Mechanism analysis and improved model for stick-slip friction behavior considering stress distribution variation of interface

Studying the evolution of interface contact state, revealing the "black box" behavior in interface friction and establishing a more accurate friction model are of great significance to improve the prediction accuracy of mechanical system performance. Based on the principle of total reflection, a visual analysis technology of interface contact behavior is proposed. Considering the dynamic variation of stress distribution in interface contact, we analyze the nonlinear characteristics of contact parameters in different stages of stick-slip process using the above-mentioned experimental technology. Then, we find that the tangential stiffness of the interface is not a fixed value during the stick-slip process and the stress distribution variation is one of the important factors affecting the tangential stiffness of interface. Based on the previous experimental results, we present an improved stick-slip friction model, considering the change of tangential stiffness and friction coefficient caused by the stress distribution variation. This improved model can characterize the variation characteristics of contact parameters in different stages of stick-slip process, whose simulation results are in good agreement with the experimental data. This research may be valuable for improving the prediction accuracy of mechanical system performance.     

Modeling of the dynamic contact in stick-slip microdrives using the method of reduction of dimensionality

In this work we present a new method to describe movements of stick-slip microdrives. On the microscopic scale we model the contact between actuator and slider as a dynamic tangential contact using the method of reduction of dimensionality. On the macroscopic scale simple one- and three-dimensional equations of motion are derived. An algorithm to solve these equations will be introduced. The results of the simulation will be compared qualitatively and quantitatively to experimental investigations. Even for the simplest assumed model it proves that experimental and numerical values correlate excellently.     

First-order phase transition between the liquidlike and solidlike structures of a boundary lubricant

A thermodynamic model for characterization of the first-order phase transition between the structural states of a boundary lubricant is suggested. It is shown that melting of the lubricant is due both to a rise in its temperature and to shear experienced by friction surfaces when elastic strains (stresses) exceed a critical value. A phase diagram with regions of dry and sliding friction is constructed. Using a mechanical analogue of the tribological system, the dependence of the friction force on the lubricant temperature and relative shear rate of the friction surfaces is analyzed. The observed conditions of stick-slip friction, which is the main reason for friction parts wear, are described. Reasons for stick-slip friction are revealed.     

Critical Velocity of Controllability of Sliding Friction by Normal Oscillations for an Arbitrary Linear Rheology

The application of ultrasonic vibrations is an established procedure in industry in order to significantly reduce and control sliding friction. One of the main characteristics of this phenomenon is that, beyond a certain critical sliding velocity, the friction is no longer controllable—although oscillations are still being externally applied. an a previous series of related studies, closed-form solutions of the critical velocity have been derived with respect to pure elastic and specific viscoelastic models. In the present paper we present a universal formula of the critical velocity which is valid for arbitrary linear rheology. The derivation relies on the same theoretical basis of the previous studies, where the reduction of friction is ascribed to a stick-slip motion of the contact. Therefore, all previous results represent limiting and special cases of this universal equation. In the second part of this paper we pursue the numerical analysis of the previous studies by investigating the reduction of friction for a viscoelastic Kelvin material for the first time.     

Stochastic theory of ultrathin lubricant film melting in the stick-slip regime

Melting of an ultrathin lubricant film under friction between atomically smooth surfaces is studied in terms of the Lorentz model. Additive noise associated with shear stresses and strains, as well as with film temperature, is introduced, and a phase diagram is constructed where the noise intensity of the film temperature and the temperature of rubbing surfaces define the domains of sliding, dry, and stick-slip friction. Conditions are found under which stick-slip friction proceeds in the intermittent regime, which is characteristic of selforganized criticality. The stress self-similar distribution, which is provided by temperature fluctuations, is represented with allowance for nonlinear relaxation of stresses and fractional feedbacks in the Lorentz system. Such a fractional scheme is used to construct a phase diagram separating out different types of friction. Based on the study of the fractional Fokker-Planck equation, the conclusion is drawn that stick-slip friction corresponds to the subdiffusion process.     

Transition from stick-slip to continuous sliding in atomic friction: entering a new regime of ultralow friction

A transition from stick-slip to continuous sliding is observed for atomically modulated friction by means of a friction force microscope. When the stick-slip instabilities cease to exist, a new regime of ultralow friction is encountered. The transition is described in the framework of the Tomlinson model using a parameter eta which relates the strength of the lateral atomic surface potential and the stiffness of the contact under study. Experimentally, this parameter can be tuned by varying the normal load on the contact. We compare our results to a recently discussed concept called superlubricity.     

