Measurement method of spherical radius size of differential planetary gear tooth surface based on 3D vision

Abstract

In order to accurately measure the spherical radius dimensions of planetary gear tooth surfaces, we propose a non-contact measurement method based on 3D vision technology. Firstly, the point cloud data of the planetary gear captured by the laser 3D profiler is preprocessed, and the tooth surface point cloud is extracted. Next, based on the structural characteristics of the planetary gear tooth surface, a uniform slicing and sampling algorithm is used to extract circular contour points where the tooth surface point cloud intersects with the slicing planes. These points are then projected onto a two-dimensional plane, where an improved RANSAC algorithm is used to precisely fit each circular cross-section. Contour points associated with significant fitting errors are removed based on a set tolerance value. Finally, an improved differential evolution algorithm is used to perform a three-dimensional spherical fitting on the contour points that meet the tolerance criteria, achieving accurate measurement of the spherical radius of the planetary gear tooth surfaces. Experimental results demonstrate that the repeatability error of the proposed method is ±0.02 mm, with a maximum absolute error of 0.026 mm and an average measurement time of 4.76 s. The method exhibits high robustness and measurement accuracy, meeting practical engineering measurement requirements.