Soft Elastohydrodynamic Lubrication Research Articles

Implementation of a New Smart-Lubricant Model Using Generalized Newtonian Approach in Soft Elastohydrodynamic Lubrication

Abstract This is an inceptive attempt to replace the classical Bingham fluid model with a continuous double Newtonian power-law-based constitutive equation for smart lubricants like magneto-rheological, electro-rheological, and ferro-fluids. The implementation of Bingham model in hydrodynamic (HD) and elastohydrodynamic (EHD) lubrication analyses is highly challenging and inconvenient due to its inherent discontinuity. Therefore, the present work demonstrates the use of an already existing rheological model with an appropriate set of parameters to describe the flow behavior of smart lubricants in a soft-EHD lubrication algorithm based on the generalized Newtonian approach. The formation of both floating and adherent cores validates the proposed model. An extensive parametric study is also performed to explore the effects of operating speed, load, and slide-to-roll ratio on the soft-EHL characteristics. The results are very promising, showing that it's possible to customize smart lubricants to match specific operating conditions. This is achieved by adjusting the yield stress value accordingly, allowing for the desired variation in lubrication characteristics.

Polymer Lubrication: Pressure–Viscosity–Temperature Dependence of Film Thickness for Highly Loaded Compliant Contacts in Elastohydrodynamic Lubrication Regime

Abstract The relevance of the compliant contacts operated in elastohydrodynamic lubrication regime has increased during the last decades. Polymers and elastomers have been preferred because of their low-cost production or their tribological performance in many mechanical and bioengineering applications, where the metals originally dominated. Especially, in high-performance applications, such as polymer gears, the current subject of interest covers the transition between Piezoviscous-elastic and Isoviscous-elastic regimes of elastohydrodynamic lubrication. Here, it is necessary to precisely determine operating conditions and lubricant properties such as rheology whose contribution to film thickness formation may be influenced by attributes of individual lubrication regimes. The high-pressure viscosimeter and the optical tribometer were used, the former to establish the pressure–viscosity–temperature relationship of two reference lubricants, natural Squalane and synthetic tri(2-ethylhexyl) trimellitate, and the latter to determine the central and minimum film thickness in the circular contact between the PMMA disc and the steel ball using the optical chromatic interferometry method. Experimental results of film thickness demonstrated a significant deviation from the soft elastohydrodynamic lubrication (EHL) models, independently of the lubricant used, load, entrainment speed, and temperature because the pressure–viscosity–temperature response of lubricant was not included. Due to this, film thickness data were regressed, and new power coefficients of dimensionless parameter G¯ were derived. Outcomes confirmed the operation of the compliant circular contact in the transition region between the Piezoviscous-elastic and Isoviscous-elastic regimes with the minimum film thickness identified on the side lobes of the horseshoe shape.

Solving transient problems in soft Elasto-Hydrodynamic lubrication

Many important problems in elasto-hydrodynamic lubrication arise when one of the contacting bodies is elastically soft. An example is the squeezing of a thin liquid film between a rigid sphere/cylinder and a soft elastic substrate, in which the sphere may not be sliding and be subjected only to normal loads (stationary contact), or it can be sheared at the same time and undergo steady or non-steady sliding. These problems are notoriously difficult to solve for soft solids under large loads and thin lubricant films. For this reason, indentation and sliding problems have usually been analyzed separately, and solutions for transient sliding problems are few. Here we develop a numerical method that avoids difficult-to-converge iterative methods and is able to solve both normal indentation and/or transient sliding lubrication problems. The scheme is fully automatic, stable, and efficient and requires only a linear matrix equation to be solved at every time step. We present solutions of two transient sliding problems: in the first of which, a rigid sphere undergoes transient normal lubricated contact followed by transient sliding on an elastic half space. In the second, a rigid cylinder undergoes transient lubricated sliding on an elastic foundation.

