The surface reconstruction of logarithmic spiral bevel gear is to construct a real logarithmic spiral bevel gear tooth surface by interpolation using the discrete data points of the tooth surface collected. The tooth surface reconstruction of logarithmic spiral bevel gear is the core part of the whole digital model. The accuracy of tooth surface reconstruction of logarithmic spiral bevel gear will directly affect the establishment of the model. It is the bottleneck of CAD / CAM system technology. The significance of logarithmic spiral bevel gear tooth surface reconstruction is to compare and analyze the established logarithmic spiral bevel gear real tooth surface with the theoretical tooth surface. Therefore, the established logarithmic spiral bevel gear tooth surface must be based on the real tooth surface and collect data on the logarithmic spiral bevel gear tooth surface according to the needs of establishment, The tooth surface model of logarithmic spiral bevel gear established by reverse engineering software must conform to the real tooth surface shape.
At present, in the research of reverse engineering, the modeling of free-form surface is divided into two categories: one is the reconstruction method using triangular Bezier surface as surface; The other is the rectangular parameter interpolation method based on NURBS (non-uniform rational B-spline) curves and surfaces. In fact, these two methods have their own advantages and disadvantages. Triangular Bezier surface is widely used in some scattered data points because of its wide application and good flexibility. However, there is a problem. The tooth surface of logarithmic spiral bevel gear reconstructed by triangular Bezier surface does not meet the surface forming standard and cannot exchange data with CAD system. Therefore, it is necessary to convert triangular Bezier surface into NURBS surface with unified standard. Now, almost all CAD software systems at home and abroad use NURBS surface standard, and some IGES and pddi as data exchange use NURBS curves and surfaces as their own industrial standards.