Stiffness Modelling for One Curvic Coupling Considering Contact Details

Curvic couplings have been widely used in precise mechanical devices at high loading and high rotate speed, such as aircraft engines, because of its high torque transmission capacity and precise auto centering. So far, most stiffness models for curvic couplings are created to implement the qualitative stiffness analysis, neglecting the detailed features and the contact stiffness, which limit their precision. In this study, the stiffness analysis of curvic couplings is simplified as the plane-strain problem, to determine both the tensile–compressive stiffness of one tooth, taking into account their detailed features, and contact stiffness. All possible deformation factors: tooth deformation, dedendum deformation, flange deformation and contact deformation of the tooth surface are included during stiffness modelling. Based on the M-B elastic–plastic fractal model of rough contact interfaces, the contact stiffness is introduced. The non-uniform distributed load and the contact status on the tooth surface are obtained by adopting the finite-element method. In addition, the effects of the uniformly distributed load and the non-uniformly distributed load on the deformation of the curvic couplings are studied using a local equivalent stiffness model. And then, the deformation distribution on the tooth surface is solved to build two tensile–compressive stiffness models under different distributed load. The theoretical stiffness models show that the axial compression deformation of the tooth is the most influential factor at the pitch circle of the curvic coupling, followed by the contact deformation, and others have little influence. Therefore, it is necessary to consider the effect of the contact status and the compression load in the stiffness analysis of the curvic couplings, in particular for double-row large-radius arc curvic couplings with short bolts. The results of the tensile–compressive stiffness constitutive model and the unit-sector finite-element model under different distributed load are compared. The result shows that the nonlinearity stiffness of the curvic coupling is mainly determined by the uneven distribution of the contact stress. Under the non-uniform load distribution of the tooth surface, the compression stiffness of the curvic coupling increases as the axial pressure increases. On the contrary, the compressive stiffness, which is obviously larger than the tensile stiffness, decreases as the axial tension increases. Although all possible factors have been considered in the improved analytical modeling, the stiffness of tooth surface is four times higher than that of the verified simulation finite-element results. Therefore, the authors don’t recommend the constitutive modelling way to obtain curvic couplings stiffness, which is much more complex and not precise enough either. It can be better to model it in the phenomenological ways using experiments data, and the verified finite-element model is also better than the constitutive model.