三维匹配是复杂曲面零件加工余量分配与轮廓误差评估的基础，现有方法难以克服固有测量缺陷（测点分布不均、密度不均、局部缺失等）对匹配精度的影响。提出一种基于方差最小化原理的三维匹配数学建模与计算方法，可线性求解运动变量，具有二次收敛性；研究方差最小化匹配与传统TDM （Tangent distance minimization）匹配的等效条件，推导匹配参数误差和测点位置误差的定量表示；以叶片机器人磨抛视觉定位、螺旋桨桨叶加工余量分配、曲轴轮廓检测等为例验证所提方法，试验表明方差最小化方法可解决匹配目标函数倾向于满足高密度测点或噪音点平方距离最小化问题。
3D matching is the basis for machining allowance distribution and profile error evaluation of complex surface, but existing methods are hard to guarantee stable matching accuracy, due to inherent measurement defects such as uneven point distribution, uneven density and local point missing. This paper proposes a novel 3D matching method of mathematical modeling and parameter calculation based on the variance minimization principle. It can linearly calculate the motion variables during each iteration, and appear quadratic convergence. The equivalent condition between the variance minimization matching and the TDM matching is derived, and the quantitative representations of both matching parameter error and point position error are analyzed. In addition, the effectiveness of the proposed method is demonstrated by the experiments of visual localization in robot grinding, allowance distribution in propeller machining and profile analysis in crankshaft inspection. It shows that the variance minimization has the advantage of overcoming the wrong squared distance minimization with respect to the high-density points or noisy points.
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