A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments

Straight lines, or G01 blocks, are the most widespread representation form for the tool path in CNC machining. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. To solve this problem, a real-time path-smoothing method is proposed, which adopts a curvature-continuous B-spline with five control points to blend the adjacent straight lines. The advantage of the transition scheme is that, G² continuity, analytical calculation of the curvature extrema, approximation error control and real-time performance are considered simultaneously. Then, a bidirectional scanning algorithm for jerk limited S-shape feedrate profile is proposed to evaluate the feedrate constraints. On this basis, a real-time look-ahead scheme, which comprises of path-smoothing, bidirectional scanning and feedrate scheduling, is developed to acquire a feedrate profile with smooth acceleration. Also, an arc-length based interpolation algorithm for mixed linear and parametric segments is proposed to overcome the difficulty of crossing different segments. With these schemes, the smoothness of both tool path and feedrate is guaranteed. Simulation and experiments on an X–Y–Z platform are conducted. The results demonstrate the feasibility and efficiency of the present algorithms.     

Development and implementation of a NURBS interpolator with smooth feedrate scheduling for CNC machine tools

Parametric interpolation for Non-Uniform Rational B-Spline (NURBS) curve has become more important than ever before in the control of CNC machine tools. An effective NURBS interpolator not only can obtain accurate contour trajectories, but also have smooth dynamics performance. This paper proposes a numerically efficient NURBS interpolation scheme which consists of two stages namely preprocessing and interpolating. In the stage of pre-processing, the parameter interval is split into several blocks at breakpoints and an iterative numerical quadrature method is applied for each block. By means of the iterative quadrature method, the initial parameter intervals of each block are divided into several subintervals according to the arc length approximation error. Meanwhile, the curvature of each knot and the cubic polynomial coefficients of each subinterval are obtained. Then the critical points with large curvature of each block are found from the candidate points and the tolerated speed of each critical point is calculated according to the constraints of chord error and centripetal acceleration. Hence, the feedrate scheduling based on the S-shaped acceleration profile for each block can be preplanned via the approximate arc length of each subinterval, the tolerated speed of each critical point and kinematics characteristics such as acceleration/deceleration and jerk limits of the machine tools. In the stage of interpolating, the parameter of the next interpolation point can be calculated directly using the cumulative arc length and the cubic polynomial coefficients of each subinterval. Finally, a series of numerical simulations and real machining experiments are conducted, and the simulation and experimental results have showed the good performance of the proposed NURBS interpolator both in efficiency and accuracy.     

Real-time generation and control of cutter path for 5-axis CNC machining

This paper presents a new approach to real-time generation and control of the cutter path for 5-axis machining applications. The cutter path generation method comprises real-time algorithms for cutter-contact path interpolation, cutter offsetting, and coordinate conversion. In addition, a global feedback loop is closed by the CNC interpolator so as to augment the controlled accuracy in practical cutter path generation. An error compensation algorithm and a feedrate adaptation algorithm for the control loop are developed, respectively.     

The feedrate scheduling of parametric interpolator with geometry,process and drive constraints for multi-axis CNC machine tools

Parametric interpolator has been widely adopted in machining sculptured parts. Accordingly, the feedrate scheduling of parametric interpolator plays a role in CNC machine tools especially for multi-axis machines with linear and rotary axes, since a smooth movement is beneficial for achieving better surface geometry as well as shorter machining time. This paper presents a new feedrate scheduling method for the five-axis machining of geometrically complex part with geometry, process and drive constraints. The satisfaction conditions of constraints are first built and the proportional adjustment of feedrate sensitive regions is proved to be suitable for simultaneously reducing the magnitudes of constraints such as angular acceleration, linear acceleration, axis accelerations and jerks. The initial feedrate profile is first constructed with confined chord error, angular velocity and axis velocities owing to the independence of these constraints. Then, for each iterative adjustment a curve evolution strategy is used to deform the target feedrate profile to the adjusted positions instead of the re-interpolation of feedrate profile, until the final desired feedrate profile is achieved without violated constraints. Simulations and experiments are conducted and the results validate the performances of the proposed method.     

Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm

In this paper, a dynamics-based interpolator with real-time look-ahead (DBLA) algorithm is proposed to generate a smooth and jerk-limited acceleration/deceleration (ACC/DEC) feedrate profile. The interpolator consists of three modules: geometric, dynamics-based, and jerk-limited modules. The geometric module can detect the local maximum/minimum (max/min) curvatures, and divide a NURBS curve into small segments according to the information of sharp corners. The feedrates at the sharp corners are determined based on confined chord errors and curvatures of the curve. The dynamics-based module utilizes a dynamics feedrate modification equation (DFME) to estimate contour errors at the sharp corners and adjusts the feedrates at the locations of the sharp corners. The jerk-limited module plans the feedrate profile of the curve according to the segments’ length and the given jerk limit. Simulations are performed to verify real-time performance of the look-ahead algorithm. Experiments using a PC-based motion controller and an X–Y table are conducted to demonstrate that high-accuracy can be achieved with the proposed dynamics-based interpolator as compared to the adaptive-feedrate and the curvature-based feedrate interpolation algorithms.     

NURBS interpolator for constant material removal rate in open NC machine tools

Conventionally used linear or circular interpolators are undesirable for the precision machining of 3D free-form surfaces for the following reasons: the transmission errors due to the huge number of point data, discontinuity of curve segmentation, and unsmooth motion speed. In this regard, modern CNC machine tools are designed with a function for machining arbitrary parametric curves. However, these systems do not consider controlling feedrate adaptively, which dominates the quality of the machining process. This paper proposes a NURBS interpolator based on the adaptive feedrate control for the constant material removal rate. This is accomplished by varying feedrate using the curvature of a surface. The curvature-compensated feedrate system has important potential applications in ensuring part accuracy and protecting the cutting tool. The simulated and experimental results show it is applicable to real machining.     

Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path

A novel analytical five-axis path-smoothing algorithm is developed for the high speed machining of a linear five-axis tool path. Segment junctions of the linear tool path in the machine tool coordinate system, which are tangent-discontinuous points, are all blended by two transition cubic Bézier curves. One cubic Bézier curve is used to smooth the segment junction of the translational path, and the other Bézier curve is used to smooth the segment junction of the rotational path. The tangency and curvature continuities are both guaranteed in the new path. The dual-Bézier transition algorithm has three advantages: (1) Compared with the path-smoothing method in the workpiece coordinate system, the new dual-Bézier transition method directly and simultaneously smooths the machine tool axis trajectories of both translational path and rotational path. The feed speed and stability will both be improved because the tool path discontinuities are the most important source of feed fluctuation. (2) The constraints of approximation error and the synchronization of parametrization of two smoothed curves, which are the most challenging problems in the smoothing of 5-axis tool path, are both considered. (3) The transition cubic Bézier curve pair has an analytical solution and can be easily integrated in the real-time interpolator. Computational examples and the cutting experiment of an impeller blade show that the novel path-smoothing method has obvious advantages in both feed smoothness and cutting efficiency over the original linear interpolator.     

CNC machine tool surface interpolator for ball-end milling of free-form surfaces

This paper presents a new type of CNC machine tool interpolator that is capable of generating the cutter path for ball-end milling of a free-form surface. The surface interpolator comprises on-line algorithms for cutter-contact (CC) path scheduling, CC path interpolation, and tool offsetting. The interpolator algorithms for iso-parametric, iso-scallop and iso-planar machining methods are developed, respectively. The proposed surface interpolator method gains the advantages for minimizing the data loaded to the CNC machine tool and maintaining the desired feedrate and position accuracy along the CC path.     

基于误差预处理的液压系统反馈线性化控制

针对液压系统的强非线性、参数时变特性,提出一种基于误差预处理的反馈线性化自适应控制器。采用RBF神经网络对液压系统进行辨识与建模;为了实现快速高精度的位置输出,对误差进行预处理,调节误差增益,使其增益能够随误差变化而变化,实现:小误差时大增益,加快响应速度,提高控制精度;大误差时小增益,防止系统超调。基于误差预处理,利用反馈线性化方法,设计了控制器及自适应律。仿真结果表明:在反馈线性化结合误差预处理的作用下,系统的响应速度及控制精度均优于反馈线性化控制。     

Smooth feedrate planning for continuous short line tool path with contour error constraint

