No abstract

This paper presents a method for designing a novel type of movable tooth drive characterized by logarithmic spiral conjugated tooth profiles, which are in almost full surface contact owing to such innovative tooth geometry, in comparison with the conventional involute or cycloidal tooth profiles creating a linear contact. Firstly, the existence conditions of the conjugated curve of the logarithmic spiral are researched by establishing the meshing equation, and its geometric and kinematic properties are identified to design the conjugated tooth profiles of the movable tooth and ring gear. Then, wave generator profile, according to the requirement that it should be completely convex and smooth, is designed and modified to ensure the consistency with load capacity of the conjugated tooth profiles. On this basis, dimensional synthesis of the mechanism is performed following the influence analysis of main factors on the force/motion transmission characteristic of the whole machine. Finally, the virtual prototype is developed and the proposed design method is validated by relevant force performance simulation. The outcomes lay a significant foundation for the design of such logarithmic spiral tooth profile transmission.

This paper presents a static model for a novel movable tooth drive with logarithmic spiral tooth profiles, to research contact force and load distribution during the meshing period. According to the geometric properties of the conjugate tooth profiles, their compatibility law considering the multi-tooth elastic meshing effect are investigated to reveal load distribution characteristic of the teeth. The static model of the mechanism is thus developed to systematically analyze variation in contact force during the rise travel. The results indicate that the contact force between the tooth and ring gear is proportional to the curvature radius of the contact point, and it increases exponentially and monotonically corresponding to the curvature radius of logarithmic spiral tooth profile; in the multi-tooth meshing condition, the load distribution of the teeth coincides with the ratio of the curvature radius of each contact point, and periodical pulsations of total contact force occur at the alternation of the teeth. Finally, the proposed model is validated by the FEM simulation of a prototype, and the influence of dimensional parameters is further discussed for the self-locking and force transmission characteristics of the tooth. The outcomes provide critical technical support for the static modelling and design of such transmission mechanism.