# Reverse engineering design of logarithmic spiral bevel gear

Using the physical reverse engineering method to collect the discrete data points of the tooth surface of the logarithmic spiral bevel gear can not only reconstruct the tooth surface of the logarithmic spiral bevel gear, but also calculate the error between the real tooth surface and the theoretical tooth surface, so as to analyze the machining error of the gear and take effective measures to improve the machining accuracy of the logarithmic spiral bevel gear.

Based on the improvement of the meshing theory of the logarithmic spiral bevel gear theory, the reverse engineering design of the logarithmic spiral bevel gear is realized by using the reverse engineering method and some equipment software. The mathematical model of the real tooth surface of the logarithmic spiral bevel gear is established by using the NURBS interpolation method. According to the characteristics of meshing theory, the tooth surface curve is constructed from the discrete data points of logarithmic spiral bevel gear tooth surface, and then the interpolation surface is constructed from the tooth surface curve. According to the selection method and principle of parametric combined boundary conditions of tooth surface of logarithmic spiral bevel gear, the real tooth surface mathematical model of logarithmic spiral bevel gear is constructed.

Based on the established real mathematical model of logarithmic spiral bevel gear, the ultimate goal is to compare the tooth surface of logarithmic spiral bevel gear with the theoretical tooth surface, so as to calculate the error between them. Therefore, it is necessary to solve the points on the tooth surface for the known logarithmic helix and logarithmic helix tooth surface equations, so as to realize the error calculation of the constructed surface and theoretical tooth surface.

The research is a part of the research of logarithmic spiral bevel gear. Through this research, we can not only reconstruct the tooth surface of logarithmic spiral bevel gear and calculate the existing tooth surface error of logarithmic spiral bevel gear, but also play a practical guiding significance for the accuracy inspection in the machining process of logarithmic spiral bevel gear, the machine tool adjustment and compensation of machining error, and the feedback compensation of heat treatment deformation, And further enrich and improve the research system of logarithmic spiral bevel gear.

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