最小区域球度误差评价的弦线截交方法

Intersecting Chords Method in Minimum Zone Evaluation of Sphericity Deviation

最小区域球度误差评价是精密测量技术中的一个非常重要并且复杂问题。针对笛卡儿坐标系下球体形状误差评价,介绍一种利用弦线截交关系求解最小区域球度误差评价方法。通过构建笛卡儿坐标系下球度误差测量模型,提出基于一般二次曲面理论的最小二乘球心计算方法。根据最小区域球度误差模型分类,利用弦线截交关系建立起最小区域球度误差评价的2+3和3+2模型,最后通过截交几何模式产生了虚拟中心,从而准确确定球度误差评价模型的最大弦线与最大截面,达到快速精确构建模型的目的。测试数据和实例应用表明,基于弦线截交关系的最小区域球度误差评价方法具有更高的计算效率,且测量空间不受测量坐标系和零件几何形状误差的影响,并显著提高了整体评价的精度与准确性。

Minimum zone evaluation of sphericity deviation is a very important and complex problem in precision measurement technology. For the evaluation of sphere form deviation in Cartesian coordinates, a new minimum zone evaluation method of sphericity deviation using the relationship of intersecting chords is introduced. First, the measurement models of sphericity deviation in Cartesian coordinates are constructed and a calculation method based on general quadratic surface theory is presented for obtaining least square center. Then, according to the classification of minimum zone sphericity deviation models, using the intersecting chord method to build the 2＋3 and the 3＋2 models of minimum zone evaluation of sphericity deviation. Finally, through the intersecting chord geometry model produces virtual center so as to accurately determine the maximum chord and the maximum section of evaluation model, meanwhile, the purpose of fast and accurate constructing model is also achieved. The results and examples indicate that intersecting chord method has high the computational efficiency and the accuracy of evaluation. In addition, the method has little influence on the measurement space from the measurement coordinate system and the geometry form error, which significantly improves the minimum zone evaluation of sphericity deviation.