Dry Friction Problems Research Articles

Numerical solution of dry friction in point contact using the unified Reynolds method combined with rarefied gas effect

Dry friction problems are widespread in engineering applications. However, the current research on the contact pressure between interfaces mainly relies on static contact mechanics solutions, neglecting the influence of the contact pressure generated by the gases in the environment. In this paper, the ambient gas is considered as a lubricant with lubricating effects. Drawing inspiration from hydrodynamic lubrication methods, a unified mixed lubrication equation for dry friction problems is developed, taking into account the influence of gas rarefaction effects. This study computes the dry friction contact pressure under different winding speeds and loads. The advantage of this method lies in its ability to automatically distinguish between the contact and noncontact regions during the calculation process, enabling the determination of the contact pressure over the entire contact area. The computational results demonstrate that at low entrainment velocities, there is minimal deviation in contact pressure and contact area compared to Hertzian contact. However, as the entrainment velocity increases, the actual pressure-bearing area enlarges compared to static contact, and there is a smooth transition of pressure at the contact edge, which cannot be obtained from static contact analysis. Finally, the numerical solution of the contact pressure when the sliding speed spans several orders of magnitude is given, and the calculation results show that the numerical model has good robustness. This numerical approach offers valuable insights for guiding the design of air bearings in practical applications.

Shear oscillations of bridge on sliding foundation during earthquake

The article investigates the vibration of the railway bridge on the sliding foundation with dry friction under the action of real earthquake records at the intensity of 7, 8, 9, and over 9 on the MSK-64 scale. Dynamic dry friction problems are non-linear since each slip's start and end times are determined during the problem-solving process; they depend on many design parameters and external influences. The simplified model of vertical and shear deformation of the bridge is proposed as oscillating intermediate support with the mass of the span connected to the girth rail by a rubber bearing part. In this case, all elements in the structural model are connected to each other, taking into account eccentricities. The finite element method discretizes the coordinate variables and the Newmark time method with matrices built at each step. Structural vibrations are studied based on four real earthquake records. It is shown that using a sliding foundation can significantly reduce the shear forces in the bridge supports depending on the structure mass, the dry friction coefficient, and the nature of the seismic effect.

Strictly localized bounding functions for vector second-order boundary value problems

The solvability of the second-order Floquet problem in a given set is established by means of C 2 -bounding functions for vector upper-Carathéodory systems. The applied Scorza–Dragoni type technique allows us to impose related conditions strictly on the boundaries of bound sets. An illustrating example is supplied for a dry friction problem.

Indeterminacy of a dry friction problem with viscous damping involving stiction

AbstractWe study a usual friction law for one degree of freedom solid where the dynamical friction coefficient is smaller than the static friction coefficient. We show that this law can be dangerous, because it can lose all predictive power. We first study a passage to the limit to prove that the limit is strongly depending on the data. We secondly study the obtained limit law, which is written with a non maximal monotone multivalued graph; this property implies that the differential inclusion possesses a set of solutions, whose diameter is too big to know the solution with precision. Moreover, the associated numerical scheme does not have a unique solution.

Influence of harmonically varying normal load on steady-state behavior of a 2dof torsional system with dry friction

A nonlinear dry friction problem with harmonically varying normal load is formulated, in the context of a two-degree of freedom torsional system, since virtually all of the prior literature focuses on the topic of time-invariant normal load. First, pure stick, pure slip and stick–slip motions are computationally and analytically determined when excited by a sinusoidal torque, in the presence of harmonically varying saturation torque; mean terms are included in both. These analyses yield both transient and steady-state time histories under various conditions. Second, the effects of time-varying normal load on steady-state responses have been investigated and nonlinear spectral maps (including super-harmonics) are developed. Results show that the actuation system parameters could affect steady-state stick–slip motions in different ways over the lower and higher frequency regimes, as a result of time-delay in slip motions with respect to the torque excitation. In particular, the negative slope characteristics in the friction law exaggerate the stick–slip vibration problems, and it is the major cause of bifurcations and quasi-periodic or chaotic motions. Around the super-harmonic peak frequencies, the nonlinear system tends to lose stability as abrupt jumps in the spectral maps take place. An equivalent viscous damping model is considered to analytically investigate the instability mechanism. Further, the periodicity of the system response under harmonically varying actuation is conceptually by employing the harmonic balance method. Finally, steady-state behavior is examined for the nonlinear, time-varying dry friction problem.

