Nowadays, the bevel gears are widely applied in the industry for the intersected-axial transmission system. But the applications of the bevel gears are mostly limited to the usage of involute bevel gears. In this thesis, the bevel gear with circular-arc tooth profiles is derived by using general theorem of conjugate surfaces, coordinate transformation, constrained meshing equation, and spherical trigonometry. According to the bevel gears with circular-arc tooth profile derived above, the analyses and discussions of the interference are proposed. The interference situation is detected by applying the phase lead-lag concept while circular-arc curve is moving on the spherical cross-section. Furthermore, the ideal conditions to avoid occurrence of interference are proposed. Design charts for the maximum values of tooth profile angle are also constructed as a reference for designers. The 3D solid models of the bevel gear with circular-arc tooth profiles are constructed by using the computer software (Pro/E). Finally, the transmission ability is verified through the computer animation using CAE software (Visual Nastran). It is believed that the mathematical models and design method developed in the thesis will provide a useful foundation for the further studies.

Curvic couplings have been widely applied to various industrial applications. Presently the Gleason No.120 special grinding machine developed by Gleason Works Co. is one of the commonly used machine tool for the curvic coupling manufacturing. On the other hand, in response to the issue of improving the domestic design and manufacturing ability, an alternative manufacturing method of curvic coupling is introduced in this study. In this study the geometrical characteristics of the novel gear profile are investigated. Firstly, applying the spatial transformation matrix theorem to the relationship between the cutting tool path and the cutting tool position, the cutting tool profile equation of curvic coupling is successfully derived. Secondly, the mathematical model of the envelope surface of the generating tool, or generally being called the gear surface, is constructed based on the trajectory equation of the generating tool motion and the tool-workpiece meshing equation. Finally, the solid model is established based on the obtained mathematical model, and the comparison works with the conventional curvic coupling are also carried out. The analysis of gear surface is graphically depicted with respect to the various machining parameters. It is believed that this thesis provides a useful tool for the following studies of curvic couplings for the different demand of application fields.

The bevel gears have been widely used for the intersected-axial transmission system for a long time. But mostly them are limited in the category of involute tooth profiles. It is believed that bevel gears with circular-arc tooth profile, similar to the Wildhaber-Novikov circular-arc helical gears, will improve the load capacity of the gear set. The bevel gears with circular-arc tooth profiles was firstly proposed by Kuo and Tsai in 2001. Although these new type of bevel gears can increase the load capacity of transmission, the expensive manufacturing process is still the problem. In this paper, the design parameters of bevel gear with circular-arc profiles developed by Kuo and Tsai are modified. Bevel gear set with spiral point contact path is developed. This improvement makes it possible to manufacturing the newly developed bevel gears in just a simple milling or/and grinding process with circular cutting edges. The manufacturing process is then cost down quit a lot. A method for checking the gear interference is also proposed. Finally, the 3D solid models of the bevel gear with circular-arc tooth profiles as well as the grinding wheel are constructed by using the computer software ¡§Pro/E¡¨. It is believed that the mathematical models and the design method developed in the thesis will provide a useful foundation for the further studies.

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