Contouring controller design based on iterative contour error estimation for three-dimensional machining

Recently, there has been a growth of interest in high precision machining in multi-axis feed drive systems, subjected to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. To guarantee high precision machining in modern computer numerical controlled (CNC) machines, CNC's controllers do its control efforts to reduce contour error. One of the common approaches is to design a controller based on the estimation of contour error in real time. However, for complex contours with severe curvatures, there is a lack of effective algorithms to calculate contour errors accurately. To address this problem, this paper proposes an accurate contour error estimation procedure for three-dimensional machining tasks. The proposed method is based on an iterative estimation of the instantaneous curvature of the reference trajectory and coordinates transformation approach, and hence, it is effective for complex reference trajectories with high curvatures. In addition, contour error controller is presented to reduce the estimated contour error. The feasibility and superiority of the proposed model as well as contour error controller are demonstrated through experimental system using a desk-top three-axis CNC machine.     

Hierarchical optimal force–position–contour control of machining processes

There has been a tremendous amount of research in machine tool servomechanism control, contour control, and machining force control; however, to date these technologies have not been tightly integrated. This paper develops a hierarchical optimal control methodology for the simultaneous regulation of servomechanism positions, contour error, and machining forces. The contour error and machining force process reside in the top level of the hierarchy where the goals are to (1) drive the contour error to zero to maximize quality and (2) maintain a constant cutting force to maximize productivity. These goals are systematically propagated to the bottom level, via aggregation relationships between the top and bottom-level states, and combined with the bottom-level goals of tracking reference servomechanism positions. A single controller is designed at the bottom level, where the physical control signals reside, that simultaneously meets both the top and bottom-level goals. The hierarchical optimal control methodology is extended to account for variations in force process model parameters and process parameters. Simulations are conducted for four machining operations that validate the developed methodology. The results illustrate the controller can simultaneously achieve both the top and bottom-level goals.     

Contour error reduction for free-form contour following tasks of biaxial motion control systems

In modern machining applications, reduction of contour error is an important issue concerning multi-axis contour following tasks. One popular approach to this problem is the cross-coupled controller (CCC). By exploiting the structure of CCC, an integrated control scheme is developed in this paper and an in-depth investigation on the issue of contour error reduction is also conducted. The proposed motion control scheme consists of a feedback controller, a feedforward controller, and a modified contour error controller (CCC equipped with a real-time contour error estimator). In addition, a fuzzy logic-based feedrate regulator is proposed to further reduce the contour error. The proposed feedrate regulator is designed based on the real-time estimated contour error and the curvature of the free-form parametric curves for machining. Several experiments are conducted to evaluate the performance of the proposed approach. Experimental results demonstrate the effectiveness of the proposed approach.     

A new approach to z-level contour machining of triangulated surface models using fillet endmills

Precision z-level contour machining is important for various computer-aided manufacturing (CAM) applications such as pocket machining and high-speed machining (HSM). This paper presents a new z-level contour tool-path generation algorithm for NC machining of triangulated surface models. Traditional approaches of z-level machining rely on the creation of accurate CL (cutter location) surfaces by surface offsetting or high-density z-map generation, which is computationally expensive and memory demanding. In contrast, this paper presents a novel approach to the generation of CL data directly from the section polygon of a triangulated surface model. For each polygon vertex of the contour, the offset direction is determined by the normal to the edge, while the offset distance is not fixed but is determined from the cutter shape and the part surface. An interference-free tool-path computation algorithm using fillet endmills is developed. Since there is no need to create a complete CL surface or high-density z-map grids, this proposed method is highly efficient and more flexible, and can be directly applied to triangulated surfaces either tessellated from CAD models, or reconstructed from 3D scanned data for reverse engineering (RE) applications.     

Hierarchical optimal force-position control of complex manufacturing processes

A hierarchical optimal controller is developed in this paper to regulate the machining force and axis positions, simultaneously, in a micro end milling process. The process is divided into two levels of decision making. The bottom level includes the measurable states, which in this work comprises the axis positions. The top level includes the higher order objectives, which can be derived from the bottom level objectives by an aggregation relationship. In this work, the top level's objective is to regulate the machining force. A series of simulations were conducted in which the weighting between the top and the bottom level objectives is adjusted within the feasible range. The results demonstrated that excellent tracking of both axis positions and machining force are achieved during the steady state regardless of the weighting. However, the transient performance of the system could be systematically shaped to achieve better performance of either objective. For the purpose of comparison a decentralized optimal controller was constructed and simulated for the feasible range of controller weights. When the axis position errors were weighted heavily, both controllers were able to regulate the axis errors well, while the hierarchical controller had smaller machining force errors. When the machining force errors were weighted heavily, although the machining force error decreased for the decentralized controller the axis position errors increased significantly. However, with heavy machining force weighting, the hierarchical controller was able to manipulate the axial errors in a way that while the machining force error was reduced, the contour error (i.e., smallest deviation from the tool tip to the desired contour) remained small.     

