Nonequilibrium kinetics of phase transitions in the boundary friction mode

A nonequilibrium evolution thermodynamic model is presented, which describes the processes developing in the boundary friction mode. The excessive volume parameter is introduced to describe the lubricant state; it has a minimum value in the case of the solid-like structure of the lubricant and increases during melting. The source of entropy growth which results from the external energy inleak during the deformation of the lubricant owing to the shear of the rubbing surfaces, is taken into account. It is shown that the stick-slip mode of motion occurs within wide ranges of the parameters; this is caused by periodic phase transitions of the first-order between the structural states of the lubricant. The effect of the shear velocity, load, and temperature on the pattern of stick-slip friction is studied.     

Nonlinear thermodynamic model of boundary friction

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied. An excess volume parameter is introduced, the value of which is related to the presence of defects and inhomogeneities in the lubricant. Via minimization of the free energy, the Landau-Khalatnikov kinetic equation is obtained for this parameter. The kinetic equation is also used for relaxation of elastic strains, which in its explicit form contains the relative shear velocity of the rubbing surfaces. With the numerical solution of these equations, a phase diagram with domains corresponding to the sliding and dry stationary friction regimes is built at a fixed shear velocity. A simple tribological system is used to demonstrate that in the dynamic case, three friction regimes can occur, namely, dry, stick-slip, and sliding friction. It is shown that a lubricant can melt when the shear velocity exceeds a critical value and with elevation of its temperature. The dependence of the dynamic friction force on the pressure applied to the surfaces, the temperature of the lubricant, and the shear velocity is considered. It is shown that growth of pressure leads to the forced ordering and solidification of the lubricant.     

Hysteresis Behavior in the Stick–Slip Mode at the Boundary Friction

A tribological system is considered that consists of two atomically smooth solid surfaces separated by an ultrathin lubricant film. A thermodynamic model based on the Landau theory of phase transitions is built that describes the behavior of this system in the boundary friction mode. The free energy density for an ultrathin lubricant film is given in the form of expansion in series in terms of the powers of order parameter that is reduced to the shear modulus of the lubricant. The kinetics of the system is studied on the basis of a model describing first-order phase transitions between kinetic modes of friction. It is shown that in the presence of spring between the external drive and block the width of temperature hysteresis increases versus fixed coupling.     

A stochastic model of stick-slip boundary friction with account for the deformation effect of the shear modulus of the lubricant

The melting of an ultrathin lubricating film during the friction of two solid atomically smooth surfaces is studied within the limits of the Lorentz model that approximates a viscoelastic medium, the deformation effect of the shear modulus being taken into account. It is shown that the action of a random force representing additive non-correlated noise results in the sustained oscillation mode that corresponds to stickslip friction. The numerical modeling of the process yields the ratios between the relaxation times at which the stick-slip mode is characterized by a high amplitude. The amplitude of stick-slip transitions is found to decrease as the shear modulus of the lubricant increases.     

Synergetic representation of stick-slip mode of boundary friction

The melting of an ultrathin lubricating film clamped between two atomically smooth solid surfaces that are in relative motion is studied based on the Lorentz model for the approximation of a viscoelastic medium. An equation of motion for the stresses has been derived in the form of a three-order differential equation and analyzed at various friction surface temperatures. In all cases, the phase portraits and the time dependences of the stresses have been plotted. It has been found that, depending on the temperature and the lubricant parameters, either the damped oscillation mode or the stochastic oscillation mode may occur. The stochastic oscillation mode is presented in the phase plane as a strange attractor. It has been shown that initial conditions have a critical effect on the system behavior. Based on the model, the behavior of two types of tribosystems, i.e., with the unidirectional shear of the surfaces and under an alternating external effect, has been described.     

Mechanism of Crack Growth in Lubricated Rolling/Sliding Contact

In order to explain the mechanism of rolling-contact fatigue crack growth analytically, fracture mechanics are applied to a semicircular surface crack inclined at an angle to the elastic half-space loaded by Hertzian stresses.

It is shown that the surface traction is the controlling factor for lubricant seepage into the crack and for shear mode crack growth rate. It is also clarified that the generation of pits results from tensile mode crack growth mainly due to the oil hydraulic pressure action.     

