿行距方向的法曲率，给出了后跟角的自动计算方法。算例表明，所提出的走刀行距及刀具倾角的计算方法合理可行，能够有效提高计算精度和加工效率。     

自由曲面数控加工刀具的研究

对自由曲面数控加工中的刀具进行了较深入的研究。从刀具有效半径和切削速度的角度,对平头立铣刀在五坐标自由曲面加工中的加工效率与切削性能进行了分析。提出了球头刀和平头刀的刀位计算方法,并对叶片曲面的刀具轨迹进行了仿真模拟。     

基于广域空间的自由曲面宽行加工方法

为提高自由曲面环形刀五轴精加工的效率,在广域空间中分析刀具的干涉误差,对曲面宽行加工的刀具方位优化方法进行研究。首先根据环形刀刀具特性,定义曲面可能干涉的区域为广域空间,然后将广域空间离散点集变换至刀具坐标系中,计算刀具刀刃曲面的干涉误差,从而构建刀具的实际切削轮廓,并在此基础上精确计算有效的加工带宽。最后,通过建立刀具方位与加工带宽的函数关系,以加工带宽最大化为目标,实现环形刀五轴宽行加工刀具方位的自动优化。算例及试验表明,在相同的残留高度要求下,广域空间方法较之现有的二阶泰勒逼近方法,切触点轨迹长度减少了15.74%,说明基于广域空间的刀轴优化方法是实现自由曲面宽行加工的有效途径。     

带倾斜回转工作台的四坐标后置处理方法

针对带倾斜回转工作台的四坐标数控加工的后置处理,提出了一种非正交多轴联动数控机床的逆运动学求解方法。基于矢量绕任意轴线的旋转变换,建立了非正交情况下四坐标机床各运动坐标同刀位数据之间的映射关系,从而实现了机床平动坐标和转动坐标的计算。该方法同样适用于非正交情况下五坐标机床的逆运动学求解。利用刀具同加工表面相切的控制方式,给出了实际加工中进刀及退刀过程的构造方法。本文方法稳定可靠,并已成功应用于工程实际中。     

基于临界约束的四轴数控加工刀轴优化方法

针对自由曲面四轴加工中复杂刀具运动导致的干涉和刀具运动不连续等现象,提出一种基于临界约束的刀轴优化方法。基于刀具与工件约束曲面之间的相对位置关系,利用曲线上的点搜索算法确定切触点处的临界刀轴矢量,并计算当前切触点刀轴摆动的可行域;以切削行内所有切触点的刀轴可行域为基础,建立当前切削行内无干涉且相邻刀轴变化最小的刀轴矢量优化模型,实现了自由曲面四轴加工无干涉刀轴矢量的光顺控制。整体叶盘四轴加工试验表明,利用此方法获得的刀轴矢量可以显著改善机床运动的连续性,并避免刀具干涉的产生,提高了加工质量。     

五坐标端铣数控加工计算理论分析

本文介绍了五坐标端铣数控加工中的后跟角计算方法及刀位计算方法,分析了加工误差,包括直线逼近误差和刀轴摆动误差,提出了刀轴摆动误差补偿方法——刀具切触点偏置法,给出了走刀步长、走刀步距及刀具半径计算公式。     

基于正向杜邦指标线的五坐标侧铣加工

为实现叶轮类零件的多坐标侧铣加工,通过引入正向杜邦指标线,利用鼓锥形刀对自由曲面的五坐标侧铣加工进行研究。针对具有严格凸切削刃的侧铣加工刀具,提出不发生局部干涉的充要条件是切触点处刀具曲面的正向杜邦指标线位于被加工曲面的正向杜邦指标线之内。给出利用鼓锥形刀侧铣加工自由曲面时实施干涉检查的判断准则以及消除干涉的修正方法,推导出具有严格凸切削刃的刀具在给定的残留高度下侧铣加工带宽的计算方法。在此基础上,利用等残留高度法实现鼓锥形刀侧铣加工自由曲面无干涉刀具轨迹的生成。算例表明,在相同残留高度下,鼓锥形刀侧铣较之球头刀加工效率提高37.44%,说明侧铣加工是提高切削效率和加工质量的一种有效途径。     