数控加工自动编程中的边缘矢量化技术

针对目前数控激光加工自动编程系统存在的问题，对边缘跟踪得到的点阵边界图形进行了矢量化处理，在保持图象特征的基础上，使自动编程系统生成的数控加工文件大大压缩，避免了边缘噪声，使数控激光加工的效率进一步提高。     

Estimation of tool orientation contour errors for five-axismachining

Recently, there has been a growth of interest in high-precision machining in multi-axis feed drive systems, which are subject to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. Tracking errors in an individual driving axis during five-axis machining result in tool tip contour error and tool orientation contour error. Based on the conventional definition of the tool orientation contour error, that is, it is the deviation in the normal direction from the desired orientation in spherical coordinates, even if the tool tip and tool orientation contour errors are very small, a mismatch between the tool tip position and tool orientation causes an overcut or undercut when these errors are treated independently. To address this problem of mismatch, this paper presents a new definition of the actual tool orientation contour error. This definition considers synchronization between the tool tip and tool orientation contour errors. In addition, we propose an estimation model for the tool orientation contour error. Experimental results demonstrate that the proposed model provides a better indication of the actual tool orientation contour error than the conventional definition.     

PID position domain control for contour tracking

Contour error reduction for modern machining processes is an important concern in multi-axis contour tracking applications in order to ensure the quality of final products. Many control methods were developed in time domain to deal with contour tracking problems, and a proportional–derivative (PD) position domain control (PDC) was also proposed by the authors. It is well known that proportional–integral–differential (PID) control is the most popular control in applications of control theory. In this paper, a PID PDC is proposed for reducing contour tracking errors and improving contour tracking performances. To determine proper control gains, system stability analysis is conducted for the proposed PDC. Several experiments are conducted to evaluate the performance of the developed approach and are compared with the PID time domain control (TDC) and the cross-coupled control. Different control gains are used in the simulations to explore the robustness of PID PDC. Comparison results demonstrate the effectiveness and good contour performances of PID PDC for contour tracking applications.     

Iterative learning control for integrated system of robot and machine tool

This study is concerned with the integrated system of a robot and a machine tool. The major task of robot is loading the workpiece to the machine tool for contour cutting. An iterative learning control (ILC) algorithm is proposed to improve the accuracy of the finished product. The proposed ILC is to modify the input command of the next machining cycle for both robot and machine tool to iteratively enhance the output accuracy of the robot and machine tool. The modified command is computed based on the current tracking/contour error. For the ILC of the robot, tracking error is considered as the control objective to reduce the tracking error of motion path, in particular, the error at the endpoint. Meanwhile, for the ILC of the machine tool, contour error is considered as the control objective to improve the contouring accuracy, which determines the quality of machining. In view of the complicated contour error model, the equivalent contour error instead of the actual contour error is taken as the control objective in this study. One challenge for the integrated system is that there exists an initial state error for the machine tool dynamics, violating the basic assumption of ILC. It will be shown in this study that the effects of initial state error can be significantly reduced by the ILC of the robot. The proposed ILC algorithm is verified experimentally on an integrated system of commercial robot and machine tool. The experimental results show that the proposed ILC can achieve more than 90% of reduction on both the RMS tracking error of the robot and the RMS contour error of the machine tool within six learning iterations. The results clearly validate the effectiveness of the proposed ILC for the integrated system.     

Robot vision by a contour sensor with associative memory

Advancing automation can only cope with the rising cost of labour.For visual inspection a minicomputer sustained optical contour sensor checks automatically whether all contours of an assembled part are present and lie within prefixed tolerances.Automation of welding or machining often requires high precision feeding of parts, causing prohibitive costs and thus rendering automation uneconomical. The optical contour sensor catches edges without mechanical contact and controls the machining or welding process relative to these edges.With associative retrieval of data stored in a training phase, the contour sensor recognizes and positions straight parts in arbitrary orientations on a conveyor belt, even if they touch and partly cover each other. This allows automation of many pick-and-place operations at the inputs of automated production lines.     

