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.     

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.     

Virtual machining considering dimensional,geometrical and tool deflection errors in three-axis CNC milling machines

Virtual manufacturing systems can provide useful means for products to be manufactured without the need of physical testing on the shop floor. As a result, the time and cost of part production can be decreased. There are different error sources in machine tools such as tool deflection, geometrical deviations of moving axis and thermal distortions of machine tool structures. Some of these errors can be decreased by controlling the machining process and environmental parameters. However other errors like tool deflection and geometrical errors which have a big portion of the total error, need more attention. This paper presents a virtual machining system in order to enforce dimensional, geometrical and tool deflection errors in three-axis milling operations. The system receives 21 dimensional and geometrical errors of a machine tool and machining codes of a specific part as input. The output of the system is the modified codes which will produce actual machined part in the virtual environment.     

基于轮廓最优圆逼近方法的轮廓误差控制

设计并实现了基于轮廓最优圆逼近方法的轮廓误差估计模型,该模型克服了常规方法对于任意加工曲线,廓误差计算过程复杂、计算量大、难以应用到实时任务的缺点,通过实时读取数控机床的位置反馈值和插补器的指令数据估算出轮廓误差值,结合双模糊变论域自适应控制算法,应用于两轴数控系统并实时补偿各单轴控制器,实现对复杂加工过程轮廓误差实时估算并补偿。在实验数控机床上加工两种典型轮廓,对比实验表明,所提出的基于轮廓最优圆逼近方法的双模糊变论域轮廓误差控制方法能有效减小加工轮廓误差,有更高的轮廓精度。     

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.     

Influence of High-Speed Machine Tool Control Parameters on the Contouring Accuracy. Application to Linear and Circular Interpolation

In this paper, we investigate the servo parameters and axis dynamics influences on the contouring accuracy for practical applications such as contouring control of manufacturing systems (robot, machine tool...). The analytical formulation of contouring error in the case of straight line, circle and corner crossing is derived using a simplified axis drive model including the main servo parameters and dominating mechanical mode. The effectiveness of the proposed formulation in estimating the evolution of the final contour error is demonstrated experimentally on a two-axis machine tool.     

Iso-planar piecewise linear NC tool path generation from discrete measured data points

This article presents a method of generating iso-planar piecewise linear NC tool paths for three-axis surface machining using ball-end milling directly from discrete measured data points. Unlike the existing tool path generation methods for discrete points, both the machining error and the machined surface finish are explicitly considered and evaluated in the present work. The primary direction of the generated iso-planar tool paths is derived from the projected boundary of the discrete points. A projected cutter location net (CL-net) is then created, which groups the data points according to the intended machining error and surface finish requirements. The machining error of an individual data point is evaluated within its bounding CL-net cell from the adjacent tool swept surfaces of the ball-end mill. The positions of the CL-net nodes can thus be optimized and established sequentially by minimizing the machining error of each CL-net cell. Since the linear edges of adjacent CL-net cells are in general not perfectly aligned, weighted averages of the associated CL-net nodes are employed as the CL points for machining. As a final step, the redundant segments on the CL paths are trimmed to reduce machining time. The validity of the tool path generation method has been examined by using both simulated and experimentally measured data points.     

Design and application of a sliding mode controller for accurate motion synchronization of dual servo systems

This paper presents a continuous time sliding mode controller (SMC) design to deal with the problem of motion synchronization in dual spindle servo systems. Synchronization error is defined as the differential position error between the two servo drives that follow identical reference motion trajectory. Proposed SMC controller penalizes three error states; namely individual axis tracking errors and the synchronization error for accurate synchronization. The control law is derived from Lyapunov energy function without switching condition. The controller shows robust motion synchronization against disturbances and parameter variations. Proposed SMC control is implemented in conventional double-sided machining operation.     

Five-axis tool path generation for a flat-end tool based on iso-conic partitioning

