Kinematic modelling of a 3-axis NC machine tool in linear and circular interpolation

Machining time is a major performance criterion when it comes to high-speed machining. CAM software can help in estimating that time for a given strategy. But in practice, CAM-programmed feed rates are rarely achieved, especially where complex surface finishing is concerned. This means that machining time forecasts are often more than one step removed from reality. The reason behind this is that CAM routines do not take either the dynamic performances of the machines or their specific machining tolerances into account. The present article seeks to improve simulation of high-speed NC machine dynamic behaviour and machining time prediction, offering two models. The first contributes through enhanced simulation of three-axis paths in linear and circular interpolation, taking high-speed machine accelerations and jerks into account. The second model allows transition passages between blocks to be integrated in the simulation by adding in a polynomial transition path that caters for the true machining environment tolerances. Models are based on respect for path monitoring. Experimental validation shows the contribution of polynomial modelling of the transition passage due to the absence of a leap in acceleration. Simulation error on the machining time prediction remains below 1%.     

五轴联动数控加工的刀具路径优化方法研究

为解决五轴联动加工复杂曲面过程中的刀具路径不连续问题,提出了五轴数控的刀具路径优化方法。通过五轴NC代码的坐标变换还原有效切削路径,对切削路径进行误差约束下的非均匀有理B样条(NURBS)曲线拟合。对旋转轴路径采用五次样条曲线进行插值,建立切削路径和旋转轴路径的参数映射关系,通过机床逆运动变换求解C2连续的平动轴路径。实验表明,经过该方法优化后,切削路径和各驱动轴运动路径具有良好的平滑性,显著提高了五轴加工曲面精度和表面质量。     

Influence of interpolation type in high-speed machining (HSM)

The recourse to the high-speed machining for the manufacture of warped shapes imposes an evolution towards a very high technicality of the CAM methods and of the machining operation execution. Due to its own characteristics, the high-speed machining (HSM) implies the use of new machining interpolations, in such a way that it assures the continuity of advances in the best way possible. Among these interpolations, we mention the polynomial interpolation. In this article, we propose a complete study of the interpolation type influence on the HSM machine dynamic behavior and also on the generated errors. For this, we have measured the feed rate of the cutting tool path for each type. Then, in terms of accuracy, we have measured the errors. In order to validate our approach, we have compared the simulated results to the experimental ones.     

A control strategy with motion smoothness and machining precision for multi-axis coordinated motion CNC machine tools

The advanced manufacture technology requires that multi-axis coordinated motion computer numerical control (CNC) machine tools have the capability of high smoothness and high precision. At present, the study of the motion smoothness mainly concentrates on the acceleration and deceleration control method and the look-ahead process of velocity planning in the interpolation stage. The control strategy of the contouring error mainly focuses on tracking error control, cross-coupling control, and optimal control. In order to improve the motion smoothness and contouring precision for multi-axis high-speed CNC machine tools, a multi-axis modified generalized predictive control approach was presented in this paper. In the control strategy, the estimation models of tracking error, contouring error, velocity error, and acceleration error were structured separately. A new improved quadratic performance index was proposed to guarantee the minimum of these errors. Generalize predictive control was also introduced, a multi-axis generalized predictive control model was deduced for motion smoothness and machining precision for multi-axis coordinated motion CNC system, and an approved multi-axis generalized predictive controller based on the model was designed in this paper. The proposed predicted control approach was evaluated by simulation and experiment of circular, noncircular, and space line trajectories, respectively. These simulative and experimental results demonstrated that the proposed control strategy can significantly improve the motion smoothness and contouring precision. Therefore, the new position control method can be used for the servo control system of multi-axis coordinated motion CNC system, which increases motion smoothness and machining precision of CNC machine tools.     

