自由曲面五轴等残余高度高精度加工的路径规划

针对自由曲面的加工，提出了等残余高度的路径规划算法：当刀具沿切削路径运动时，刀刃上与曲面法向距离等于加工精度的点形成了过渡路径；通过此路径求得一条相邻的刀具路径．消除了传统的路径规划算法中对相邻路径的切削方向及局部几何信息的近似，相应地提高了路径规划的精度．实例表明，这对改善刀具路径的精度有很大地帮助．     

数控仿真中的实时碰撞检测算法的研究

碰撞干涉检测是数控加工仿真中的重要组成,文章提出了一种实现数控仿真加工的实时碰撞检测算法,该方法是通过测试线与刀具扫掠体包络面求交的交点来判断刀具或刀柄在加工过程中是否和夹具发生了碰撞,以及碰撞发生在哪些控制代码所对应的刀具移动上;算法的关键在于实时性,满足了数控加工过程中的实时碰撞检测,同时也给出了实例说明了算法的有效性。     

基于改进边界距离变换的路径提取算法研究*

针对虚拟内窥镜中心路径提取算法时间效率不高的问题,通过改进边界距离变换,提出了中心路径的快速提取算法。首先建立最小距离场,在边界内推过程,仅扫描并处理与边界点面连接的点并对其设标记属性,每次向里剥离一层体素标记属性随之增加,直到对内部点集都置到边界的最小边界距离值（DFB）;然后找到DFB值不小于其所有面邻接点DFB值的体素点,即3D局部最大值;最后用最短路径相连3D局部最大值,形成中心线。实验结果表明,改进的中心路径提取算法的时间效率较传统距离变换算法有很大提高。     

利用特征刀位点的三角网格表面NURBS刀轨生成

为了提高数控加工的加工效率和精度,提出一种利用特征刀位点的NURBS刀轨生成算法.采用截平面和三角网格模型的等距模型求交来计算直线刀轨的刀位点,由等距模型的顶点曲率估算刀位点处沿刀轨和刀轨间隔方向的曲率半径,并根据残留高度确定刀轨行距;对基于特征刀位点的NURBS曲线拟合算法进行改进,采用阈值分割的方法选取初始特征刀位点,采用相邻直线段夹角最大原则确定新特征点,并用刀位点的投影点参数对特征点参数进行修正.采用文中算法对直线刀轨的刀位点进行NURBS曲线拟合,并在刀轨行间采用NURBS曲线过渡,以减小数控程序量并提高刀轨光顺性.实验结果表明,文中算法效率高,采用其生成的刀轨具有较少的控制顶点、较高的拟合精度以及较好的光顺性.     

离散曲面的等距面生成算法

离散曲面的等距面生成问题是一个不同于传统的等距面计算的新问题。拟对该问题展开研究并提出一个有效的离散曲面的等距面生成算法。该算法通过计算离散曲面的包络面上的离散体元而生成等距面。所提算法可以有效地解决等距计算过程中发生的拓扑、自相交等现象。实验结果表明了该算法的有效性。     

数控加工中刀具补偿的应用

在数控机床的加工过程中,可以清楚看出刀具（或电极丝、激光等,以下统称为刀具）中心的运动轨迹与工件已加工轮廓不重合,这是因为工件轮廓是刀具以运动包络的方式形成的。刀具的中心（底端面与轴线相交点）称为刀具的刀位点,刀位点的运动轨迹即代表刀具的运动轨迹。     

带折痕的Loop细分曲面等距面处理算法

Loop细分曲面不同细分层次的网格面可作为不同加工工序的加工模型.现有等距面生成算法因未考虑折痕和边界的特殊情况,当折痕或边界存在时将会生成与预期结果有较大差别的等距面.给出了折痕等尖锐特征处极限等距位置的计算方法,以及根据尖锐特征点极限位置反求初始网格等距位置的Gauss-Jacobi迭代公式,并证明了其迭代收敛性.采用文中算法得到的等距网格面令人满意.     

