基于截面数据的B样条曲面光顺拟合

分析了B样条曲线的光顺拟合方法，针对按截面测量所得数据，将B样条曲线光顺拟合的方法扩展到B样条曲面的光顺拟合，并给出了数值算例。     

基于Matlab曲线拟合工具箱的列表曲线拟合

数控列表曲线存在编程繁琐、拟合精度低等缺点，提出了采用Matlab曲线拟合工具箱进行数控列表曲线拟合的方法，通过汽车活塞裙部纵向型线曲线的拟合，介绍了曲线拟合工具箱的应用方法。该方法具有方便、快捷和拟合精度高等特点。     

基于升阶的B样条曲面光顺拟合

分析了B样条曲线的光顺拟合方法和均匀B样条曲线的升阶方法，针对截面线上数据点个数变化较大的情况，提出了曲面光顺拟合的方法，并给出了计算实例。     

Clothoid曲线拟合及插补方法

为了提高自由曲线、曲面的加工性，在对自由曲线、曲面拟合方法研究的基础上，介绍一种曲率连续的自由曲线、曲面拟合法——Clothoid曲线法，并详细推导了Clothoid曲线插补算法。     

PTCR伏安特性测试曲线中的数学模型

详细分析了正温度系数热敏电阻(PTCR)静态伏安特性曲线的特征，在此基础上介绍了处理伏安特性测试数据的数学方法——最小二乘法和自然样条函数法。并将实际测试数据用本方法拟合结果与通用数据拟和软件Origin拟舍结果进行了比较。结果表明：本方法拟合的曲线跟Origin拟合的结果趋势非常接近，绘制的曲线更加平滑，更加接近实际。     

高精度非圆曲线轮廓铣削宏程序的研究

针对高精度非圆曲线加工节点计算延时的问题，提出了圆弧拟合节点坐标先计算、存储，后提取的加工编程方法，设计了椭圆圆弧拟合节点计算、存储宏程序，给出了应用实例。结果表明，该方法能保证高精度非圆曲线加工精度，提高了加工效率。     

基于B3样条曲线的高精度凸轮反求设计

在对各种反求工程中的关键技术——曲线曲面拟合方法进行比较的基础上，深入研究了描述能力强、拟合计算量相对比较小的B3样条曲线，以此理论为基础推导了B3样条曲线进行插值的算法，并将其成功地应用于高精度凸轮反求设计中。     

基于最小二乘法的液压泵特性曲线的绘制

提出一种基于最小二乘法原理的液压泵特性曲线的拟合方法,并用Visual Basic 6.0语言编制了曲线绘制用软件。利用该软件对试验数据进行处理并实现了特性曲线的绘制。试验结果表明,基于最小二乘法的液压泵特性曲线的拟合方法不仅可以快速地绘制出特性曲线,提高了试验效率,而且拟合误差较小、精度高,是一种较好的液压泵特性曲线的拟合方法。     

一种直线拟合法中拟合误差的简便计算方法

介绍了一种数控加工中用直线拟合非圆曲线时拟合误差计算的基本原理和具体方法。采用这种方法，可以手工进行拟合误差的计算，为手工编程带来极大的方便。     

列表曲线零件数控线切割自动编程的研究

介绍了一种在AutoCAD中拟合列表曲线的方法，论述了3B代码格式与DXF文件的数据处理算法，提出了列表曲线零件数控线切割自动编程的设计方法，有利于列表曲线零件的集成制造。     

变曲率零件拉弯模数控加工的数据处理

讨论了变曲率零件拉弯模数控加工的数据处理问题，包括列表曲线的获得与数据平滑校正，离散曲线的连续化拟合，数控编程中节点与插补长度的计算等。为实现变曲率零件拉弯模的数控加工奠定了基础。     

基于离散点截形螺旋面加工原理研究

提出了基于离散点的圆柱螺旋面成形刀具计算方法，分别建立了已知螺旋面工件截形离散点数据计算成形刀具廓型的数学模型及已知刀具截形离散点数据计算由其加工的螺旋面工件的数学模型。利用累积三次参数样条法计算螺旋面工件截形及成形刀具廓型各离散点的倾斜角。分析了成形刀具的计算误差，对成形刀具数据型值点以累积三次参数样条进行插值，用双圆弧样条拟合的方法进行光顺处理。实例证明，两模型是正确性的、可行的，能够满足离散点条件下螺旋面高效率、高精度的加工要求。     

