【作者】 孟兰会；

【导师】 孙玉文；

【作者基本信息】 大连理工大学 ， 机械设计及其理论， 2006， 硕士

【摘要】 近年来,关于自由曲面的刀具轨迹规划问题的研究已经很深入,但是针对离散三角网格曲面的规划方法并不多,通常只有等截面法,往往不能满足实际加工的需要。针对于此,本论文提出了一种基于映射建模的刀具轨迹规划方法,其基本思路是先选择恰当的映射方法将离散三角网格映射到参数曲面,在参数域进行轨迹规划,然后将生成的轨迹映射回原三角网格曲面,即得到所需的刀具轨迹。 首先,探讨了映射方法的选择。此步骤是整个规划方法的基础。协调映射因为具有变形小、网格不会重叠等优点,被作为最佳选择。根据协调映射的理论,建立了平面上圆形域、矩形域、多边形域等参数域的映射模型,可根据轨迹规划的需要来选择映射的边界。由于协调映射时所需处理的数据量很大,本文给出了编程时具体的数据结构,其中大型稀疏矩阵采用三元组压缩存储。 其次是在参数域上规划刀具轨迹,并提出了一种基于平面螺旋线制导的螺旋型刀具轨迹的生成新方法。针对网格曲面,建立了曲面上任一点处的法矢和曲率的计算模型,进而确定网格曲面路径间距及步长,建立相应的计算模型。根据协调映射及相关理论,建立了原网格曲面和参数域曲面的路径间距及步长的对应关系。采用B样条技术,实现了离散型刀触点轨迹的解析表达。 最后,为生成原网格域上的刀具轨迹。根据协调映射求解得到其逆映射,将刀触点轨迹由参数域逆映射回网格曲面。还给出了三角形面积坐标法简化此步骤。根据所选择的刀具——平底刀,推导得到刀触点转化为刀位点的公式,建立计算模型。并对干涉问题进行研究,探讨调整刀轴矢量来解决干涉的问题。最后根据模型将刀触点轨迹转化为刀位点轨迹,即刀具轨迹。 本方法还可以生成等参数线轨迹、Piano轨迹等轨迹,对其具体应用作了进一步的探讨。本文还就所列出的轨迹线的类型给出了相应的例子。随后根据一个实例——自行车座,给出了螺旋型轨迹、等参数线轨迹以及截面线轨迹。通过编程进行了轨迹线的长度和加工时间的仿真,并且就所得试验结果进行分析,给出结论。更多还原

【Abstract】 Significant research has been carried out to generate tool path for free-form surface recently. However few of them are for triangular meshes except iso-planar tool path. It can’t satisfy all demands for machining. So this paper presents a method of generating tool path for triangular meshes based on maps. The method’s main process is mapping triangular meshes to parameter region by conformal maps firstly, generating tool path on parameter region secondly and finally mapping tool path back from parameter region to triangular meshes.Firstly, the choice of maps is discussed. The map is the foundation of the whole method. Conformal map is the best choice because it has merits such as little deformation and no grid overlapping, etc. Based on the theory of conformal map, map model is built for planar parametric circle, rectangle and polygon regions. The boundary of parametric region rests with the need of tool path planning. The data structure is presented for the vast data while constructing conformal map. The large-scale sparse matrix is stored as three-number sets.Secondly, tool path is generated in parametric region and a new method for generating spiral tool path guided by spiral in planar is presented. A mathematic model is established to calculate normal vector and curvature of a point on the triangular surface. The calculating model for path interval and step length is developed, too. According to conformal map and relative theory, the relation of path interval between triangular meshes and parametric region is built. Adopting B-spline technology, it is implemented to analytic expression of discrete cutter contact tool path.Finally, tool path is generated on triangular meshes. Cutter contact tool path is mapped from parametric region to triangular meshes by means of conformal map and its reverse map. It can be easily solved by barycenter coordinate, too. The formula is given for calculating cutter location point from cutter contact point. The problem about interference is discussed and solved by adjusting the vector of tool axe. Lastly, cutter location points are calculated according to the calculating model.By using this method, it can generate iso-parametric tool path, Piano tool path, etc. This method’s application is deeply discussed and corresponding examples are given. Taking the bicycle seat as an actual example, the spiral tool path, iso-parametric tool path and iso-planar tool path are generated. In addition, every kind of tool path’s length and machining time are simulated and the comparison result is analyzed to draw the conclusion.更多还原