A Model for Wall Slip Prediction of Confined n-Alkanes: Effect of Wall-Fluid Interaction Versus Fluid Resistance

It is shown via molecular dynamics simulations that the occurrence of wall slip for linear alkanes confined between geometrically smooth surfaces depends on the wall-fluid interactions and the chain length of the lubricant molecules. A wall slip model based on the competition between these two factors is introduced. A surface parameter accounts for the wall-fluid interaction and commensurability, and is valid for both canonical and complex crystal lattices: this quantity is then linked to the shear stress transferred to the fluid molecules. The lubricant internal cohesion under confinement is described by a bulk viscosity term. Finally, a semi-analytical law for wall slip prediction including both the fluid viscosity and the surface characterization parameter is proposed.     

Lubricant oils additivated with polymers in EHD contacts: Part 1. Rheological behaviour

This paper reports on the influence of a polymer additive on the traction behaviour of a mineral oil investigated using a two‐disc machine at different temperatures and contact pressures. A semi‐empirical approach was used for determining the effective lubricant rheological parameters ‐ the elastic shear modulus, the viscosity of the lubricant, and the limiting and Eyring stresses ‐ in elastohydrodynamic contacts. Using this approach, the effect of polymer concentration on the rheological parameters that appear in both the Johnson‐Tevaarwerk and Bair‐Winer models was quantified. The influence of operating conditions, such as pressure, oil temperature, and polymer concentration, on the traction coefficient, limiting shear stress (from the Bair‐Winer model), Eyring stress (from the Johnson‐Tevaarwerk model), shear modulus, and apparent viscosity was also investigated.     

Design considerations for cushion form bearings in artificial hip joints.

Lubrication mechanisms and contact mechanics have been analysed in a new generation of 'cushion form' bearings for artificial hip joints, which comprise low elastic modulus layers on the articulating surfaces. Comparisons have been made with 'hard' bearings used in existing prostheses and also with the natural hip joint. Lubricating film thicknesses are enhanced by larger contact areas and lower contact pressures. For a fixed contact area, simultaneous changes in layer thickness and radial clearance have been shown to have a small effect on elastohydrodynamic film thickness. Hard bearings designed with the same contact area as the cushion bearings produced a similar film thickness, but lubricant film thickness is not optimized in current designs. The main advantage of using a cushion bearing with low elastic modulus layers was found to be associated with microelastohydrodynamic lubrication. Careful selection of the elastic modulus is important in order to ensure that this lubrication regime was effective. Low elastic modulus layers may also produce local deformations, which enhance squeeze film action. The elastic modulus of the material should not be lower than necessary to produce effective microelastohydrodynamic lubrication, as a further reduction in modulus only increases the strain distribution in the material. A lubricant film thickness of 0.3 microns has been predicted for a cushion hip prosthesis with a femoral head diameter of 32 mm and radius of contact zone of 16 mm, using a 2 mm thick layer with an elastic modulus of 20 MPa.     

含增粘剂润滑油粘弹性的实验研究

本文将系统分析原理引入到对润滑剂本构方程的研究中来,进而提出了一种对本构方程研究的新的实验方法。通过实验得到了含增粘剂润滑油的本构方程的频谱特征图,从而证实了该方法的可行性。将四种增粘剂润滑油在不同增粘剂含量不同温度下的实验数据按照Maxwell流变模型进行回归,得到流变参数(剪切弹性模量)与增粘剂含量、温度之间的关系,给出了回归公式。该公式在一定范围内反映了流变参数的变化规律。     

环形金属橡胶隔振器弹性参数的确定

以实验研究为基础，通过对大量实验结果的分析，借助于金属元件抗拉弹性模量和剪切模量的计算方法，推导出环形金属橡胶隔振器在承受扭剪应力时，抗拉弹性模量以及扭剪弹性模量与金属丝直径、环形隔振器的几何参数、金属橡胶元件的相对密度之间的关系的理论计算公式。研究结果证明，利用该计算公式和有限元计算方法，可以直接求得具有不同结构参数的相应形状金属橡胶隔振器的弹性性能参数，所得计算结果与实验结果具有良好的一致性，因而大大减少了实验工作量，为金属橡胶隔振器的系列化生产奠定了基础。     

The lubrication of lightly loaded cylinders in combined rolling, sliding and normal motion with couple stress fluid

The lubrication of lightly loaded cylinders with combined rolling, sliding and normal motion is investigated with a couple stress fluid as lubricant under cavitation boundary conditions. It is shown that the major bearing performance characteristics can be accounted for by means of a dimensionless parameter, q, involving the “normal” and “entraining” velocities, the minimum film thickness and the radius of the geometrically equivalent cylinder near a plane. The load capacity and frictional drag increase as the squeeze velocity increases. This increase is enhanced by decreasing the couple stress parameter, τ. However, when the two surfaces move apart these results are reversed. It is convenient to adopt the least-squares procedure for the accurate representation of the line of cavitation and the line of maximum pressure. The effect of couple stresses on the point of cavitation is quite significant compared with viscous fluid of the same viscosity.     

