基于三维凸包的公差基准平面拟合方法

发布时间：2018-06-11 20:46

本文选题：基准平面 + 拟合　；参考：《机械工程学报》2015年23期

【摘要】：针对目前基于离散采样点进行基准平面拟合时没有考虑基准平面受约束的问题,提出一种基于三维凸包的带约束的基准平面拟合方法。该方法利用计算几何中的凸包理论,使用增量算法快速构建平面特征离散采样点的三维凸包。其次根据基准平面的定义,确定基准平面处于不同基准优先级时被其他基准特征约束的自由度以及建立基准的方法。在此基础上利用三维凸包建立基准平面无约束、转动约束、平动约束的数学模型,结合基准的相关实体要求实现了基准平面变动空间的求解。试验结果表明:采用一组采样数据建立基准平面时,所提出的算法与传统的最小二乘法进行比较更加符合基准平面的建立原则,保证了基准平面的准确性,满足了工程需求。
[Abstract]:In order to solve the problem that the reference plane is not constrained when fitting the datum plane based on discrete sampling points, a method of fitting the datum plane with constraints based on 3D convex hull is proposed. Based on the convex hull theory in computational geometry, the incremental algorithm is used to construct the 3D convex hull of discrete sampling points with plane features. Secondly, according to the definition of the datum plane, the degree of freedom of the datum plane being constrained by other datum features and the method of establishing the datum are determined when the datum plane is at different datum priority. On this basis, the mathematical model of the unconstrained, rotational and translational constraints of the datum plane is established by using the three-dimensional convex hull, and the solution of the variable space of the datum plane is realized according to the requirements of the datum entities. The experimental results show that when a set of sampling data is used to establish the reference plane, the proposed algorithm is more in line with the principle of establishing the reference plane compared with the traditional least square method, which ensures the accuracy of the reference plane and meets the engineering requirements.
【作者单位】：北京理工大学机械与车辆学院;
【基金】：国家自然科学基金(51275047) 国防基础科研(A2220110008) 总装预先研究(51318010102)资助项目
【分类号】：TG801

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