In the machining program for free form surfaces, the tool path is usually represented as continuous short lines. For the computer numerical control, the feedrate profile for short line tool path should be smooth and optimized in order to achieve high machining quality and high speed. In high speed machining, the feedrate profile also has a strong influence on contour accuracy. This paper presents a new real-time smooth feedrate planning algorithm for short line tool path, in which the contour error constraint is included. To realize contour error control, the feedrate is adaptively adjusted based on the curvature radius of the tool path, which is directly estimated from the short lines. The 7-phase jerk-limited look-ahead planning is employed to generate a smooth feedrate profile. The target feedrate filter (TFF) and planning units merging techniques are developed to improve the smoothness of the feedrate profile and reduce the overhead on look-ahead. The advantage of the proposed algorithm is that it is not only convenient to achieve the balance among accuracy, smoothness and productivity by adjusting parameters, but also efficient in design, which makes it possible to be implemented on low cost hardware platforms. Experiment results demonstrate the feasibility of the proposed algorithm on smooth feedrate planning and contour error control for continuous short line tool path.     

叶片造型网格扭曲的校正方法研究

叶片曲面造型中的网格扭曲严重影响其性能，使得叶片数控加工质量降低。本文分析了叶片造型扭曲的原因，提出了一种叶片造型网格扭曲的校正方法。详细论述了叶片截面线数据点离散、截面数据点参数域变换、近似弧长参数化等关键问题的解决措施，通过在叶片高效螺旋铣数控编程中的应用实例，对本方法进行了验证。结果表明：本方法能有效地消除叶片造型中的网格扭曲现象，显著提高叶片曲面的品质和数控加工质量。     

直线电机伺服系统精密数字控制方法研究

直线电机是实现非圆截面类零件数控车削加工的关键,针对其跟踪目标轨迹已知和对外部干扰及模型参数摄动敏感的特点,研究了一种具有离散时域扰动观测器的数字预见控制方法。首先,通过在最优状态反馈控制的基础上增加目标预见前馈项,减小了直线电机伺服系统的位置跟踪误差;其次,将外部干扰和模型参数摄动作为等效控制输入,设计了一种离散时域扰动观测器加以抑制,增强了预见伺服系统的鲁棒性。仿真结果表明,该控制方法能够满足高速高精度条件下对非圆截面零件的车削加工要求。     

力反馈设备运动学分析及轨迹规划

针对于人体的复杂组成,要求力反馈设备必须具有精确稳定的工作性能。介绍了设备的构件组成和工作方式,运用D-H参数法建立每一个杆件的坐标系,得到了相邻杆件之间的齐次变换矩阵。经过运动学分析,得到了力反馈设备运动学特征方程。利用ADAMS进行设备的轨迹规划,理论分析和实际仿真结果表明该力反馈设备结构具有良好的运动特性。     

Sliding mode cutting force regulator for turning processes

Continuous sliding mode control is applied to turning processes for cutting force regulation. The motivation of the use of the slide mode control scheme is to solve the nonlinearity problem caused by the feedrate override command element in the commercial CNC machine tool. When the adaptive control algorithm is applied to the commercial CNC machine tool, it is one of the practical methods that the programmed feedrate is overridden after the control algorithm is carried out. However, most CNC lathe manufacturers offer limited number of data bits for feedrate override, thus resulting in nonlinear behavior of the machine tools. Such nonlinearity brings ‘quantized' or discrete effect so that the optimal feedrate is rounded off before being fed into the CNC system. To compensate for this problem, continuous sliding mode control is applied. Simulation and experimental results are presented in comparison with those obtained from applying adaptive control which is a widely used approach in cutting force regulation. Adaptive control loses its effectiveness in the presence of nonlinearity since it generally requires linear parametrization of the control law or the system dynamics. Experiments are conducted under various machining conditions, subject to changes in spindle speed, material of work-piece, and type of machining process. The suggested slide mode controller shows smoother cutting force fluctuation, which cannot be achieved by the conventional adaptive controller. The experimental set-up reflects the emphasis on the practicality of the sliding mode controller. In order to avoid the use of a dynamometer in the course of measuring the cutting force, the indirect cutting force measuring system is used by means of feed drive servo-motor current sensing.     