超精密机床的变增益交叉耦合控制研究

超精密加工的轮廓精度控制直接影响到工件的加工精度,交叉耦合控制算法通过对2轴进行协调而影响轮廓控制精度。在分析超精密数控机床误差模型的基础上,将变增益交叉耦合控制算法引入超精密数控机床的伺服控制。实验结果表明变增益交叉耦合控制算法可以在不改变位置环的情况下,有效提高系统的轮廓精度。     

Computer aided contouring operation for traveling wire electric discharge machining (EDM)

This paper develops a computational method for numerical control (NC) of traveling wire electric discharge machining (EDM) operation from geometric representation of a desired cut profile in terms of its contours. Normalized arc length parameterization of the contour curves is used to represent the cut profile and a subdivision algorithm is developed together with kinematic analysis to generate the required motions of the machine tool axes. In generating the tool motions for cutting sections with high curvatures such as corners with small radii, a geometric path lifting method is presented that increases the machining gap and prevents gauging or wire breakage.     

Tool-path generation from measured data

Presented in the paper is a procedure through which 3-axis NC tool-paths (for roughing and finishing) can be directly generated from measured data (a set of point sequence curves). The rough machining is performed by machining volumes of material in a slice-by-slice manner. To generate the roughing tool-path, it is essential to extract the machining regions (contour curves and their inclusion relationships) from each slice. For the machining region extraction, we employ the boundary extraction algorithm suggested by Park and Choi (Comput.-Aided Des. 33 (2001) 571). By making use of the boundary extraction algorithm, it is possible to extract the machining regions with O(n) time complexity, where n is the number of runs. The finishing tool-path can be obtained by defining a series of curves on the CL (cutter location) surface. However, calculating the CL-surface of the measured data involves time-consuming computations, such as swept volume modeling of an inverse tool and Boolean operations between polygonal volumes. To avoid these computational difficulties, we develop an algorithm to calculate the finishing tool-path based on well-known 2D geometric algorithms, such as 2D curve offsetting and polygonal chain intersection algorithms.     

Tool-path generation for Z-constant contour machining

For the Z-constant contour machining, a tool-path generation procedure is presented. The suggested procedure consists of two parts; (1) calculating the contours (tool-path-elements) by slicing the CL-surface with horizontal planes and (2) generating a tool-path by linking the contours. For the slicing algorithm, two algorithms are suggested, one is to slice a triangular mesh and the other is for a Z-map model. The second part, the linking problem, is approached from the technological requirements, such as considering the machining constraints among the tool-path-elements, minimizing the tool-path length and reflecting the oneway/zigzag linking options. To simplify the linking problem, we develop a data structure, called a TPE-net, providing information on the machining constraints among the tool-path-elements. By making use of the TPE-net, the tool-path linking problem becomes a touring problem so that every node has been traversed.     

A newly developed corner smoothing methodology based on clothoid splines for high speed machine tools

Continuous linear commands are widely executed in computer numerical control (CNC) machining. The tangential discontinuity at the junction of consecutive segments restricts the machining efficiency and deteriorates the surface quality. Corners of linear segments have been successfully blended by inserting parametric splines. There still exists challenges when the common methods are employed in the line-segment commands due to part of the following restrictions: (1) the stringent computation for iteratively calculating the arc-length; (2) the unwanted feedrate fluctuation; (3) the oversize contour deviation for separately completing curve fitting and velocity planning.A novel smoothing method based on a clothoid pair to synchronously accomplish planning of geometry blending and speed scheduling is proposed, the spline parameter of which is arc-length-parameterized. The arc-length, curvature extreme, and geometric shape of the transition curve are analytically expressed by the transition length. On these bases, the transition curve and the velocity profile are concurrently constructed based on the predefined approximation error, the reachable velocity, and normal kinematic constraints in the look-ahead stage. Then, a real-time interpolation scheduling is developed to overcome the crossing difficulties between the linear and parametric segments. Compared with existing methods, the proposed method can analytically calculate the length of transition curves for the arc-length-parameterized expression form. Furthermore, the feedrate fluctuation is eliminated in the fine interpolation. Moreover, the overlarge contour derivation produced by corner smoothing is significantly avoided. It is friendlier to the CNC system for the on-line executing smooth motion since more computing resources can be released to handle other tasks, smoother motion can be achieved and higher contour accuracy can be obtained. The experimental results also demonstrate its practicability and reliability.     

