B样条曲面造型设计新方法的研究

根据构造均匀双三次Ｂ样条曲面的基本理论，提出用扫描变换形式自动获取Ｂ样条曲面的特征网格顶点信息及直接生成各种Ｂ样条曲面的新方法，并研究其实用程序设计方法。     

NURBS曲面造型中曲线曲面分割问题的研究

提出一种基于ＮＵＲＢＳ齐次坐标表示来计算曲线曲面分割问题的方法,把ＮＵＲＢＳ总是转化为四维空间非有理Ｂ样条问题,就用Ｂ样条分割算法来解决,其几何意义明确,求解过程简便易行,便于在ＣＡＤ／ＣＡＭ系统中实现。     

用于非均匀有理B样条曲面裁剪的扫描线算法

提出一种用于非均匀有理B样条曲面裁剪的算法。首先在非均匀有理B样条曲面的参数域中定义曲面的裁剪曲线;然后自上而下地分析曲面参数域中的每一条U（或V）向线段（扫描线）;通过这些扫描线与裁剪曲线的相交关系来判定曲面的裁剪域;再将其映射到三维空间中;从而显示出裁剪操作的结果。由于可以通过定义扫描移动最小步距值来控制曲面裁剪操作的精度;该算法适用于各种精度需求的裁剪操作场合。此外;也可以根据需要对扫描进行定位操作来实现各种裁剪特效。     

曲线曲面的B3样条拟合及其实现

在计算机辅助几何设计(CAGD)中,曲线、曲面拟合多采用多项式作为基函数,本文通过几种曲线、曲面生成算法分析,提出了一种B3样条的拟合方法.它具有B样条的主要优点,耳通过所有型值点,这一方法适用于自由曲线、曲面的设计.还结合拱坝体形设计实例说明了用此方法进行造型设计的技术.     

B样条曲线的局部自动光顺算法

针对工程上广泛应用的Ｂ样条曲线,给出了一种新的曲线局部自动光顺算法。该算法基于Ｂ样条曲线的曲率,提出两种光顺度的概念,并据此建立曲线的几何光顺准则,通过自动搜寻光顺点,重复删除与插入这些光顺点,便可使Ｂ样条曲线满足光顺性要求。     

自由曲线曲面造型技术的综述

随着航空、造船等行业的发展,对曲线曲面造型技术提出了更高的要求。论述了曲线曲面造型技术的产生、发展及其应用过程和曲线曲面造型技术的现状以及发展趋势,介绍了几种CAD/CAM系统的曲面功能。     

高次曲线的B样条插值

在激光切割加工的工件轮廓中,有些是由复杂的参数曲线构成。用传统的直线或圆弧插值,由于在分割节点附近进给量波动,使高速切割的效果欠佳。若采用B样条插值,然后实现B样条的直接插补,就能够解这个问题。B样条曲线是一种CAGD形状数学描述的基本方法。它具有局部性、几何不变性以及造型灵活性等优点,更重要的是它的连续性,B样条曲线是分段曲线,在每一段内部无限次可微,在曲线段的端点处为(n—r)次可微(n为样条曲线次数,r为该端点的重复度)犤1犦。因此考虑用三次B样条曲线对高次曲线进行插值。1型值点的生成根据函数的几何特性,可以将整条…     

曲面上曲线的精确及近似求解法

在计算机辅助几何设计领域，曲面上曲线是非常重要的一个元素。鉴于它的重要性，提出了一种计算曲面上曲线的方法。在求出曲面上曲线后，利用曲线逼近的原理，再求出曲面上曲线的近似解。     

NURBS曲线,曲面造型过程的可视化设计

由于ＮＵＲＢＳ曲面,曲线构造的复杂性,描述ＮＵＲＢＳ曲线,曲面必然采用复杂的数据结构,这样给人－机交互带来很大的困难。本文利用ＶＣ＋＋编写的ＮＵＲＢＳ曲线,曲面造型系统可以实时观察曲线等操作,这对ＮＵＲＢＳ曲线曲面造型无颖 会带来极大的方便。     

B样条曲面的T样条裁剪法

针对B样条曲面裁剪法中的裁剪曲面定义与裁剪边界修改问题,提出一种T样条曲面裁剪法,并用于多边矩形域上的曲面裁剪。先将B样条曲面转换为一张全行列T样条曲面,然后再利用T样条曲面的局部均匀细分和控制点移除,得到一张T样条裁剪曲面。裁剪后的T样条曲面建立在一个多边T网格上,具有完整的曲面定义,并且可以局部修改其裁剪边界。最后通过实例验证了T样条裁剪曲面在曲面定义和边界修改上都优于B样条裁剪曲面。     

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented.The symme- try property is realized by using symmetric knot vector and symmetric control points.Firstly,data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points.Then the divided data points are pararaeterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions.Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane.Lastly,the constrained least squares fitting problem is solved with the Lagrange multiplier method.Two examples from industry are given to show that the proposed method is efficient,robust and able to meet the general engineering requirements.     

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.     

FAIRING TECHNIQUE OF THE CURVES AND SURFACES IN INDUSTRIAL STYLING DESIGN

To many industrial products such as cell phone, family appliance, vehicle, a pretty shape of nice visual effect is indispensable. To fulfill this target, designers are endeavoring to make the curve and surface of the products smooth and continuous during the shape design. Through the analysis and generalization of the present smoothing methods, the energy optimization method which combines the merits of energy method and least squares method together is studied, the target function of energy optimization method is derived, the solution to the target function and steps of curve fairing is introduced, the skills and methods building A-class surface which are based on cloud data measured from 3D scanning are studied, the validity of energy optimization method is verified with the example of the shape design ofa mini-EV as well.     