Effect of correlated temperature fluctuations on the phase dynamics in an ultrathin lubricant film

The melting of an ultrathin lubricant film at friction between atomically smooth surfaces is studied with allowance for fluctuations of its temperature, which are described by the Ornstein-Uhlenbeck process. The behavior of the most probable types of shear stresses arising in the lubricant is considered, and phase diagrams for second-and first-order phase transformations (the melting of an amorphous lubricant and that of a crystalline lubricant, respectively) are constructed. It is shown that, in the former case, lubricant temperature fluctuations lead to the formation of a stick-slip friction domain separating the domains of dry and sliding friction, which is typical of first-order transitions. In the latter case, three domains of stick-slip friction arise, which mark the transitions between dry friction and metastable and stable sliding friction. As the time of correlation of lubricant temperature fluctuations gets longer, the temperature of rubbing surfaces rises to the point where sliding friction sets in.     

Modelling of a two-dimensional Coulomb friction oscillator

Xia proposes a model for investigating the stick-slip motion caused by dry friction of a two-dimensional oscillator under arbitrary excitations. Instead of the harmonic balance method used by most investigators, a numerical approach to investigate the system is provided. The concept of the friction direction angle is introduced to determine the components of the static and kinetic friction force vector and the hyperbolic secant function is introduced to deal with the transition of the friction force from the static to the kinetic state. The friction direction angle is determined by either relative velocities or input forces. With this method the switch conditions for stick state, slip state and stick-slip state can be easily derived. The orbits of the responses, which are either straight line segments, circular or elliptic are obtained. In the general case, the orbit of the response is a complex planar curve. Zero-stop, one-stop, two-stops and more than two-stops per cycle are also found.     

Texture-induced modulations of friction force: the fingerprint effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.     

Modeling friction on a mesoscale: master equation for the earthquakelike model

The earthquakelike model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach naturally describes stick-slip and smooth-sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the studies of the properties of the contacts.     

Modeling of dry sliding friction dynamics: from heuristic models to physically motivated models and back

After giving an overview of the different approaches found in the literature to model dry friction force dynamics, this paper presents a generic friction model based on physical mechanisms involved in the interaction of a large population of surface asperities and discusses the resulting macroscopic friction behavior. The latter includes the hysteretic characteristic of friction in the presliding regime, the velocity weakening and strengthening in gross-sliding regime, the frictional lag and the stick-slip behavior. Out of the generic model, which is shown to be a good, but rather computationally intensive, simulation tool, a simpler heuristic model, which we call the generalized Maxwell-slip friction, is deduced. This model is appropriate for quick simulation and control purposes being easy to implement and to identify. Both of the generic and heuristic model structures are compared, through simulations, with each other and with experimental data.     

基于滑动势能面的二维材料原子尺度摩擦行为的量化计算

近年来,二维材料优异的摩擦特性成为人们关注的焦点,然而目前缺乏理论上对其摩擦力进行快速、有效、精确的计算预测方法.本文提出采用密度泛函理论计算真实体系的滑动势能面,利用得到的"数值型势能面"替代传统的解析势函数,并结合Prandtl-Tomlinson模型,量化求解具有复杂形状势能面的真实二维材料体系的摩擦行为.基于该方法,揭示了原子力显微镜实验中观察到的石墨烯Moire纹超晶格结构的双周期"黏-滑"摩擦现象;理论预测了二维材料异质结构的层间超低摩擦现象,相对于同质材料,其静摩擦力和滑动摩擦力均成数量级降低,发现势能面起伏和驱动弹簧刚度均会影响层间相对滑动路径,进而对层间的摩擦行为产生影响.该方法同样可拓展到其他van der Waals作用主导的界面摩擦体系.     

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.     

A numerical study on stick-slip motion of a brake pad in steady sliding

A numerical model for an elastic brake pad sliding under constant load and with constant velocity over a rigid surface is investigated by finite element analysis. The geometry is taken to be two-dimensional, the contact is assumed to follow the laws of continuum mechanics and temporal and spatial resolution are such that dynamical effects localized at the interface are resolved. It turns out that at the contact interface localized slip events occur either in the form of long-lasting slip pulses, or in the form of brief local relaxations. Macroscopically steady sliding, macroscopic stick-slip motion or slip-separation dynamics occurs, depending on the macroscopic relative velocity. While structural oscillations of the brake pad do not seem to play a significant role during steady sliding at least one structural oscillation mode becomes synchronized with the interfacial dynamics during stick-slip or slip-separation motion. Assuming a given friction law for the interface, the macroscopically observed friction coefficient depends considerably on the underlying dynamics on the interface.     

