The Processing Method Of Logarithmic Spiral Bevel Gear

Based on the principle of gearing angle function, the base curve equation of logarithmic spiral curve was established, and the formation principle of the curve was demonstrated, and the mathematic characteristics of the curve were analyzed. According to the requires of curves in gearing analysis, when logarithmic spiral curve is used as flank curve and pitch curve, the basic qualities, such as velvet characteristic, nonintervention characteristic, continuous characteristic, was demonstrated; conjugate curve equation of logarithmic spiral curve was calculated, then the conclusion that the conjugate curve of logarithmic spiral curve is logarithmic spiral curve was drew.According to the theory of Batrand curves, it is appropriate to analyze the conjugated curves on the pitch cone instead of conjugated profiles, consequently it was proved respectively that the contacting curve is logarithmic spiral and conjugated profiles is logarithmic spiral profiles. These assured fully the researching significance that the spiral angle is equal in every contacting point. The system of meshing theory of logarithmic spiral bevel gear was established by analyses, such as the meshing boundary function of conjugate flank, the induced normal curvature of conjugate flank mesh, etc.Based on analyses of both similarities and differences between logarithmic spiral bevel gear and conventional spiral bevel gear, the design methods of bevel gears were studied, and the definition of geometric parameters and confirmation of basic parameters were given and computational methods of strength were analyzed. Based on above these, for bevel gears, the theory of gear-cutting and the processing methods in NC (Numerical Control) machine tools were researched further. After the questions, such as the positional relation, the relative motion between tools and gears to be machined, etc., were analyzed fully, the gearing equation of the bevel gear was verified from processing point of view, consequently the feasibility that the logarithmic spiral bevel gear is machined was proved, and the processing programme of the bevel gear was programmed in multi-axis NC machines, so the processing of the bevel gear was achieved. After the finished gear was examined and measured, it is true that the new type of spiral bevel gear, logarithmic spiral bevel gear, has the characteristic of well contact areas and the desired design purpose was achieved, so the transmission of logarithmic spiral bevel gear can be a new one in the area of spiral bevel gear transmission.