基于等参数线法离散NURBS曲面的插补算法

在模具和航空等制造业,常会遇到复杂曲线曲面的数控加工。为满足提高加工NURBS曲线曲面精度和高速加工的要求,提出了将NURBS曲面采用等参数线法离散成一族NURBS曲线的直接插补算法。优点是可将一阶、二阶导矢和控制弓高误差而自动调整进给速度的计算放在插补前的预处理中集中进行。     

数控加工刀具轨迹生成方法探讨

目前，零件造型的方法主要有三种：线架造型、曲面造型和实体造型。在数控加工中，通常采用曲面造型和实体造型相结合的方法来进行。本文就在CAXA制造工程师软件中进行实体造型零件的数控加工曲面时，刀具轨迹生成的方法进行探讨。例中的零件是一个模具型芯，由实体造型方法的拉伸到面的方式生成，如图1所示。该零件上表面的曲面可以采用多种方式进行加工。一、利用参数线加工方法1(1) 单击主菜单中的“应用”→选“轨迹生成”→选“参数线加工”→弹出“参数线加工参数表”对话框，选择和填写参数→按“确定”按钮。(2) 拾取待加工曲面。…     

未知曲面数控加工干涉区域求取算法研究

质量和效率是自由曲面零件数控加工所追求的一对相互矛盾的目标,曲面的分片加工可以较好地解决这这一问题,而自由曲面零件分片加工方法中一个关键问题是如何求取自由曲面的干涉区域,提出了在对自由曲面密集采样测量的基础上,利用未知曲面测点信息,通过参数曲面局部逼近和干涉区域测点问几何关系遍历求取干涉区域的算法,该方法避开了烦琐的自由曲面重建处理,仿真和实验研究的结果验证了算法的有效性。     

基于Z-map模型的自由曲面无干涉刀具轨迹生成算法研究

刀具轨迹生成是自由曲面零件数控加工中重要的研究内容.本文分析了自由曲面数控加工中常用的刀具轨迹生成策略和方法,设计和实现了一种基于Z-map结构的自由曲面无干涉刀具轨迹生成算法.本算法采用进化算法进行刀具干涉检测,不仅解决了生成刀具轨迹时因走刀步长不合理而产生的过切问题,而且也确保了生成的刀具轨迹为无干涉刀具轨迹.     

离散数据复杂曲面的粗加工

提出一种基于离散数据的复杂曲面数控粗加工方法，被加工曲面用多面体模型来描述，采用分层切削方法加工，基于二维等值平面图的拓扑结构，求出各层的有效加工区域，利用数控编程自动生成刀具轨迹。该方法成功地解决了层切法加工复杂曲面时不能处理岛中岛的难题，经实践检验，效果良好。     

MasterCAM编程和CNC数控铣床巧妙结合在雕刻加工中的应用

该文通过对圆弧曲面数控雕刻加工的实例表述,给出了圆弧曲面数控雕刻的编程加工应用步骤,在圆弧曲面数控雕刻加工中,针对于编程软件的特点和数控铣床的特点,采用了灵活实用编程方案和可靠有效的数控加工工艺,从而保证零件加工质量和加工效率,也使企业经济效益和生产水平得以提高。     

曲面数控加工的虚拟仿真实现

本文采用VisualBasic.NET语言编程对AutoCAD2004进行二次开发,对零件模型的表面进行三角形三维面化处理并计算刀具基点空间位置坐标.用刀具模型与零件毛坯模型进行布尔差运算形成过程模型,从而实现了曲面数控加工的虚拟仿真.     

