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一引言在圆度评定与回转精度评定中,最小二乘圆由于其数学式严谨,几何意义与统计意义清晰而一直得到广泛的应用。根据定义,最小二乘圆圆心C点坐标x_0y_0与半径R为优化问题(见(1)式)的解。式中x_i=p_icosθ_i;y_i=p_isinθ_i;而p_i=ro+r(θ_i);ro为工件(测回转精度时为基准球)的公称半径;r(θ_i)为测量值r(θ)的第i点采样值,即θ_i=2π/(n)i;n为每2π的采样点数。当x_c~2+y_c~(2)~(1/2)《ro时,对(1)式早已有近似解。
I. INTRODUCTION In the assessment of roundness and accuracy of rotation, the least-squares circle has been widely used due to its mathematical rigor, clear geometric meaning and statistical significance. By definition, the coordinates of the point C in the center of the least squares circle x_0y_0 and the radius R are solutions to the optimization problem (see (1)). Where p_i = ro + r (θ_i); ro is the nominal radius of the workpiece (reference ball when measuring the rotation accuracy); r (θ_i) is the nominal radius of the i Point sampling value, that is, θ_i = 2π / (n) i; n is the number of sampling points every 2π. When x_c ~ 2 + y_c ~ (2) ~ (1/2) "ro, there is already an approximate solution to (1).