Pre-compensation of contour errors in five-axis CNC machine tools

This paper presents an analytical prediction and compensation of contouring errors in five-axis machining of splined tool paths. The position commands are first fitted to piecewise quintic splines while respecting velocity, acceleration and jerk continuity at the spline joints. The transfer function of each servo drive is kept linear by compensating the disturbance effect of friction with a feed-forward block. Using the analytically represented five-axis, splined tool path, splined tracking errors and kinematic model of the five-axis machine tool, contouring errors are predicted ahead of axis control loops. The contouring errors are decoupled into three linear and two rotary drives, and the position commands are modified before they are sent to servo drives for execution. The proposed method has been experimentally demonstrated to show significant improvement in the accuracy of contouring five-axis tool paths.     

Integral design of contour error model and control for biaxial system

This paper focuses on the contour following accuracy improvement for biaxial systems using cross-coupled control (CCC). It proposes an integral design method including contour error model, contour control effort distribution and the CCC algorithm. First, a contour error model using the contour algebraic equation and its partial derivatives is established without the small tracking error assumption. This model satisfies the condition that it equals to zero if and only if the real contour error value vanishes, which makes perfect contour following become possible in theory. Then, in order to decouple the contour following the feed-direction tracking, contour control effort distribution is decided to be in line with the normal vector at the desired point. Through expanding the proposed contour error model with Taylor series to make it be related to tracking errors of both axes, the stability condition of CCC is analyzed by the contour error transfer function (CETF). Experiments are carried out on an X–Y motion stage to verify the proposed method. The results show that it improves the contour following accuracy greatly in various conditions, even when large tracking errors occur.     

数控伺服系统跟踪及轮廓误差分析

分析了数控加工中伺服系统跟踪误差和轮廓误差的计算方法,详细讨论了双轴数控加工中轴跟踪误差和轮廓误差之间的关系。指出了多轴加工中轮廓误差建模和误差控制方法的理论意义和应用价值。     

Pre-compensation of servo contour errors using a model predictive control framework

Methods for pre-compensating contour errors in servo systems by adding components of the predicted contour error to the reference position command have recently been proposed in the literature. Such methods are very effective when the curvatures of the desired path are small but their performance degrades at locations of sharp curvature because they lack look-ahead capabilities. This paper presents an improved method for pre-compensating contour errors in servo systems by modifying reference position commands using a model predictive control framework. The pre-compensation value at any given location along the desired path is defined as a weighted average of contour errors within a prediction horizon, and the weights are selected to minimize the sum of squares of the estimated contour errors over the chosen prediction horizon. Constraint enforcement functionalities are also built into the proposed method to ensure that the pre-compensated reference commands stay within specified velocity and acceleration limits. Simulations and experiments are used to compare the performance of the proposed method to a recently proposed pre-compensation approach which lacks look-ahead and constraint enforcement capabilities. Significant improvements in contouring accuracy over the existing method are demonstrated.     

Precise contour following for biaxial systems via an A-type iterative learning cross-coupled control algorithm

This paper proposes an A-type iterative learning cross-coupled control (CCC) algorithm for biaxial systems. An algebraic equation based contour error model is used as the CCC input. This model has the advantage that it is zero if and only if the real value vanishes. The iterative learning CCC is designed to make its input converge to zero. Hence, it is expected to that the contour error will converge to zero as well. After analyzing the control algorithm convergence condition in the frequency domain, the proposed method is implemented on a motion stage. Experimental results show that the algorithm perfectly follows contours as the cycles approach infinity regardless of whether tracking errors are small or large.     

A neural network approach for force and contour error control in multi-dimensional end milling operations

The problem of controlling the average resultant cutting force together with the contour error in multi-dimensional end milling operations is considered in this study. Two sets of neural networks are used in the control system. The first set is used to specify the feed rate to maintain a desired cutting force. This feed rate is resolved along the feed axes using a parametric interpolation algorithm so that the desired part shape is obtained. The second set is used to make corrections to the feed rate components specified by the parametric interpolation algorithm to minimize the contour error caused by the dynamic lag of the closed-loop servo systems controlling the feed drives. In addition, the control system includes a feedforward input to compensate for static friction effects. Experimental results are presented for machining two-dimensional circular slots and a three-dimensional spherical surface to show the validity of the proposed approach.     