Periodic intermittent regime of a boundary flow

Melting of an ultrathin lubricant film during friction between two atomically smooth surfaces is investigated using the Lorentz model for approximating the viscoelastic medium. Second-order differential equations describing damped harmonic oscillations are derived for three boundary relations between the shear stresses, strain, and temperature relaxation times. In all cases, phase portraits and time dependences of stresses are constructed. It is found that under the action of a random force (additive uncorrelated noise), an undamped oscillation mode corresponding to a periodic intermittent regime sets in, which conforms to a periodic stick-slip regime of friction that is mainly responsible for fracture of rubbing parts. The conditions in which the periodic intermittent regime is manifested most clearly are determined, as well as parameters for which this regime does not set in the entire range of the friction surface temperature.     

Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction

We propose an archetypal self-excited system driven by moving belt friction, which is constructed with the smooth and discontinuous(SD) oscillator proposed by the Cao et al. and the classical moving belt. The moving belt friction is modeled as the Coulomb friction to formulate the mathematical model of the proposed self-excited SD oscillator. The equilibrium states of the unperturbed system are obtained to show the complex equilibrium bifurcations. Phase portraits are depicted to present the hyperbolic structure transition, the multiple stick regions, and the friction-induced asymmetry phenomena. The numerical simulations are carried out to demonstrate the friction-induced vibration of multiple stick-slip phenomena and the stick-slip chaos in the perturbed self-excited system. The results presented here provide an opportunity for us to get insight into the mechanism of the complex friction-induced nonlinear dynamics in mechanical engineering and geography.     

Minimal models for disk brake squeal

Numerous publications on the modeling of disk brake squeal can be found in the literature. Recent publications describe the onset of disk brake squeal as an instability of the trivial solution resulting from the non-conservative friction forces even for a constant friction coefficient. Therefore, a minimal model of disk brake squeal must contain at least two degrees of freedom. A literature review of minimal models shows that there is still a lack of a minimal model describing the basic behavior of disk brake squeal which can easily be associated to an automotive disk brake.Therefore, a new minimal model of a disk brake is introduced here, showing an obvious relation to the technical system. In this model, the vibration of the disk is taken into account, as it plays a dominant role in brake squeal. The model is analyzed with respect to its stability behavior, and consequences in using it in the optimization of disk brake systems are discussed.     

Stick-slip regime of melting of boundary lubrication taking into account spatial inhomogeneity

The processes of boundary friction between two atomically smooth solid surfaces with an ultrathin layer of lubricant between them are studied in the context of the model of the first-order phase transitions, taking into account the spatial inhomogeneity. The stick-slip regime of motion, which is often observed experimentally for such systems, is considered. Such a regime is represented as the periodic first-order phase transitions between the structural states of the lubricant. It is shown that during motion, the lubricant tends to assume a homogeneous structure over the sliding plane, which results in the periodicity of time dependences of the basic parameters in the stick-slip regime. The dependence of the order parameter on the shear rate is analyzed and it is shown that this dependence has the same shape for all the regions on the contact plane.     

Finite element modelling for the investigation of in-plane modes and damping shims in disc brake squeal

Squeal propensity of the in-plane modes and the constrained-layer type damping shims for disc brake system is investigated by using the finite element method. Theoretical formulation is derived for a rotating disc in contact with two stationary vibrating pads attached to the damping shim components. By the conversion from the theoretical to FE brake model, the full equations of motion for the actual disc brake system describes the disc rotation, the in-plane friction characteristics and damping shims in association with squeal vibration. It is concluded from the results that the in-plane torsion modes can be generated by the negative friction slope, but they cannot be controlled by the damping shims. The in-plane radial mode is also investigated and found to be very insensitive in squeal generation.     

Tribological system in the boundary friction mode under a periodic external action

A mechanical analog of a tribological system in the boundary friction mode is studied. A thermodynamic model is used to analyze the first-order phase transition between liquidlike and solidlike structures of a lubricant. The time dependences of the friction force, the relative velocity of the interacting surfaces, and the elastic component of the shear stresses appearing in the lubricant are obtained. It is shown that, in the liquidlike state, the shear modulus of the lubricant and the elastic stresses become zero. The intermittent (stick-slip) friction mode detected experimentally is described. It is shown that, as the lubricant temperature increases, the frequency of phase transitions between the lubricant structural states decreases and the total friction force and elastic stress amplitudes lower. When the temperature or the elastic strain exceeds the corresponding critical value, the lubricant melts and a kinetic slip mode in which the elastic component of the friction force is zero takes place.