五轴龙门数控铣床转动轴联动中的动态轨迹误差仿真分析

针对刀具两摆的五轴龙门数控铣床,对一转动轴与一平动轴联动及两转动轴联动加工圆弧时的动态轨迹误差分别进行了分析。采用D-H(Denavit-Hartenberg)法对轴的输入的进给指令位置计算公式进行了推导,并将进给指令位置输入到由动态仿真工具Simulink构建的进给伺服系统仿真模型中,得到了圆弧上动态轨迹误差的分布曲线。通过对转动轴联动加工圆弧的动态轨迹误差分析,可为五轴龙门数控铣床转动轴动态误差的检测提供指导,使得机床的检测与调整更加快速和便捷。     

Real-time P-H curve CNC interpolators for high speed cornering

In this paper, real-time Pythagorean hodograph (P-H) curve CNC interpolators are used for high speed corner machining. There are large contouring errors around sharp corners when low-bandwidth servo controllers (such as P-PI control) are used. In order to decrease the amount of the cornering errors, an improved interpolation method is proposed. The first deceleration phase of motion and the over-corner P-H curve constructed for regions with sharp corners are devised by quadratic and constant velocity interpolation algorithms, respectively. The geometric parameters of the over-corner P-H curve and the feed rate along the modified tool path are computed by pattern search algorithm in order to reduce the maximum cornering error. The proposed interpolation algorithm is implemented for symmetrical and unsymmetrical corners. The results of simulation, such as the cornering error and the total cornering time, are compared with previously published methods. It has been observed that the developed over-corner P-H approach can substantially reduce the amount of cornering error.     

An intelligent feedrate scheduling based on virtual machining

Off-line feedrate scheduling is an advanced methodology to automatically determine optimum feedrates for NC code modification. However, most existing feedrate scheduling systems have limitations in generating the optimised feedrates because they use the material removal rate or the cutting force model which is dependent on cutting conditions. This paper proposes a feedrate scheduling system based on an improved cutting force model that can predict cutting forces accurately in general end milling situations. Original blocks of NC code were divided into smaller ones with the optimised feedrates to adjust the peak value of cutting forces to a constant value. The acceleration and deceleration characteristics for a given machine tool were considered for realistic feedrate scheduling. Moreover, a modified type of Z-map model was developed to reduce the entry/exit angle calculation error in the cutting force prediction and named the moving edge node Z-map (ME Z-map). Pocket machining experiments show that the proposed method is accurate and efficient in maintaining the cutting force at a desired level.     

A local smoothing interpolation method for short line segments to realize continuous motion of tool axis acceleration

In traditional processing, a large number of G01 blocks are adopted to discretize free surface or curve for NC machining. But, the continuity of G01 line segments is only C⁰, which may lead to discontinuity of axis acceleration, resulting in the frequent fluctuation of tool motion at the junctions in high-speed machining, deteriorating the quality of work piece, and reducing processing efficiency. To solve this problem, a local smoothing interpolation method is proposed in this paper. At first, the analytic relationship between the continuity of the trajectory and the continuity of the axes motion is first systematically described by formula. Based on this relationship, a local smoothing algorithm and a feed-rate scheduling method are proposed to generate a C² continuous tool path motion with axis-acceleration continuity. The local smoothing algorithm smoothes the corners of G01 blocks by the cubic B-spline according to the cornering error tolerance specified by the user. After the feed rate at critical points of smoothed tool path was determined by a modified bidirectional scanning algorithm by considering constrains of chord error and kinematic property, an iterative S-shape feed rate scheduling is employed to minimize residual distance caused by round of time while ensuring the continuity of feed rate and acceleration. Then, a look-ahead interpolation strategy combined with smoothing algorithm and feed-rate scheduling as mentioned is proposed for real-time interpolation of short line segments. At last, simulations are conducted to verify the effectiveness of the proposed methods. Compared with the traditional G01 interpolation, it can significantly improve the processing efficiency and shorten the processing time within error tolerance.     

