叶片类复杂型面电解加工的等几何数值分析方法研究

以航空发动机涡轮叶片的电解加工为研究对象,研究了其加工间隙的基于NURBS基函数的参数化几何建模方法,用以更好的逼近表达叶片的复杂边界曲面。建立了加工间隙内电场分布的数学模型,分析了加工间隙阴极工具和阳极叶片工件需要满足的边界条件,利用与几何建模相同的NURBS基函数作为逼近电势分布解空间的基函数。解决了边界条件施加时的非插值性困难。最后通过实验证明了等几何法在叶片电解加工中较传统有限元法具有统一数学模型,收敛速度更快等优势。     

基于等几何拓扑优化的柔性机构设计

等几何分析能够将几何建模的基函数与结构数值分析的形函数统一,从而得到高精度的结构数值分析结果。面向柔性机构,提出了一种基于等几何拓扑优化的柔性机构设计方法：通过NURBS基函数和Shepard函数构造增强密度分布函数,该函数的高阶连续性可确保优化结构边界的光滑清晰;然后根据密度分布函数建立柔性机构的等几何拓扑优化模型;最后,将该方法应用于柔性机构设计。通过算例结果可知,等几何拓扑优化方法特有的计算原理可提高数值计算的精度和效率,能有效避免由网格依赖、棋盘格现象等产生的边界问题,确保了优化结构均具有较好的光滑性和连续性,验证了提出的方法能有效避免柔性机构的铰链现象。     

基于等几何边界元法和粒子群优化算法的结构形状优化

等几何边界元法是将计算机辅助几何设计(CAGD)中描述几何边界的非均匀有理B样条(NURBS)基函数作为边界元法中的形函数。该方法不仅能精确地描述几何边界,且几何设计、仿真分析和形状优化采用统一的数学描述即NURBS,从而避免了重复地划分网格和优化中的网格畸变问题,提高设计、仿真和优化效率。本文将等几何边界元法和粒子群优化算法相结合,讨论了二维线弹性结构的形状优化。相对基于梯度的优化算法,无梯度的粒子群优化算法可以避免繁杂的敏感性分析过程,使优化的实现过程更为简便。数值算例验证了基于粒子群优化算法的等几何边界元法在结构形状优化中的有效性和精度。     

采用非线性电解液的叶片电解加工阴极设计

工具阴极设计是航空发动机叶片电解加工工艺过程中的关键环节。本文采用有限元数值算法求解加工间隙内的电场分布,考虑非线性电解液对成型规律的影响,进行叶片的阴极设计计算。对加工间隙分布的分析表明,将非线性电解液的影响带入阴极求解中,能使所研究的问题更接近实际情况,从而能提高阴极设计的精度。     

高频窄脉冲电流电解加工叶片过程的耦合场数值模拟

与传统直流电解加工相比,高频窄脉冲电流电解加工在复制精度、重复精度、表面质量、加工效率、加工过程的稳定性等方面均有显著提高,特别适用于要求高精度和高表面质量的具有复杂几何轮廓零件的精密加工。文中在建立叶片电解加工区域二维模型的基础上,分别进行了直流电解加工和高频窄脉冲电流电解加工的电场与流场的耦合数值模拟,对比结果验证了高频窄脉冲电流电解加工较传统直流电解加工的优越性。     

发动机叶片电解加工变间隙阴极修正法

为了提高叶片电解加工的精度,提出变间隙阴极修正方法,建立该方法数学模型,分析加工间隙与阴极修正量的对应关系,通过在型面误差中代入间隙补偿量来修正阴极。提出阴极沿型线修正量的计算公式和插值逼近的试验方法。结合自行研制的新型叶片电解加工机床,进行了叶片电解加工阴极修正的试验,通过变间隙修正方法修改阴极。试验过程中阴极经过3次计算机修正,可使叶片电解加工精度提高到0.05 mm,表明该阴极修正方法合理有效,数学模型与试验情况吻合。     

航空叶片电加工多物理场耦合仿真及实验研究

针对涡轮转子叶片电解加工过程参数分布复杂、型面难以预测的问题,分析电解加工过程中电场、流场、温度场特性,建立多场耦合数学模型并利用Matlab ode45函数求解多物理场耦合数值解;利用COMSOL软件对叶片电解加工过程多物理场进行数值模拟,得到加工间隙内电解液流速、温度、电解质电流密度的分布规律;选择合适的工艺参数完成了Inconel 718叶片电解加工试验,用三坐标测量机得到叶片轮廓曲线的实测值,与单电场仿真的理论值与多物理场耦合后仿真的理论值进行对比。结果表明,多物理场耦合仿真的理论值更接近于试验检测的实测值,能够准确模拟实际电解加工过程,可以为实际加工过程阴极工具设计、参数优化等提供理论依据,对提高电解加工质量和效率有重要意义。     

