双球渐开线样板的理论分析和应用

Theoretical analysis of double-ball artifact and its applications

为确保齿轮测量仪器的高精度校准,国际标准ISO/TR 10064-5:2005推荐了新型的双球渐开线样板。该样板采用高精度球体的部分圆弧代替渐开线,通过误差补偿,获得高精度渐开线以实现渐开线溯源。研究了该样板相关的理论问题,为双球样板设计与应用提供了理论基础。针对数控齿轮测量仪器常釆用的电子展成法,分析并给出了理想安装条件下和存在安装误差时双球渐开线样板的原理误差及其计算公式;根据最优圆弧思想,使用最小二乘法推导出双球中心距的优化公式;最后给出了原理误差的补偿方法。基于上述基本理论,开发了双球样板设计软件并研制了一块模数为2.268 1mm、齿数为40、压力角为20°的双球渐开线样板。

To ensure high-precision calibration of gear measuring instruments,the international standard ISO / TR 10064-5：2005 recommends a Double-Ball Artifact（DBA） as calibration reference.The DBA employs a high-precision sphere to replace the involute and uses an error compensation technique to obtain a high-precision involute to realize the involate traceability.The theoretical issues relating to the DBA are discussed to provide a theoretical basis for the design and application of the DBA.The error of measurement principle of DBA and its calculation function are given under the conditions of ideal installation and with installed errors for the electronic generative metrology.According to the optimized arc thoughts,the formula of the optimized center distance between the two balls is derived by the least square method.Finally,the error compensation method is described.The DBA software is designed based on the above theory and a DBA is developed with a parameter of module in 2.268 1 mm,number of teeth in 40,and a pressure angle in 20 °.