Research on Modeling of Spiral Bevel Gear without Accurate Solving Initial Value

Spiral bevel gear transmission is widely used in automotive, aerospace, shipbuilding and other fields due to its advantages of contact ratio, stable transmission, and strong carrying capacity. This paper aims at the complex shape of the tooth surface of the spiral bevel gear in the digital modeling process based on the machine kinematic relationship and the principle of gear meshing during the actual machining of the spiral bevel gear. In some mathematical modeling methods, the gear tooth surface equation usually needs accurate initial values to solve and obtain the tooth surface coordinate values steadily. An algorithm that does not require accurate initial values is proposed to solve gear tooth surface coordinates of a spiral bevel gear machined under a universal machine model, and determine the relative positions of the convex and concave surfaces of the gear by surface projection and coordinate transformation to establish a solid model of the spiral bevel gear, so as to achieve the purpose of obtaining three-dimensional digital models at the parameter design stage of the spiral bevel gear, which is convenient for the design of the model, analysis and gearing analysis.