Traditionally, for the flat-end tool, due to the intertwined dependence relationship between its axis and reference point, most 5-axis tool-path generation algorithms take a decoupled two-stage strategy: first, the so-called cutter contact (CC) curves are placed on the part surface; then, for each CC curve, tool orientations are decided that will accommodate local and/or global constraints such as minimum local gouging and global collision avoidance. For the former stage, usually simplistic “offset” methods are adopted to determine the cutter contact curves, such as the iso-parametric or iso-plane method; whereas for the latter, a common practice is to assign fixed tilt and yaw angle to the tool axis regardless the local curvature information and, in the case of considering global interference, the tool orientation is decided solely based on avoiding global collision but ignoring important local machining efficiency issues. This independence between the placement of CC curves and the determination of tool orientations, as well as the rigid way in which the tilt and yaw angle get assigned, incurs many undesired problems, such as the abrupt change of tool orientations, the reduced efficiency in machining, the reduced finishing surface quality, the unnecessary dynamic loading on the machine, etc. In this paper, we present a 5-axis tool-path generation algorithm that aims at alleviating these problems and thus improving the machining efficiency and accuracy. In our algorithm, the CC curves are contour lines on the part surface that satisfy the iso-conic property — the surface normal vectors on each CC curve fall on a right small circle on the Gaussian sphere, and the tool orientations associated to a CC curve are determined by the principle of minimum tilt (also sometimes called lead) angle that seeks fastest cutting rate without local gouging. Together with an elaborate scheme for determining the step-over distance between adjacent CC curves that seeks maximum material removal, the presented algorithm offers some plausible advantages over most existing 5-axis tool-path generation algorithms, particularly in terms of reducing the angular velocity and acceleration of the rotary axes of the machine. The simulation experiments of the proposed algorithm and their comparison with a leading commercial CAM software toolbox are also provided that demonstrate the claimed advantages.     

The Domain of Admissible Orientation concept: A new method for five-axis tool path optimisation

This work deals with the optimisation of tool paths in five-axis machining. The objective is to improve the kinematic behaviour of machine tools during milling. The orientation of the tool axis at each point of a tool path is optimised while ensuring quality constraints. These are modelled using the Domain of Admissible Orientation (DAO) concept expressed in the P-System and transformed into the M-System. This article aims at defining the DAO and presents an example of optimisation using this concept. This optimisation is a minimisation of the movement generated by each rotation axis and is applied to two test parts.     

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。     

Improving machining accuracy in precision line boring

There is an ever-growing demand for high precision machining to obtain increased accuracy and surface finish, as they are key factors in product quality and performance. Machining operations, in general, are associated with errors of varying magnitude originating from different sources. As a result, the sizes of the machined features usually deviate from their desired, nominal values. Identification of error sources, techniques of measurements (on/off line), and efficient strategies for their compensation are the steps required to minimize, and, in some cases eliminate process errors. This paper focuses on modeling and compensation of geometric errors in machining operations specific to the line boring process. It is part of an undergoing research project focused on design and development of an agile precision line boring station for machining of long bores. After a brief overview of sources of geometric errors and their components, a methodology for their calculation is introduced. In this regard, error equations reflecting the effects of machine tool geometric errors at the tool tip are derived. It is shown that these equations can be further simplified without significantly affecting computational accuracy of the results. This makes the approach more attractive for real-time applications. A set of experimental data obtained from a prototype of the machine is used to study the effectiveness of the proposed approach and the results are reported. The paper concludes with discussions and presentation of different methods and available tools for real time compensation of these errors.     

Adaptive learning control for thermal error compensation of 5-axis machine tools

The research presented in this paper shows an adaptive approach for long-term thermal error compensation of 5-axis machine tools (MT). A system of differential equations is used to compute the model based compensation values. The model can predict thermal displacements of the tool center point (TCP) based on changes in the environmental temperature, load-dependent changes and boundary condition changes and states, like machining with or without cutting fluid. The model based compensation of the rotary axis of a 5-axis MT is then extended by on-machine measurements. The information gained by the process-intermittent probing is used to adaptively update the model parameters, so that the model learns how to predict thermal position and orientation errors and to maintain a small residual error of the thermally induced errors of the rotary axis over a long time. This approach not only increases the MT accuracy but also reduces the amount of time spent on preproduction model parameter identification. Additionally an algorithm has been developed to dynamically adjust the length of the on-machine measurement intervals to maintain a high productivity and a constant deviation of the machined parts.Experimental results confirm that the adaptive learning control (ALC) for thermal errors shows a desirable long-term prediction accuracy.     

A physically-based model for global collision avoidance in 5-axis point milling

Although 5-axis free form surface machining is commonly proposed in CAD/CAM software, several issues still need to be addressed and especially collision avoidance between the tool and the part. Indeed, advanced user skills are often required to define smooth tool axis orientations along the tool path in high speed machining. In the literature, the problem of collision avoidance is mainly treated as an iterative process based on local and global collision tests with a geometrical method. In this paper, an innovative method based on physical modeling is used to generate 5-axis collision-free smooth tool paths. In the proposed approach, the ball-end tool is considered as a rigid body moving in the 3D space on which repulsive forces, deriving from a scalar potential field attached to the check surfaces, and attractive forces are acting. A study of the check surface tessellation is carried out to ensure smooth variations of the tool axis orientation. The proposed algorithm is applied to open pocket parts such as an impeller to emphasize the effectiveness of this method to avoid collision.     

Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface

This paper presents a global optimization method to generate a tool path for flank milling free-form surfaces with a generic cutter based on approximation using the tool envelope surface. It is an extension of our previous work [Gong Hu, Cao Li-Xin, Liu Jian. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Computer Aided Design 2005; 37:1205–13]. First, given initial tool path or tool axis trajectory surface, the grazing points of the tool envelope surface can be calculated. Second, the errors between the tool envelope surface and the designed surface along the normal direction of the tool envelope surface are calculated. Based on this new definition of error, an optimization model is established to get the global optimized tool axis trajectory surface. In order to simplify the calculation, two variants of this method based on the least square criterion are proposed to solve this model. Since this method is really based on the tool envelope surface, it can reduce the initial machining errors effectively. The proposed method can be used not only for cylindrical cutters and conical cutters, but also for generic cutters with a surface of revolution. In addition to ruled surfaces, it also can be used for machining non-ruled surfaces. Finally, several examples are given to prove its effectiveness and accuracy. The generated tool paths and calculated grazing points for test are available in supplementary files for the readers’ convenience in verifying this work in different CAD/CAM systems.     

Tool selection for five-axis curvature matched machining

This paper presents an automatic cutting tool selection methodology for five-axis finish surface machining based on the techniques of curvature matched machining. The criterion for cutter selection is to minimize the machine errors and to maximize material removal rate using an optimal filleted end mill selected from a standard cutting tool library. Tool parameters investigated include cutter radius, cutter corner radius and cutter length. The maximum swept silhouette of the inclined tool is proposed and implemented as tool radii selection protocols for matching the change in surface curvature. Algorithms for detection and correction of local tool gouging and global tool interference are presented. The local distance between the cutter bottom and the surface is used to detect and correct local tool gouging. Global tool interference detection and correction is solved by studying the shortest distance between the part surface and the cutter body axis. A faceted approach is used to accelerate the distance calculations. The solution to the local and global gouging problems leads to the shortest, most rigid, tool in the library. These methods of automatic tool selection have been implemented in ROBLINE using the C-language on the system. ROBLINE is a precursor to CODE (Cimetrix Open Development Environment) which is a complete commercial off-line/on-line machine modeling, development and control package. Machined examples confirm the effectiveness of these methods.     

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.     

Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus

NC machining of a nonzero genus triangular mesh surface is being more widely confronted than before in the manufacturing field. At present, due to the complexity of geometry computation related to tool path generation, only one path pattern of iso-planar type is adopted in real machining of such surface. To improve significantly 5-axis machining of the nonzero genus mesh surface, it is necessary to develop a more efficient and robust tool path generation method. In this paper, a new method of generating spiral or contour-parallel tool path is proposed, which is inspired by the cylindrical helix or circle which are a set of parallel lines on the rectangular region obtained by unwrapping the cylinder. According to this idea, the effective data structure and algorithm are first designed to transform a nonzero genus surface into a genus-0 surface such that the conformal map method can be used to build the bidirectional mapping between the genus-0 surface and the rectangular region. In this rectangular region, the issues of spiral or contour-parallel tool path generation fall into the category of simple straight path planning. Accordingly, the formula for calculating the parameter increment for the guide line is derived by the difference scheme on the mesh surface and an accuracy improvement method is proposed based on the edge curve interpolation for determining the cutter contact (CC) point. These guarantee that the generated tool path can meet nicely the machining requirement. To improve further the kinematic and dynamic performance of 5-axis machine tool, a method for optimizing tool orientation is also preliminarily investigated. Finally, the experiments are performed to demonstrate the proposed method and show that it can generate nicely the spiral tool path or contour-parallel tool path on the nonzero genus mesh surface and also can guarantee the smooth change of tool orientation.     

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.     

An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears

To transfer power, a pair of spiral bevel or hypoid gears engages. From beginning to end of two tooth surfaces engaging with each other: for their rigid property, they contact at different points; and for their plastic property, they contact at small ellipses around the points. On each surface, the contact line (or called as contact path) by connecting these points and the contact area by joining these ellipses are critical to driving performance. Therefore, to machine these surfaces, it is important to machine the contact line and area with higher accuracy than other areas. Five-axis flank milling is efficient and is widely used in industry. However, tool paths for flank milling the gears, which are generated with the existing methods, can cause overcuts on the contact area with large machining errors. To overcome this problem, an innovative approach to NC programming for accurate and efficient five-axis flank milling of spiral bevel or hypoid gears is proposed. First, the necessary conditions of the cutter envelope surface tangent with the designed surface along a designed line are derived to address the overcut problem of five-axis milling. Second, the tooth surface including the contact line and area are represented using their machining and meshing models. Third, according to the tooth surface model, an optimization method based on the necessary conditions is proposed to plan the cutter location and orientation for flank milling the tooth surface. By using these planned tool paths, the overcut problem is eliminated and the machining errors of contact area are reduced. The proposed approach can significantly promote flank milling in the gear manufacturing industry.