数控皮革裁剪的NURBS曲线切向跟随插补方法

针对数控裁剪加工中裁刀的旋转运动控制问题,分析了数控皮革裁剪机的工作原理.通过建立裁剪加工中裁刀运动的数学模型,提出了NURBS曲线的切向跟随插补方法,并对其插补精度进行了分析.在XY运动控制平台上对该算法进行了仿真分析,试验结果表明切向跟随插补方法能较好的满足裁剪加工要求.     

五轴线性插补中非线性误差补偿方法

以A-C双摆头五轴数控机床为研究对象,通过对机床的运动学求解,分析了五轴数控机床在加工过程中非线性误差产生机理并建立了非线性误差的数学模型。通过齐次坐标变换的方法,推导出计算加工过程中刀尖点实际位置的数学表达式以及其反计算公式。针对五轴数控机床的旋转轴运动所产生的非线性误差,提出了一种反求插补点的补偿方法。从五轴数控加工旋转中心位置插补算法角度考虑降低非线性误差的方法,通过理论刀尖点位置来反求旋转中心的插补的位置,使实际刀尖点更多地落在理论插补路径上。利用MATLAB进行实际数据的仿真验证,结果表明所提出方法能将非线性误差有效控制在加工允差内,可显著提高五轴数控系统的轨迹控制精度,可见本文所提出方法具有较好的可行性和实际应用价值。     

空间任意圆弧插补算法的分析

插补算法是数控技术中的关键性技术,通过分析平面圆弧的插补算法以及空间坐标的旋转算法的特点,推导出空间任意圆弧的插补算法公式。同时根据矢量分解算法求出插补算法中刀具的坐标增量和速度增量。     

实时快速NURBS直接插补技术

为了解决基于泰勒展开式的NURBS插补算法存在的速度波动问题,提高NURBS插补实时性,深入研究了NURBS曲线直接插补方法。根据插补原理,提出了一种不同于泰勒展开式的插补计算方法,并研究了一种NURBS快速计算方法。在满足插补过程精度要求的前提下,由进给速度直接计算插补点坐标,并采用递推矩阵对NURBS进行快速求值求导计算,有效地减小了速度波动,而且提高了计算速度和插补实时性。仿真结果证明了该方法的可行性和有效性。     

一种直线插补算法及其在机器人中的应用研究

针对基于PLC控制器的机器人实现直线插补的问题,对在降低控制器硬件配置和性能要求的条件下实现机器人直线插补的方法进行了研究,提出了一种基于等时间间隔的直线插补算法,即等时间周期法。该算法可以通过改变插补周期调整插补精度,从而改变插补算法所需的控制器运行速度和数据存储空间。在自主研发的四关节冲床上下料机器人上,采用松下FP-X型PLC作为控制器,对提出的插补算法进行了实验和验证,对插补误差进行了定性和定量分析。研究结果表明,所提出的插补算法完全能够在无插补指令的PLC上运行,并满足直线插补精度的要求,这对降低机器人的开发成本具有重要意义。     

CNC系统数据采样插补的新算法

插补是CNC系统中重要的功能模块,插补算法的优劣直接影响着加工速度和精度.本文论述了直线和圆弧的数据采样法的基本原理插补算法及终点判别方法.利用圆的参数方程,提出了一种先计算插补点再计算进给量的新算法.最后利用LabVIEW软件进行了插补仿真,结果表明此方法大大提高了插补的精度和速度.     

新型并联机床数控系统插补算法的研究

提出一种用于新型并联机床的粗、精插补策略和算法 ,粗插补采用直接对加工曲面进行插补的方法。以NURBS曲线为例 ,运用合理计算方法推导出粗插补计算公式 ,并对粗、精插补进行了误差分析。插补实例结果表明 ,该插补算法具有恒速进给、加工表面轮廓误差易于控制等特点     

基于最大移动量的高效DDA数控插补系统的设计与开发

传统DDA插补方法的进给速度波动较大,误差亦较大.因此提出一种用C语言实现的高效DDA数控插补方法,该方法采用传统DDA插补的原理,并在此基础上予以扩展和改进,能实现多轴线性联动插补和圆弧插补,以最大移动量作为计算速度的依据,并采用左移规格化数据的方法提高了插补效率,保证了机床移动速度的均匀性.运用最大移动量的高效DDA数控插补系统加工平面类零件和球面时取得了满意的效果.     

