Complete solutions of plasticity theory in the task of pressing a flat rigid punch into a surface plastic layer adhered to a hard base

A complete solution of the mathematical plasticity theory on pressing a flat rigid punch into a surface, relatively soft, plastic layer has been obtained. The solution finds practical application for calculating the load-carrying ability of a friction bearing. The slip-line fields and the velocity hodographs satisfying the problem boundary conditions have been defined. Extreme contact pressures were determined, and a graph of how the numerical values depend on the relative length of the contact area has been plotted.     

Plotting and analysis of hodographs for studying the electrophysical parameters of objects using attachable eddy-current transducers

The results of experimental studies during the eddy-current testing of conducting (including ferromagnetic) objects are considered. A data correcting procedure was suggested; it allows one to decrease the requirements for the phase and frequency stability characteristics of the measuring circuit and to relate experimental results to a theoretic model. Initial and corrected hodographs for a number of materials with different electrophysical properties are reported. The magnetic permeability magnitudes of steel 30X13 were calculated for two electromagnetic-field exciting frequencies (15 kHz and 1 MHz).     

Test results of friction factor for round-hole roughness surfaces in closely spaced channel flow of water

For examining friction-factor characteristics of round-hole pattern surfaces which are usually applied on damper seals, flat plate test apparatus is designed and fabricated. The measurement method of leakage and pressure distribution along round-hole pattern specimen with different hole area is described and a method for determining the Fanning friction factor is discussed. Results show that the round-hole pattern surfaces provide a much larger friction factor than smooth surface, and the friction factor vs. clearance behavior yields that the friction factor generally decreases as the clearance increases unlike the results of Nava’s flat plate test. As the hole depth is decreased, the friction factor is increased, and maximum friction factor is obtained for 50% of hole area. Since the present experimental friction factor results show coincident characteristics with Moody’s friction factor model, empirical friction factors for round-hole pattern surfaces are obtained by using the Moody’s formula based on curve-fit of the experimental data. Results of Villasmil’s 2D CFD simulation support the present experimental test result.     

Influence of Ultrasonic In-Plane Oscillations on Static and Sliding Friction and Intrinsic Length Scale of Dry Friction Processes

The force of friction between plates of different materials (steel, brass, copper, titanium, glass, aluminum, rubber, and Teflon, among others) and a steel sample oscillating in the sliding plane at a frequency of 40–70 kHz has been studied. The measured friction coefficient as a function of sliding velocity and velocity oscillation amplitude fits well with theoretical predictions based on the simple Coulomb friction law at sliding velocities larger than the actuation velocity. However, the friction coefficient tends to a finite value at small sliding velocities, which is contrary to the theoretical prediction. The static limit has been studied in detail. A strong decrease in the static friction force takes place at oscillation amplitudes of 20–60 nm. Such amplitudes are enough to control the friction coefficient. The experimental data for both static and sliding friction are interpreted within the framework of a microscopic model and a phenomenological macroscopic model. The notion of intrinsic friction slip length is introduced.     

Analytical Models for Atomic Friction

In this methods article, we describe application of Prandtl–Tomlinson models and their extensions to interpret dry atomic-scale friction. The goal is to provide a practical overview of how to use these models to study frictional phenomena. We begin with the fundamental equations and build on them step-by-step—from the simple quasistatic one-spring, one-mass model for predicting transitions between friction regimes to the two-dimensional and multi-atom models for describing the effect of contact area. The intention is to bridge the gap between theoretical analysis, numerical implementation, and predicted physical phenomena. In the process, we provide an introductory manual with example computer programs for newcomers to the field, and an illustration of the significant potential for this approach to yield new fundamental understanding of atomic-scale friction.     

