Frictional contact mechanics | EPFL Graph Search

Contact mechanics is the study of the deformation of solids that touch each other at one or more points. This can be divided into compressive and adhesive forces in the direction perpendicular to the interface, and frictional forces in the tangential direction. Frictional contact mechanics is the study of the deformation of bodies in the presence of frictional effects, whereas frictionless contact mechanics assumes the absence of such effects. Frictional contact mechanics is concerned with a large range of different scales.

At the macroscopic scale, it is applied for the investigation of the motion of contacting bodies (see Contact dynamics). For instance the bouncing of a rubber ball on a surface depends on the frictional interaction at the contact interface. Here the total force versus indentation and lateral displacement are of main concern.
At the intermediate scale, one is interested in the local stresses, strains and deformations of the contacting bodies in and near the cont

Planar Equilibria of an Elastic Rod Wrapped Around a Circular Capstan

Harmeet Singh

We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact - namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of finite length wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the classic capstan problem to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan.

SPRINGER2022

An elastic rod in frictional contact with a rigid cylinder

Paul Grandgeorge, Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano

We investigate the load transmission along an elastic rod of finite cross-section in contact with a rigid cylinder, as system often referred to as the generalized capstan problem. In the presence of friction, the idealized classic capstan equation predicts that the tension along a perfectly thin and flexible filament increases exponentially along the contact region. In practical applications, however, the validity of the idealized capstan equation is compromised due to the interplay between finite rod thickness, bending stiffness, and the forces applied at the rod extremities. Here, we combine precision model experiments, finite element simulations, and theoretical modeling to investigate the contact mechanics and the force transmission along an elastic rod in frictional contact with a rigid cylinder. We study two cases when the rod is either static or sliding. First, we focus on the static case, in the absence of friction, by considering equal loads at both extremities of the rod. We show that as the loading force is increased, the nature of contact transitions from a localized region to an extended band at the surface of the cylinder. The latter is characterized by double-peaked contact force distribution. In the sliding case, friction is activated by inducing a relative motion between the rod and the cylinder. We applied a fixed loading force at one rod extremity while pulling the other extremity at a constant velocity. The driving force is monitored during sliding. For increasing loading forces, we find that the force ratio is non-monotonic and displays a local minimum, in contradiction with the constant ideal capstan prediction. This minimum force ratio coincides with the transition from a single contact point to an extended contact region. A theoretical analysis based on Euler's elastica serves to rationalize the results from the physical and numerical experiments. In addition to predicting the nature of the contact region (single point versus extended line), our model provides quantitative predictions for the wrapping angle and the driving-to-loading force ratio. Finally, we leverage our mechanics-based framework to predictively understand the force ratio at the ends of two commercially available engineering belts (spring-steel and polyurethane) in sliding contact with a steel cylinder.

PERGAMON-ELSEVIER SCIENCE LTD2022

Frictionless electrostatic rotary stepper micromotor for microrobotic applications

Marc Stranczl

We present the modeling and experimental characterization of a monolithic 3-phase rotary stepper micromotor which employs a flexure suspension to guide the rotor. The monolithic structure avoids any frictional contact during operation, providing a precise, repeatable and reliable bidirectional stepping motion without feedback control. We have performed finite element analysis (FEA) simulations of the mechanical static and dynamic properties. These studies are consistent with the extensive experimental characterization performed in the quasi-static, transient, and dynamic regimes. Dynamic nonlinearities have been observed and compared to a complete mathematical model including the electrostatic actuation and the mechanical properties of the system. The analytic model is consistent with the simulations and the experiments. The monolithic 3-phase rotary stepper micromotor has been modified to increase its torque and we have included a differential capacitive angular sensor. The implementation of this micromotor in a microgripper has also been studied and designed. These designs have been fabricated in a single-crystal silicon, using a simple single-mask process, based on standard Silicon-On-Insulator technology. The fabrication was performed in the cleanroom of the EPFL Center of MicroNanoTechnology (CMi) and has conducted to the preliminary experimental characterization of prototypes which validated the single-mask process.

2011

An elastic rod in frictional contact with a rigid cylinder

Paul Grandgeorge, Pedro Miguel Nunes Pereira de Almeida Reis, Tomohiko Sano

PERGAMON-ELSEVIER SCIENCE LTD2022