Noncircular bevel gear is applied to intersecting axes, realizing given function of transmission ratio. Currently, researches are focused mainly on gear with involute tooth profile and straight tooth lengthwise, while that with free-form tooth profile and curvilinear tooth lengthwise are seldom touched upon. Based on screw theory and equal arc-length mapping method, this paper proposes a generally applicable generating method for noncircular bevel gear with free-form tooth profile and curvilinear tooth lengthwise, covering instant screw axis, conjugate pitch surface, as well as the generator with free-form tooth profile and curvilinear tooth lengthwise. Further, the correctness of the proposed method is verified through illustrations of computerized design.

Noncircular bevel gears are applied in variable-speed transmissions with intersecting axes. Since dedicated machines for manufacturing noncircular bevel gears are not available, noncircular bevel gears are normally manufactured using universal computer numerically controlled (CNC) machining centers, resulting in poor productivity. This paper describes a face-milling method for generation of noncircular spiral bevel gears, which is analogous to the generation of spiral bevel and hypoid gears using CNC hypoid gear generators, such as Gleason free-form hypoid generators. As a result, the productivity is significantly improved. Based on the theory of gearing, this paper first describes the basic concept of generation of conjugate noncircular spiral bevel gears. Generation of the tooth surfaces using crown-gear generation concept is analytically discussed with association to the face-milling process of generation of the proposed noncircular spiral bevel gears. The tooth surface geometries are represented by the position vectors and normals. The kinematical model of free-form machines is developed. The machine motion parameters are determined based on the theoretically defined tooth surfaces using the crown-gear generation concept. The developed method is verified by manufacturing a real pair of noncircular spiral bevel gears with satisfactory contact patterns which agree well with those modeled using a commercial cae software program.

Cold rotary forging is an advanced but complicated metal forming technology with continuous local plastic deformation. Investigating the wear is significant for effectively predicting the life of the dies and improving the workpiece surface quality. This paper is aimed to use the FE method to predict the wear response over the surfaces of the dies and the workpiece in cold rotary forging. For this purpose, a 3D elastic-plastic dynamic explicit FE model of cold rotary forging of 20CrMnTi alloy is developed using the FE software ABAQUS/Explicit and its validity is verified theoretically and analytically. Based on this valid 3D FE model, a systematic study has first been conducted, modeling and explaining the contact pressure and slip distance response. Then, the wear response that occurs at the surfaces of the dies and the workpiece is achieved. Finally, the effect of the process parameters, rotational speed n of the upper die, feed rate v of the lower die, outer/inner diameter of the ring workpiece, on the wear response is revealed. The results of this research help us better understand the complicated wear mechanisms in cold rotary forging. Moreover, the modeling methods proposed in this paper have the general significance to study the wear problems in other complicated metal forming processes.