基于MLS改进算法的曲线拟合技术研究

针对散乱点拟合曲线的算法问题,分析了移动最小二乘逼近法（MLS）的特点,提出了用MLS改进算法对散乱点进行曲线拟合,并结合实例进行了验证。结果表明,MLS改进算法在拟合曲线时,选取不同阶的基函数和不同的权函数,在保证精度和光滑度的基础上,解决了传统曲线拟合方法在拟合曲线时出现的运算不稳定现象,显示了MLS改进算法在曲线拟合中的优越性。     

一种基于插值拟合的复杂刀具轨迹在线平滑压缩算法

提出了一种基于插值拟合的在线复杂刀具轨迹平滑压缩算法,该算法依据主导点的选取策略,对原始数据点进行离线预处理,然后进行主导点的在线插值拟合以及非主导点的误差检测,进而生成一条满足拟合精度要求的B样条曲线。主导点依据离散数据点的曲率阈值、曲率极大值、曲线拐点,以及分段Bezier曲线逼近拟合后的误差最大值点进行选取。在具有C2连续性的分段Bezier曲线逼近拟合前,需要利用长度均分策略,提取长度突变点作为新增的主导点,以保证拟合的准确性。对主导点进行B样条插值拟合后,利用轮廓误差跟随法对非主导点到拟合曲线的误差进行检测。该方法与牛顿迭代法相比,其计算速度更快且能提高算法效率。仿真结果表明,提出的算法可对复杂刀具轨迹进行平滑压缩,且误差检测的精度能够满足要求。     

基于MATLAB单双圆弧混合逼近曲线的算法及实现

讨论了单圆弧和双圆弧逼近的特点,结合两者的优点,用优化三点圆弧以允差逼近曲线和单双圆弧混合逼近的算法,理论上使得曲线有拐点和极值点时整个逼近圆弧的光滑连接,并保证了圆弧逼近的段数达到最少。基于Matlab采用比例法、一维搜索和优化相结合的方法进行程序的编翩求解节点,算法简单,可靠,程序运行快速高效。为数控加工复杂的曲线和CAD系统提供了参考。     

基于B样条曲线节点插入算法的拟合优化

在逆向工程中对叶片进行非接触式测量,为了更好得到叶片型线的数据,需要用曲线对有序的点云进行拟合.为了满足精度要求,提出了用节点插入算法来对拟合出B样条曲线进行优化.该方法首先通过最小二乘法拟合出曲线,然后根据误差和曲率信息以及节点插入算法不断插入节点,所得结果与上一次进行对比,直到达到拟合要求.实验表明,该方法考虑到局部曲率及误差,得到的拟合曲线逼近效果更好.     

基于UG曲线光顺拟合二次开发算法

为了解决涡轮叶片曲面不光顺而造成的数控加工刀轨生成失败的问题,本文针对叶片曲面截面线进行光顺拟合,提出了一种三次非均匀B样条曲线整体光顺逼近算法。该算法建立了一个由最小二乘法、型值点曲率和、型值点曲率变化和三项组成的目标函数,并利用高斯消元法求出最优控制顶点坐标序列。该算法可以使曲线在给定的逼近误差范围内,实现型值点曲率和降低的同时,曲率变化也更加均匀。最后将算法程序嵌入UG5.0二次开发程序中实现自动光顺拟合模块的开发,并通过与已存在的算法进行光顺效果对比实验,验证了本文算法更有效。     

非圆二次曲线等误差曲率圆法拟合算法的研究

综合比较多种非圆曲线逼近拟合方法,等误差曲率圆法是最佳方法.文中对等误差曲率圆法进行了数学描述,提出了可行的拟合算法,并基于该算法编制出程序流程图.利用该程序流程图,为数控编程人员编制非圆曲线程序提供了思路,具有一定应用价值.     

