Adaptable geometric patterns for five-axis machining: a survey

The paper presents a survey of five-axis computer numerical controlled (CNC) machining optimization methods employing adaptable geometric patterns. First, the survey introduces evolution of CNC interpolators from the simplest Taylor series-based routines to sophisticated procedures based on constraint minimization from dynamic systems control theory. Furthermore, a variety of methods based on spline interpolation, NURBS interpolation and Farouki’s Pythagorean–hodograph curves is presented and analyzed. Next, the survey deals with techniques to optimize the positions and orientations of the tool in a particular neighborhood of the part surface. The most important application of these techniques is cutting by a flat-end or a fillet mill while avoiding local overcuts or undercuts due to the curvature interference and rear gouging. This section is supplemented by detection of global interference using visibility cone schemes and their recent modifications and improvements. Solutions offered by solid modeling are presented as well. Finally, adaptable geometric patterns employed for tool path generation are considered and analyzed. The adaptation is performed using certain criteria of the tool path quality, such as kinematics error, scallops, possible undercuts or overcuts, and the continuity of the path. Also covered are complex pocket milling employing geometric patterns capable of following the boundary, such as the offset methods, regional milling, the potential path methods, and clustering. The chapter also presents tool path optimization based on the adaptable curvilinear grids connecting the cutter location points. Finally, navigation approaches and the shortest-path schemes are considered, along with the adaptive space-filling curve algorithms and their combinations with grid generation.     

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.     

Elasto-geometrical error modeling and compensation of a five-axis parallel machining robot

Parallel manipulators have the potentials of high efficiency and high precision in the field of machining and manufacturing. However, accuracy improvement of the parallel manipulator is still an essential and challenging issue, encountering two important problems. Firstly, the ignorance of elastic deformation caused by gravity or deviations of static stiffness model restricts further improvement of accuracy. To solve this problem, an elasto-geometrical error modeling method is proposed. The comprehensive effects of structural errors, elastic deformation under gravity and compliance parameter errors on pose deviations are disclosed. On this basis, the identification equation of actual structural errors and compliance parameter errors can be established. Secondly, the ill-conditioned identification matrix and the identification equation with anisotropic residual error can lead to inaccurate identification results. To solve this problem, a weighted regularization method is proposed. The identification equation with isotropic residual error is built, and accurate identification can be realized with the regularization method. Based on the proposed methods, the error compensation experiment is conducted on the prototype of a five-axis parallel machining robot using a laser tracker. Experiment results show that the accuracy of the machining robot is significantly improved after compensation. An M1_160 test piece and an S-shaped test piece are machined and measured to further validate the effectiveness of the proposed methods. The elasto-geometrical error modeling method and the weighted regularization method can be applied to other parallel manipulators’ accuracy improvement.     

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.     

五轴数控机床几何误差建模与分析

基于多体系统基本理论推导出相邻体理想坐标变换以及误差变换矩阵并通过拓扑方法拓展到任一体理想坐标及误差变化公式。进而应用到五轴机床对应的零部件进行机床几何误差建模。最后推导出刀具形成点与工件被加工点的空间位置误差模型。并结合实验探究五轴数控机床37项误差参数对实际运动中的刀具形成点的位置误差影响,为之后的误差补偿和机床精度预测奠定理论基础。     

鞋楦五轴数控加工中的刀具半径补偿算法

在切触点信息缺失的情况下,以刀心点法向量为刀具半径补偿方向可能导致工件表面质量较差,为此提出一种全局法向量光顺方法.首先通过拟合平面求刀心点法向量,然后以前一个刀心点的法向量方向为基准调整当前刀心点的法向量方向,使法向量方向一致.针对相邻刀心点法向量方向偏差较大的问题,将与当前刀心点切平面不垂直的和在Z方向与周围刀心点...     

A methodology for systematic geometric error compensation in five-axis machine tools

To enhance the accuracy, an efficient methodology was developed and described for systematic geometric error correction and their compensation in five-axis machine tools. The methodology is capable of compensating the overall effect of all position-dependent and position-independent errors which contribute to volumetric workspace. It was implemented on a five-axis grinding machine for error compensation and for the check of its effectiveness. Error compensation algorithm was designed, and a routine was written in Matlab software. The developed technique and software are based on an error table which interprets the function of axis through cubic spline technique and synthesis modeling of a machine tool. Recursive compensation methodology was used to remove the machine errors from the actual tool path and inverse technique was implemented to find the corrected positions of prismatic and rotary joints. Moreover, it can convert the corrected tool paths into practical compensated NC codes. The generated, corrected and modified NC codes directly fed to the controller of a five-axis machine tool. Validation of the technique was preceded by repeated experimentation of measurement and through machining of typical standard workpieces with some additional specific features. Experimental results exhibit effective compensation and remarkable improvement in the parametric and volumetric-workspace accuracy of the five-axis machine tool.     