Generalized Taylor series expansion for free-form two-dimensional contour error compensation

The model-based Taylor series expansion error compensation (TSEEC) method has been shown to be capable of eliminating contour errors in biaxial CNC machines. However, it has been developed for only linear and circular contours. In this paper, an extension of TSEEC, a generalized TSEEC or GTSEEC, is proposed which is capable of compensating for the contour errors of arbitrary two-dimensional contours. A new real-time algorithm is used to estimate the contour error so that GTSEEC can be applied even in cases where the function of the contour is unknown. Simulation results using linear, circular and parabolic contours are presented which show that, with perfect knowledge of the axial dynamics, GTSEEC can perfectly eliminate the contour errors for any contour, even when there is significant mismatch in the axes' dynamics. Experiments on a small two-axis computer-controlled machine indicate the effectiveness and better performance of GTSEEC in reducing contour errors for free-form contour following tasks when compared with two other leading approaches, the zero phase error tracking control (ZPETC) and cross-coupled control (CCC).     

高速轮廓运动综合位置误差控制的研究

高速轮廓运动控制技术已广泛应用于工业中。目前研究主要从减少伺服跟随误差和采用交叉耦合控制减少轮廓误差两个方面来提高运动精度。文章对几种常见的控制方法进行了讨论，并给出了一种综合位置误差控制的方案。该控制方案可在不改变原位置环的基础上大大提高位置伺服的性能，减小高速运动和参数扰动时的轮廓误差。控制理论分析和仿真结果表明了其有效性，且该方案容易实现。     

Machining contour errors as ensembles of cutting, feeding and machine structure effects

CNC machining has been studied from the perspective of either cutting or feeding. However, machining quality is the outcome of both of these processes. This work investigates the contour errors of a complete CNC machine system. A system model is developed to cover all groups of functions, including trajectory planning, trajectory tracking, cutting process and machine structure. Analysis results reveal the limitations of traditional studies. The dependence of contour errors on trajectory curvature, feed-rate, cutting depth and tracking control is investigated as well. A new model of CNC machining is developed.     

Position command shaping control in a retrofitted milling machine

A position command shaping controller, hybrid structure of feedforward controller and cross-coupling controller, for accurate contouring in motion control is proposed in this paper. The feedforward controller can improve tracking performance of single axis and the cross-coupling controller guarantees the reduction in contour error for multi-axis motion. When compared with the conventional motion system, this new structure has the advantage that the compensators have a simpler design process than conventional ones and so does its stability analysis. The proposed compensators (or controllers) are evaluated and compared experimentally with a traditional controller on a microcomputer controlled dual-axis positioning system. The experimental results show that the new hybrid structure reduces remarkably the tracking error and contour error. In addition, this new controller can be implemented easily on a majority of motion systems in use today via reprogramming the reference position command subroutine.     

High speed servo control of multi-axis machine tools

Advances in high-speed machining technology, including those in spindle speeds and cutters, are out-pacing advances in the servo control performance of machine tools. To close this gap, new machine tools and improved controls must be developed. Improvements to machine tools under development include special-purpose machine tools, the use of advanced materials, the replacement of ball screws and ways with linear motors and roller guides, and the use of parallel link actuators. This paper focuses on the control issues that will become increasingly important as these high-speed machining and high-speed machine tool advances are realized.The main issues in high-speed servo control are feed rate planning, and servo loop control laws. A method is developed in this paper which takes advantage of the full performance envelope of each axis in an arbitrary path. This near-complete usage of the servo capabilities of a machine tool results in reduced cycle time or reduced path error. A servo loop control law is then developed that uses the axis performance envelope as well as instantaneous position, velocity, and acceleration information of the target path and machine axis to improve servo performance in the presence of disturbances.     

电液伺服系统无模型轨迹跟踪控制算法的研究与实现

对于具有往复运动特征的电液伺服系统，由于存在很强的非线性，依靠模型分析，求解将是十分复杂的，本文提出了一种基于Fourier级数的无模型的电液伺服系统轨迹跟踪控制算法，该算法轨迹跟踪问题在Fourier空间转化为调节器问题，并给出了控制器的详细设计及系统的稳定性分析，最后给出控制器在注塑机上的实际应用，实验结果表明该方法对改善注塑机动模的运动特性有较好的效果。     

