NURBS插补方式对数控铣削加工质量的影响

针对自由曲面加工误差较大的问题,从插补方式的角度进行了对比研究。对相同的二维抛物曲线分别以直线插补、直线-圆弧插补和NURBS插补三种插补方式进行实际加工,利用三坐标测量仪对所加工曲面轮廓进行测量,并获取相应的加工误差分布曲线。分析结果表明,NURBS插补刀具路径可以改善零件的加工精度和表面光顺性,有效地提高生产效率,并能够减少曲面后续抛光的工作量,较好地满足自由曲面高性能数控加工的需要。     

Implementation of online NURBS curve fitting process on CNC machines

The study aims to develop a method for implementing an online non-uniform rational B-spline (NURBS) curve fitting process on CNC machines for improving the quality and efficiency of machining. Conventional CAD/CAM/CNC systems usually induce some machining difficulties and limit the machining results in real applications. Therefore, some researchers have proposed various methods for improving the machining results. An online NURBS curve fitting process consists of the fetching and fitting stages for CNC machines is developed in this paper. The fetching stage fetches a block of NC code and generates motion commands for obtaining data points. The fitting stage executes the NURBS curve fitting method along with a given set of data points. Moreover, the optimal search method is designed for obtaining good results in the NURBS curve fitting process. Simulations and machining tests carried out on a vertical machining center show that the proposed approach reduces the machining time to about 23% while maintaining the machining quality for the sample test.     

The design of a NURBS pre-interpolator for five-axis machining

A non-uniform, rational B-spline (NURBS) interpolator has great advantages for free-form surface machining compared to the conventional linear/circular interpolator. However, the existing NURBS interpolators can only handle the NURBS trajectory given in a customized NURBS G code. Also, it is limited to three-axis applications. In this paper, a NURBS pre-interpolator with three function options is proposed for a computer numerical control (CNC) system so that the NURBS interpolator can be thoroughly applied for five-axis machining. The first function is called the NURBS converter function, which is used to convert a series of linear/circular segments exactly into a NURBS curve. The second function is the NURBS smoother function, by which, a series of linear segments are fitted to a NURBS curve. The third option provides two kinds of NURBS G codes definition, by which, the NURBS trajectory with five axes can be represented directly. Upon using the three options of the NURBS pre-interpolator, a unified NURBS curve can be obtained for further interpolation. Two actual machining cases are conducted to evaluate the feasibility of the proposed pre-interpolator.     

Simultaneous 3D machining with real-time NURBS interpolation

Increasing demand on precision machining using computerized numerical control (CNC) machines have necessitated that the tool move not only with the smallest possible position error but also with smoothly varying feedrates in 3-dimensional (3D) space. This paper presents the simultaneous 3D machining process investigated using a retrofitted PC-NC milling machine. To achieve the simultaneous 3-axis motions, a new precision interpolation algorithm for 3D Non-Uniform Rational B-Spline (NURBS) curve is proposed. With this accurate and efficient algorithm for the generation of complex 3D shapes, a real-time NURBS interpolator was developed using a PC and the simultaneous 3D machining was accomplished satisfactorily.     

基于NURBS最小二乘逼近的微段平滑加工算法

在微段加工方式下,通常需要借助CAM(Computer Aided Manufacturing,计算机辅助)软件的后置处理将连续的加工路径离散化为大量微小直线段,并生成数控程序,数控系统则根据由微小直线段组成的加工路径进行插补和加工。但是,该方式具有加工程序量过大和需要频繁加减速来满足加工精度要求的两大不足。因此,为了实现微小直线段的高速平滑加工,提出了带权因子和一阶导数约束的NURBS曲线最小二乘逼近算法并加以了初步验证。算法的实质是将由微小直线段组成的加工路径拟合成一条连续的NURBS曲线,作为新的加工路径,然后利用NURBS实时插补对新的加工路径进行插补,实现微小直线段的高速平滑加工。经初步验证,算法有助于改善微段加工方式的加工质量和效率。     

基于UG的NURBS曲线插补技术的应用研究

高速切削加工作为模具制造中重要的一项先进制造技术,NURBS曲线插补技术逐步得到应用。在UG中通过对连结分段、角度公差、拟合公差等参数的设置以及对UGCAM后处理器的修改,生成了NURBS曲线插补指令,从而驱动CNC机床实现了NURBS曲线插补的高速加工。     

Real-time variable feed rate NURBS curve interpolator for CNC machining

This paper presents a real-time control algorithm based on Taylor’s expansion for implementing variable feed rate non-uniform rational B-spline (NURBS) curve interpolators using a digital signal processor for precision CNC machining. To efficiently compute the NURBS curve and its derivatives in real-time, an effective method is proposed. The variable feed rate NURBS curve interpolator can be used to realise the ACC/DEC before feed rate interpolation in which the ACC/DEC (acceleration/deceleration) planning on the feed rate command executes before the interpolation takes place, so that the path command errors caused by conventional ACC/DEC planning using the post feed rate interpolation can be effectively eliminated. To demonstrate the performance of the proposed algorithm, an X-Y table driven by two servomotors is controlled to track command paths represented by multiple blocks of NURBS curves. Experimental results verify the effectiveness of the proposed method.     