Kinematic error separation on five-axis NC machine tool based on telescoping double ball bar

The theory and algorithm of the homogeneous transformation matrix (HTM) method are applied in establishing the kinematic error model of five-axis machining tool with two-axis turntable. Based on this model, a new method for the kinematic error separation in five-axis numerical control (NC) machining tool is proposed. In this study, three types of simultaneous three-axis control motions are designed for each rotary axis to identify the deviations. In the measurement, two translational axes and one rotary axis are simultaneously controlled to keep a constant distance between the tool and the worktable. Telescoping double ball bar is used to measure the relative distance between the spindle and the worktable in the motion of NC machining tool. Finally, the value measured by telescoping double ball bar is substituted into the model to obtain kinematic error of NC machining tool. Comparison has confirmed that the proposed method is high precision and can be applied to effectively and conveniently measure the five-axis machining tool.     

复杂曲面五轴侧铣加工的运动学优化方法

针对五轴侧铣加工中刀轴的运动可能导致加工材料过切与效率低下的问题,提出采用多约束自适应的刀轴运动学优化方法来解决该问题。建立球头铣刀在刀具路段上的运动学模型,通过分析刀轴运动对刀刃微元去除材料的影响,确定刀轴运动优化的约束条件。在虚拟环境中仿真复杂曲面五轴侧铣加工过程,通过自适应控制器调整刀轴运动速度,使机床在多约束加工条件下最大限度地发挥其工作潜能。整个刀轴运动规划过程随刀具与工件接触区域的变化而不断优化,最后将优化结果存储在每个刀位点上。仿真与实验结果表明,刀轴自适应控制的运动学优化方法有效可行,为五轴侧铣加工过程提供了有力的分析工具。     

A cutter orientation modification method for five-axis ball-end machining with kinematic constraints

Cutter orientation modification with kinematic constraints is very necessary and effective for five-axis machining especially machining at high speed. It is very helpful for achieving a smooth cutter motion and keeping the process steady. Therefore, a cutter orientation adjustment method is proposed to obtain an optimized tool path which makes best use of the kinematic characteristics of angular feed for five-axis machining. For the given five-axis cutter location path and the feed profile of cutter tip point both expressed by b-spline formats with the same parameterization, the analytic relations of angular feed, angular feed acceleration, and jerk with respect to the geometric and tangential feed parameters of the cutter tip trajectory are first derived. Then, the conditional inequalities of these kinematic constraints used for orientation adjustment are built. Subsequently, the determination method of feasible cutter orientation and detailed algorithm of orientation adjustment are given. Finally, illustrated examples are conducted to validate the proposed orientation adjustment method. The results show that the developed method is effective and can be applied to optimize geometrically complex five-axis tool path by taking the angular feed, angular feed acceleration, and jerk into account.     

Machinability and set-up orientation for five-axis numerically controlled machining of free surfaces

In this paper, we investigate the problems of determining machinability and part set-up orientation for a given surface model. We first develop kinematic models of the five-axis machines, based on the axis configuration, then develop algorithms for determining the feasibility of one-set-up machining (machinability) and the part orientation for types C-A and A-B tool configurations. Machinability is determined by a computationally efficient procedure for finding the intersection of the feasible tool motion on the sphere and a visibility map which we call the binary spherical map (BSM). The part set-up is so chosen as to give the smallest rotational range among all feasible configurations. The algorithms developed have been tested via numerical simulations. The results show that they can be readily implemented in a CAD/CAM system, as an automated process planner selecting the efficient machine type and part set-up for NC machining.     

A postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation

Improvements in the machine tool and the machining process technologies increased the need for generic postprocessors in order to exploit the capabilities of the machine tools. Contrary to conventional machining approach, next-generation machining technologies such as force-based feedrate scheduling and toolpath optimization requires the implementation of the variable feedrate during toolpath which constitutes the aim of this article. Therefore, this paper introduces a postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation. Furthermore, a practical yet effective method for avoiding kinematic singularities by spherical interpolation and NC data correction is presented as well. Proposed approach is validated for various five-axis machine tools with different kinematic configurations via virtual machine simulation module. Results of the verification tests show that presented postprocessing approach can accurately convert the cutter location information into NC codes and it is demonstrated that integrated virtual simulation module can simulate toolpaths with large number of blocks.     