Form error estimation in ball-end milling of sculptured surface with z-level contouring tool path

This paper presents a flexible model for estimating the form error in three-axis ball-end milling of sculptured surface with z-level contouring tool path. At an interval of feed per tooth, the whole process of sculptured surface machining is treated as a combination of sequential small inclined surface milling. For ball-end milling of the inclined surface with z-level contouring tool path, at surface generation position, an analytical model is proposed to identify the feedback effect of tool deflection on cutting edge engagement. The deflection-dependent cutting edge engagement is determined by using an iterative procedure. And ultimately, the form error is obtained from the balanced tool deflection and associated surface inclination angle. In a validation experiment, the estimated form errors are compared with both the measurements and the predictions of a rigid model. It is shown that the proposed flexible model gives significant better predictions of the form error than rigid model. Good agreement between the predicted and measured form errors is demonstrated for the ball-end milling of sculptured surface with z-level contouring tool path.     

Linear Interpolation of machining tool-paths with robust vibration avoidance and contouring error control

This paper presents a reference trajectory (command) generation scheme to robustly avoid residual vibrations that occur due to rapid acceleration of machine axes in high-speed machining and positioning tasks. A robust Finite impulse response (FIR) filter is designed to generate reference motion commands for accurate real-time interpolation of linear toolpaths along point-to-point (P2P) and non-stop contouring trajectories. The designed FIR filter generates reference acceleration profiles with wide attenuation bands in the frequency spectrum to avoid unwanted vibrations. Design and tuning principles for the robust FIR filter are presented, and kinematics of the generated reference trajectories are analyzed. Contour errors that occur during rapid non-stop linear interpolation are estimated from the filter dynamics. A feedrate scheduling method is introduced to analytically confine those interpolation contour errors within user specified tolerances. Effectiveness of the proposed trajectory generation scheme is validated in actual machining tests, and it is benchmarked against the state-of-the-art technique. It is shown that developed FIR-based trajectory generator can robustly avoid unwanted inertial vibrations to produce smoother surfaces without elongating cycle times.     

High-speed contouring enhanced with P-H curves

In this paper, Pythagorean hodograph (P-H) curve theory is used for high-speed contouring applications. There are large contouring errors around sharp corners when low-bandwidth servo controllers (such as P-PI control) are used. It is possible to construct a P-H curve in the region of sharp corners in order to decrease the amount of cornering error. The developed algorithm is implemented for various corners with different angles. With respect to sharp tool paths, the total machining time is increased by a small amount, but the cornering error is reduced to the allowable tolerance limit. The results of simulation, such as the total cornering time and the cornering error, are compared with previously published methods. It has been shown that the over-corner P-H approach will substantially decrease the amount of cornering error.     

The influence of friction on contouring accuracy of a Cartesian guided tripod machine tool

This paper is focused on the friction-induced contouring errors of a three-axis parallel kinematic machine (PKM) called a Cartesian-guided tripod (CGT). A dynamic model of the CGT including the nonlinear dynamic, mechanical compliance and mechanical friction has been formulated. Servo control characteristics of the formulated CGT dynamic model are analyzed based on the conventional P-PI controller and feedforward friction compensation implemented in the joint level control scheme. Quantitative analysis and comparison of the various friction sources from the actuated joints (ballscrew/nut) and passive joints (balljoint and guideway) have been conducted. Analysis results show that the ballscrew/nut friction produces the most significant friction-induced contouring errors. The ball-joint friction and linear-guide friction induced contouring errors are two-order and one-order, respectively, lower than the errors by the ballscrew friction. The main reason is that the equivalent friction torques of these two friction sources coupled into the servo drive loop are reduced by the leverage effect of the driving leg length. It was also found that the conventional feedforward friction compensation can effectively reduce the ballscrew-friction-induced contouring errors. However, if not properly compensated, ballscrew friction could excite significant platform-leg structural vibration because the tripod-based PKM usually has a high compliance vibration mode in the horizontal platform-leg direction. The friction-excited structural vibration can be reduced by putting vibration absorbers on the guideways of the passive leg to damp out the platform-leg vibration. From the primary analysis results, it can be seen that the proposed tripod based PKM has high potential for high-speed 5-axis machining applications.     

