Dependent Friction Model Research Articles

Prediction of factor of safety of a slope with an advanced friction model

Landslides and other mass movements are quite prevalent phenomena in hilly areas, and sometimes cause huge losses of both life and property [1]. To mitigate these natural calamities, a precise scientific study that can predict the slope failures is required. Prediction of the mechanical stability of slopes both man made as well as natural is a tedious task after considering the complexity involved in the physical behaviour of the slope forming material as well as their intricate failure mechanisms [1–4]. Traditional approaches to predict stability of a slope are generally based on evaluation of a factor of safety through limit equilibrium analysis (LEA) [1–4]. The factor of safety (FOS) of a slope is defined as the ratio of shear strength to driving stress generally due to gravitational force along the failure plane [1–3]. Physically, FOSo1 signifies the slope to be unstable; however it is stable if FOS41 [1]. The limitation of the LEA is that the analysis is carried out with a single fixed value of shear strength of solids such as rocks and soils, while ignoring the sliding rate dependent failure strength. Experiments on rocks have shown that failure strength (also known as frictional strength) does depend on sliding velocity and time of stationary contact (also known as waiting time) of the sliding interface [5–7]. Moreover, based on these experimental observations, an advanced friction model has been proposed which is known as the rate and state dependent friction (RSF) model. The RSF model is basically a modified form of the Mohr–Coulomb failure criterion [13]. It is to be noted that the RSF model has been extremely successful in recent times for predicting the frictional behaviour of hard and rough solids such as rocks, soils, hard polymers etc. [8–11]. As a result, the RSF model has found widespread applications in the study of mechanics of earthquakes and faulting [10].

Simulation of Frictional Strength and Steady Relaxation Using the Rate and State Dependent Friction Model

In this paper, frictional strength of hard solids, such as rock–rock sliding surfaces, is studied as a function of waiting time and shearing velocity. A one dimensional spring–mass sliding system is numerically simulated under the quasistatic condition using the rate and state dependent friction model. It is established that frictional strength varies linearly with the logarithm of waiting time (also known as time of stationary contact or relaxation time, etc.) as well as logarithm of shearing velocity. Analytical expression developed for frictional strength is found to be valid only in the case of high stiffness of the connecting spring. In the steady relaxation simulation, a steadily sliding mass is suddenly brought to zero velocity and relaxation of the interfacial stress and corresponding velocity at the sliding interface is studied as a function of relaxation time in the velocity strengthening regime of friction. A mathematical relation is derived between state variable and waiting time using the concept of steady relaxation. The relaxation model is also compared with the experimental data from the literature. Finally, the present study enables one to unify the slide–hold–slide friction experiments.

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.

A load dependent friction model for fully plastic contact conditions

In fully plastic contact conditions where nominal contact pressure is relatively high, like in metal forming processes, individual summits join together to form contact patches. The geometry of these contact patches depends on the contact pressure, which results in load-dependent frictional behaviour. This paper describes a model that takes into account this effect, and calculates contact and coefficient of friction in such conditions based on a good description of the shapes of contact patches instead of individual summits. The results show that as the nominal contact pressure increases, the effect of surface topography becomes less significant while the effect of the interfacial shear strength remains important.

Simulation of fluid transients, for nonlinear fluids, with a lumped parameter model

AbstractThis paper deals with the modeling of transients in low pressure transmission lines. Modeling of low pressure lines becomes more and more important for increasing efficiency of fast switching applications and performance of pumps e.g. common rail diesel injection systems and suction pipes of pumps. One simulation method is the lumped parameter model. For example a straight pipe can be modeled as a cascade of inertia, friction and compressibility blocks. In this paper, the idea of cascades is adopted for transient simulation of nonlinear fluids. The model includes a nonlinear fluid law of an oil‐air mixture and the balance equations i.e. the compressibility and the inertia of the fluid. Friction is modeled by the frequency dependent friction model of Kagawa et.al. Comparison of simulation results with measurements from a test rig shows good correlation. Finally the scope of this simulation model is discussed and compared with measurements. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

State and Rate Dependent Friction Laws for Modeling High-Speed Frictional Slip at Metal-on-Metal Interfaces

In the present paper the applicability of state and rate dependent friction laws in describing the phenomena of high speed slip at metal-on-metal interfaces is investigated. For the purpose of model validation, results of plate-impact pressure-shear friction experiments were conducted by Irfan in 1998 and Irfan and Prakash in 2000 using a Ti6Al4V and Carpenter Hampden tool-steel tribo pair are employed. In these experiments high normal pressures (1-3GPa) and slip speeds of approximately 50m∕s were attained during the high-speed slip event. Moreover, these experiments were designed to investigate the evolution of friction stress in response to step changes in normal pressure and also in the applied shear stress during the high-speed slip event. A step drop in normal pressure is observed to result in an exponential decay of the friction stress to a new steady-state characteristic of the current normal pressure and the current slip velocity. A step drop in applied shear stress is observed to lead to an initial drop in friction stress, which later increases toward a new steady-state friction stress level. In response to the step drop in applied shear stress the slip velocity initially increases and then decreases to a new steady-state level consistent with the new friction stress level. A modified rate and state dependent friction model that employs both velocity and normal stress dependent state variables is used to simulate the experimental results. A good correlation is found between the experimental results and the predictions of the proposed state and rate dependent friction model.

