Frictional Motion Research Articles

How frictional slip evolves

Earthquake-like ruptures break the contacts that form the frictional interface separating contacting bodies and mediate the onset of frictional motion (stick-slip). The slip (motion) of the interface immediately resulting from the rupture that initiates each stick-slip event is generally much smaller than the total slip logged over the duration of the event. Slip after the onset of friction is generally attributed to continuous motion globally attributed to ‘dynamic friction’. Here we show, by means of direct measurements of real contact area and slip at the frictional interface, that sequences of myriad hitherto invisible, secondary ruptures are triggered immediately in the wake of each initial rupture. Each secondary rupture generates incremental slip that, when not resolved, may appear as steady sliding of the interface. Each slip increment is linked, via fracture mechanics, to corresponding variations of contact area and local strain. Only by accounting for the contributions of these secondary ruptures can the accumulated interface slip be described. These results have important ramifications both to our fundamental understanding of frictional motion as well as to the essential role of aftershocks within natural faults in generating earthquake-mediated slip.

Transient postseismic slip and aftershock triggering: A case study of the 2008 MW7.9 Wenchuan Earthquake, China

In this study, we investigate how a stress variation generated by a fault that experiences transient postseismic slip (TPS) affects the rate of aftershocks. First, we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion, that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law, and that the TPS can be explained by a continuous creep process undergoing reloading. Second, we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS. For the Wenchuan sequence, we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law (MOL), the Dieterich model, and the specific TPS model. The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12, where A and B are the parameters in the rate- and state-dependent friction law respectively. Moreover, the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance, respectively. Because the B/A ratio in the current model is always larger than 1, the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1. Finally, the influence of the background seismicity rate r on parameters is studied; the results show that except for the apparent aftershock duration, other parameters are insensitive to r.

Oil density and viscosity affect emulsion stability and destabilization mechanism

The effects of the oils density and viscosity (DV) on the emulsions kinetic stability and destabilization mechanisms were revealed from the perspective of droplets movement and emulsions viscosity. With the extension of storage time, severe creaming (20.20 ± 0.73 × 10−4 mm/s), flocculation and coalescence (7.26 ± 0.82 μm−2 min−1) occurred in emulsions prepared with oils of lowest DV; the extent of creaming (15.90 ± 0.68 × 10−4 mm/s) and coalescence (1.36 ± 0.10 μm−2 min−1) were alleviated upon increasing oils DV, accompanied by the occurrence of acute Ostwald ripening (17.03 ± 1.72 μm3 min−1); and only slight creaming (2.26 ± 0.24 × 10−4 mm/s), flocculation, coalescence (0.70 ± 0.09 μm−2 min−1) and Ostwald ripening (6.14 ± 0.42 μm3 min−1) occurred in emulsions prepared with oils of highest DV. This was because oils with higher DV (especially density) restricted the droplets fluidity due to an increased motion friction, leading to a more homogeneous internal network and a higher apparent/macroscopic viscosity (0.31 ± 0.04 Pa·sn and 0.1 nm−2 s) of emulsions. These impeded the Brownian motion and diffusion of droplets to decrease the collision frequency/efficiency and mass transfer respectively, which in turn conduced to retarding droplets size enlargement and stabilizing the emulsions against different destabilization mechanisms.

Development and analysis of magnet-engaged piezoelectric energy generator under friction-induced vibration

Piezoelectric energy transducers, which can be an efficient solution for the power supply of wireless devices, have been widely researched. This study investigated the characteristics of a magnet-engaged nonlinear piezoelectric energy generator stimulated by friction-induced vibration (FIV), in two distinct design configurations (in-parallel and in-series). A mathematical model was developed, and the dynamic response of the mechanical system and voltage output from the piezoelectric shear deformation were solved using an iterative method. A friction model considering the Stribeck effect was introduced to describe the friction motion. The emergence of a stick-slip motion induced limit cycle and its vanishing delineates the unstable and stable regions of the system, respectively. A critical sliding velocity vc splits the regions. When the sliding velocity exceeds vc, the system remains in stable region with exclusive slip friction behavior. Parameter studies were conducted to explore the effect of decay factor β, dynamic friction coefficient μk, static friction coefficient μstatic, and normal force FN on vc. The results indicate that increasing β and μk can reduce the unstable region and generation of FIV, whereas, increasing FN and μstatic can promote the occurrence of FIV. The energy generation was evaluated by a transient charging simulation that has been experimentally validated in a previous study. The influence of β, μk, μstatic, and FN on the energy generation was also investigated relative to the operating velocity range (OVR) and sum of root mean square charging power (SRCP). The in-parallel systems exhibit a higher SRCP within the same OVR, whereas the in-series systems are more likely to excite FIV with a wider OVR. Additionally, the simulation results of fluctuating working conditions show that both fluctuating FN and v0 have negative effects on the energy generation. The nonlinear in-series system exhibits better robustness with the least affected SRCP and almost unchanged OVR under fluctuating FN and v0.

