The Effect of Boundary Condition Variations on the Rolling Resistance of a Hard Sphere on Rubber Sheets

A growing body of evidence suggests that limited accuracy can be expected from analytical and computational tools relying on linear viscoelasticity for the prediction of rolling resistance in real systems presenting material and geometric nonlinearities. A set of experimental data for the viscoelastic resistance to motion incurred by a rigid sphere rolling between two parallel sheets of rubber, in realistic in-service conditions, was determined, in a previous work [Zéhil and Gavin, 2019]. The tests involved different elastomers (a Urethane rubber and a Neoprene rubber) and different sheet thicknesses, ball diameters, loading levels and rolling speeds. The accuracy of linear models in predicting such practical data is assessed in this work. To this aim, the elastomers are described by general linear viscoelastic models whose master-curves are characterized by: (i) High Frequency Thermo-Viscoelastic Spectroscopy, under very small strain amplitudes and (ii) Dynamic Mechanical Analysis under relatively larger deformations. In both cases, rolling resistance predictions are obtained using computational tools based on linear viscoelasticity [Zéhil and Gavin, 2013a, 2013b] and compared to the measurements. Conclusions are drawn regarding: (i) the practical limitations of linear rolling resistance models and (ii) influences of nonlinearities such as those due to large deformations, to the Mullins effect [Mullins, 1969] and to the Payne effect [Payne, 1962], on predictions.

Rolling Resistance of a Hard Sphere on Rubber Sheets: Limitations of Linear Viscoelastic Modeling and Influence of Nonlinearities

Zéhil

Gavin

2019

A New Contact Model of Joint Surfaces Accounting for Surface Waviness and Substrate Deformation

Yun

et al. 2019

The joint surfaces in the computer numerically controlled (CNC) machines play a crucial role in transmitting load and energy in operations. In this paper, a new contact model between rough surfaces of a joint is proposed by considering the influence of surface waviness and substrate deformation. A contact model for a single asperity system is first established, in which the asperity and substrate deformations are calculated based on the Hertz theory. Then, it is extended to an entire rough surface by a statistical method, where the contact of rough surfaces is treated as the contact between a smooth waviness and a rough surface. The numerical results showed that when contact deformation is constant, the real contact area and the normal load of joint surfaces increase with increasing radius of the waviness peak while the normal load decreases with the increase of surface roughness. When a rough surface contains a coating layer or a surface film, the deformation of the joint surface has to consider both substrate deformation and asperity deformation. The substrate deformation will generate larger influence for a stiffer or harder coating. Compared with other models, the results obtained from the proposed model show better agreements with the experimental data.

Analytical-Based Assessment of Effect of Highly Deformable Elements on Tunnel Lining Within Viscoelastic Rocks

Shao

Qin

et al. 2020

The utilization of highly deformable elements in lining has been proved to be an effective measure to control large deformations occurring in tunnels excavated in severe squeezing rocks. However, there exists no practiced method to transfer these benefits into engineering design. In this paper, the effect of highly deformable elements on tunnel responses is analytically conducted. The whole deformation of lining is divided into two parts to process, consisting of the first deformation of highly deformable elements and then that of segmental lining. Viscoelastic analytical solutions for lining pressure and tunnel displacement in the two deforming stages are derived, respectively. In addition, the analytical solutions are validated by comparing the predicted results with corresponding existing solutions. Good agreements between them can be achieved. Furthermore, a parametric investigation on the influence of highly deformable elements on tunnel performance is carried out. Results show that in linear viscoelastic rocks, there exists a linear relationship between lining pressure or tunnel displacement and length of the highly deformable elements with their numbers in lining remaining constant. The same lining pressure or tunnel displacement can be achieved under the condition of equal total length of highly deformable elements. Lining pressure or tunnel displacement linearly changes with Young’s modulus of highly deformable elements as well. This paper can provide a new trail to quickly and reliably evaluate the response of a tunnel where highly deformable elements are applied.