In this article, logarithmic spiral curve is successfully applied to bevel gear transmission and used as dentiform line of helicoid bevel gear. Put forward a novel logarithmic spiral bevel gear drive. Because spiral angle on each point of logarithmic spiral curve is constant, the problem of variational spiral angle is solved faultlessly. Analyze the basic characteristics of logarithmic spiral curve and demonstrates the condition of the logarithmic spiral curve used as pitch curve. Put forward the new kind of transmission form of logarithmic spiral bevel gear and it makes up the deficiency in current bevel gear transmission area.
In this article it constructs tooth surface equation of a new type of bevel gear which is logarithmic spiral bevel gear by the tooth trace and the tooth profile curve with space geometric knowledge. By means of the CAD software which can intuitively understand the complex curves and surfaces and the MATLAB software platform, it makes the complex mathematical theory be easier to understand and apply correctly, and verifies the correctness of the tooth surface equations.
For a new type of bevel gear—logarithmic spiral bevel gear, establish its tooth direction curves and the mathematical model of tooth surface equation. With CAD software platform which can intuitive understanding of complex curves and combined with conical logarithmic spiral parameter equation build the logarithmic spiral on cone surface. Then array logarithmic spiral to make them evenly distributed in the cone surface, without any interference and to meet the strength distribution on both ends of circular truncated cone equally. Use two logarithmic spirals from different starpoint as tooth direction curves of lift and right tooth surface. Finally, use space geometric knowledge to build tooth surface equation by tooth direction curves and tooth profile curves.
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