自由曲面实时插补技术及其改进研究

本文指出了传统离线编程方法的不足,提出了自由曲面直接插补控制方法,提出了对传统插补方法的修正偏置算法及针对实时插补技术的速度修调,阐述了实时插补算法轨迹的生成过程、该插补算法基于曲面曲率等几何信息控制加工误差及切削步长、切削行宽,生成的刀具路径具有一定的自适应性。     

提高曲轴非圆磨削精度的插补方法

为提高曲轴非圆磨削的精度,提出了一种分段多项式插补方法。这一插补方法引入中间参数P来构造函数,并根据磨削点的恒线速度确定插补参数步长ΔP。对这一插补方法的轮廓误差进行了分析与验证,确认这一插补方法的误差小,插补精度高。     

An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.     

Performance Evaluation of a Real-Time Interpolation Algorithm for NURBS Curves

This paper presents a real-time interpolation algorithm for NURBS curves. In contrast to the existing linear and circular interpolators, the proposed interpolator can maintain small contour errors and feedrate fluctuations. Feedrate components, acceleration components and the servomotor driving force for each axis are precalculated from the given curve shape and themachine tool dynamic properties. As a sudden change in the geometrical properties of the tool path can increase contour errors and cause a sudden change of driving force of each servomotor, a new strategy of variable feedrate machining based on the geometrical properties of tool path is suggested. Real-time performance measurement of this interpolator is performed to demonstrate its practical feasibility.     

Self-adjustment computing method for time-partition interpolation in motion trajectory control of CNC machine tools

For time-partition interpolation in computer numerical control of the motion trajectory of a machine tool, the trajectory in a sampling cycle is approximated by a line segment from the current position of the tool to another on the expected trajectory; and locating the terminal of the line is the goal of the interpolation. In this paper, a self-adjustment computing method applicable to any explicit curve type is proposed. With the method, the terminal of the linear moving path in a cycle is first estimated by the motion information in the previous cycle, then adjusted according to the ratio of the desired moving distance to the computed linear path length. The result of the computation is fairly accurate, and it can be further enhanced with more adjustments performed in a sampling cycle, which is demonstrated in the simulation results. Furthermore, an adaptive feedrate adjustment algorithm is also introduced to enable the proposed method to control the trajectory contour errors.     

A NURBS interpolation algorithm with continuous feedrate

The high-speed precision machining of a part requires minimal feedrate fluctuation and contour error, and parametric spline interpolations have proven to be superior over linear and circular interpolations. However, parametric spline interpolations may result in large feedrate fluctuation due to an inaccurate mapping between the spline parameter u and the displacement S. This paper presents a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error. Since the cubic or quintic polynomials expressing the u-S mapping are acquired, they can be calculated by two consecutive interpolation points with the continuity condition. Thus, the parameter u can be calculated quickly and accurately by substituting the desired displacement S into the cubic or quintic polynomials. Simulation shows that the feedrate fluctuation of the proposed algorithm is much smaller than that of Taylor interpolation algorithms and Feed correction algorithm.     

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.     

Feedrate scheduling strategy for free-form surface machining through an integrated geometric and mechanistic model

In free-form surface machining, it is essential to optimize the feedrate in order to improve the machining efficiency. Conservative constant feedrate values have been mostly used up to now since there was a lack of physical models and optimization tools for the machining processes. The overall goal of this research is the integration of geometric and mechanistic milling models for force prediction and feedrate scheduling in five-axis CNC free-form surface machining. For each tool move, the geometric model calculates the cut geometry, and a mechanistic model is used along with a maximum allowable cutting force to determine a desired feedrate. The results are written into the part NC program with optimized feedrates. When the integrated modeling approach based feedrate scheduling strategy introduced in this paper was used, it was shown that the machining time can be decreased significantly along the tool path.     