Friction Reduction and Motion Stability of Setal Array Sliding on Rough Surface

Friction Reduction and Motion Stability of Setal Array Sliding on Rough Surface

The linear and non-linear study of effect of rotation and internal heat source/sink on Bénard convection

The primary objective of this study is to investigate non-linear Bénard convection in a single-walled carbon nanotube suspension saturated in a rotating porous medium with an internal heat sink/source. The modified Buongiorno model is utilized to formulate the governing equations for the flow. Both linear and weak non-linear stability analyses are conducted in this investigation. The linear stability analysis employs the truncated Fourier series transformation, while the weakly non-linear stability analysis utilizes the Lorenz model, assuming weak thermophoresis, porous friction, and small-scale convective motion. The cubic Ginzburg–Landau equation is formulated and subsequently solved to derive the expression for the amplitude. The influence of various parameters, such as the Taylor number, heat sink/source parameter, and viscosity parameter, is discussed in relation to the threshold criteria of convection, as well as heat and mass transport rates. Based on the linear stability analysis, it is determined that the introduction of a rotating frame of reference delays the initiation of convection, whereas the energy supplied to the system accelerates the onset of convection. The heat transfer rate increases by when the nanofluidic system is placed in the rotating frame of reference under the presence of an internal heat source.

Towing couplers of a multi-sectional vehicle

BACKGROUND: The most difficult stage in the operation of a tractor with heavy towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, the use of the initial kinetic energy of the tractor, which can develop when using limited elastically deformable towing couplers, can be considered. AIMS: Analysis of efficiency of using elastically deformable towing couplers for a road train with heavy towed objects at the starting mode. METHODS: The analytical research of the developed mathematical model of the initial stage of starting of a road train with elastic couplings was carried out for optimization of properties of these devices with regard to the process efficiency improvement. In order to assess the effectiveness of using elastically deformable towing couplers, the results obtained should be compared with similar results corresponding to absolutely rigid towing couplers. RESULTS: Comparison of displacements, velocities and energies testifies to the high efficiency of the elastically deformable towing coupler. The use of elastically deformable towing couplers gives the ability to accumulate the initial kinetic energy of an airfield tractor, which makes it possible to overcome the static friction force and ensure the starting of heavy towed objects. CONCLUSIONS: Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with completely rigid and elastically deformable towing couplers shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable towing couplers can cause oscillations of the tractor-towed objects system. In order to prevent them, the towing couplers must be locked at the time of their greatest deformation.

Numerical Study on Vibration Response of Compressor Stator Blade Considering Contact Friction of Holding Ring

There are many kinds of assembly structures in heavy-duty gas turbine compressor stator blades which have significant influence on the complex damping vibration characteristics. At present, compressor design is becoming more and more compact, so it is very meaningful to accurately obtain stator blade vibration characteristics of structures with contact damping. Firstly, a fretting slip friction dynamic model was introduced, and then a vibration analysis model of the compressor stator blade with outer ring structure was established based on the slip friction theory. Then, the vibration response of the compressor stator blade was obtained according to various working conditions, and the main factors affecting the vibration characteristics of the stator blade were revealed. Finally, the vibration response of the blade under a particular exciting force condition was simulated. The results show that the damping vibration characteristics of the compressor stator blades were affected by the excitation force and the normal load of the contact surface. The vibration response curve of the stator blade and the equivalent stiffness coefficient of the contact surface were analyzed, and the friction motion of the contact surface changed with the change of the working condition. The model can simulate the nonlinear vibration characteristics of stator blades. This method provides a reference for the vibration safety analysis of compressor stator blades.

Physical and chemical properties of amaranth grain as affected by the varietal characteristics and humidity

