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In this work the quasi-static model of the three-dimensional geometrical non-conjugate contact problem for two C1surfaces is studied. The set of contact equations is formulated by using a new parameterisation that enables to reduce the conventional system of five nonlinear equations with five unknown position and contact parameters to just two nonlinear equations with two changeable parameters. The novel model is computationally efficient and demonstrates increased accuracy and stability of the numerical solution, compared to the conventional model described by Litvin, which suffers from convergence problems and requires a high computational effort. The new model is implemented to spur gear with crowned tooth surfaces to parametrically estimate the susceptibility to diverse misalignments of the contact pressure, transmission error and path of contact.

We elaborate a SDOF time-domain model for elastic hysteretic damping, by modifying the viscous damping model to introduce an instantaneous correction factor that recursively depends on the state variables of the system, such that the response exhibits weak dependency on frequency, corresponding to a large array of engineering materials. The effect of different formulations for calculating the instantaneous correction factor on the predicted hysteresis loops and the potential manifestation of singularities is studied. Hysteresis loops anticipated by the model are plotted and forced vibration responses to harmonic and other periodic non-harmonic excitations are simulated and discussed, also in comparison to the conventional viscous and Reid’s damping models.

The design of a novel gear system based on a Rzeppa joint internal interface is presented and analysed. The joint allows the transmission of torque loads while allowing real-time re-alignment of the gear to eliminate non-torque loads arising from misalignment. This gear, when part of a misaligned pair, is shown by means of quasi-static FE simulations to remain essentially under the same stress conditions, even when under considerable misalignment, and to outperform crowned gears. The trade-off is increased contact stress at the ball elements of the joint interface. In addition, the mesh stiffness for the conventional and the novel design are estimated, showing that the proposed design produces a lower but nearly constant stiffness throughout the mesh cycle.