路径拟合在服装切割中的研究与应用

针对服装样片在裁剪过程中提出的快速性要求,给出了一种服装样片切割方案:通过三次准均匀B样条拟合PLT文件中的加工数据,获得服装样片的轮廓曲线,并采用混合圆弧-直线逼近法逼近拟合曲线,在误差允许的前提下,重新离散化刀具加工点,减少了在拟合曲线上的刀具加工点数量,从而提高了服装裁剪的速率。重点讨论了运用三次准均匀B样条拟合样片轮廓曲线以及采用混合圆弧-直线逼近法逼近拟合曲线,突出了其在大曲率线段加工中的优势。     

等误差面积法三点圆圆弧段逼近非圆曲线

详细介绍等误差面积法圆弧段逼近非圆曲线节点的计算方法 ,并通过编程误差的分析 ,建立逼近误差面积相等的三点圆圆弧段逼近非圆曲线节点坐标计算的算法     

基于NURBS曲线拟合的刀具路径优化方法

为解决复杂曲面高速、高精度加工中由于微小直线段链逼近自由曲线产生的刀具路径不连续问题,提出一种基于非均匀有理B样条曲线拟合的刀具路径优化方法.在该方法中,通过分析刀具路径的几何特征鉴别需要平滑的连续直线段链,对其分段进行基于最小二乘法的非均匀有理B样条曲线拟合优化,并设置相邻段连接点处的边界平滑条件,还原刀具路径应有的连续性.拟合算法采用特征点搜索法设定曲线参数,通过误差控制的曲线节点向量和控制顶点调整保证拟合曲线精度.实验表明,经过该算法拟合优化后的刀具路径具有良好的平滑性,显著提高了曲面加工的精度和效率.     

基于曲率及误差分布的点云逼近曲线优化算法

为提高利用形状信息优化点云逼近曲线的准确性,提出了一种基于曲率及误差分布的点云逼近曲线优化算法.该算法首先快速地创建满足误差限的非最优样条曲线,据此获得较为准确的曲率分布作为形状信息;然后,以大于所给曲率阈值的角点作为种子点,构建出点云的三次序号参变量样条逼近曲线.当逼近曲线误差不满足误差限时,以误差的分布情形确定型值点的添加位置.使得每一次型值点添加后最大误差均减小.通过数条点云曲线实验表明,该算法显著地减少了逼近曲线的控制点数目.     

PROFILE TOLERANCE EVALUATION OF PARAMETRIC CURVES AND SURFACES

The profile error evaluation of complex curves and surfaces expressed in parametric form is considered. The linear error model is established on the base of two hypotheses firstly. Then the profile error evaluation is converted into one of these optimal formulations: MINIMAX, MAXMIN and MINIDEX problems, which are easier to be solved than the initial form. To each one of them, geometric condition and algebraic condition are presented to arbitrate whether the ideal element reaches to the optimal position. Exchange algorithm is proven highly effective in searching for solutions to these optimization problems. At last some key problems in tolerance evaluation of freeform surfaces and curves in B spline method are discussed.     

基于环形补偿参数曲线插补算法

对于数控加工中参数曲线的加工,提出了一种新的插补算法,该算法利用泰勒展开对曲线方程进行重构,引入误差补偿思想,对插补过程中产生的误差反复补偿,从而满足目标要求,通过仿真和实际切削实验,表明该算法简单实用、通用性强、算法精度高,能够保证参数曲线的光滑性,有利于提高参数曲线加工质量和加工效率.     

Algorithms of wavefront generation for aspheric surface measurement

For aspheric surface measurement with wavefront sensing technology, after obtaining the slope or curvature as the measurement raw data, the data processing algorithm must be re-studied for high performance in practical application. This paper designs, analyzes and compares five different algorithms to generate wavefront for aspheric surface measurements, especially for practical measurements with noises and missing data. Simulation and experimental results show that in ideal condition without any noise in the system, direct fitting yields perfect results without error; the algorithms including Southwell reconstruction achieve better results under practical conditions, where there exist real issues such as noise and abnormal data. Reconstruction is therefore an essential step as it significantly improves the measurement stability and reliability, and enables the system feasible for practical applications. Furthermore, Southwell algorithm is extended for applications with missing data, which is most likely happen when the surfaces to be measured possess large dynamic range.     

基于阻尼粒子群优化的地磁场测量误差补偿

针对三轴磁力仪在磁场测量过程中的磁干扰问题,提出了基于阻尼粒子群优化算法的磁测误差补偿方法。建立了磁力仪误差和载体磁干扰的一体化误差补偿模型,分别采用阻尼粒子群算法和Two-step方法对非线性观测模型进行参数估计。以质子磁力仪数据作为真值,借助无磁转台充分连续采样,实验结果显示,阻尼粒子群算法对于磁场测量误差具有良好的抑制作用。补偿后,由阻尼粒子群算法和Two-step方法得到的均方根误差分别由1 025.7降至60.304 4、581 n T。结果表明,阻尼粒子群算法取得了更好的补偿效果,补偿精度提高了至少一个数量级,为磁场测量误差提供了一种非常有效的补偿方法。     