基于NURBS曲线的数控机床几何误差实时补偿研究

阐述了一种基于NURBS曲线的数控机床几何误差补偿技术,利用误差模型计算预设的NURBS路径与控制点之间的位置偏移能得到NRUBS误差补偿函数控制点,通过插入新的节点产生新的函数控制点,并提高NURBS曲线表达误差补偿函数的柔度,从而得到更高的补偿精度。结果表明,在公差精度为0．00057mm的情况下,沿3种不同工作路径的误差补偿精度都小于1mm。     

混气电解加工探讨

电解加工是利用金属在电解液中发生阳极溶解反应而去除工件上多余的材料、将零件加工成形的一种方法。电解加工的加工精度不仅与加工间隙有关,还与机床、工艺装备、工具阴极、工件、工艺参数等诸多因素有关,通常采用混气电解加工、脉冲电解加工、小间隙电解加工和改进电解液等措施提高加工精度。其中混气电解加工是将具有一定压力的气体与电解液按一定比例混合在一起,然后将这种混合物加入到工件的加工间隙中去进行电解加工的一种方法。混气电解加工可以缩小加工间隙,提高电解加工的加工精度和复制精度,但混气电解加工的微观不平度和不直度还不理想。从气液混合比、混气电解加工的特性以及混气电解加工的工艺三个方面对混气电解加工的原理进行一定的探讨,希望摸索一种提高电解加工精度的方法。     

电解加工微小孔误差分析及特征检测研究

针对电解加工微小孔特征检测问题,对影响加工精度的因素、特征检测方法、数字图像处理等问题进行了研究,对电解加工时工作圈长度与径向间隙、孔内电解液体积之间的函数关系进行了归纳,提出了一种基于Matlab数字图像处理技术的微小孔特征检测方法;对电解加工得到的微小孔图片进行了滤波、去噪、边缘检测和特征提取,得到了所加工微小孔圆度、锥度、粗糙度等几何特征参数值,根据检测结果定量评定了加工误差,及时调整了电解加工时的各项参数。研究结果表明:该检测方法设计合理,错检率、漏检率低,检测时间短。     

等几何分析中Dirichlet边界条件的配点施加方法

相对于传统有限元,等几何分析使用NURBS基函数统一表示几何和分析模型,它能消除传统有限元的网格离散误差,容易构造高阶协调单元。但是由于NURBS基函数缺乏插值性,控制顶点也不一定位于几何边界上,使得难以直接施加Dirichlet边界条件。针对这一问题,提出一种基于样条拟合的Dirichlet边界条件施加方法,通过引入一组边界配点来拟合边界条件。注意到不合适的配点策略会使得边界插值方程组奇异或者条件数过大,详细讨论配点选取的基本准则,提出两种鲁棒的配点方案:Greville横标和Chebyshev插值点法。并且将配点方法扩展到最小二乘形式,设计一种快速的场变量消去算法。通过实例验证上述方法的可行性和有效性。试验结果表明,各种配点策略的收敛率基本保持在一个量级,因此配点法的关键是选择稳定的配点方案。     

Isogeometric bending analysis of composite plates based on a higher-order shear deformation theory

This research paper presents an isogeometric plate finite element formulation for analysis of thick composite plates. Isogeometric finite element method which is based on non-uniform rational B-splines (NURBS) basis functions, is a novel numerical procedure developed to bridge the gap between CAD and FEM modeling of structures. In order to investigate the behavior of isogeometric plate elements under static loading, plate kinematics is based on third order shear deformation theory (TSDT) of Reddy, which is free from transverse shear locking. This paper discusses accurate transverse stress recovery procedures for TSDT isogeometric finite elements. Numerical experiments with quadratic, cubic and quartic elements are presented and obtained results are compared to other available ones.     