A mixed soft elastohydrodynamic lubrication model of textures in a rotary lip seal

A two-dimensional elastohydrodynamic numerical analysis is conducted for a rotary lip seal with a textured shaft by coupling flow, deformation and contact equations. In this analysis, an elastic deformation equation is used to obtain the displacement of the discrete lip surface and a correction process is proposed to calculate the contact pressure in operation. Considering the effects of circular and elliptical dimples respectively, the contact pressure distribution, lip deformation, oil film load support and leakage of the lip seal are obtained, and a parametric study for textures is performed. The results show that the effects of textures reshape the lip surface topography and generate secondary fluid pressure. Micro-dimples with appropriate size can significantly reduce the contact pressure.

Validity of Winkler's mattress model for thin elastomeric layers: beyond Poisson's ratio.

Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point-indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness, which itself depends on the problem under consideration.

The Effect of Texture Floor Profile on the Lubricant Film Thickness in a Textured Hard-On-Soft Bearing With Relevance to Prosthetic Hip Implants.

Polyethylene wear debris limits the longevity of prosthetic hip implants. We design a pattern of axisymmetric texture features to increase hydrodynamic pressure and lubricant film thickness and, thus, reduce solid-on-solid contact, friction, and wear in hard-on-soft prosthetic hip implant bearings. Specifically, we study the effect of the texture floor profile on the lubricant film thickness using a soft elastohydrodynamic lubrication model. We compute the optimum texture parameters that maximize the lubricant film thickness for different texture floor profiles, as a function of bearing operating conditions. Flat texture floor profiles create thicker lubricant films than sloped or curved texture floor profiles for their respective optimum texture design parameters. We find that the texture feature volume is the most important parameter in terms of maximizing the lubricant film thickness, because a linear relationship exists between the texture feature volume with optimum texture parameters and the corresponding optimum lubricant film thickness, independent of the texture floor profile.

Maximizing the Lubricant Film Thickness Between a Rigid Microtextured and a Smooth Deformable Surface in Relative Motion, Using a Soft Elasto-Hydrodynamic Lubrication Model.

We design a pattern of microtexture features to increase hydrodynamic pressure and lubricant film thickness in a hard-on-soft bearing. We use a soft elastohydrodynamic lubrication model to evaluate the effect of microtexture design parameters and bearing operating conditions on the resulting lubricant film thickness and find that the maximum lubricant film thickness occurs with a texture density between 10% and 40% and texture aspect ratio between 1% and 14%, depending on the bearing load and operating conditions. We show that these results are similar to those of hydrodynamic textured bearing problems because the lubricant film thickness is almost independent of the stiffness of the bearing surfaces in full-film lubrication.