基于数值方法的内超环面齿轮齿廓离散建模

超环面行星蜗杆传动系统中的关键零件内超环面齿轮的齿面是一种复杂的 空间曲面。为了实现复杂曲面的数控加工和采用有限元方法对其进行接触分析时,能否获得 精确的内超环面齿轮的实体模型是解决问题的关键。本文针对内超环面齿轮数字化建模问 题,根据内超环面齿轮的数学模型,对其螺旋齿面进行网格划分,提出基于数值方法的内超 环面齿轮离散建模方法。该方法采用截平面蔟将内超环面齿轮模型离散成数据点云,从而获 得内超环面齿轮离散模型,为后期的复杂曲面插值重构提供了基础。     

应用构形空间理论处理自由曲面加工的干涉问题

文中简述了自由曲面数控另工编程中干涉检查的各种方法，利用构形空间概念，提出一种自由曲面加工的干涉检查算法，该算法先得到刀位面和保护面的离散三角表示，然后根据三角的上包络求刀位轨迹，从而避免干涉，算法适合于用球头刀，圆角刀和平底端刀的任意加工方式的三轴铣削，且实用，稳定，可靠。     

三维复杂型腔的数控加工新方法

提出了一种适用于三维复杂型腔数控加工的新方法，该方法包括偏置曲面求交，偏置曲面裁剪和曲面参数域内刀具轨迹规划等三部分，其中计算刀具定位数据的算法精确，高效，不仅可用于由雕塑曲面构成的复杂型腔的数控加工，也适用于单张曲面的区域加工和组合曲面的三轴数控加工。     

数控加工中加工误差预测模型的研究

提出了一个在球头端铣加工中预测复杂曲面加工误差的理论模型.在理论模型的基础上,计算出了曲面各个部分的由刀具变形引起的加工误差.对影响加工误差的诸如切削模式、铣削位置角、曲面几何形状等各种切削状况进行了研究.最后,使用加工中心,在各种加工状况下.通过一系列实验对理论模型进行了验证.并利用计算机图形学工具对二者进行了建模仿真,结果显示理论值与实验值非常吻合.恰好证明了趣论模型在预测表面加工误差方面的适应性非常好.     

A new Steiner patch based file format for Additive Manufacturing processes

Additive Manufacturing (AM) processes adopt a layering approach for building parts in continuous slices and use the Standard Tessellation Language (STL) file format as an input to generate the slices during part manufacturing. However, the current STL format uses planar triangular facets to approximate the surfaces of the parts. This approximation introduces errors in the part representation which leads to additional errors downstream in the parts produced by AM processes. Recently, another file format called Additive Manufacturing File (AMF) was introduced by ASTM which seeks to use curved triangles based on second degree Hermite curves. However, while generating the slices for manufacturing the part, the curved triangles are recursively sub-divided back to planar triangles which may lead to the same approximation error present in the STL file. This paper introduces a new file format which uses curved Steiner patches instead of planar triangles for not only approximating the part surfaces but also for generating the slices. Steiner patches are bounded Roman surfaces and can be parametrically represented by rational Bezier equations. Since Steiner surfaces are of higher order, this new Steiner file format will have a better accuracy than the traditional STL and AMF formats and will lead to lower Geometric Dimensioning and Tolerancing (GD&T) errors in parts manufactured by AM processes. Since the intersection of a plane and the Steiner patch is a closed form mathematical solution, the slicing of the Steiner format can be accomplished with very little computational complexity. The Steiner representation has been used to approximate the surfaces of two test parts and the chordal errors in the surfaces are calculated. The chordal errors in the Steiner format are compared with the STL and AMF formats of the test surfaces and the results have been presented. Further, an error based adaptive tessellation algorithm is developed for generating the Steiner representation which reduces the number of curved facets while still improving the accuracy of the Steiner format. The test parts are virtually manufactured using the adaptive Steiner, STL and AMF format representations and the GD&T errors of the manufactured parts are calculated and compared. The results demonstrate that the modified Steiner format is able to significantly reduce the chordal and profile errors as compared to the STL and AMF formats.     

A Method for Displaying Metaballs by using Bézier Clipping

For rendering curved surfaces, one of the most popular techniques is metaballs, an implicit model based on isosurfaces of potential fields. This technique is suitable for deformable objects and CSG model. For rendering metaballs, intersection tests between rays and isosurfaces are required. By defining the higher degree of functions for the field functions, richer capability can be expected, i.e., the smoother surfaces. However, one of the problems is that the intersection between the ray and isosurfaces can not be solved analytically for such a high degree function. Even though the field function is expressed by degree six polynomial in this paper (that means the degree six equation should be solved for the intersection test), in our algorithm, expressing the field function on the ray by Bézier functions and employing Bézier Clipping, the root of this function can be solved very effectively and precisely. This paper also discusses a deformed distribution function such as ellipsoids and a method displaying transparent objects such as clouds.     