Purpose. To establish the peculiarities of the formation of physicochemical properties of amaranth grain under the effect of varietal characteristics and humidity. Methods. Laboratory methods for determination of physicochemical and physicomechanical properties of grain; calculation for determination of volume, area and sphericity of grain; mathematical and statistical methods for the analysis of the experimental data. Results. The research shows that the carbohydrate content of amaranth grain varied from 63.1 to 68.7%. At the same time, the content of carbohydrates in the grain of variety ‘Kharkivskyi-1’ was significantly higher compared to ‘Atstek’ and ‘Helios’. The content of protein in the grain of the studied varieties varied significantly. The highest protein content was in the grain of 'Lera' and ‘Kharkivskyi-1’ varieties (20.2–24.9%). It should be noted that the lysine content in the grain of these varieties was also the highest (0.85–0.91%). Grain moisture content in the studied varieties was low (8.3–11.1%). The highest grain quality was in the ‘Helios’ variety – 819 g/dm3, while in the rest of the studied varieties it ranged from 748 to 775 g/dm3. 1000-kernel weight and 1000-kernel volume were almost equal in the studied amaranth varieties. At the same time, the angle of the natural slope varied reliably. The coefficients of external friction at rest and the coefficient of external friction in motion for the grain of the varieties ‘Kharkivskyi-1’, ‘Lera’ and ‘Atstek’ were significantly higher compared to ‘Helios’. The geometric parameters of grain changed reliably depending on their humidity: as the humidity of the grain increases, its geometric parameters increase. An increase in the moisture content of the grain increases the linear dimensions. At the same time, the volume and surface area of the grain increases, thanks to which the sphericity increases. Conclusions. It was established that the physicochemical properties of amaranth grain reliably change as affected by varietal characteristics and humidity. The grain of amaranth varieties ‘Lera’ and ‘Kharkivskyi-1’ has the highest protein content (20.2–24.9%) and lysine (0.85–0.91%). The carbohydrate content is 65.3–68.7%. ‘Helios’ variety has the highest grain quality – 819 g/dm3. 1000-kernel weight is 0.664–0.710 g, depending on the variety. The grain of varieties ‘Kharkivskyi-1’, ‘Lera’ and ‘Atstek’ is characterized by a higher angle of natural slope, coefficients of external friction at rest and external friction in motion. An increase in grain moisture significantly increases its geometric parameters.

Analysis and rationale of TOW units for tractors with massive towed objects

The most difficult stage in the operation of a tractor with massive towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, we can consider the use of the initial kinetic energy of the tractor, which can be developed when using limited elastically deformable tow units. To optimize the mathematical model, the following assumptions are made: traction force F on the hook of the tractor is a constant value; the inertial masses of the tractor and towed objects are the same and equal m. The dynamics of a tractor and massive towed objects is described by means of theoretical mechanics, taking into account the elastic deformation of tow units. The composed systems of linear homogeneous differential equations with right-hand sides are solved by the method of elimination of functions with increasing of exponential order, as a result of which differential equations of the fourth and sixth power are formed. Initial conditions at t = 0: since the tow unit is not deformed and no force is applied to the towed object. The periods t2 and t3 are determined, during which the tow units will undergo maximum deformation. To assess the effectiveness of the use of elastically deformable tow units, the results obtained should be compared with similar results corresponding to absolutely rigid tow units. Comparison of displacements, speeds and energy testifies to the high efficiency of the elastically deformable tow units. The use of elastically deformable tow units makes it possible to accumulate the initial kinetic energy of an aircraft tow tractor, which makes it possible to overcome the static friction force and ensure the starting of heavy towed objects. Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with absolutely rigid and elastically deformable tow units shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable tow units can cause oscillations of the tractor-towed objects system. To prevent them, the tow units must be blocked at the moment of their maximum deformation.

INITIAL TRACTOR DYNAMICS WITH MASSIVE TOWED OBJECTS

It is noted that the most difficult stage in the operation of a tractor with massive towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, we can consider the use of the initial kinetic energy of the tractor, which can develop when using elastically deformable towing devices. Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with absolutely rigid and resiliently deformable traction coupling devices shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable towing devices can cause oscillations of the tractor–towed objects system. To prevent them, the towing devices must be blocked at the moment of their greatest deformation.

Analysis of heat transfer and thin film flow of Au−Np over an unsteady radial stretching sheet

The analysis of heat transfer and thin film flow over an unsteady radial stretching surface is the primary focus of this work. For the two-dimensional motion of the pair stress nanofluid made of gold nanoparticles, a mathematical model is put forth. Nonlinear governing partial differential equations for momentum and energy are converted into a set of ordinary differential equations via similarity transformations. By using the BVP4c method, the resulting nonlinear differential equations were calculated. The relationship between the Nusselt number, temperature, skin friction, and fluid motion velocity is examined and graphically analyzed. This study suggests that thin film thickness increases for rising values of volume fraction whereas it dropped for increasing values of the magnetic parameter and unsteadiness parameters Maximum heat transfer rate and skin friction coefficient has been observed for blade and cylinder shaped nanoparticles and minimum for brick shape.

