Existence Judgement And Solving Of Fully Conjugated Tooth Surface Of Spiral Bevel Gear

In the measuring process of spiral bevel gears, the design tooth surfaces which are used as the basis for calculating the tooth surface error are changing with the difference of gear processing methods and machine adjustment parameters,As the result, the use of the measurement results and the comparison of the measurement results between different measuring instruments are restricted severely. In the case of ensuring meshing relationship of a pair of spiral bevel gears, the goal of this study is to solve the equation and to explore the existence of fully conjugated tooth surface, which is not affected by processing method and machine tool adjustment parameters. The following are the main research contents:Firstly, in order to explore the existence of complete conjugate tooth surface, the sufficient condition is derived and the solving of the fully conjugated tooth surface equation is proposed.Secondly, the tooth surface of spiral bevel gear is projected into the shaft section, and the mapping relation between the two dimensional points and the spatial tooth surface is established. The tooth surface calculate path is planned, and the initial data is given, the correctness of the numerical model is verified by comparing the numerical examples.Thirdly, the design tooth surface which is processed by the milling/tilt method is compared with the fully conjugated tooth surface, the design tooth surface showing convex characteristics, which conform with the idea of tooth surface optimization design, the complete conjugate tooth surface can be used for the measurement of the actual tooth surface is verified.