TOOTH CURVES AND ENTIRE CONTACT AREA IN PROCESS OF SPLINE COLD ROLLING

In spline rolling process, the contact area between roller and workpiece plays an important role in calculating rolling-force and rolling-moment. For the purpose of studying the contact area, contact state between roller and workpiece in process of spline cold rolling based upon cross rolling is analyzed. According to the suitable hypothesis, the mathematic model of roller-tooth-curve in optional position of rolling process is established. Combing the theory of conjugate curves with the theory of envelope curve, the corresponding mathematic model of workpiece-tooth-curve is established. By utilizing establishing mathematic models, the algorithm of entire contact area in rolling process is created. On the basis of the algorithm, calculation-program is compiled under MATLAB program language environment. The calculation-program actualizes quantitative analysis and quantitative calculation of contact areas. Utilizing the calculation-program, the influence of parameters on contact area is analyzed, and the tendency is consistent with the manufacturing experience. In consideration of rolling-force optimization, the primary process parameters may be selected according to results of calculation. The result of the present study may provide basis for research on rolling-force and rolling-moment.     

基于力密度方法的NURBS曲线和曲面变形框架

提出基于力密度方法的统一求解策略,实现NURBS曲线和曲面的精确变形.将控制网格类比为空间索网结构,分别建立外载荷变化最小、外载荷最小、杆阻尼长度最小和节点位移最小等四种表达不同几何和物理意义的最小化模型来驱动变形,并以控制顶点在变形前后的位移为变量,建立统一表达的目标函数方程,便于多个最小化模型组合使用,满足特定的变形需要.由于目标函数的二次性以及约束的线性化处理,优化问题可以通过Lagrange乘子法转化为线性问题进行求解.在计算中引入目标函数快速求解算法,使变形设计可以满足实时交互操作的需要.应用实例表明,该算法可以应用于细节特征设计和反求建模等复杂曲面造型.     

PRINCIPLE AND TRANSMISSION TECHNOLOGY OF BERTRAND CONJUGATE SURFACES

Bertrand surface is presented by abstracting and subliming the common characteristic of the usual surfaces including rotational surfaces, developable surfaces, normal circular-arc surfaces, etc. Basic characteristic of Bertrand surface is that normals along generator are coplanar. Bertrand conjugate principle is studied and its basic characteristic is that the instantaneous contact line between a pair of Bertrand conjugate surfaces is generator. Bertrand conjugate can be divided into three kinds of typical conjugation forms in terms of the generators that are general plane curve, circular-arc and straight line. Basic conjugate condition is given respectively, and structure condition, which reflects transmission forms and directrix characteristic of this kind of conjugation, is researched. As typical engineering application of Bertrand conjugate surface principle, transmission technology of loxodromic-type normal circular-arc bevel gear is studied.     

EXPERIMENTAL STUDY ON OPEN－DIE COLD EXTRUSION FORMING TECHNIQUE FOR INVOLUTESPLINE SHAFTS

ＥＸＰＥＲＩＭＥＮＴＡＬＳＴＵＤＹＯＮＯＰＥＮ－ＤＩＥＣＯＬＤＥＸＴＲＵＳＩＯＮＦＯＲＭＩＮＧＴＥＣＨＮＩＱＵＥＦＯＲＩＮＶＯＬＵＴＥＳＰＬＩＮＥＳＨＡＦＴＳＥＸＰＥＲＩＭＥＮＴＡＬＳＴＵＤＹＯＮＯＰＥＮ－ＤＩＥＣＯＬＤＥＸＴＲＵＳＩＯＮＦＯＲＭＩＮ...     

多轴机床加工复杂自由曲面的刀底干涉避免

为快速、有效地解决复杂自由曲面加工中存在的刀底干涉问题,通过刀底干涉特征分析,得出能否快速、有效地划分出刀底干涉范围是影响刀底干涉避免总体效率和精度的关键。其次,以切削点的局部几何性质为基础, 提出了刀底干涉范围的快速划分方法。第三,以切削点的切平面为媒介定义了刀底干涉特征点,该干涉特征点与刀具的刀轴矢量无关,因此这些干涉特征点既可作为初始刀轴定位的依据又可作为刀轴调整的约束。同时又构造了刀底干涉特征点的快速搜索算法。以搜索的少量干涉特征点为基础,最终得出了无刀底干涉的快速刀轴定位算法。实例分析表明,算法的应用不仅能快速、有效地解决刀具加工自由曲面的刀底干涉问题,而且刀底干涉特征点的存在也为其他形式的干涉避免打下了坚实基础。     

MECHANICS ANALYSIS ON PRECISE FORMING PROCESS OF EXTERNAL SPLINE COLD ROLLING

According to the suitable assumption, the deformation process of external spline cold rolling is analyzed. By the graphing method, the slip-line field of plastically deforming area in process of external spline cold rolling is set up. Different friction-conditions are used in different contact areas in order to realistically reflect the actual situation. The unit average pressure on contact surface of the rolling process is solved according to the stress filed theory of slip-line. And the formulae of the rolling-force and rolling-moment are established. The theoretical result is well consistent with the finite element analysis. A theoretical basis is provided for the precise forming process of spline cold rolling and the production of external splined shafts.     

模具曲面抛光时表面去除的建模与试验研究

提出用表面去除廓形来描述模具表面在垂直于抛光轨迹方向的抛光去除量。在假设抛光工具与模具自由曲面的接触服从椭圆赫兹接触的前提下,利用提出的抛光去除系数推导了表面去除廓形的理论方程。仿真和试验结果揭示了抛光表面去除的规律,验证了表面去除廓形的理论模型。