基于通用五坐标数控机床螺旋锥齿轮NC加工研究

基于空间面共轭原理,确定齿轮切齿矢量关系,建立了螺旋锥齿轮的齿面矢量方程。利用空间坐标系的变换,确定出刀具相对工件的位置和姿态,实现刀具与工件的相对运动,从而将传统的螺旋锥齿轮机床加工调整参数转换为适合NC机床加工的运动参数,进行了五轴加工的刀具扫描体计算,在计算机上,对螺旋锥齿轮数控加工进行了仿真,给出了相应的计算和实验结果。在通过五坐标数控机床上实现螺旋锥齿轮加工,确定出螺旋锥齿轮NC加工方法。     

A novel kinematic model for five-axis machine tools and its CNC applications

In conventional five-axis CNC machining, the machine structure is treated as a single kinematic chain just like a robotic manipulator while the cutter is treated as an end effector. In this paper, besides the machine kinematic chain, a cutter kinematic chain is introduced, and the two subkinematic chains are combined to form one machine–cutter kinematic chain. Forward, inverse kinematics and constrained inverse kinematics for the proposed machine–cutter kinematic chain are further put forward. Two applications are presented to demonstrate the advantages and effectiveness of the proposed kinematic model. The proposed kinematic model unifies the structure of the machine and cutter; therefore, the flexibility of the five-axis machine tool can be fully explored.     

Influence of position-dependent geometric errors of rotary axes on a machining test of cone frustum by five-axis machine tools

A machining test of cone frustum, described in NAS (National Aerospace Standard) 979, is widely accepted by machine tool builders to evaluate the machining performance of five-axis machine tools. This paper discusses the influence of various error motions of rotary axes on a five-axis machine tool on the machining geometric accuracy of cone frustum machined by this test. Position-independent geometric errors, or location errors, associated with rotary axes, such as the squareness error of a rotary axis and a linear axis, can be seen as the most fundamental errors in five-axis kinematics. More complex errors, such as the deformation caused by the gravity, the pure radial error motion of a rotary axis, the angular positioning error of a rotary axis, can be modeled as position-dependent geometric errors of a rotary axis. This paper first describes a kinematic model of a five-axis machine tool under position-independent and position-dependent geometric errors associated with rotary axes. The influence of each error on machining geometric accuracy of a cone frustum is simulated by using this model. From these simulations, we show that some critical errors associated with a rotary axis impose no or negligibly small effect on the machining error. An experimental case study is presented to demonstrate the application of R-test to measure the enlargement of a periodic radial error motion of C-axis with B-axis rotation, which is shown by present numerical simulations to be among potentially critical error factors for cone frustum machining test.     

五轴工具磨床通用后置处理研究

数控机床后置处理能将刀位轨迹转换为机床数控加工程序,其先进程度对零件加工质量和效率有重要影响。目前五轴工具磨床后置处理大都专机专用或另外购买专用后置处理模块。通过对五轴工具磨床的结构类型分析,建立通用五轴工具磨床运动模型,并采用机床运动创成函数将砂轮的位姿转换为机床各轴的运动量,从而得到五轴工具磨床通用后置处理方法,提高了五轴工具磨床后置处理算法的通用性。     

基于VERICUT的五轴数控加工仿真与优化

虚拟加工平台的构建、数控加工程序的正确性验证及加工过程的仿真与优化及是五轴数控机床实现高效加工的重要基础技术。基于VERICUT数控加工仿真与优化平台,以非正交五轴数控机床DMC70ev为研究对象,构建了数控加工仿真平台;以曲面加工为例,建立了基于恒定体积去除率和恒定切屑厚度的优化设计数学模型,进行了刀位轨迹的优化。应用表明:研究成果实现了五轴数控加工过程仿真及数控加工程序的正确性验证,减少了刀具磨损,提高了加工效率与加工质量,可以较好地提升企业数控加工技术的应用水平、应用质量,推动现代制造技术的发展。