Design of a real-time NURBS interpolator with constant segment length for milling EDM

The utilization of the non-uniform rational B-spline (NURBS) toolpaths becomes more important than ever before. However, in traditional milling electrical discharge machining (EDM) of parametric curves, there commonly exist problems such as speed loss and an overincreased sampling period, which directly cause a decrease in machining efficiency. Moreover, traditional approaches normally suffer from a complex toolpath planning. In this paper, a real-time interpolator with a constant segment length is proposed to improve the milling EDM of NURBS curves. The proposed interpolator can directly process NURBS curves with their definition information. The toolpath planning can thus become simpler. A new two-stage interpolation method is adopted such that both a high speed accuracy and a relatively short sampling period can be achieved, and the magnitude of chord errors can also be reduced. While the first-stage interpolation samples a NURBS curve with a constant-length segment, the second-stage interpolation, or the re-interpolation, executes multiple interpolations in a sampling period to generate the required feed rate. A loop buffer is designed for the implementation of the real-time interpolator. Experimental results show that the proposed interpolator demonstrates a superior machining performance to that by traditional interpolators, especially in terms of chord errors and erosion rate.     

A Study on an Open Architecture CNC System with a NURBS Interpolator for WEDM

This paper deals with the design and implementation of an open architecture CNC system for wire electrical discharge machining (WEDM) with a consideration of the differences between WEDM and NC cutting machines. Work using open architecture controllers (OACs) has focused mainly on metal cutting machines. WEDM has many aspects similar to milling machines. However, there are differences in the machining processes and control strategies. To close the gap between previous general work on OAC and the WEDM specific needs, an open architecture NC model for WEDM comprised of a synchronisation kernel and an NC functional module is proposed. The proposed CNC system is applied to an existing commercial WEDM system by a retrofitting method. A precise NURBS interpolation function is implemented and sample runs are conducted with a NURBS interpolator that is added to the proposed system.     

基于速度指令波动的NURBS曲线插补算法研究

由于NURBS曲线的弧长是曲线参数的非解析积分形式,因而曲线弧长的准确参数化是插补计算的关键。通常,基于泰勒展开或曲线弧长多项式拟合的近似求值方法被用于插补计算;然而,截断误差的引入最终会导致速度指令波动,影响数控加工精度。针对具有最小速度指令波动的NURBS曲线插补算法研究,首先提出了曲线参数-弧长的三阶拟合多项式方法;然后以该方法计算结果为初值,并提出了求取精确曲线参数的弦截速度校正方法;最后进行了仿真验证。仿真结果表明,所提出的方法计算量小,提高了曲线参数的计算精度,相比于现有的方法,速度指令波动有很大减小。     

NURBS插补技术在复杂曲面数控加工中的应用

分析了NURBS(Non-Uniform Rational B-Spline)曲线直接插补技术相对于传统数控系统中采用的直线或圆弧逼近对NURBS曲线数控编程的优越性;探讨采用NURBS曲线插补技术的CNC机床曲线曲面的加工方法以及实际应用中需要进一步解决的问题。     

基于STEP-NC的CNC系统中插补技术研究

STEP-NC是一个新的数控编程接口,基于STEP-NC的CNC系统是未来数控技术发展方向之一.在该系统中不但具有直线和圆弧插补功能,而且还具有样条曲线插补功能.开发了一个统一的 基于NURBS样条曲线插补的通用插补器,推导出一个简洁的NURBS几何数据预处理算法,详细论述了基于等弧长的插补技术和插补原理.最后,通过仿真和实例加工验证了上述算法的有效性和可靠性.     

