Variance-Minimization Iterative Matching Method for Free-Form Surfaces—Part II: Experiment and Analysis

Abstract

In the first part of this paper, a free-form surface matching method called variance-minimization matching (VMM) was proposed to address uneven/open point distributions and measuring noise. The convergence property and sensitivity to measuring defects were theoretically studied. In the second part of this paper, a series of experiments are presented to verify the feasibility of the proposed method in free-form surface matching. The experiments are divided into four sets: a measuring defects experiment, a noise experiment, a convergence experiment, and an artificial experiment. In the first set of experiments, the existing methods are prone to becoming trapped in a local optimum affected by uneven/open point distributions, which shows that measured points incline toward dense areas. However, in VMM, there is little inclination regardless of the increase in the number of measuring defects. In the second set of experiments, sensitivity to varying noise is tested. The results show that VMM helps prevent unstable sliding in the presence of Gaussian noise. In the third set of experiments, we compare convergence speed and convergence stability under different initial positions. It is verified that VMM exhibits the quadratic convergence. Finally, a set of artificial experiments is implemented, revealing that the proposed method is appropriate for use in automated manufacturing processes such as geometric inspection and allowance distribution. Note to Practitioners —Measuring defects usually occur when using a scanning device to obtain the measured points of a workpiece. Weakening the effect of measuring defects on matching results is critical to promoting manufacturing automation. This paper proposes a new method called variance-minimization matching (VMM) that considers measuring defects. In the first part of this paper, the modeling and theoretical analysis of VMM were introduced. In the second part of this paper, simulated experiments are performed to verify the feasibility of VMM in addressing uneven/open point distributions, measuring noise, and large initial positions. Next, artificial experiments employing VMM in geometric inspection and allowance distribution are presented. The proposed method also applies to other automated manufacturing processes, such as workpiece localization, deformation analysis, and complex parts repair.