CHAOS IN NONAUTONOMOUS DIFFERENTIAL INCLUSIONS

The existence of a continuum of many chaotic solutions are shown for certain differential inclusions which are small nonautonomous multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems.

Analysis of a dry friction problem under small displacements: application to a bolted joint

This study presents an analysis of the problem of macroscopic contact of steel upon steel with dry friction, in the specific case of a bolted joint. The configurations of these types of joints result in very small displacements and interface sliding velocities. To understand how the system formed by the two surfaces in contact works, an experiment was carried out. The analysis of the results obtained made it possible to define the behavior of the system and to model the variations of the main parameters by original and continuous laws. These laws accurately correlate to all the results of the tests effectuated.

Résolution de problémes de rafle et application á un probléme de frottement

In this paper we study the sweeping processes by convex sets depending on time and the solution. We do some application to a dry friction's problem.

Singular perturbation approach to an elastic dry friction problem with non-monotone coefficient

In this paper we study a one-dimensional dynamic model of dry friction with slip velocity dependent coefficient. In many cases, this model has more than one solution. We introduce a perturbed friction condition which allows us to regain the uniqueness of the solution. We show that the perturbed problem’s solutions pointwise converge to a particular solution of the initial problem when the perturbation parameter tends to zero. The singular perturbation approach provides the analysis of a criterion used to select a solution of the problem, and suggests a method to study more elaborated dry friction problems.

Chaotic solutions in differential inclusions: chaos in dry friction problems

The existence of a continuum of many chaotic solutions is shown for certain differential inclusions which are small periodic multivalued perturbations of ordinary differential equations possessing homoclinic solutions to hyperbolic fixed points. Applications are given to dry friction problems. Singularly perturbed differential inclusions are investigated as well.

Perturbation singulière d'un problème de frottement sec non monotone

In this Note we deal with a singularly perturbed system constituted by a differential inclusion which has a unique solution for each value of the perturbation parameter. The associated degenerated problem, that corresponds to a dynamic dry friction problem, has many solutions. We show that perturbed problem solutions converge to a particular solution of the degenerated problem when the perturbation parameter goes to zero. The singular perturbation approach allows an analysis of a criterion used to select a solution of the degenerated problem, and suggests a method to study more elaborated dry friction problems.

Chaos in ordinary differential equations with multivalued perturbations: Applications to dry friction problems

This note is a survey of recent results based on the papers [6, 7, 8]. Dry friction forces acting on a moving particle due to its contact to walls have in certain situations the form #(x)(g0(:~) + sgn £'), where x is displacement from rest, k is velocity, # and go are non-negative bounded continuous, and sgnr = r/Ir [ for r • R {0}, see [1, 5, 13]. When there are also restoring and external forces, the following equation is studied ;~ + g ( x ) + ~1 sgn~ ~-~ ~2 ,z~(t), (1.1)

Bifurcation of periodic solutions in differential inclusions

Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.

Bifurcation from homoclinic to periodic solutions in singularly perturbed differential inclusions

The existence of periodic solutions is studied for certain singularly perturbed differential inclusions. Applications are given to dry friction problems.

Bifurcation from Homoclinic to Periodic Solutions in Ordinary Differential Equations with Multivalued Perturbations

The existence of periodic solutions are studied for certain differential inclusions. Applications are given to ordinary differential equations with multivalued perturbations embodying also dry friction problems. Singularly perturbed differential inclusions are investigated as well.

Periodic solutions of dry friction problems

Dry friction problems lead to discontinuous differential equations, e.g. to $$x'' + xx' + \mu \operatorname{sgn} x' + \beta ^2 x = \varphi (t),$$ where sgn γ=γγ for γ ≠ 0 and sgn (0)=[ − 1. 1]. We study existence of ω-periodic solutions of (1) in case ϕ is ω-periodic. Results forx> 0 are given in the book “Multivalued Differential Equations” (K. Deimling: De Gruyter 1992). and preliminary ones forx=0 are contained in K. Deimling “Multivalued differential equations and dry friction problems” (Proc. Conf. Differential & Delay Equations. World Sci. Publ. 1992). Based on the latter and considerable additional analysis, we give a complete description of the resonant casex=0.β=1. ϕ(t)=sint. In particular, it turned out that for μ e (π 4. 1) there is a unique globally asymptotically stable 2π-periodic solutionxgm, which necessarily has deadzones (i.e.xμ (t) ≡c in certain intervals). In addition, the nonresonant case is solved by means of degree theory for multivalued maps, since in this situation a priori bounds can be found easily.