多种参数对自由曲面形态优化的影响研究

自由曲面结构的形态优化通常是在给定材料参数和曲面厚度的情况下进行的，因此有必要对材料参数和曲面厚度取值对曲面形态优化的影响进行研究。基于梯度法，采用非均匀有理B样条（NURBS）技术生成自由曲面，以最小应变能为优化目标，对自由曲面进行形态优化，并研究了材料弹性模量、泊松比和曲面厚度对优化结果的影响。研究表明，弹性模量的取值对曲面的优化结果几乎没有影响，而材料泊松比和曲面厚度的取值对曲面形态优化均有影响，其中曲面厚度的影响最为显著。     

BIM-to-IGA: A fully automatic design-through-analysis workflow for segmented tunnel linings

Both planning and design phase of large infrastructural project require analysis, modelling, visualization, and numerical analysis. To perform these tasks, different tools such as Building Information Modelling (BIM) and numerical analysis software are commonly employed. However, in current tunnel engineering practice, there are no systematic solutions for the exchange between design and analysis models, and these tasks usually involve manual and error-prone model generation, setup and update. In this paper, focussing on tunnelling engineering, we demonstrate a systematic and versatile approach to efficiently generate a tunnel design and analyse the lining in different practical scenarios. To this end, a BIM-based approach is developed, which connects a user-friendly industry-standard BIM software with effective simulation tools for high-performance computing. A fully automatized design-through-analysis workflow solution for segmented tunnel lining is developed based on a fully parametric design model and an isogeometric analysis software, connected through an interface implemented with a Revit plugin. The IGA-Revit interface implements a reconstruction algorithm based on sweeping teachnique to construct trivariate NURBS lining segment geometry, which avoids the burden to deal with trimmed geometries.     

基于NURBS曲面的管道三维成像技术研究

管道的三维成像是处理变形检测数据最直观但也是最复杂的方式,而曲面的三维重建算法是实现管道三维成像的关键。为此,基于非均匀有理B样条(NURBS)曲面的三维成像技术,通过管道检测数据反求双三次NURBS曲面的节点矢量与控制点,并对管道机器人在检测过程中可能发生的周向转动进行优化处理,使用C++编程语言与OpenGL生成管道的三维模型,并对比了相同变形管道中,是否考虑检测机器人的周向转动对于成像效果产生的影响。研究结果表明:基于NURBS曲面的三维重建算法对于管道局部变形(凹陷变形、挤压变形)的表面重构精度较高,其成像效果清晰、逼真,且考虑检测机器人的周向转动时,所生成的三维模型表面过渡更加圆滑。研究结果可为油气输送管道三维成像技术的进一步研究提供参考。     

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。     

三次NURBS曲线轮廓的数控加工编程处理

在给定具体型值点的条件下 ,通过反求工程 ,构造出三次NURBS曲线的参数方程 ,并提出了一种利用最小二乘圆对NURBS曲线进行分段圆弧逼近的数控编程方法 ,它基于NURBS曲线的矩阵表示 ,在满足精度的要求下 ,可使拟合圆弧段数最少 ,并能够减小拟合误差、简化数值计算和编程 ,从而减少CAD系统与CNC系统的数据传送 ,提高了加工效率和质量     

基于NURBS曲线的逼近研究

介绍了直线逼近和圆弧逼近2种NURBS曲线逼近算法,并在两者的基础上,提出对NURBS曲线进行混和逼近的新算法,最后,通过实例验证了该算法的正确性与可行性。     

基于NURBS算法的工业机器人轨迹规划研究

轨迹规划是工业机器人研究领域的重要内容之一。为解决使用直线与圆弧逼近不规则曲线方法带来较大误差的问题,提出使用NURBS拟合自由曲线,并使用S形速度曲线来控制机器人末端的运动速度和加速度,使各个插补点的位置、速度和加速度能够连续,将之反推到关节空间可以得到各个关节的角度、角速度和角加速度。最后以IRB2600工业机器人为仿真本体,通过MATLAB仿真证明:NURBS和S形速度曲线相结合的方法可以得到在关节空间连续、平稳的运行轨迹、速度曲线、加速度曲线,减弱了因各关节角度、角速度、角加速度突变带来的冲击影响,优化了机器人运行轨迹。     

Equiareal parameterizations of NURBS surfaces

The equiareality of NURBS surfaces greatly affects the results of visualization and tessellation applications, especially when dealing with extruding and intruding shapes. To improve the equiareality of given NURBS surfaces, an optimization algorithm using the Möbius transformations is presented in this paper. The optimal Möbius transformation is obtained by computing the intersection of two planar algebraic curves, whose coefficients are computed explicitly for Bézier and B-spline surfaces, while numerically for NURBS surfaces. Examples are given to show the performance of our algorithm for visualization and tessellation applications.     

An improved feedrate scheduling method for NURBS interpolation in five-axis machining

Five-axis machining plays an important role in manufacturing by dint of its high efficiency and accuracy. While two rotation axes benefit the flexibility of machining, it also brings limitations and challenges. In order to further balance machining precision and efficiency, an improved feedrate scheduling method is presented considering geometric error and kinematic constraints for the Non Uniform Rational B-Spline (NURBS) interpolation in five-axis machining. A simplification method is proposed to calculate the geometric error which describes the deviation between the ideal tool path and the real tool path induced by the non-linear movement. A linear relation between geometric error and feedrate is built to limit the feedrate. The constraints determined by single axis kinematic performance and tangential kinematic performance are also considered. Under these constraints, a constrained feedrate profile is determined. Aiming to get more constant feedrate in the difficult-to-machine areas, this work proposes a scheduling method which combines morphological filtering and S-shape acceleration/deceleration (acc/dec) mode. Simulations and experiments are performed to compare the proposed feedrate scheduling method with two previous feedrate scheduling method and the results prove that the proposed feedrate scheduling method is reliable and effective.