Temperature-Dependent Friction of Gemini Hydrogels

Discussion and hypotheses regarding the dominant dissipation mechanisms in Gemini hydrogel sliding have often implicated viscous dissipation through shear rate and mesh size—essentially, if the dissipation is simply a result of viscous shear through a single mesh dimension at the surface, increasing viscosity, increasing sliding speed and decreasing mesh size will all increase the frictional shear. Based on the measurements of gel shrinking coupled with increasing viscosity with decreasing temperature, the expectation is that the friction will increase dramatically with decreasing temperature. Potential frictional dissipation mechanisms in hydrogel sliding were investigated by measuring friction coefficients over a range of temperature from − 20 °C (253 K) to + 20 °C (293 K). The gels were run in the Gemini configuration and were made from 7.5 wt% polyacrylamide (PAAm) formulations swollen in water. After casting, the hydrogel solvent (water) was exchanged with a 40:60 dimethyl sulfoxide (DMSO)–water solution by volume, which permitted experiments to be conducted below the freezing point of water alone (0 °C). The hydrogels were found to shrink as the temperature decreased, and measurements suggest that the mesh size changed from roughly ξ = 16 nm at + 20 °C to ξ = 10 nm at − 20 °C. The viscosity of the 40:60 DMSO–water solution was measured on a parallel plate rheometer over the range in temperature and found to increase from η = 1 mPa-s at + 20 °C to η = 12 mPa-s at − 20 °C. Experiments were conducted with 2-mm-radius spherical probes on flat sheets under reciprocating contact at a normal load of 2 mN, sliding speeds of either V = 10 µm/s or V = 1 mm/s and over a temperature range of − 20 °C to + 20 °C, at 5 °C increments. The entire system was allowed to equilibrate at each temperature, and the friction coefficients and associated uncertainties are reported. The friction behavior at V = 10 µm/s increased in proportion to the changes in viscosity and mesh size following the models, and had friction coefficients of µ = 0.01 at + 20 °C that increased to µ = 0.16 at − 20 °C. The high-speed sliding experiments at V = 1 mm/s were in the soft elastohydrodynamic lubrication regime, and the friction coefficient increased in proportion to the ratio of the viscosity changes, µ = 0.01 at + 20 °C to µ = 0.09 at − 20 °C. In the high-speed experiments, there was a dramatic shift in behavior from low to high friction around T = − 3 °C (270 K). Following the hypotheses of thermally activated friction, plots of the natural log of normalized friction (ln(µ/µo)) versus 1/RT were analyzed for both data sets and give activation energies of Ea = 16 ± 2 kJ/mol at V = 1 mm/s and Ea = 20 ± 2.5 kJ/mol at V = 10 µm/s. These activation energies are within the range of the activation energy of the viscosity for the DMSO–water solution, Ea = 15.9 ± 0.3 kJ/mol. Overall, these experiments clearly demonstrate that Gemini hydrogel friction increases with decreasing temperature and suggest that both viscosity and mesh size contribute to friction under direct contact sliding.

Soft-Elastohydrodynamic Lubrication Line Contact Analysis on a Strip of Bio-Materials

Abstract The characteristics of anisotropic material, finite deformation, and lubrication in biological system diminish the friction and wear between soft tissues with relative motion. In this research, the lubrication between pleura surfaces in relative motion is analyzed by soft elastohydrodynamic lubrication (soft-EHL) line contact with an equivalent model. The model is a soft, transversely isotropic (TI) elastic strip with finite thickness sliding under a rigid sinusoidal surface, which is used to simulate the surface irregularities, with lubricant in between. The material nonlinearity and the curvature effects due to finite deformation, which are significant in soft-EHL, are considered in the present study. The pressure distribution, film thickness, von Mises stress, and material deformation are analyzed and discussed under various combinations of elastic moduli and Poisson's ratios for the transversely isotropic models. The simulation results reveal that the soft-EHL modeling fit actual result better than the traditional EHL (t-EHL) modeling. The Poisson's ratio νp = 0.1 and νpz = 0.49 situation will have more gentle stress distribution. The present soft-EHL solver can be used to realize some desired stress distributions and to identify the mechanical properties bio-materials under the aids of experiments.

Simulation of the effects of non-Newtonian fluid on the behavior of a step hydraulic rod seal based on a power law fluid model

The rheological characteristics of the oil film on the rod-seal interface in the sealing zone have a major influence on the behavior of reciprocating seals. Because of the addition of polymers, the viscosity and temperature properties of hydraulic oil have improved and the fluid presents non-Newtonian characteristics. To investigate the influence of these characteristics on seal behavior, a soft elastohydrodynamic lubrication (EHL) numerical model is introduced to simulate a step seal under a mixed lubrication condition. A modified Reynolds equation is derived for calculating the fluid film pressure distribution more accurately. The equation is based on the power law fluid model and Jakobsson-Floberg-Olsson (JFO) cavitation theory. Results are presented to gain insight into the effect of non-Newtonian fluid characteristics on seal behavior, and the simulated results are compared to those of a Newtonian fluid to reveal the seal mechanism. The influence of operating parameters and the seal surface root mean square (RMS) roughness on sealing performance under different power law indexes is also investigated and discussed.