A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry

In an attempt to construct an isogeometric analysis-suited geometry for isogeometric analysis, a new surface parameterization method using the one-step inverse forming (SPIA) is proposed. Initial generation of watertight analysis-suitable geometry (NURBS surfaces) with complex shapes can be a significant bottleneck for isogeometric analysis because computer-aided design models often include ambiguities such as gaps and overlaps. Most of traditional surface parameterization techniques are based on geometric method and limited to finite meshes, while SPIA is a physics-based method using sheet metal forming technique with large elastic–plastic deformation and robust enough and rapid to deal with the finite elements mesh with over 100,000 nodes within 2 min without the necessity to simplify the meshes. Using Coons surface parameterization, global mesh parameterization, and NURBS reconstruction, we can rebuild new computer-aided design models with errors under any tolerance to which isogeometric analysis can be applied. The NURBS surfaces after reconstruction are also used for computer-aided manufacturing.     

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.     

基于等几何分析的自由曲面壳体包容式节点力学分析方法

包容式节点作为一种曲面壳体结构的新型节点,展示出优越的抗疲劳力学性能及承载能力.文中针对包容式节点曲面渐进优化设计过程中有限元网格不易调整等问题,将等几何分析理论引入包容式节点这类自由曲面壳体结构的分析.首先从包容式节点曲面的NURBS曲面模型出发,基于Reissner-Mindlin退化壳理论,建立对应的壳体单元,然...     

雷诺方程的数值计算方法概述

作为流体力学中的基本公式,雷诺方程的数值求解一直是流体润滑领域研究的重要方向之一。以雷诺方程的基本形式为基础,分别介绍有限差分法、有限元法和有限体积法求解雷诺方程的过程,讨论各自的特点及存在的问题;介绍多重网格法同上述方法结合在求解雷诺方程中的应用,指出多重网格法在求解雷诺方程的高效性方面有了很大程度的突破,但在求解精度上并未有显著改善;讨论等几何分析方法在求解雷诺方程上的应用,指出等几何分析方法求解雷诺方程具有较高的效率和求解精度,但仍存在如样条基函数的不可插值性和IGA在雷诺方程求解方面的普适性等问题,探讨IGA的研究方向,如针对特定雷诺方程引入适于IGA的新型样条表征求解空间、修改IGA理论与雷诺方程的离散模式引入新型边界条件加载模式等;因数值求解雷诺方程时在边界处理、复杂求解域等问题上仍没有一个稳定适用面广的方法,建议可尝试联合IGA与多重网格法来求解雷诺方程,以进一步提高求解效率和精度。     

求解复杂轴扭振动力特性的一种近似分析方法

应用模态摄动法求解非均质变截面复杂轴的扭转振动的模态特性。在这一方法中,选择与复杂轴约束条件相同、等截面均匀轴的扭转振动解析模态函数作为近似分析的基函数,采用Ritz展开和摄动分析相结合的方法,把复杂轴扭振的变系数微分方程的求解,转化为一组代数方程组的求解。虽然这一方法应用了结构振动分析中常用的Ritz展开原理,但避免了关于模态广义坐标的特征值问题的求解,通过代数方程组的求解,可逐一求得复杂轴的扭转振动的模态特性,简化了求解的难度。通过2个算例的分析表明,该方法简单实用,且具有较高的精度。     

Laminar and turbulent channel flow simulation using residual based variational multi-scale method

We present a residual-based isogeometric variational multiscale method to solve laminar and turbulent channel flow. Residual-based variational multiscale method is a new finite element formulation for solving turbulent flows using a large-eddy simulation type modeling. Isogeometric analysis, a new finite element method using CAD blending functions as its basis functions, is employed for higher order approximation of the solution. First, laminar flow with Re _τ 0.55 = through flat channel is considered and linear, quadratic and cubic basis functions, which are C ⁰, C ¹, and C ²-continuous across element boundaries, respectively are employed and their accuracy is presented by the comparison with analytical result. Next, same methodology is applied to the turbulent channel flow with Re_r = 180. Current results are validated by the comparison of turbulence statistics using available DNS data.     

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.     

基于灵敏度分析的三维结构等几何形状优化方法

以等几何分析为数值分析方法,针对三维结构的线弹性问题,以优化边界控制点坐标为设计变量,通过Coons体插值方法得到插值控制点对优化边界控制点的坐标导数,推导了单元刚度矩阵对控制点坐标变量的形状优化灵敏度方程,并对应力灵敏度和位移灵敏度方程进行了推导。数值算例证明该方法具有较高的优化效率,优化结果良好。