一种用于数控机床进给系统的迭代学习轮廓控制器的设计

数控机床进给系统产生的轮廓误差对产品质量有着严重的影响。为了对轮廓误差进行补偿,设计一种迭代学习轮廓控制器,用以提高进给系统的轮廓跟随效果。对数控机床进给系统进行分析后,获取其跟踪误差以及轮廓误差的模型。在该模型的基础上,设计线性插值法和圆域插值法,用来计算轮廓误差的大小。接着对进给系统在s域的闭环传递函数进行分析,采用PID反馈补偿器,设计迭代学习轮廓控制器,利用该控制器对实际轮廓误差进行补偿。仿真结果显示:采用此方法跟踪期望轨迹时,产生的最大跟踪误差为6.57%,较PID方法减小了5.7%;在跟踪期望轮廓时,产生的最大轮廓误差为0.8 mm,较PID方法减小了0.7 mm。由此说明此方法对轮廓误差的补偿性能较好,能够对数控机床进给系统的轮廓跟随准确度进行较好的控制。     

Thermal error mode analysis and robust modeling for error compensation on a CNC turning center

In this paper a novel concept of thermal error mode analysis is proposed in order to develop a better understanding of the thermal deformation on a turning center. The thermal error of the machine can be treated as the superposition of a series of thermal error modes with corresponding mode shapes and time constants. The selection of sensor location can then be improved based on the thermal error mode analysis. A robust modeling approach is also proposed to minimize the errors due to temperature measuring noise and the adverse effect of environmental changes. Through the use of thermal error mode analysis and the robust modeling approach, the number of thermal sensors has been reduced from 16 to four. The thermal error compensation system has been applied to a turning center in daily production for more than two years and it has kept year-round accuracy. The thermal drift in workpiece diameter on the turning center has been reduced from 35 μm to 6 μm from its center of tolerance.     

数控手机玻璃磨边机控制算法及误差分析研究

为了去除手机玻璃边的瑕疵以提高其抗冲击力,设计一种数控磨边机。针对手机玻璃轮廓外形,采用了几何图形分析法,提出了基于极坐标系下的直线插补算法和圆弧插补算法。讨论了影响手机玻璃轮廓磨削加工精度的主要误差因素,推导出离散系统时间跟随误差公式和综合轮廓误差公式,采用了三次样条插值法,利用MATLAB软件对恒角速度磨削进行动力学仿真分析,并进一步提出恒角速度磨削改进策略。实践证明：采用上述控制算法的数控磨边机能有效地提高手机玻璃轮廓的磨边精度,满足工艺要求。     

FANUC系统Cs轮廓控制功能在数控机床中的应用

本文阐述了Cs轮廓控制功能基本原理、硬件配置,梯形图编写,参数设置以及调试中的注意事项。对FANUC数控系统在扩展功能方面进行实际应用作了介绍,对其他数控系统在数控机床应用有指导作用。     

基于双模同步预测的机械臂末端轮廓精确跟踪控制

为减小机械臂末端在进行轨迹跟踪运动时的轮廓误差,提出一种机械臂轮廓误差同步预测控制策略。该策略将操作空间轮廓误差映射到关节空间,从而定义机械臂各关节的同步行为,有效减小了末端轮廓误差,提高了机械臂各关节的运动协调性。为解决常规预测控制器不能保证系统稳定的问题,提出双模同步预测控制方法,通过在预测时域外切换到局部控制率来保证控制器的稳定性。实验结果表明:所设计的控制器能有效减小末端轮廓误差并使关节输出力矩更加平稳。     

伺服刀架系统的反复反馈误差补偿控制

对于具有滞后特性的伺服刀架系统,采用自校正ＰＩＤ控制。在此基础上,为进一步提高伺服刀架系统的跟踪精度,提出了反复反馈误差补偿控制方法。理论分析和实验结果都表明,该控制方法以有效地提高伺服刀架的跟踪精度。     

数控机床神经元自适应位置控制算法

基于神经元的自学习特性,提出了适用于数控机床位置伺服控制的神经元控制器,算法的显著特点是不需要系统建模,而且运算简单,非常适用于工程实际应用。仿真和数控机床伺服系统的实时控制实验说明本文提出的控制算法的有效性。     

电液位置伺服系统的高精度神经网络控制研究

提出了一种采用CMAC神经网络的自学习控制器,以解决具有参数不确定和时变外扰动的电液位置伺服系统的高精度控制问题,该控制器采用动态误差作为CMAC的激励信号,从而使基于CMAC的控制器跟踪连续变化的信号成为可能。仿真结果证明了该控制器不仅是有效的,而且具有很强的鲁棒性。