The Initiation of Frictional Motion—The Nucleation Dynamics of Frictional Ruptures

AbstractFrictional interfaces lose stability via earthquake‐like ruptures, which are close analogues of shear cracks that are well‐described by fracture mechanics. Interface ruptures, however, need to be first formed—or nucleated. Rupture nucleation therefore determines the onset of friction, replacing the concept of a characteristic “static friction coefficient”. Utilizing rupture arrest at an imposed barrier, we experimentally determine nucleation locations, times and stresses at the origin of each subsequent rupture event. This enables us study the nucleation process via real‐time measurements of real contact area and local strain. Nucleation events initiate as 2D patches that expand at nearly constant velocities, vnuc, that are orders of magnitude lower than the dynamic rupture velocities described by conventional fracture mechanics. We find that: (a) Nucleation has location‐dependent stress thresholds, (b) vnuc is roughly proportional to the local stress level, (c) the nucleation process continues until the patch size reaches Ltran ∼ LG, the Griffith length for the onset of dynamic fracture (d) scaling time by τ = Ltran/vnuc, nucleation patches exhibit self‐similar dynamics (e) dynamic ruptures' cohesive zones are not fully established until significantly beyond Ltran. Many details of nucleation are governed by the local contact area topography, which is roughly invariant under successive rupture events in mature interfaces. Topography‐dependent details of the nucleation process include: precise nucleation site location, patch geometry, critical stress thresholds and the proportionality constant of vnuc with stress. We believe that these results shed considerable light on both how frictional motion is triggered and earthquake initiation.

Deterministic and stochastic chaos characterize laboratory earthquakes

We analyze frictional motion for a laboratory fault as it passes through the stability transition from stable sliding to unstable motion. We study frictional stick-slip events, which are the lab equivalent of earthquakes, via dynamical system tools in order to retrieve information on the underlying dynamics and to assess whether there are dynamical changes associated with the transition from stable to unstable motion. We find that the seismic cycle exhibits characteristics of a low-dimensional system with average dimension similar to that of natural slow earthquakes (<5). We also investigate local properties of the attractor and find maximum instantaneous dimension ≳10, indicating that some regions of the phase space require a high number of degrees of freedom (dofs). Our analysis does not preclude deterministic chaos, but the lab seismic cycle is best explained by a random attractor based on rate- and state-dependent friction whose dynamics is stochastically perturbed. We find that minimal variations of 0.05% of the shear and normal stresses applied to the experimental fault influence the large-scale dynamics and the recurrence time of labquakes. While complicated motion including period doubling is observed near the stability transition, even in the fully unstable regime we do not observe truly periodic behavior. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics. As applied to tectonic faults, our results imply that even small stress field fluctuations (≲150 kPa) can induce coefficient of variations in earthquake repeat time of a few percent. Moreover, these perturbations can drive an otherwise fast-slipping fault, close to the critical stability condition, into a mixed behavior involving slow and fast ruptures.

Mechanical Properties and Friction Dynamics of Organogels Solidified with Rice Paraffin.

Raw materials suitable for a sustainable society have attracted interest in the cosmetics industry. We focused on rice bran as a sustainable material and evaluated the gelation behavior of paraffin extracted from rice bran (rice paraffin) against liquid paraffin, squalane, jojoba oil, and silicone oil. In addition, the frictional properties of the prepared organogel on an artificial skin surface were evaluated using a sinusoidal motion friction evaluation system. Rice paraffin solidified all oils even at the lowest wax concentration of 5 wt%. The hardness and kinetic friction coefficient μ k increased with an increase in the wax composition. The hardness and μ k of organogels solidified with rice paraffin were smaller than those of gels solidified with petroleum-derived paraffin. These differences are caused by the smaller carbon amount of rice paraffin. The friction parameters depended on the type of oil: the μ k of RLG composed of rice and liquid paraffin was greater than that of the other three oils (R, L, and G denote rice paraffin, liquid paraffin, and gel, respectively). These findings promote the development of lipsticks and cleansing gels consisting of sustainable development goal-responsive raw materials.

Friction Dynamics of Organogels on Artificial Skin Surfaces

Organogels are attractive formulations in cosmetics, food, and pharmaceuticals. They exhibit characteristic frictional and mechanical responses during the collapse of a mesostructure. In this study, the friction dynamics of organogels composed of five different waxes (paraffin wax, microcrystalline wax, ceresin, candelilla wax, and carnauba wax) and liquid paraffin were evaluated using a sinusoidal motion friction evaluation system. All organogels exhibited a velocity dependence of friction coefficient that increased with the acceleration of the contact probe. Depending on the ease of the crystal formation of the waxes in liquid paraffin, hydrocarbon-based waxes formed soft organogels with a low-friction coefficient, whereas ester-based, highly polar waxes formed organogels that were hard and had a high-friction coefficient.