Modelling three-dimensional soft elastohydrodynamic lubrication contact of heterogeneous materials

Abstract This paper presents an approach for modelling three-dimensional soft elastohydrodynamic lubrication (EHL) contact of heterogeneous materials. In this approach, a hydrodynamic interface element is developed to achieve the coupling of elastic deformation of heterogeneous contacting bodies and the steady-state hydrodynamic lubrication at the contact interface. The deformation behaviors are simulated by the finite element method, while the hydrodynamic lubrication is dealt with by solving the Reynolds equation. This approach can enable the simulation of soft EHL contact between bodies with heterogeneous materials and complicated geometric configurations. Predicted lubrication performances of soft EHL contacts show good agreement with the experimental measurements reported in literature. Analysis and discussion are also conducted on various cases of soft EHL contact between an elastic ball and a coating-substrate system with or without inhomogeneities.

Analysis of Soft-Elastohydrodynamic Lubrication Line Contacts on Finite Thickness

Soft elastohydrodynamic lubrication (soft-EHL) is an important mechanism in biotribological systems. The soft-EHL has some distinct differences from the traditional hard-EHL, and a systematic analysis factoring in key features of the “softness” appears to be lacking. In this paper, a complete soft-EHL line-contact model is developed. In the model, the half-space approximation is replaced by the finite thickness analysis; the geometrical and material nonlinearity due to finite deformation is factored in; the surface velocities altered by the curvature effect are considered, and the load balance equation is formulated based on the deformed configuration. Solutions are obtained using a finite element method (FEM). The film thickness, pressure distributions, and material deformation are analyzed and discussed under various entraining velocities, elastic modulus, and material thickness of the soft layer. Comparisons are made between soft-EHL and hard-EHL modeling assumptions. The analyses show that the classical EHL modeling is not suitable for soft materials with high loads. The results show that the finite deformation (Green strain) should be considered in soft-EHL analysis. In the contact region, the hard EHL solver overestimates the pressure distribution and underestimates the film thickness and deformation.

Transitional behaviour between biphasic lubrication and soft elastohydrodynamic lubrication of poly(vinyl alcohol) hydrogel using microelectromechanical system pressure sensor

The soft hydrogel material is expected for a candidate material as biomimetic artificial cartilage with synergistic functionalities of adaptive multimode lubrication. In boundary lubrication mode of hydrogel material, the biphasic lubrication mechanism cooperatively exerts its functionality. In hydrodynamic lubrication mode, it is preferable that the lubricating surfaces be impermeable to trap the fluid pressure in contact surfaces, whereas the actual biphasic material like a hydrogel is a permeable material with surface porosity. It is indicated that the interstitial fluid pressurisation in the permeable biphasic material can contribute to significant fluid load support under lower sliding speed condition. So, the authors examined how the contrary fluid pressure effect appears in the transition from the boundary lubrication mode to soft elastohydrodynamic lubrication mode. In the experiment, a small pressure sensor was utilised to measure the in-situ fluid pressure in sliding condition. Although the experimental condition of this study was selective, the result showed a possibility of the negative effect of the biphasic surface, in which the permeable surface diminished the hydrodynamic fluid pressure. This means that one should manage and enhance the biphasic lubrication abilities in wide operation range when the hydrogel material was used as a load bearing material.

Observation on the deformation of dimpled surface in soft-EHL contacts

Abstract In order to study the deformation of a textured surface in soft elastohydrodynamic lubrication (EHL) contacts, observation of the deformed surface around the dimple was realized and conducted under a sliding condition with various loads by using optical interferometry. The results show that uneven deformation emerges around the dimple. Both the applied load and sliding velocity have significant influence on the deformation of the soft surface, especially on the deformation pattern. Contrary to the usual assumption, the effect of shear strains in the soft slider on the total surface deformation is increasingly noticeable, and it results in unexpectedly deformation patterns around the dimple.

