Abstract: To research the mathematical verification for M-M coaxiality,the geometric characteristic of real gauge were analyzed according to the engineering semantics of M-M coaxiality,and the mathematical model of virtual gauge based on boundary was established.Through analyzing the used process of real gauge in conformity assessment,a mathematical model of M-M concentricity error was established in the form of constrained optimization problem based on established virtual gauge and rigid body kinematics,and the solution method was given.An application of the proposed method in the evaluation of M-M coaxiality error of staircase was carried out,and the results showed that the proposed method could realize the mathematical evaluation of M-M Coaxiality error,which was more accurate than the existing methods.

Key words: mathematical model, error verification, maximum material requirement, datum, coaxiality

摘要： 为了研究M-M同轴度误差的数学评定方法,根据M-M同轴度误差的工程语义分析真实量规的几何特性,建立了基于边界的虚拟量规数学模型。通过分析真实量规在合格性评定中的使用过程,基于建立的虚拟量规和刚体运动学,以有约束目标优化问题的形式建立了M-M同轴度误差的评定数学模型,并给出了求解方法。最后给出了该方法在阶梯轴M-M同轴度误差评定中的应用实例,结果说明所提方法能够实现M-M同轴度误差的数学评定,而且比现有方法更准确。

关键词: 数学模型, 误差评定, 最大实体要求, 基准, 同轴度