数控系统连续微段重构与插补算法研究

针对目前微段加工研究中采用的非重构微段加工方法存在的加工轨迹与设计曲线轮廓误差较大,轮廓加工精度较低,及微段节点处速度方向不连续,因此加工表面质量不高,加工过程机床振动较大的问题。在计算机数控（Computerized Numerical Control,CNC）中采用实时曲线重构与插补算法进行连续微段加工以实现对曲面的高速高精度加工。微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足加减速要求的可以直接递推的插补样条曲线的重构条件。应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到um级精度的同时,加工速度提高了2~2.4倍。实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内进行整体加减速速度规划,提高加工效率,而且加工轨迹的进给速度的衔接平滑,轨迹光滑,表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了平衡了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度。     

一种实时轮廓误差估算方法的研究

针对于现有的轮廓误差估算方法通常会将光滑的参考曲线处理成为微小直线段,从而导致估算的轮廓误差值精度较低的问题。采用了一种将参考曲线近似为圆弧,在圆弧上估算轮廓误差的方法。为了证明此方法的有效性,在Simulink环境下对此估算方法进行预补偿仿真。仿真结果显示,此方法可以实时估算并补偿轮廓误差,并且其估算精度高,能够在很大程度上提高数控机床的加工精度。     

Computer numerical control for assuring the machining accuracy of contour milling

In this paper, a software technology for improving the machining accuracy in contour milling is discussed, in which the continuous path control is thoroughly investigated from the viewpoint of system synthesis, and the computer numerical control is effectively used. It is shown that the proposed “real-time cutter path rectification” offers an effective means to overcome the serious problem of the thermal deformation of workpieces. In this case, it is necessary to take many factors into consideration; the diversity of shapes, the change of cutting conditions, the unstable thermal situation, and so on. Therefore, the adaptive control is applied to compensate the thermal displacement of the contour during the cutting process. Relating to this subject, the effective cutter radius, which depends on cutter wear, is also evaluated in real-time operation; and the cutter diameter compensation is included in the “cutter path rectification”. In order to assure the machining accuracy, a new approach to contour measurement is proposed, in which the continuous path control by CNC system is used. It is certified through some experiments that the method proposed in this paper is useful to realize the flexible automation with high machining accuracy.     

航空叶片打磨余量分析及轨迹生成

针对航空发动机叶片打磨加工前,叶身余量分布不均且较小的问题,提出一种基于毛坯点云配准的加工余量分析和自适应打磨轨迹生成方法。利用精确扫描测绘技术获取毛坯三维点云,形成了毛坯/零件数模二者点云配准方法;通过基准对齐、点云轮廓包含等条件约束,实现了毛坯三维加工余量分析;在余量分布点云基础上,通过截面获取加工点云轨迹,对轨迹点云进行珠链排序,将轨迹排序点有效化,计算出连续合适的打磨路径,实现自适应余量打磨。最后在Vericut软件中进行了打磨仿真,验证了提出方法的有效性。     

High aspect ratio meso-scale parts enabled by wire micro-EDM

Micro-electro discharge machining (EDM) is a subtractive meso-scale machining process. The Agie Excellence 2F wire micro EDM is capable of machining with a 25 micron diameter wire electrode and positioning the work piece to within ±1.5 microns. The over-burn gap can be controlled to within 3 microns to obtain a minimum feature radius of about 16 microns while achieving submicron surface finish and an imperceptible recast layer. For example, meso-scale gears that require vertical sidewalls and contour tolerances to within 3 microns can be wire EDMed into a variety of conductive materials. Material instabilities can affect the dimensional precision of machined meso-scale parts by material relaxation during the machining process. A study is done to investigate the machining performance of the wire micro EDM process by machining a high aspect ratio meso-scale part into a variety of metals (e.g. 304L stainless steel, Nitronic 60 Austentic Stainless, Beryllium Copper, and Titanium). Machining performance parameters such as, profile tolerance, perpendicularity, and repeatability are compared for the different materials. Pertinent inspection methods desirable for meso-scale quality assurance tasks are also evaluated. Sandia National Laboratories is developing meso-scale electro-mechanical components and has an interest in the assembly implications of piece parts fabricated by various meso-scale manufacturing processes. Although the wire EDM process is typically used to fabricate 2½ dimensional features, these features can be machined into a 3 dimensional part having other features such as hubs and chamfers to facilitate assembly.