基于纬线法的鼓形刀具刀位误差分布计算

Calculation of tool position error distribution of barrel cutter based on latitude approach

刀具误差分布是描述刀具表面与设计曲面之间相对位置关系的重要表达方式,在刀具姿态调整与行宽优化中具有重要应用价值。为提高鼓形刀具刀位误差分布的计算效率与精度,提出了一种基于纬线法的新算法,即纬线圆圆心定位法。该方法通过刀具表面一系列纬线圆的圆心来计算刀具表面与设计曲面之间的最短距离,进而求解其刀位误差分布曲线。针对纬线圆圆弧包络法、纬线圆圆弧离散法和纬线圆圆心定位法,讲解了3种计算方法的基本原理,并详细地分析了影响3种方法计算效率与精度的主要因素。然后,对比分析了纬线圆数量对3种方法计算效率与精度的不同影响。最终,利用某叶片零件加工表面进行了实验验证。结果证明,3种算法皆可满足行宽计算误差不大于5%的要求。但是,3种算法中,纬线圆圆弧离散法所需计算时间最长,纬线圆圆弧包络法其次,所需计算时间减少约50%,纬线圆圆心定位法的计算效率最高,所需计算时间减少约80%。在计算精度方面,纬线圆圆弧离散法与纬线圆圆心定位法精度较好且准确度相差不大,但是比纬线圆圆弧包络法精度提升不足5%。

The tool position error distribution plays an important role in the strip-width calculation and the description of the spatial relationship between the cutter surface and designed surface.In order to improve the efficiency and precision about the tool position error distribution calculation of barrel cutter,a latitude circle center location algorithm based on the latitude separation approach is presented in this paper.The shortest distances between cutter surface and designed surface are calculated according to the center of a series of latitude circles in the new algorithm,then the tool position error distribution curve can be obtained.There are three different means dealing with latitude circles,namely latitude circle arc envelope algorithm,latitude circle arc discretization algorithm,and latitude circle center location algorithm.Firstly,the fundamental principles of three algorithms are introduced respectively while the main factors on the calculation efficiency and precision are analyzed.Secondly,the different influences of latitude circle number on the calculation efficiency and precision are compared in three algorithms.Finally,agiven example verifies the validity of the concepts and algorithms in this paper.The results show that the strip-width calculation errors of the three algorithms are less than 5%.The latitude circle discretization algorithm is the most time-consuming,and the calculation time of latitude circle envelope algorithm is reduced by 50% while the calculation time of latitude circle center location algorithm is reduced by 80%.The latitude circle center location algorithm and latitude circle discretization algorithm are similar in terms of the calculation precision,but the improvement of calculation precision is less than 5% compared to the latitude circle envelope algorithm.