Nonlinear dynamics of mechanical system with external excitation

Abstract This paper attends to the problem of vibration of a self-excited mechanical system with a relatively complicated, history dependent dry friction model. The experimentally identified friction model allows description of various cases of stationary and transient motion. The system is composed of a lumped mass that interacts with a belt by means of dry friction. The system is additionally subjected to an external harmonic excitation through elastic element. The main objective of the experimental research has been focused on the analysis of the system behaviour for various values of the excitation frequency. This paper includes also computer simulation of the vibration of the considered system and comparison between the results of experimental and theoretical analysis. The comparison enables the assumed friction model for steel-polyester pair to be verified. It was another goal of the investigations.

Low-velocity friction between macroscopic solids

We analyze the physical mechanisms taking place in unlubricated friction between surfaces of micrometric roughness at sliding speeds <100 μm ·s −1 . This analysis is based on extensive experimental investigations of the time and velocity dependences of static and dynamic friction forces, and of non-stationary sliding. It fully supports the state and rate dependent friction model first proposed by Rice and Ruina.

A New Compensator for Servo Systems With Position Dependent Friction

In this study, we present a new compensator design for systems with position dependent friction. Position dependent friction occurs between revolving parts that are conventionally used in mechanical systems. Because the friction force changes with the position, the conventional servo controller can not maintain consistent performance. In this paper, a modified Karnopp function is proposed to more accurately describe the friction force’s position dependency. A control methodology then exploits this position dependent friction model in order to cancel out the friction force variation and achieve ultimate boundedness [18]. Experimental results demonstrate that the controller achieves consistently good performance. Based on these results, a compensator design procedure is provided.

A position dependent friction model for solution reactions in the high friction regime: Proton transfer in triosephosphate isomerase (TIM)

A position dependent friction model based on Grote–Hynes theory is developed to describe activated rate processes in the high friction regime. The model is employed to determine the transmission coefficient, which corrects the transition state theory rate constant for recrossing of the transition state. A simple expression is derived for the transmission coefficient in the limit of a slow response of the thermal bath. The model is applied to the initial proton transfer step in the reaction catalyzed by triosephosphate isomerase, for which the standard Grote–Hynes theory was found to be inappropriate. The predictions of the position dependent friction model are in a good agreement with results of detailed molecular dynamics simulations. The method used to determine the transmission coefficient should be generally applicable to reactions that are strongly coupled to a slow thermal bath.

Dilatancy, compaction, and slip instability of a fluid‐infiltrated fault

We analyze the conditions for unstable slip of a fluid infiltrated fault using a rate and state dependent friction model including the effects of dilatancy and pore compaction. We postulate the existence of a steady state drained porosity of the fault gouge which depends on slip velocity as ϕss = ϕ0 + εln(v/v0) over the range considered, where v is sliding velocity and ε and v0 are constants. Porosity evolves toward steady state over the same distance scale, dc, as “state.” This constitutive model predicts changes in porosity upon step changes in sliding velocity that are consistent with the drained experiments of Marone et al. (1990). For undrained loading, the effect of dilatancy is to increase (strengthen) ∂τss/∂lnv by μssε/(σ – p)β where μss is steady state friction, σ and p are fault normal stress and pore pressure, and β is a combination of fluid and pore compressibilities. Assuming ε ∼ 1.7×10−4 from fitting the Marone et al. data, we find the “dilatancy strengthening” effect to be reasonably consistent with undrained tests conducted by Lockner and Byerlee (1994). Linearized perturbation analysis of a single degree of freedom model in steady sliding shows that unstable slip occurs if the spring stiffness is less than a critical value given by kcrit = (σ‐p)(b‐a)/dc ‐ εμssF(c*)/βdc where a and b are coefficients in the friction law and F(C*) is a function of the model hydraulic diffusivity c* (diffusivity/diffusion length2). In the limit c* →∞ F(c*) → 0, recovering the drained result of Ruina (1983). In the undrained limit, c* → 0, F(c*) → 1, so that for sufficiently large ε slip is always stable to small perturbations. Under undrained conditions (σ – p) must exceed εμss/β(b ‐ a) for instabilities to nucleate, even for arbitrarily reduced stiffness. This places constraints on how high the fault zone pore pressure can be, to rationalize the absence of a heat flow anomaly on the San Andreas fault, and still allow earthquakes to nucleate without concommitant fluid transport. For the dilatancy constitutive laws examined here, numerical simulations do not exhibit large interseismic increases in fault zone pore pressure. The simulations do, however, exhibit a wide range of interesting behavior including: sustained finite amplitude oscillations near steady state and repeating stick slip events in which the stress drop decreases with decreasing diffusivity, a result of dilatancy strengthening. For some parameter values we observe “aftershock” like events that follow the principal stick‐slip event. These aftershocks are noteworthy in that they involve rerupture of the surface due to the interaction of the dilatancy and slip weakening effects rather than to interaction with neighboring portions of the fault. This mechanism may explain aftershocks that appear to be located within zones of high mainshock slip, although poor resolution in mainshock slip distributions can not be ruled out.

A study of instantaneous flow rate measurement in a high-frequency region, based on hydraulic pipe line dynamics.

Concerning the dynamic characteristics of oil hydraulic pipe lines, experimental research from the view point of focusing on the unsteady flow rate through a pipe is insufficient because of the lack of adequate flowmeters. The authors develop a new system to measure the unsteady flow rate of oil through a circular pipe. The sampling frequency of the measurement is 1.28 kHz. The frequency responses and the transient responses of the oil hydraulic pipe lines are obtained by measuring the flow rate through a certain cross-section of the pipe and the pressure at the section simultaneously. The experimental results are compared with the theoretical results, which are calculated by making use of the so-called frequency dependent friction model. As a result, it is verified for the first time that the theory predicts the rate of the instantaneous flow rate measuring system is sufficient for the general dynamic test of oil hydraulic circuits and equipment.