转台-摆头式五轴机床几何误差测量及辨识

为降低转动轴几何误差对转台-摆头式五轴机床精度的影响,提出了基于球杆仪的位置无关几何误差测量和辨识方法。基于多体系统理论及齐次坐标变换方法建立了转台-摆头式五轴机床位置无关几何误差模型,依据旋转轴不同运动状态下的几何误差影响因素建立基于圆轨迹的四种测量模式,并实现10项位置无关几何误差的辨识。利用所建立的几何误差模型进行数值模拟,确定转动轴的10项位置无关几何误差对测量轨迹的影响。最后,采用误差补偿的形式实验验证所提出的测量及辨识方法的有效性,将位置无关几何误差补偿前后的测量轨迹进行比较。误差补偿后10项位置无关几何误差的平均补偿率为70.4%,最大补偿率达到88.4%,实验结果表明所提出的建模和辨识方法可用于转台-摆头式五轴机床转动轴精度检测,同时可为机床精度评价及几何精度提升提供依据。     

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.     

加工中心热误差补偿的研究

热误差是加工中心的最大误差源。通过对机床热特性的实验和分析，利用神经网络模型对热误差进行了补偿，取得比较好的效果。     

Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties

In precision machining of free-form surfaces at high speed, it is very important to ensure part accuracy and machining properties. To achieve this, this paper develops a guide spline-based feedrate scheduling method for machining along curvilinear paths with simultaneous constraints of chord errors and ac/deceleration. Based on two metrics about feedrate scheduling from the view of geometric and kinematic properties, the nonlinear relationships between the arc-length parameter and path parameter are subsequently established with a parameter correction spline. Then a guide spline associated with the modified curvature radius of paths is constructed to the schedule feedrate. It is shown that determining the largest safe feedrate with constant chord error can be reduced to the issue of changing the feedrate proportionally with the square root of path curvature radii and ensuring the safe feed acceleration can be converted into the issue of presetting the largest slope of guide spline. The simulation results prove that the proposed feedrate scheme has potential applications in the field of finish machining.     

NC codes optimization for geometric error compensation of five-axis machine tools with one novel mathematical model

The International Journal of Advanced Manufacturing Technology - This paper presents the optimization compensation based on the mathematical expressions of geometric error model for the accuracy...     

基于LS-SVM的机床加工误差预测模型探讨

提出一种基于最小二乘支持向量机(LS-SVM)的机床加工误差回归模型和预测方法,给出了相应的步骤和算法.通过与BP神经网络和RBF神经网络预测方法比较,仿真结果表明,在较少的误差数据条件下,该模型能够有效的描述和预测加工误差的变化,且模型预测误差比神经网络模型小60%左右;应用该预测模型预测机床加工误差有更高的预测精度,对其实施补偿和控制,将有效提高机床的加工精度.     

Identification and measurement of geometric errors for a five-axis machine tool with a tilting head using a double ball-bar

Geometric errors are one of the primary potential sources of error in a five-axis machine tool. There are two types of geometric errors: position-dependent geometric errors and position-independent geometric errors. A method is proposed to identify and measure the position-independent geometric errors of a five-axis machine tool with a tilting head by means of simultaneous multi-axis controlled movements using a double-ball bar (DBB). Techniques for identifying position-independent geometric errors have been proposed by other researchers. However, most of these are based on the assumption that position-dependent geometric errors (such as linear displacement, straightness, and angular errors) are eliminated by compensation, once the position-independent geometric errors have been identified. The approach suggested in this paper takes into account the effect of position-dependent geometric errors. The position-dependent geometric errors are first defined. Path generation for circle tests with two or three simultaneous control movements is then carried out to measure the position-independent geometric errors. Finally, simulations and experiments are conducted to confirm the validity of the proposed method. The simulation results show that the proposed method is sufficient to accurately identify position-independent geometric errors. The experimental results indicate that the technique can be used to identify the position-independent errors of a five-axis machine tool with a tilting head.     

Influence of manufacturing errors in a metal-cutting machine with parallel kinematic structure on its machining precision

Possible manufacturing and assembly errors in a metal-cutting machine with parallel kinematic structure that affect its kinematic model are analyzed. On the basis of the manufacturing tolerances for the metal-cutting machine, the equations of the direct and inverse kinematic transformations are refined. An algorithm is derived for simulating the influence of geometric errors on the positioning precision of the actuator in the metal-cutting machine.     

Estimation of three-dimensional volumetric errors of machining centers by a tracking interferometer

A tracking interferometer is a laser interferometer with the mechanism to steer the laser direction to automatically follow a target retroreflector. This paper experimentally investigates the performance of the tracking interferometer prototype, developed by a part of the authors, in estimating the volumetric accuracy of a machining center based on the multilateration principle. Then, the prototype's technical issues are discussed based on the measurement uncertainty analysis. This paper briefly reviews the direct algorithm to calculate the three-dimensional position of the target, as well as the indirect algorithm to estimate geometric error parameters of the machine's kinematic model. Their comparison is also presented based on the uncertainty analysis.     

车铣复合加工中心综合误差检测及补偿策略

根据五轴车铣复合加工中心的结构及其运动链构型特点,设计了综合误差检测方案。检测包括车主轴床身至铣主轴运动链的空间误差检测以及车主轴的热误差检测两部分。由于检测方案使刀具-工件之间构成了完整的运动链,解决了单纯的空间误差检测方法未考虑车主轴运动链误差影响的问题。文中同时提出了车铣复合加工中心综合误差补偿策略以及运用神经网络算法的几何误差和热误差综合补偿模型。采用分步体对角空间误差检测后,实施了空间误差补偿。补偿后四条体对角线的空间误差都明显减小,减小幅度从15.24 μm到50.83 μm,误差补偿效果从39.10%提高到78.06%。本文提出的方法极大地改善了空间误差补偿精度。