Calculating frictional force with considering material microstructure and potential on contact surfaces

A method based on the energy dissipation mechanism of an Independent Oscillator model is used to calculate the frictional force and the friction coefficient of interfacial friction. The friction work is calculated with considering the potential change of contact surfaces during sliding. The potential change can be gained by a universal adhesive energy function. The relationships between frictional force and parameters of a tribo-system, such as surface energy and microstructure of interfacial material, are set up. The calculation results of the known experimental data denote that the frictional force is nearly proportional to the surface energy of the material, nearly inversely proportional to the scaling length, and independent of the lattice constant. The results agree with that of adhesion friction equations. They also agree with the experimental results performed with an atomic-force microscope under the ultra high vacuum condition. __________ Translated from Tribology, 2006, 26(2): 159–162 [译自: 摩擦学学报]     

Hodographs of Magnetic Permeability of Cylindrical Rods in Homogeneous AC Magnetic Field

The effective magnetic permeability of cylindrical rods is derived from experimental data by solving the inverse problem for cylindrical samples under a homogeneous ac magnetic field. The complex magnetic permeability is plotted as a function of the frequency of the ac field. The graphs are presented in the form of hodographs. Some parameters of the hodographs are very important for determination of electromagnetic parameters of materials and sort of steel. Studies of the effective magnetic permeability of rods from various materials versus frequency demonstrated that this characteristic provides a good basis for a multiparametric technique of nondestructive examination.     

Speed and Atmosphere Influences on Nanotribological Properties of NbSe<Subscript>2</Subscript>

Nanotribological properties of NbSe₂ are studied using an atomic friction force microscope. The friction force is measured as a function of normal load and scan speeds ranging from 10 nm s⁻¹ to 40 μm s⁻¹ under two atmospheres (air and argon). At low speed, no effect of atmosphere is noticed and a linear relationship between the friction and normal forces is observed leading to a friction coefficient close to 0.02 for both atmospheres. At high speed, the tip/surface contact obeys the JKR theory and the tribological properties are atmosphere dependent: the shear stress measured in air environment is three times lower than the one measured under argon atmosphere. A special attention is paid to interpret these results through numerical data obtained from a simple athermal model based on Tomlinson approach.     

A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the “true” asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07–0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.     

Frequency Dependence of the Effective Magnetic Permeability of Plates in Homogeneous Magnetic Field

The paper reports on calculations of the magnetic permeability of plates in a longitudinal homogeneous ac magnetic field based on experimental data. The corresponding curves and hodographs of the effective magnetic permeability are given.     

Bridging the Gap Between the Atomic-Scale and Macroscopic Modeling of Friction

A short survey of a modern view on the problem of friction from the physical viewpoint is presented. An atomically thin lubricant film confined between two substrates in moving contact has been studied with the help of molecular dynamics (MD) based on Langevin equations with coordinate- and velocity-dependent damping coefficient. Depending on model parameters, the system may exhibit either the liquid sliding regime, when the lubricant film melts during sliding (the “melting-freezing” mechanism of stick-slip motion), the “layer-over-layer” sliding regime, when the film keeps a layered structure at sliding, or the solid sliding regime, which may provide an extremely low friction (“superlubricity”). Atomic-scale MD simulations of friction, however, lead to a “viscosity” of the thin film, as well as to the critical velocity of the transition from stick-slip to smooth sliding, which differ by many orders of magnitude from the values observed in macroscopic experiments. This contradiction can be resolved with the help of the earthquakelike (EQ) model with a continuous distribution of static thresholds. The evolution of the EQ model is reduced to a master equation which can be solved analytically. This approach describes stick-slip and smooth sliding regimes of tribological systems within a framework which separates the calculation of the friction force from the atomic-scale studies of contact properties.     

Embedding Wear Models into Friction Models

Frictional behavior in dry or boundary-lubricated tribosystems is commonly time-dependent. Examples include phenomena like running-in, scuffing initiation, adhesive transfer, coating wear-through, and lubricant starvation. Fundamental models for the sliding friction coefficient usually focus either on determining a steady–state value or on predicting periodic behavior like stick-slip. They often neglect the details of long- and short-period frictional transients, some of which are quite repeatable. In addition to generating heat, frictional work is known to be dissipated in several ways, including roughness changes, wear particle generation, tribomaterial evolution, and microstructural alteration. Pairs of materials can display identical average friction coefficients but significantly different wear processes because frictional work is dissipated differently from one pair of materials to the next. The attributes of friction-versus-time behavior for combinations of metals, ceramics, and polymers can be comprised of stages whose understanding may require the development of piecewise friction models that include wear. This paper discusses past work on the subject, exemplifies embedding a simple wear model into a friction-versus-time model, and indicates how friction process diagrams can play a role.     