Development of a real-time trajectory generator for NURBS interpolation based on the two-stage interpolation method

This paper deals with the real-time NURBS interpolation method in which the interpolation error between the ideal curve and the interpolated curve is compensated within the machine basic length unit (BLU). Parametric curve interpolation methods are based on the Taylor series expansion of curve parameters and an approximation. This approach enables effective feed command generation following the target curve. However, the interpolation error caused by the curve segmentation cannot be controlled.In this research, a two-stage interpolation method that compensates for interpolation errors within machine BLU is proposed. The interpolation result was filtered by an acceleration/jerk limitation equation. Through this two-stage interpolation, both the interpolation error condition and the motion dynamics can be satisfied.Using computer simulations in which interpolation results are revaluated by a numerical iteration method, it is shown that the two-stage interpolation algorithm can interpolate target curves precisely with geometric and dynamic contentment. The proposed algorithm was implemented in the CNC simulator system and an experimental run was conducted to identify the real-time adaptation.     

双曲柄连续轨迹生成机构的优化综合

本文首先提出从动杆杆长结构误差的概念，然后基于该结构误差建立优化综合模型，采用改进遗传算法获取综合结果。从前杆杆长结构误差不仅计算便利，且能有效反映出实际生成的轨迹曲线与预期的理想轨迹曲线间的差异，避免了在两轨迹曲线上选择对应比较点的困难。改进遗传算法保证了获得全局最优解。综合实例结果表明了本方法的有效性。     

SR253Z智能调节仪在热电偶检定系统炉温控制中的应用

热电偶群炉自动检定系统用于自动检定各种工作用热电偶,能满足短时间内检定大批量热电偶的要求,该控温系统采用RS485总线智能仪表和SSR进行控温,先进的专家PID算法,有效地防止控温过程中的超调和欠调现象,实现自然、平稳的温度过渡,既可减少不必要的等待时间,又可得到理想的恒温指标.     

Batch circular form error characterization and evaluation

In practice, it is necessary to understand the general quality status of a batch of circular features machined under the same or similar conditions. In particular, it is necessary to understand the possible worst case among such a batch of circular features. To this end, a brand-new concept called “batch circular form error” is presented in this paper. Detailed definitions of batch circular form error including batch circular form error with ideal conditions and batch circular form error with realistic conditions are provided. Accordingly, the evaluation algorithms of batch circular form error are developed. The algorithms include the characterization of the deterministic profile of circular features and the evaluation of batch circular form error based on a given profile confidence level. Case studies with simulation and experimental data are used for demonstration. The results show that the batch circular form error can be estimated with the data measured from any circular feature in the batch, as long as the sample size is large enough and random ratio is not too large.     

无线传感器网络中一种改进的DV-HOP定位算法

在无线传感器网络中,节点定位技术占有非常重要的地位。为了提高节点定位精度,在研究和分析传统DV-HOP定位算法的基础上提出了一种改进算法。该改进算法中,每个信标节点通过分析实际距离和估计距离之间的误差,可进一步修正平均每跳距离;然后在未知节点坐标计算过程中引入二维双曲线定位算法代替传统的三边测量法,可减少节点计算误差。仿真结果表明,在无需增加额外的硬件设备的条件下,改进的DV-HOP算法与传统的DV-HOP算法相比,能够更加有效地提高节点的定位精度。     

A study on motion of machine tools’ hexapod table on freeform surfaces with circular interpolation

Accuracy is greatly affected by nonlinear motion of hexapods. This need is more obvious when these mechanisms are used in machining environments where precision and surface qualities are of critical importance. In this paper, comprehensive algorithm for hexapod tool path programming is developed. Using C#.Net, this algorithm is developed based on circular motion and rotation of the table which has the capability of checking nonlinear error and keeping it in a controlled limit as well. Improved Tustin algorithm is used for interpolating circular path. To evaluate the accuracy of the developed algorithm on a freeform surface, a turbine blade is scanned, and its CAD model is developed. Taking zigzag strategies, movement on turbine blade surface is approximated with smaller circles using the algorithm presented in this paper. The output accuracy resulted from interpolation algorithm for passing on turbine blade surface is studied in SimMechanics of MATLAB software. Using Total Station camera, motion path of two turbine blades with different radius curves on the hexapod table is experimentally obtained. Finally, it can be stated that the developed algorithm based on circular interpolation has the capabilities of motion on freeform curves.