Elastohydrodynamic Lubrication of Rough Surfaces under Oscillatory Line Contact with Non-Newtonian Lubricant

This paper presents the results of a transient analysis of elastohydrodynamic lubrication (EHL) of two parallel cylinders in line contact with a non-Newtonian lubricant under oscillatory motion. Effects of the transverse harmonic surface roughness are also investigated in the numerical simulation. The time-dependent Reynolds equation uses a power law model for viscosity. The simultaneous system of modified Reynolds equation and elasticity equation with initial conditions was solved using the multigrid, multilevel method with full approximation technique. The film thickness and the pressure profiles were determined for smooth and rough surfaces in the oscillatory EHL conjunctions, and the film thickness predictions were verified experimentally.

For an increase in the applied load on the cylinders or a decrease in the lubricant viscosity, there is a reduction in the minimum film thickness, as expected. The predicted film thickness for smooth surfaces is slightly higher than the film thickness obtained experimentally, owing primarily to cavitation that occurred in the experiments. The lubricant film under oscillatory motion becomes very thin near the ends of the contact when the velocity goes to zero as the motion direction changes, but a squeeze film effect keeps the fluid film thickness from decreasing to zero. This is especially true for surfaces of low elastic modulus. Harmonic surface roughness and the viscosity and power law index of the non-Newtonian lubricant all have significant effects on the film thickness and pressure profile between the cylinders under oscillatory motion.     

A non-averaging method of determining the rheological properties of traction fluids

Traction machines have been frequently used to study the rheological responses of lubricants in elastohydrodynamic lubrication (EHL) contacts. Fundamental properties are inferred from EHL traction measurements based on the average pressures and temperatures in the contact. This average approach leads to uncertainty in the accuracy of the results due to the highly nonlinear resonse of the fluid such as viscosity to both pressure and temperature. A non-averaging method is developed in this paper to study the elastic and plastic properties of traction fluids operating in EHL contacts at small slide-to-roll ratios. A precision line-contact traction rig is used to measure the EHL traction at a given oil temperature and Hertz pressure. By choosing a sensible pressure-property expression, the parameters of the expression can be determined through the initial slope and peak traction coefficient of the traction measurements. The elastic shear modulus and the limiting shear stress of the lubricant corresponding to a single pressure can then be calculated for a range of pressures and temperatures of practical interest. Two high-traction fluids are studied, and their elastic moduli and limiting shear stresses presented.     

Couple stresses in the elastohydrodynamic film in rolling bearings

Couple stresses may appear, when additives are present in a lubricant or when the lubricant molecules are long chains. Couple stresses are particularly probable in the elastohydrodynamic lubrication of gears or of heavily loaded rollers, where the film thickness is exceptionally small. For simplicity, the Grubin-type approximation is used in the present analysis to study the effect of couple stresses on the minimum film thickness between elastic rollers. A new parameter is defined and used to study the effects of couple stresses. The appearance of couple stresses has the desirable effect of increasing the minimum film thickness, especially when the chain length of the additive molecule or of the lubricant molecule is large.     

Effects of transverse atomic steps on bilayer lubricating films of simple hydrocarbons

Molecular dynamics (MD) simulations were conducted in order to study the dynamic behavior and traction of bilayer lubricating films of n-hexane, cyclohexane, and n-hexadecane. Lubricants were confined between bcc iron surfaces with and without transverse grooves of mono-atomic depth. Once the system equilibrated statically, one of the solid surfaces was moved to shear the film. The results demonstrated that the traction coefficient was governed by structures of the films, which depended on the molecular structures of the lubricants and on the atomic scale geometry of the solid surfaces. Traction was high when interfacial slip between lubricant layers and solid walls occurred. Evolution of the layered structure by gradual rearrangement of the molecules and resulting slip between the lubricant layers, caused significant reduction in the traction coefficient. The atomic steps enhanced the molecular rearrangement of n-hexadecane, while they retarded or inhibited those of n-hexane and cyclohexane resulting in a relatively higher traction coefficient for stepped surfaces. Molecular orientation of the normal alkanes under shear is described by the orientational order parameter, which has a strong correlation with the traction coefficient. The steady state traction coefficient of all the three simple hydrocarbons was highest when both of the surfaces had steps, and lowest when both of the surfaces were flat.     