计算多边形交集、并集面积的算法

平面多边形交集与并集面积的计算机算法可以利用多边形裁剪算法来实现。本文提出的算法思想是利用Weiler-Atherton多边形裁剪算法中的多边形链表,在遍历链表时遇到交点就改变跟踪方向,这样可以求出并集顶点表,求交集时只要从入点开始跟踪遇到交点再改变跟踪方向;最后,通过交集和并集表求出它们的面积。多边形可以是凸的或凹的、甚至是带孔的。     

在GPU上实现基于高斯映射的通用刀具扫描体建模

以针对数控加工仿真的需要,以高斯映射理论为基础、GPU为主要硬件平台,提出一种基于并行计算的快速通用刀具空间扫描体建模方法.首先结合通用刀具的数学模型,利用高斯映射理论分析刀具平动时的扫描体建模原理;然后分析刀具做任意空间运动时的刀具表面点法向量和对应的接触映射,推导求解扫描体包络边界的表达式;再根据GPU上的通用计算方法和GPU图形绘制管线设计基于GPU实现刀具空间扫描体建模的算法流程,并利用C++、Open GL和Open GL着色语言GLSL实现了该方法.通过刀具扫描体建模实例,验证了文中方法的正确性与实时性.     

等残留高度曲面加工刀具轨迹生成算法验证

对等残留高度曲面加工刀具轨迹规划方法进行实验,以验证这种算法的有效性.     

Constant scallop-height tool path generation for three-axis sculptured surface machining

This paper presents a new approach for the determination of efficient tool paths in the machining of sculptured surfaces using 3-axis ball-end milling. The objective is to keep the scallop height constant across the machined surface such that redundant tool paths are minimized. Unlike most previous studies on constant scallop-height machining, the present work determines the tool paths without resorting to the approximated 2D representations of the 3D cutting geometry. Two offset surfaces of the design surface, the scallop surface and the tool center surface, are employed to successively establish scallop curves on the scallop surface and cutter location tool paths for the design surface. The effectiveness of the present approach is demonstrated through the machining of a typical sculptured surface. The results indicate that constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches.     

三角网格表面等残留高度刀轨生成算法

针对截平面法规划的三角网格表面的刀轨长度较长、加工表面残留高度不均匀的问题,提出一种基于改进截平面法的等残留高度刀轨生成算法.首先在估算刀触点轨迹线垂直方向曲率半径的基础上,计算刀触点轨迹投影线并对其进行修正,去除其中冗余的投影点;然后由修正后的刀触点轨迹投影线构造驱动表面,利用驱动表面和网格表面迭代计算刀触点轨迹线;最后由刀触点轨迹线计算无干涉刀轨.与截平面法生成的刀轨进行比较分析的结果表明,文中算法生成的刀轨长度较小且获得的残留高度保持均匀,适合于三角网格表面表示的复杂表面的精加工.     

Generating cutter swept envelopes in five-axis milling by two-parameter families of spheres

This paper presents an efficient parametric approach of determining the shape of the envelope surface by a generalized cutter that follows five-axis tool path during NC machining. In this approach the cutter is modeled as a canal surface. By considering the tool motions the cutter is decomposed into a set of characteristic and great circles which are generated by two-parameter families of spheres. The center of a sphere from these families is described by two parameters which represent the spine curve and the tool path, and the radius of the sphere is described by one parameter representing the spine curve. Considering the relationship between characteristic and great circles the grazing points on the tool surface are identified. Analytically it is proven for the NC cutter geometries that any point on the envelope surface is located at the intersection of the characteristic and great circles. Then based on the proofs a closed-form solution for computing the grazing points generated by a surface of revolution is presented. The presented methodology is reduced to a simpler parametric form when the NC cutters are described by pipe surfaces.     

Computing of the actual shape of removed material for five-axis flat-end milling

This paper describes an algorithm that predicts the shape of material removed by a flat-end milling tool, and this may be used to compute machining strip width and scallop height at different positions of the tool path track. The algorithm computes swept sections, profiles which are swept by a moving tool bottom by passing through given planes. The technique is applicable for finish and semi-finish multi-axis milling strategies that use flat-end tools. For these strategies, the algorithm complexity can be reduced from computation of the 3D envelope of swept volumes to computation of plane-circle intersections. A new adaptive derivative-free method to sample tool motion provides robust means to generate intermediate tool positions. The step length is constrained by and dependent on different geometrical measures. At each point of a tool path, in the plane perpendicular to the cutting direction, the bottom profile of the swept section is an estimate of the profile of material left. By calculating the distance between part geometry and the computed profile of removed material, machining strip width and a scallop profile can be derived. These results can be used by tool path generation and validation routines to accurately determine the step-over between tool path tracks and surface quality.     

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.     

