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Gear wear is a progressive material removal process that gradually changes the tooth profile shape and dynamic mesh force, where the dynamic mesh force affects the tooth surface wear. To describe this process, a spur gear dynamic model that includes the mesh stiffness and unloaded static transmission error (STE) of the worn tooth profile is proposed for calculating the dynamic mesh force. Then, based on the finite element method (FEM), a dynamic contact analysis model that considers the dynamic mesh force is proposed for calculating the time-varying contact stress and relative sliding distance of the tooth surface mesh point. Finally, combined with the Archard wear model, a tooth wear depth calculation method that considers the worn tooth profile and the dynamic mesh force is proposed. In addition, the wear depth and dynamic characteristics under different wear times are studied.

Bending deformation gives rise to interwire slippage for spiral strands subjected to multi-axial loads, and further induces wear or fatigue phenomena in practice. The interwire friction would resist bending deformation and lead to uneven tension distribution of individual constituent wires but little research has quantified these effects. To figure out this issue, a beam finite element (FE) is established, into which a penalty stiffness algorithm and a Coulomb friction model are incorporated. A series of free bending simulations are developed for parametric study on deflection near the terminations and tension distribution of individual wire for strands with different levels of length and friction coefficient as well as external loads. Based on the simulation results, it is found that strand length has little influence on bending deformation and tension distribution if the strand length exceeds six times the pitch length. A deflection formula extended from the classical Euler beam model well predicts the sag deflections and the relative error with respect to experimental measurements is less than 10%. Furthermore, additional axial tension induced by the friction is clearly characterized and an approximate expression is proposed to estimate tension distribution for outer layer wires. Its predictions are encouraging for longer strands.

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