A new quasi-static friction model for the spherical hinge bearing in structural engineering

Abstract

For most frictional issues in structural engineering, the classical friction law named after Coulomb is a reliable and convenient tool, but it cannot be used to predict a slippage-related quasi-static process due to the lack of relevant items. In this paper, based on some commonly used dynamic friction models, a new rate-independent friction model is proposed to describe a quasi-static frictional process in structural field, e.g., the motion of a spherical hinge bearing in a pedestrian bridge under reciprocal pedestrian and temperature loads. Most quasi-static processes happen at the pre-sliding regime when a friction contact tends to slide slightly before the Coulomb friction is reached. The well-known Dahl model, LuGre model, and other test-based dynamic models are surveyed, and their shortcomings in engineering use are summarized subsequently. The new model, the same as the Dahl model, is rate-independent, but adopts a more engineering-oriented form. On the basis, it can be easily applied on a finite element analysis by adjusting a built-in ideal elastoplastic model. Meanwhile, the accuracy has no obvious decrease according to a test-based comparison between the Dahl model and the new. The coefficient of stiffness deviation, defined as the deviation of the pre-sliding friction stiffness from the initial friction stiffness, is introduced into the new model, which makes the model possible to predict the energy dissipation at the pre-sliding regime and can be well explained by the asperity-based theory at microscopic level. The impacts from the curvature and the coverage of a contact on the coefficient of static friction are assessed by the finite element method. It is shown that the curvature has very few impacts while the coverage is highly positively related to the observed coefficient of friction. A friction test of a spherical hinge is then carried out to verify the new model. By data regression, the coefficient of stiffness deviation for the proposed model and the exponent for the Dahl model are identified as 0.492 and 2.272, respectively. A comparison of friction torque-slippage hysteresis loops shows both the Dahl model and the proposed model have good predication as the normal force is large enough and the proposed one is even better in some load cases. Finally, a brief application on a pedestrian bridge of the new model is introduced. It indicates that there will be some mechanical residuals when a spherical hinge is applied with a reciprocating load, but the residuals tend to be limited.