复杂三角网格模型刀具组合优化加工研究

在满足复杂三角网格模型数控加工的精度要求下,为提高加工效率,提出了刀具组合优化方法。该方法以刀具轨迹长度最短为目标,并综合考虑模型微分几何信息对加工效率和精度的影响。首先根据面片法矢和曲率将模型分割为多个特征子区域,不同类型的特征子区域采用不同的刀具轨迹生成策略;建立各类型子区域的精确轨迹长度估算模型;选取合适的标准刀具组合并估算轨迹长度,拟合三次B样条曲线,求取曲线一阶导矢得到最小值,选择对应的标准刀具尺寸作为最优刀具尺寸。算法在VC++环境下进行了编程实现和算例验证,结果表明该方法是可行有效的。     

Tool-path generation from measured data

Presented in the paper is a procedure through which 3-axis NC tool-paths (for roughing and finishing) can be directly generated from measured data (a set of point sequence curves). The rough machining is performed by machining volumes of material in a slice-by-slice manner. To generate the roughing tool-path, it is essential to extract the machining regions (contour curves and their inclusion relationships) from each slice. For the machining region extraction, we employ the boundary extraction algorithm suggested by Park and Choi (Comput.-Aided Des. 33 (2001) 571). By making use of the boundary extraction algorithm, it is possible to extract the machining regions with O(n) time complexity, where n is the number of runs. The finishing tool-path can be obtained by defining a series of curves on the CL (cutter location) surface. However, calculating the CL-surface of the measured data involves time-consuming computations, such as swept volume modeling of an inverse tool and Boolean operations between polygonal volumes. To avoid these computational difficulties, we develop an algorithm to calculate the finishing tool-path based on well-known 2D geometric algorithms, such as 2D curve offsetting and polygonal chain intersection algorithms.     

Direct 5-axis tool-path generation from point cloud input using 3D biarc fitting

In reverse engineering, geometrical information of a product is obtained directly from a physical shape by a digitizing device. To fabricate the product, manufacturing information (usually tool-path) must be generated from a CAD model. The data digitized must be processed and in most cases, a surface model is constructed from them using some of the surface fitting technologies. However, these technologies are usually complicated and the process for constructing a surface patch from a massive digitizing data is time-consuming. To simplify the process for getting tool-path information, a simple algorithm is proposed in this paper. The algorithm is used to generate a 5-axis machining tool-path. Instead of implementing any complicated surface fitting techniques, a direct method is proposed for constructing three-dimensional (3D) triangular mesh from the digitizing data with the mesh points considered as the tool contact locations. Depending on the locations of the points digitized, a decimation procedure is applied such that some of the digitizing data will be filtered out. Then, the tool axis orientations which must be determined in 5-axis tool-path are calculated and the tool center locations are determined accordingly. A 3D biarc fitting technique is applied for all the tool center locations so that a complete 5-axis tool-path is obtained.     

A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining

Geometrically, a tool path can be generated by successively offsetting its adjacent path on the surface with a given path interval, which preferably starts from one of the surface boundaries or a primary curve. The key issues involved in offset path planning are the generation of raw offset paths and the elimination of the self-intersection of raw offset paths. Most researches available in this area are focused on how to generate the raw offset paths, however, the latter, especially how to eliminate the self-intersection of the offset paths on mesh surfaces, has not been sufficiently addressed. In this paper, a mapping-based approach to eliminating the self-intersection of offset paths is proposed for the CNC machining of mesh surfaces. The method first flattens the mesh surface onto a predefined plane by using a mesh mapping technique, and then taking the mapping as a guide, the offset paths are also naturally mapped onto the plane, from which those invalid self-intersection loops can be effectively identified and eliminated. To handle the issue of self-intersection for all types of offset path, a notion of local loop is introduced to detect and eliminate the invalid self-intersection loops. After that the planar paths are inversely mapped into the physical space and the final tool paths used for the machining of mesh surface are obtained. Meanwhile, in order to improve the kinematic and dynamic performance of the machine tool when machining along the generated offset paths, a method for rounding the sharp corners of tool paths, which result from the process of eliminating the self-intersection of raw offset paths, is also preliminarily investigated. Finally, the proposed method is validated by the results of simulations and machining experiments.     

一种基于STL模型的5轴高速加工刀轨优化策略

针对线性插补刀轨不连续且插补点多的缺点,提出了一种基于STL模型的口腔修复体5轴高速铣削数控加工刀轨优化策略。以去除不必要的插补点,简化加工刀轨的数量,优化刀轴矢量包络的曲面为平滑变化的规则面,实现了一种支持HEIDENHAIN数控系统的样条插补新方法。运用该策略线性插补的G代码成功地被转换成样条代码,基于Vericut仿真器,仿真加工出了磨牙冠修复体。结果表明,该优化策略不仅能缩短切削时间、提高加工质量,而且可避免切削颤振。