Curve interpolation with variable feedrate for surface requirement

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This function, called a NURBS interpolation, adopts a feedrate optimizing strategy based on both the geometrical information of the curved path and dynamic properties such as the curvature of the curve, the allowable acceleration and the time constant. However, in the case of a finish cut using a ball-end mill, the curve interpolator needs to take the machining process into account for improved surface roughness, while reducing the polishing time. This surface roughness on high-speed machining is theoretically defined by the feed per tooth and the pickfeed at the given radius of the tool. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A curve interpolation algorithm is proposed for generating particular feedrate commands that are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented. A feedrate scheme that depends on the inclination angle has important potential application in part finishes consistent with prescribed surface roughness. The results show that the proposed algorithm is potentially useful for roughness-controlled machining of curved surface products.     

5轴联动数控系统速度控制方法

高速加工过程中,在刀具路径上容易产生过冲,影响加工精度,因此必须提前对加工速度进行优化处理.基于数据采样法,利用当量位移和坐标轴方向系数实现了5轴联动线性插补;利用直线加减速原理进行插补前加减速控制;对速度前瞻控制方法进行了深入探讨,实现了相邻程序段转接处速度优化、连续微小程序段速度计算、减速点提前预测及前瞻程序段数动态选择等.仿真结果表明,速度平滑连续,有效地解决了5轴联动线性插补中的速度控制问题,提高了加工精度和加工效率.     

High accurate interpolation of NURBS tool path for CNC machine tools

Feedrate fluctuation caused by approximation errors of interpolation methods has great effects on machining quality in NURBS interpolation, but few methods can efficiently eliminate or reduce it to a satisfying level without sacrificing the computing efficiency at present. In order to solve this problem, a high accurate interpolation method for NURBS tool path is proposed. The proposed method can efficiently reduce the feedrate fluctuation by forming a quartic equation with respect to the curve parameter increment, which can be efficiently solved by analytic methods in real-time. Theoretically, the proposed method can totally eliminate the feedrate fluctuation for any 2nd degree NURBS curves and can interpolate 3rd degree NURBS curves with minimal feedrate fluctuation. Moreover, a smooth feedrate planning algorithm is also proposed to generate smooth tool motion with considering multiple constraints and scheduling errors by an efficient planning strategy. Experiments are conducted to verify the feasibility and applicability of the proposed method. This research presents a novel NURBS interpolation method with not only high accuracy but also satisfying computing efficiency.     

Feedrate planning for synchronized movements involving rotary axes in multi-axis EDM for shrouded blisks

As compared to traditional machining approaches, multi-axis electrical discharge machining (EDM) has its unique advantages in machining components which are made of difficult-to-cut materials and have complex structures, such as shrouded blisks. Manufacturing processes of such complex parts involve synchronized movements of both linear and rotary axes. Due to different dimensions of angular and linear velocities, there is a discrepancy between demanded and actual feedrates. This feedrate discrepancy, on the one hand, can cause feedrate fluctuations leading to a machining instability, and on the other hand, can cause inaccurate heights of electrode jumps. In order to ensure the machining stability, this paper proposes a feedrate planning method for multi-axis EDM of shrouded blisks. In this method, CAD models of both an electrode and an shrouded blisk are utilized to extract characteristic radii for feedrate planning in G-code generations. A feedrate post-processing algorithm for multi-axis EDM for shrouded blisks is proposed to reduce feedrate fluctuations and achieve a proper electrode jump height. Data analysis demonstrates the resultant feedrate can be kept in a proper range. In comparative multi-axis EDM for shrouded blisks, the machining time has been reduced by up to 21.43 % by using the proposed feedrate planning method.