Spherical gear couplings are mechanical components that allow transmitting torque between misaligned shafts by means of equally spaced teeth. For instance, they are used in roll-levelling machines in order to transmit power from the main gearbox to the levelling rolls. Modern roll-levelling machines are characterized to level high strength steels by using small rolls under high torque requirements (up to 1000 Nm). The small size of the rolls decreases the space between the spline couplings causing high misalignments up to 7 degrees. In aligned conditions the whole tooth flank surface is in contact, while in such misaligned conditions only some part of the tooth width is in contact, generating complex load behavior and decreasing fatigue life. In order to accommodate high misalignments and reduce the stress in tooth engagement along the tooth width direction, crowned teeth are manufactured (i.e. the hobbing tool describes a circular arc combining the axial and radial motion).

Classical coupling load models, but still used, assume a number of teeth in contact for a certain amount of misalignment. However, these models do not account for the tooth stiffness, the applied torque or manufacturing errors, which produce a sequential engagement of spline teeth. Therefore stresses could be overestimated and thus fatigue life predictions be inaccurate. Recently, several studies have been performed in order to account for tooth stiffness and tooth spacing errors of such couplings. However, they were only applied in relatively small misalignments (approx. up to 1 degree) comparing with the case studied in this research (up to 7 degrees).

In this work, a numerical model has been developed in order to predict the fatigue life of highly crowned spline coupling geometry. First, the number of teeth in contact has been evaluated for different misalignment and torque conditions. Then, the fatigue life predictions have been calculated based on the numerically obtained stresses. Finally, fatigue tests have been performed in order to validate the developed methodology. It is observed that the numerically estimated cycles to fatigue failure are close to the experimentally measured fatigue life.