A composite fitting model of discrete handbook data for peripheral end milling

Machining data handbooks are important reference books in the machining industry, as they provide recommended process parameter values for common machining operations. The machining data, although covering a wide range of relevant cutting conditions, are only listed under discrete cutting conditions. Rough interpolation-based calculations are often needed in order to estimate the process parameter values at the desired cutting condition. In this work, a composite fitting model is presented to fit a composite functional curve through the discrete handbook data of recommended cutting speeds and feeds with respect to the cutting condition of radial depth of cut for peripheral end milling. The objective is to establish a functional relationship from the handbook data such that recommended cutting speed and feed can be obtained for any given radial depth of cut. According to the tabulated layout of the machining data, the entire range of the radial depth of cut is divided into three segments having distinctive formulations and trends. Constraints are then imposed to preserve the trends and smoothly connect the adjacent segments. As a possible application of the presented model, a case study of machining a rectangular pocket is provided. Machining time of a potential process plan is readily evaluated based on the cutting speeds and feeds obtained from the composite model.     

空间管件数控数据矢量算法及实现

介绍了空间管件的管形数据和数控加工数据信息，详细分析了矢量法从管形数据到数控加工数据的转换算法。弯管弯曲受力复杂，理论计算弯曲角和弯曲伸长量困难，采用生产现场的经验数据对数控数据进行了修正，用编程软件Delphi编写软件实现了从管形数据到数控加工数据的自动转换。在弯管机上运行转换的数控加工数据，应用表明该算法稳定，具有较大的实用价值。     

从测量的散乱数据点云直接生成数控刀具路径的研究

提出了一种直接从测量的散乱数据点云用球头刀对自由曲面进行三轴数控加工时生成刀具路径的方法。不同于现有散乱点云基于逆向工程的刀具路径生成方法,本法考虑并估计了曲面加工误差和粗糙度。将散乱数据点云向XY平面投影,以获得的投影边界为刀具路径的主方向,然后根据曲面所需的加工误差和残留高度要求划分该投影数据点云,得到一系列刀位网格单元。通过最小化每个刀位网格单元的加工误差以确定每个刀位网格的节点位置,加权平均相关联刀位网格节点来对齐相邻刀位网格单元的边缘。为了缩短加工时间,裁去刀位路径上多余的线段,最终生成高效合理的数控加工刀具路径。已用实测的数据点云验证了本法直接生成刀具路径的有效性。     

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.     

运动平滑处理技术在伺服控制系统中的应用

为研究不同加减速算法对加工精度以及电机启停或突变的影响,首先分析了两种运动平滑处理技术—梯形和S形加减速算法的基本原理,建立了离散数学模型,并在传统七段S形曲线的基础上提出了五阶段S形曲线改进;然后,通过软件实现了两种加减速算法;最后,搭建了软、硬件实验平台。实验结果表明,该研究对于保证实际加工精度和电机的平稳控制有着重要的意义,也为高效率数控加工奠定了基础。     

A Cutter Orientation Modification Method for the Reduction of Non-linearity Errors in Five-Axis CNC Machining

In the machining of sculptured surfaces, five-axis CNC machine tools provide more flexibility to realize the cutter position as its axis orientation spatially changes. Conventional five-axis machining uses straight line segments to connect consecutive machining data points, and uses linear interpolation to generate command signals for positions between end points. Due to five-axis simultaneous and coupled rotary and linear movements, the actual machining motion trajectory is a non-linear path. The non-linear curve segments deviate from the linearly interpolated straight line segments, resulting in a non-linearity machining error in each machining step. These non-linearity errors, in addition to the linearity error, commonly create obstacles to the assurance of high machining precision. In this paper, a novel methodology for solving the non-linearity errors problem in five-axis CNC machining is presented. The proposed method is based on the machine type-specific kinematics and the machining motion trajectory. Non-linearity errors are reduced by modifying the cutter orientations without inserting additional machining data points. An off-line processing of a set of tool path data for machining a sculptured surface illustrates that the proposed method increases machining precision.     

B-spline tool offset of a free-form curve in the shoe last high-speed machining CNC system

Aiming at the special requirements of a shoe last high-speed machining process and the large dataset which could be gained by the reverse engineering technique, this paper analyzes the conventional tool-offset methods and presents a B-spline tool-offset model. A simple vector-analyzed algorithm to smooth the tool-offset curve in which there are local strange points is proposed, and then the second tool-offsetting, which obtains the fine data of the machining tool’s center points, is directly processed. To reduce the error from tool offsetting of the C2 continuity curve, this paper gains a smoother curve after processing via the edge points joint algorithm, which effectively solved the overcut or undercut problems in the high-speed machining of the spline curve.     

带抛物线轮廓电极的铣削程序编制

利用数控系统的用户宏程序功能编制模具电极的抛物线轮廓加工程序,便于使用不同规格的刀具加工和修改磨损补偿值,提高了单件生产效率和产品加工精度,对编制其他非圆二次曲线轮廓加工程序具有借鉴作用。