直角坐标采样时的圆柱度误差数学模型

Mathematical Models of Cylindricality Error with Sampling Points in Rectangular Spatial Coordinates

根据国家标准中有关圆柱度误差的定义,建立了任意空间位置回转表面圆柱度误差的最小二乘数学模型,该模型的坐标原点可以任意选取,各离散采样点之间也不要求为等角度间隔·用计算机进行了仿真分析·结果表明,该模型的计算结果与仿真结果十分吻合,由评定模型引入的误差极小,可以忽略不计·在此模型基础上,采用四维无约束的最优化直接算法,可求得符合最小条件的圆柱度误差值·该模型既可用于三坐标测量机也可用于其他智能量仪测量零件的圆柱度误差·

An attempt is made to solve radically the key problem on evaluating the cylindricality error with sampling points in rectangular spatial coordinates. According to the definition of cylindricality error as specified in the national standards, a mathematical model was developed to evaluate the cylindricality error by least square method, to which the origin of coordinates can be randomly selected and no isogonal requirements for sampling points. The simulated results are found highly coincident with the calculated results by the model, and the error arising from the model is negligible. Based on the model, the cylindricality in conformity with minimum conditions can be calculated by way of four-dimensional non-restraint optimization algorithms. The model can be used on either measuring machines with rectangular spatial coordinates or other intelligent measuring instruments.