A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

G01 codes generated by CAM (Computer Aided Manufacturing) system are the most common form of tool path in CNC (Computer Numerical Control) machining. For the piecewise linear path, tangential and curvature discontinuities bring about large fluctuation of feedrate and acceleration, which produces vibration of machine tool. In recent studies, the methods for G² (curvature-continuous) tool-path smoothing and jerk-limiting feedrate scheduling were developed. However there still exist the deficiencies when these methods are employed in CNC machining. It is difficult to simultaneously ensure that the tool path is chord-error-constrained and G01-point-interpolated in real time. In addition, heavy computational load hinders realtime processing in CNC system. Recently the scholars experimentally found the potential of G³ (curvature-smooth) trajectory and jerk-continuous motion in reducing the vibration of machinery. This work proposes a realtime tool-path smoothing algorithm, generating G³ interpolative tool path composed by mixed linear and quartic Bezier segments. The purpose of the smoothing scheme is the simultaneous considerations of G³ continuity, confined chord error, G01 points interpolated, and realtime performance. And the tool path generated is optimized in curvature variation energy (CVE) and analytical curvature extrema is available. To reduce the vibration, a high-efficient algorithm of jerk-continuous (JC) feedrate scheduling for G³ tool path is provided. Finally, a realtime tool-path processing scheme is developed, including G³ interpolation and motion planning functions. As shown in the simulation, the contour error, curvature of tool path, feedrate fluctuation and machining time are reduced compared with G² transition scheme. The experiment on a machine tool is conducted to demonstrate the advantages of the proposed algorithm in vibration reduction and surface quality, compared with G² transition scheme.     

遥操作机器人力反馈双向伺服控制策略研究

针对并行机构的力反馈双向液压伺服控制中所存在的反馈力冲击大及位置跟随差的问题,提出一种以主、从手之间的力信号作为从动端控制信号,位置信号形成主手控制量的新型力觉反馈控制算法。应用阀控液压缸和力传感器构成液压力伺服控制器,构建力反馈双向伺服控制试验系统。在空载、抓轮胎和抓石块3种负载情况下,分别进行了力、位置跟随性能实验。实验结果表明:该力反馈控制方法既能保证从手对主手的位置跟随精度,又能使主手准确连续地跟随从手受力情况,明显改善了主-从控制系统的操纵性能,操作者能够获得真实的力觉临场感,提高了力反馈透明性。     

Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools

The conventional approaches for surface machining use a sequence of straight lines to approximate the part surface. These straight lines are subsequently translated into linear g-codes by a post processor, and then sent to the CNC system. This process limits the surface machining capability of CNC systems. For example, the CNC machine tool can be controlled only to follow these approximated straight lines since the machine loses the surface information. In contrast, this research utilised a real-time approach for 3-D parametric surface machining on 3-axis CNC machine tools. This real-time approach, called CNC surface interpolator, can read surface g-codes and perform surface machining interpolation. The input to the CNC surface interpolator is the surface g-code, which contains geometric information, such as the coefficients of the parametric surface, as well as cutting conditions. This results in better machining feedrate controls, interpolates more precise machining commands, and requires less machining time compared to that produced by off-line approaches.     

状态反馈条件下提高轧机伺服系统精度的算法研究

不确定性条件下的控制问题是现代控制中的一个重要课题。在大多数控制问题中,实际的控制对象和用于控制器设计的数学模型总是存在差异,这种差异来自于对象参数的不确定性和时变等。轧机液压位置伺服系统是具有参数不确定性、干扰因素多的复杂的非线性控制系统,所建模型较实际对象存在较大误差。为消除这种模型误差所产生的稳态误差,文中在稳态误差溯源及模型修正的基础上构建并联积分补偿、增益积分补偿、在线辨识自校正和动态反馈控制策略,对比仿真结果表明:动态反馈算法具有兼顾动静态性能指标的优势。     

Feedrate scheduling for free-form surface using an NC verification model

This paper describes feedrate scheduling for a free-form surface using an NC verification model that can describe the actual cutting motions. This is important from the viewpoint of verification of the free-form surface and feedrate scheduling in the same simulator. In this paper, feedrate scheduling is conducted using the chip volume per tooth and per NC block using an NC verification model in order to obtain a constant chip load. A strategy for generating new NC commands at a set number of rotations between two existing NC blocks with a constant chip volume per tooth is proposed. The travel length of acceleration/deceleration is compensated in generating a new NC command in an NC block. Chip loads for feedrate scheduling are rapidly obtained in all tool paths considering surface curvature, feedrate, and cusp height formed by the previous tool path. Experiments validated that the presented feedrate scheduling obtained a constant chip load in all tool paths by inserting new NC commands in the existing NC file.