Obtaining the pressure spike and maximum shear stress from optical interferometry data

In order to predict and optimise highly loaded contact performance, accurate lubricant data is crucial. The lubricant's high-pressure rheological behaviour is by far the least known parameter. However, this is the key factor to realistic modeling of non-Newtonian Elasto-Hydrodynamic lubrication. In this paper a new approach is described to extract such data from optical interferometric film thickness measurements of EHL contacts. The approach is relatively straightforward and cheap compared to “out of contact” rheological experiments using specialized equipment.A measured high-resolution film thickness distribution was positioned using a computed film thickness distribution as a reference. The reference is computed using the same operating conditions as the measurement. Subsequently, from the computed film thickness difference, a pressure difference file is obtained by deconvolution. Adding this pressure difference to the computed pressure file associated with the computed reference film thickness, provides a corrected pressure distribution, as it has appeared in the experimental contact. In this paper results are presented for the pressure spike region of the contact, in which significant shear stresses occur. The basic approach and its difficulties are described as well as some “tricks”, such as the reduction of (local) noise resulting from the ill-posedness of the deconvolution. It is shown that simple averaging over a circle segment in the pressure spike zone, results in significant noise reduction and a very good ‘measured’ pressure spike.     

Quantifying diffused hydrogen in AISI-52100 bearing steel and in silver steel under tribo-mechanical action: Pure rotating bending, sliding-rotating bending, rolling-rotating bending and uni-axial tensile loading

Hydrogen embrittlement is often a catastrophic phenomenon of machine elements failure under cyclic stresses. This hydrogen is generated as a result of tribo-chemical and mechanical actions on the working surfaces. This hydrogen can have three different zones or stages of behaviour under tribo-mechanical actions. Firstly, it can strongly adsorb on the mating surfaces at a shallow subsurface zone and take up the load in the boundary-lubricating regime and reduce the coefficient of friction. At a second stage, it can diffuse to the deep subsurface zone where it might work together with Hertzian stresses and embrittle the subsurface zone. The last zone of hydrogen activity is the bulk of the bearing steel where it is known to collect under the action of tensile stresses and degrade the bearing steel and hence resulting in catastrophic failure. It is important and interesting to follow up the presence of hydrogen in these zones in order to predict the safe functioning of the machine elements. In addition to this a clear distinction must be made between the internal hydrogen embrittlement and environmental hydrogen embrittlement. Two important behaviours of hydrogen are studied and quantification was made by a melting sample technique. Dependence of hydrogen diffusion on the variation of tribo-mechanical action is shown in this work. This was done by studying the pure rotating bending, rotating bending with combination of sliding and rolling motion of the mating surfaces and uni-axial tensile experiments in pure water environment to see the diffusion of hydrogen into or out of the AISI-52100 bearing steel and in silver steel. Two different approaches were adopted in order to investigate the presence of hydrogen in three zones under the action of different stress states. The two techniques are melting sample technique by using hydrogen analyser and elastic recoil detection analysis, an ion beam technique. It is believed until now that hydrogen spread is homogeneous in the bearing steel. The results obtained showed that the inherent amount of hydrogen in steel samples is non-homogeneous and it was learnt that inherent amount of hydrogen in the steel samples is very important in order to support the boundary lubrication by hydrogen. Content of hydrogen in the steel samples showed a relation to the increasing number of cyclic stresses. The sliding-rotating bending stress state showed a considerable wear of the surfaces but the content of hydrogen was not very high in that sample when compared to the samples that were run under pure rotating bending stress state.     

Wear resistance of coating materials under the frictional heating conditions

The problem of the wear of an elastic coating due to a rigid body sliding over the coating surface and heating due to contact friction has been considered. The solution of the quasi-static problem has been constructed in the form of a series over eigenvalues. The area of unstable solutions of the problem, where the thermoelastic instability of a sliding contact takes place, has been determined in the dimensionless parameter space. The wear resistance of a coating has been studied for different kinds of materials depending on the following parameters: the relative sliding velocity of contact surfaces, the mode of the contact interaction of the friction surfaces, the coating thickness, etc. taking into account the temperature and stresses developing at the contact interface.