Applications of integrated motion controllers for precise CNC machines

The error resources of precise motion control systems are basically categorized into linear and nonlinear effects. To realize the precise motion of industrial computer numerical control (CNC) machines, this paper presents an integrated motion control structure with modular algorithms, including both the linear control and the nonlinear compensation. In the linear control design, this study applies three algorithms: (1) feedforward control to address the tracking errors, (2) cross-coupled control to reduce the contouring errors, and (3) digital disturbance observer to lessen the effects of modeling errors and disturbances in real applications. The results indicate that the linear motion controller achieves greatly improved accuracy in both tracking and contouring by reducing the servo lags and mismatched dynamics of the different axes. However, the adverse effect due to friction still exists and cannot be eliminated by applying the linear motion controller only. This study further integrates the nonlinear compensator and develops friction estimation and compensation rules for CNC machines. The digital signal processors are suitable to implement all the developed linear and nonlinear algorithms, and the present controllers have been successfully applied to industrial CNC machines. Experimental results on a vertical machining center indicate that, under different feed rates, the CNC machine with the integrated motion controller significantly reduces the maximum contouring error by 135% on average.     

基于VERICUT的数控加工运动学仿真

介绍了运用VERICUT软件实现数控加工运动学仿真的过程及方法.通过加工实例实现了从三维建模、刀具管理、数控程序导入到加工运动仿真,得到了一种较理想的仿真方法.基于软件的Optimath分析模块,可以对加工程序进一步优化,提高加工效率.AUTO-DIFF分析模块通过对比仿真模型和设计模型实现仿真加工过程的过切和欠切分析.     

基于ADAMS的机床高速主轴虚拟设计系统研究

针对高速主轴在数控机床中的推广应用问题,以加工中心高速主轴系统结构设计和性能分析为重点,应用虚拟设计原理、有限元分析和优化设计技术,对加工中心高速主轴系统在ADAMS环境下进行了动态仿真研究,开发了专用于机床主轴系统设计分析软件系统,给出了部分运行实例。该系统能提高产品的设计质量和设计效率。     

基于VERICUT数控加工仿真及优化的实现

VERICUT是目前少有的一款既能实现仿真又能进行较好优化的三维CAD/CAM软件.可实现刀具轨迹仿真和机床仿真的同步显示;还可通过调整各个工序的进给率优化NC代码.结合一个"锤子加工"的典型实例展现了VERICUT4.4版本环境下数控加工仿真及优化的全过程,并通过分析其优化机理说明该软件在仿真及优化方面的优越性.     

数控加工刀具的轨迹仿真与程序传输软件

利用VC++6.0和OpenGL开发了一种基于NC加工代码的数控加工刀具轨迹仿真与程序传输软件——NCEdit。该软件可用于加工程序的校验和编辑,以减少和避免加工错误,并能计算刀具的切削行程和加工时间,便于优化工艺和生产管理,还可实现与数控机床的DNC传输。     

自由曲面数控加工动态仿真研究

在VC++6.0平台上采用OpenGL技术开发一种自由曲面数控加工过程仿真系统。该系统可根据自由曲面的不同造型,规划出适当的刀位轨迹,生成G代码;实现交互控制,完成设计曲面的成型加工,并动态显示加工路径。     

基于虚拟加工技术的数控程序优化

针对传统数控程序中进给速度固定限制加工效率的缺点,开发了面向粗铣加工的数控程序优化系统。系统基于虚拟加工技术,能完成数控程序驱动下的切削过程仿真、切削力预测、碰撞检测等。系统利用粒子群进化算法,在满足加工条件的下,实现了数控程序中进给速度和主轴转速的优化,数控程序加工效率得到显著提高。     

Development of 2-axis hybrid positioning system for precision contouring on micro-milling operation

A 2-axis hybrid positioning system was developed for precision contouring on micro-milling operation. The system was developed to overcome the micro-positioning limitations of conventional linear stage positioning system on machine tools. A 2-axis flexure hinge type piezoelectric stage was added on a standard milling machine to obtain better machining results. The control method used for the hybrid system was active error compensation type, where errors from linear stages are cancelled by the piezoelectric stage motion. Positioning experiments showed an improvement of machine accuracy which was confirmed by the machining results. A micro-pillar was fabricated for the validation of long-range and high-precision contouring capability. The system was successfully implemented on micro-milling machining to achieve high-precision machining results.