Oscillatory tribometry: transition from static to kinetic friction

Oscillatory tribometry is presented as a new method for investigations on the transition from static friction to kinetic friction. The method distinguishes between purely elastic deformations and plastic frictional motions. Friction moduli are defined which are directly proportional to the stored and dissipated energy during an oscillation cycle. The elastic deformations are represented through the elastic friction modulus, which is directly proportional to the average elastic energy over an oscillation cycle, while the frictional motions yield the dissipation friction modulus, which is directly proportional to the average dissipated energy over an oscillation cycle. Energy dissipation in the static and boundary regime can be attributed to local dissolution of contact bonds or intermolecular adhesion bonds at the contact points, and thus to local slip. The ability to measure at very small sliding distances in oscillatory tribometer tests is a crucial prerequisite for such investigations. The methodology provides access to local friction phenomena at the intermolecular level while simultaneously measuring macroscopic samples. The application examples presented show that oscillatory tribometry on a highly sensitive rheometer is particularly valuable for applications such as dry contacts between polymers, elastomers or soft materials.

Observation of enhanced nanoscale creep flow of crystalline metals enabled by controlling surface wettability

Understanding and controlling interface friction are central to many science and engineering applications. However, frictional sliding is closely related to adhesion, surface roughness, surface chemistry, mechanical deformation of contact solids, which poses the major challenge to experimental studying and theoretical modeling of friction. Here, by exploiting the recent developed thermomechanical nanomolding technique, we present a simple strategy to decouple the interplay between surface chemistry, plastic deformation, and interface friction by monitoring the nanoscale creep flow of metals in nanochannels. We show that superhydrophobic nanochannels outperforming hydrophilic nanochannels can be up to orders of magnitude in terms of creep flow rate. The comparative experimental study on pressure and temperature dependent nanomolding efficiency uncovers that the enhanced creep flow rate originates from diffusion-based deformation mechanism as well as the superhydrophobic surface induced boundary slip. Moreover, our results reveal that there exists a temperature-dependent critical pressure below which the traditional lubrication methods to reduce friction will break down. Our findings not only provide insights into the understanding of mechanical deformation and nanotribology, but also show a general and practical technique for studying the fundamental processes of frictional motion. Finally, we anticipate that the increased molding efficiency could facilitate the application of nanoimprinting/nanomolding.

Friction dynamics of human hair treated with water or cationic surfactant aqueous solution

AbstractCationic surfactants are adsorbed on the surface of human hair and exhibit a lubricating effect. Here, we evaluated the friction when the hair treated with water or 1 wt% cationic surfactant (cetyltrimethylammonium bromide) aqueous solution was rubbed by a contact probe equipped in a sinusoidal motion friction evaluation system. Because of the rough structure of the cuticle on the human hair surface, an oscillatory phenomenon with a frequency of 50–70 Hz was observed when untreated hair was rubbed with a contact probe. On the other hand, the oscillatory phenomenon was not observed when the hair contained a large amount of water because stick–slip phenomena were inhibited on the soft, swollen hair surface. Furthermore, the change in kinetic friction coefficient and delay time, which is a normalized value of the time difference between the reaction of the friction force to accelerated motion, from untreated hair, Δμk and Δδ, was almost zero. However, we found a large difference in Δμk and Δδ for the hair treated with cationic surfactant aqueous solution. The treatment with cationic surfactant reduced both friction parameters, Δμk and Δδ, indicating that the treatment induced not only the frictional force but also the profile at the beginning of frictional sliding. The significant lubrication is due to cationic surfactant adsorption on the hair surface. These data imply that the smoothness of hair treated with a cationic surfactant is related to a reduction in friction coefficient and delay time δ.

Dynamometer Testing of Energy Efficient Hydraulic Fluids and Fuel Savings Analysis for US Army Construction and Material Handling Equipment

The US Army uses MIL-PRF-2104 SAE 10 hydraulic fluid in its construction and material handling equipment. This oil meets basic performance requirements but has not been optimized for hydraulic system efficiency. Hydraulic system efficiency is important because fuel transportation has unique costs and dangers in military applications. Two energy efficient hydraulic fluids were compared to MIL-PRF-2104 SAE 10 in dynamometer testing. The higher efficiency fluids reduced internal leakage flow losses and decreased low-speed motor friction. Fleet-wide fuel savings estimates for US Army construction and material handling machines were derived from engine fuel consumption models, vehicle mission profiles, hydraulic circuit analysis and dynamometer test results. The savings due to reduced fuel consumption was estimated to be $8,000,000 per annum.