Mathmathematical models,meshing analysis and transmission design for a robust cylindrical gear set generated by two blade-discs with parabolic cutting edges

Abstract

This paper proposes mathematical models for analysing meshing characteristics and controlling a parabolic-like kinematic error function for a newly developed cylindrical gear set generated by two blade-discs with parabolic cutting edges. Unlike the former design, the proposed gear set is robust against assembly errors owing to its localized bearing contact and parabolic-like kinematic error function. Based on the proposed systematic mathematical procedures, the dimension of major axis of contact ellipse and magnitude of kinematic error can be controlled by the parameters of the blade-discs. To avoid gear undercutting, explicit functions of minimum numbers of teeth of non-undercutting for gear and pinion are derived. Equations for analysing tooth contact status, specific slide and contact ellipse are created. Based on the proposed mathematical models, a computer program has been established to analyse the effects of variation in parameters for cutting tools on meshing characteristics. The robustness of the developed gear set against various assembly errors is verified through numerical examples. With the proposed mathematical models and the computer program, gear designers can quickly determine the values of parameters for cutting tools without manual trial-and-error procedures.

Keywords

cylindrical gears curvilinear tooth traces kinematic error contact ellipse

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