The Lubricating Properties of Human Whole Saliva

We demonstrate the efficient boundary lubricating properties of human whole saliva (HWS) in a soft hydrophobic rubbing contact, consisting of a poly(dimethylsiloxane) (PDMS) ball and a PDMS disk. The influence of applied load, entrainment speed and surface roughness was investigated for mechanically stimulated HWS. Lubrication by HWS results in a boundary friction coefficient of μ ≈ 0.02, two orders of magnitude lower than that obtained for water. Dried saliva on the other hand results in μ ≈ 2–3, illustrating the importance of hydration for efficient salivary lubrication. Increasing the surface roughness increases the friction coefficient for HWS, while it decreases that for water. The boundary lubricating properties of HWS are less sensitive to saliva treatment than are its bulk viscoelastic properties. Centrifugation and ageing of HWS almost completely removes the shear thinning and elastic nature observed for fresh HWS. In contrast, the boundary friction coefficients are hardly affected, which indicates that the high-M _w (supra-)molecular structures in saliva, which are expected to be responsible for its rheology, are not responsible for its boundary lubricating properties. The saliva-coated PDMS surfaces form an ideal model system for ex-vivo investigations into oral lubrication and how the lubricating properties of saliva are influenced by other components like food, beverages, oral care products and pharmaceuticals.     

Evaluation of friction coefficient using indentation model of Brinell hardness test for sheet metal forming

This work presents an indentation model of the Brinell hardness test, which is a rigid ball-deformable plane contact model (RB-DP model), to elucidate the sliding friction mechanism of sheet metal forming. In the proposed model, the friction force can be defined as a combination of shear (shearing effect) and plough (ploughing effect) forces. The real contact area ratio α is determined from the RBDP model under sliding condition. Moreover, the lateral contact area ratio A _c /A _r can be specified as a function of the real contact area ratio α. Based on Meyer’s law and Hertz contact problem, the maximum contact area ratio α _u , a limiting condition of the real contact area ratio α, can be described as a function of the strain hardening exponent n. Additionally, a limiting condition applies: the strain hardening exponent n must be less than 0.64 in the present model. The present friction model reveals that the friction coefficient μ _d is a function of strain hardening exponent n, the real contact area ratio α and the maximum contact area ratio α _u . The calculated friction coefficient μ _d agrees with the published experimental results.     

A friction model for microforming

For the simulation of metal forming processes, input data relating to the tool–workpiece interface is necessary. For microforming applications, this input data becomes very much more critical and traditional methods are not realistic. This paper describes an approach that seeks to describe friction by modelling the geometric surface roughness of the tool. This finite-element-based model has been validated experimentally in terms of loads and metal forming using the ring test and actual surface measurements. It enables more accurate and also more flexible modelling of friction.     

Fabrication,Characterisation and Tribological Investigation of Artificial Skin Surface Lipid Films