Self-intersections of offsets of quadratic surfaces: Part II, implicit surfaces

The paper investigates self-intersections of offsets of implicit quadratic surfaces. The quadratic surfaces are the simplest curved objects, referred to as quadrics, and are widely used in mechanical design. In an earlier paper, we have investigated the self-intersections of offsets of explicit quadratic surfaces, such as elliptic paraboloid, hyperbolic paraboloid and parabolic cylinder, since not only are they used in mechanical design, but also any regular surface can be locally approximated by such explicit quadratic surfaces. In this paper, we investigate the rest of the quadrics whose offsets may degenerate, i.e. the implicit quadratic-surfaces (ellipsoid, hyperboloid, elliptic cone, elliptic cylinder and hyperbolic cylinder). We found that self-intersection curves of offsets of all the implicit quadratic surfaces are planar implicit conics and their corresponding curve on the progenitor surface can be expressed as the intersection curve between an ellipsoid, whose semi-axes are proportional to the offset distance, and the implicit quadratic surfaces themselves.     

Tetrahedra Based Adaptive Polygonization of Implicit Surface Patches

This paper presents a tetrahedra based adaptive polygonization technique for tessellating implicit surface patches. An implicit surface patch is defined as an implicit surface bounded by its intersections with a set of clipping surfaces and which lies within an enclosing tetrahedron. To obtain the polygonization of an implicit surface patch, the tetrahedron containing the patch is adaptively subdivided into smaller tetrahedra according to the criteria introduced in the paper. The result is a set of tetrahedra each containing a facet approximating the surface. The intersections between the facets and the clipping surfaces are used to locate the surface patch boundary. Ambiguous results in generating the facets for highly curved surfaces or surfaces with singular points are also addressed. The result of the polygonization is a set of triangular facets that can be used for visualization and numerical analysis. The proposed method is also suitable for locating the intersection of two implicit surfaces.     

Approximate methods for simulation and verification of numerically controlled machining programs

Algorithms for simulation and verification of Numerically Controlled (NC) machining programs are presented. Compared to NC simulation based on conventional solid modeling systems, these models are designed to give approximate results, but with a substantial decrease in computer time. The surfaces of the part are discretized into a Surface Point Set (SPS) with a point spacing dependent on cutting tool size and shape local surface curvature and the desired accuracy of the approximate simulation. The surface-surface intersection calculations of the solid modeling approach are replaced by the intersection of the surface of the tool movement envelope with straight lines emanating from the surface points. The methods are applicable to both 3 and 5 axis machining. Samples test cases are presented, and implementation and efficiency issues are discussed.     

六面体体元网格三维地质模型剖切算法

针对常用的六面体体元网格三维地质模型,提出了一种求剖切面的算法.首先,采用分层投影求交点的方式,将地质体模型与切割面投影到同一平面,三维空间下的地质体模型与切割面的剖切转化为二维平面上的四边形网格与切线段求交点的运算.为减少判交次数,先根据切线走势判断可能存在交点的区域,再对可能区域进行精确判交.其次,找到并求出不能通过投影方式得到的交点.然后,将得到的所有交点按规则组成四边形网格,对每个四边形三角化处理得到TIN形式的剖切面.最后,对该TIN面进行显示.实验证明了对六面体体元网格三维地质模型剖切的可行性.     

曲面实体造型中曲线和曲面交点的求解

求交是曲面实体造型系统中影响拼合算法效率和稳定性的重要因素，而求交算法又是和曲面的几何表示密切相关的。ＮＵＲＢＳ虽然能统一表示所有曲面，但却给二次曲面的求交带来了不必要的复杂性。二次曲面经常在机械零件的设计中被用来描述轴、孔、槽等几何特征，因此它们的求交算法应具有高精度、高效率和高稳定性。为此，对一种实用的二次曲面表示方法——几何法进行了深入研究后，给出了构成二次曲面轮廓的几种二次曲线和空间四次曲线与二次曲面交点的求法。