基于Newton-Rapson迭代法的NURBS插补算法的研究

一阶、二阶Taylor展开式求解NURBS曲线插补坐标点ui+1,存在计算量大、插补时间长等问题,该文提出了一种基于Newton-Rapson迭代法的NURBS插补算法。仿真和实验结果表明:该算法计算过程简单有效,具有可行性和实用性,可以减少插补计算量和插补时间,提高插补精度和加工效率,满足了数控系统实时、高速、高效率插补的要求,对其他数控插补的过程具有很强的借鉴意义。     

基于PLC的开放式数控NURBS插补功能的研究与实现

针对一种基于PLC的开放式数控系统,应用NURBS(Non-Uniform Rational B-Spline)曲线插补技术,对传统的自由曲线插补算法进行改进.同时根据STEP-NC标准对CAD/CAM/CNC一体化的新型数控插补方法进行研究,利用ActiveX技术实现了与CAD系统的数据交换,并在实验数控系统中加以应用.实验结果证明该插补算法可以有效地提高实时插补速度和精度,提高数控系统的工作效率.     

烟气轮机动叶片的参数化建模及加工仿真

运用NURBS曲线拟合算法将节点插入算法应用到动叶片截面型线造型中,采用UG软件中的NURBS样条曲线构造器功能在多个截面上准确绘制出动叶片的截面曲线造型,并利用NURBS曲面造型模块生成烟气轮机动叶片的实体模型。对零件结构特点进行工艺分析,运用UG的加工模块进行加工仿真,生成刀具轨迹并进行试验加工,为后续烟气轮机动叶片的数控加工提供依据。     

数控加工中基于自由曲面表面特性的刀具路径安排

目前CNC上的轨迹控制功能仍主要是直线和圆弧插补,因此当加工自由曲面时,大多只能采用直线或圆弧逼近算法来对曲线进行逼近处理。针对数控加工的实际需求,现在数控系统技术人员对数控机床插补器进行研究并开发出了许多曲线和曲面插补功能。基于曲线插补,在保持进给速度尽可能恒定的条件下,对刀位路径和刀位速度进行离线的曲线拟合,以便于得到用于数控加工的刀位文件。这种方法能有效解决进给速度的波动问题,并能有效压缩刀位文件。为此,提出几种算法来拟合刀位路径和刀位速度轮廓曲线。曲线和曲面插补在数控代码数据量和逼近误差方面都有较大的改善。     

临界曲率值分割曲线尖角的NURBS曲线插补

为兼顾插补含尖角NURBS曲线的精度与速度,提出尖角分割且速度修正插补算法。由插补弦高误差限、法向加速度及其导数约束,得满足插补精度及机床动力学性能的临界曲率;用大于临界曲率的局部极大曲率及临界曲率分割NURBS曲线为是否包含尖角的若干子段;用S曲线加减速算法规划各子段进给速度,并用段间速度及位移协调关系修正各段加速度及其导数,使各段加减速时间为整数倍插补周期。在相同约束条件下,分别用曲率单调无速度修正、尖角分割无速度修正及尖角分割有速度修正算法,规划一条含大曲率尖角NURBS曲线插补速度,并用一阶泰勒级数展开算法插补该曲线。对比结果表明尖角分割且有速度修正算法可稳定得到较高插补精度,因此该算法可用于含大曲率尖角NURBS曲线高速度高精度加工。     

基于速度平滑控制的高效非均匀有理B样条曲线插补算法

为提高曲面加工的质量和效率,提出了一种基于冗余误差和速度平滑控制的非均匀有理B样条曲线插补算法.该算法先按照曲率大小将非均匀有理B样条曲线分段,再根据数控机床最大加速度调整分段.消除了曲率突变对加工的负面影响.同时为每个分段分别设置合适的编程进给速度,提高了加工效率.最后提出两段速度平滑控制方法,使速度过渡更为平滑.模拟试验证明了该算法的有效性.     

NURBS曲线实时插补进给速度控制的研究

数控技术标志着现代制造业的核心,数控插补模块是数控技术中最为重要的模块之一。NURBS曲线是自由曲线的一种,由于其NURBS曲线的诸多优越性,使其能够很好的应用到数控领域中。NURBS曲线插补及加减速控制的精度和速度是CNC系统的重要指标。通过分析NURBS曲线的插补原理,提出了基于Taylor展开公式逼近NURBS样条参数。同时考虑速度波动于曲率的关系,弦误差与插补周期的关系,根据弓高误差调节进给速度,能够将进给速度波动控制在理想水平。     

高精度数控机床非均匀有理B样条曲线插补控制研究

在复杂曲面数控加工中,经常应用非均匀有理B样条曲线。介绍了非均匀有理B样条曲线插补原理,分析了传统非均匀有理B样条曲线插补方法,即泰勒展开法,确认泰勒展开法在计算精度和时效性等方面存在不足。针对泰勒展开法存在的不足,提出采用割线法进行非均匀有理B样条曲线插补。介绍了割线法插补原理,分析了迭代运算初值及终止判定问题。通过对比确认,割线法求解时间短,精度较高,可以满足高精度数控机床非均匀有理B样条曲线的插补控制要求。