This article deals with the tribology of lipid coatings that resemble those found on human skin. In order to simulate the lipidic surface chemistry of human skin, an artificial sebum formulation that closely resembles human sebum was spray-coated onto mechanical skin models in physiologically relevant concentrations (5–100 μg/cm²). Water contact angles and surface free energies (SFEs) showed that model surfaces with ≤25 μg/cm² lipids appropriately mimic the physico-chemical properties of dry, sebum-poor skin regions. In friction experiments with a steel ball, lipid-coated model surfaces demonstrated lubrication effects over a wide range of sliding velocities and normal loads. In friction measurements on model surfaces as a function of lipid-film thickness, a clear minimum in the friction coefficient (COF) was observed in the case of hydrophilic, high-SFE materials (steel, glass), with the lowest COF (≈0.5) against skin model surfaces being found at 25 μg/cm² lipids. For hydrophobic, low-SFE polymers, the COF was considerably lower (0.4 for PP, 0.16 for PTFE) and relatively independent of the lipid amount, indicating that both the mechanical and surface-chemical properties of the sliders strongly influence the friction behaviour of the skin-model surfaces. Lipid-coated skin models might be a valuable tool not only for tribologists but also for cosmetic chemists, in that they allow the objective study of friction, adhesion and wetting behaviour of liquids and emulsions on simulated skin-surface conditions.     

Interfacial potential barrier theory of friction and wear

An interfacial potential barrier theory to calculate friction and wear is proposed by considering the micro interaction of frictional surfaces. The theory suggests that the performance of friction and wear depends on the magnitude and distribution of the interfacial potential barrier on contact surfaces. The calculation methods of the interfacial potential barrier and standard interfacial potential barrier are then studied and the formulas to calculate the friction force, friction coefficient, and quantity of adhesion wear are derived based on the theory. With its independence and stability, the standard interfacial potential barrier can be used as an index to describe the frictional performance of materials. The calculation results of the friction force with some existing experimental data are consistent with the experimental results performed with an ultra high vacuum atomic-force microscope, which proves that the theory and method are feasible. __________ Translated from Tribology, 2007, 27(1): 54–59 [译自: 摩擦学学报]     

UHV friction of tribofilms derived from metal dithiophosphates

The friction‐reduction mechanisms of Modtp and Zndtp were highlighted by submitting tribofilms to friction in ultra‐high vacuum (UHV). The use of an UHV tribometer to understand these phenomena is justified by the fact that the friction coefficient recorded in UHV is close to the friction coefficient obtained in traditional tests in oil. After UHV friction, the transfer films on the pin were analyzed by in situ AES, XPS and AES mapping. Low friction is associated with the transfer to the pin of a sulfur‐rich film. In the case of Modtp, we observe a very thin MoS₂ film. The UHV friction coefficient approaches 0.04. In the case of Zndtp, the transfer film contains ZnS together with some phosphates. Because of the poor capacity of ZnS to reduce friction, the UHV friction coefficient recorded is near 0.15. A global model of the action of dithiophosphates in reducing friction is described on the basis of the hard and soft acids and bases (HSAB) principle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental discrimination of plowing friction and shear friction

The friction of a diamond spherical indenter sliding on CrN coated nitrided steel was investigated. A friction model was proposed that takes into account plowing and shear friction. With the model the separate contributions of substrate properties and surface condition to the friction were successfully extracted: the shear friction coefficient μ _sh was found to depend exclusively on the surface condition, i.e., not on load on the indenter, hardness of the substrate, and thickness of the coating. On the other hand, the plowing component of friction was independent on surface condition.     

Contact-induced off-track vibrations of air bearing-slider-suspension system in hard disk drives

Contact-induced vibration of air bearing-slider-suspension system is a crucial issue for slider flying stability and head positioning precision of 1 Tbit/in² hard disk drives. In this paper, the contact-induced off-track vibrations of air bearing-slider-suspension system are investigated by simulation. A dynamic simulator is developed to calculate the interactions between the air bearing dynamics and vibrations of slider-suspension assembly. The simulation model consists of a finite element model of suspension assembly, an air bearing model based on the generalized lubrication equation, and a slider–disk contact model based on the probability distributions of surface roughness. A sequential method is used to couple all these models and analyses. The time history of the slider and suspension motions, together with the time-varying forces including air bearing force, air shear forces, contact force and friction force can be obtained. The effects of different contact conditions, such as the contact intensity, friction coefficient, and disk surface waviness on off-track vibrations are investigated numerically in details. The results reveal some mechanisms on how these factors contribute to the off-track vibrations of suspension assembly.