Influence of the crowning ratio in spherical gear couplings working in misaligned conditions

Abstract

Spherical gear couplings are high power density mechanical components employed to transmit power between misaligned rotating shafts. Their main differences in comparison with conventional spline couplings are their two tooth profile modifications: the longitudinal crowning, which is defined by the amount of crowning (Chβ) and the tip crowning. Focusing on the longitudinal crowning, this is controlled in the manufacturing process by the movement (rβ) of the tool (hob) which generates a crowning radius (rc) on the hub, and enables centering the contact along the face width, preventing tooth interference in misaligned conditions (Fig. 1(a)). However, the procedure to calculate the crowning radius is unclear, since proposed equations in literature yield to different values (Fig. 1(b)). Dudley [1] and Lagutin [2] proposed equations which result in constant values regardless of the operating misalignment angle (γ) and will not enable the operation without interference (or edge contact) at high misalignment angles. In contrast, other authors [3, 4, 5], include the misalignment angle in their definitions, but differ in other variables incorporated. In conclusion, for a given misalignment angle, depending on the selected methodology from the literature there are a variety of possible hub geometries which will present different mechanical behaviors. Thus, this paper analyses the influence of the crowning radius in spherical gear couplings with the aim of achieving a design that provides the maximum contact surface, the minimum tooth root stress and the best tooth root fatigue properties.