Experimental and Numerical Analysis of Soft Elastohydrodynamic Lubrication in Line Contact

This paper describes an experimental setup that allows the observations of the stress distribution under soft elastohydrodynamic lubrication (EHL) in line contact by means of photoelasticity. This experimental method is rarely used in the EHL field. The photoelastic fringe patterns in the circular polarization are collected under different rolling speeds and loads. Numerical calculations are carried out to analyze the oil film thickness, pressure, and shear stress distribution. Compared with those results, numerical and experimental stress distribution are basically consistent. Some beneficial conclusions are obtained. These are helpful to investigate further the oil pressure distribution and directly observe the stress distribution under lubrication conditions through experiment method.

Biphasic and boundary lubrication mechanisms in artificial hydrogel cartilage: A review.

Various studies on the application of artificial hydrogel cartilage to cartilage substitutes and artificial joints have been conducted. It is expected in clinical application of artificial hydrogel cartilage that not only soft-elastohydrodynamic lubrication but biphasic, hydration, gel-film and boundary lubrication mechanisms will be effective to sustain extremely low friction and minimal wear in daily activities similar to healthy natural synovial joints with adaptive multimode lubrication. In this review article, the effectiveness of biphasic lubrication and boundary lubrication in hydrogels in thin film condition is focused in relation to the structures and properties of hydrogels. As examples, the tribological behaviors in three kinds of poly(vinyl alcohol) hydrogels with high water content are compared, and the importance of lubrication mechanism in biomimetic artificial hydrogel cartilage is discussed to extend the durability of cartilage substitute.

A Strongly Coupled Fluid Structure Interaction Solution for Transient Soft Elastohydrodynamic Lubrication Problems in Reciprocating Rod Seals Based on a Combined Moving Mesh Method

Soft elastohydrodynamic lubrication (EHL) problems widely exist in hydraulic reciprocating rod seals and pose great challenges because of high nonlinearity and strong coupling effects, especially when the EHL problems are of high dimensions. In this paper, a strongly coupled fluid structure interaction (FSI) model is proposed to solve the transient soft EHL problems in U-cup hydraulic reciprocating rod seals. The Navier–Stokes equations, rather than the Reynolds equation, are employed to govern the whole fluid field in the soft EHL problems, with the nonlinearity of the solid taken into consideration. The governing equations of the fluid and solid fields are combined into one equation system and solved monolithically. To determine the displacements of nodes of the fluid field, a new moving mesh method based on the combination of the Laplace equation and the leader–follower methods is put forward. At last, the proposed FSI model runs successfully with the moving mesh method, and the boundaries of the hydrodynamic lubrication zones and the hydrostatic zones are formed automatically and change dynamically during the coupling process. The results are as follows: The soft EHL problems show typical characteristics, like the constriction effects of the lubricating films, and the law of dynamic development of the lubricating films and the fluid pressures is revealed. The minimum stroke lengths needed to generate complete lubricating films vary with the rod speeds and movement directions, so the design of the rod seals should be paid close attention to, in particular the rod seals of short stroke lengths. Furthermore, along with the dynamic development processes of the fluid pressures during the instroke of U-cup seals, the lubricating film humps expand and locate between the fluid pressure abrupt points and the outlet zones. After the U-cup seals reach the steady-states, the fluid abrupt points disappear and no changes of the film humps are observed. Theoretically, the proposed method can be popularized to solve similar soft EHL problems.

Finite deformation effects in soft elastohydrodynamic lubrication problems

Soft elastohydrodynamic lubrication regime is typical for many elastomeric and biological contacts. As one or both contacting bodies are then highly compliant, relatively low contact pressures may lead to large deformations which are neglected in the classical EHL theory. In the paper, the related finite-deformation effects are studied for two representative soft-EHL problems. To this end, a fully-coupled nonlinear formulation has been developed which combines finite-strain elasticity for the solid and the Reynolds equation for the fluid, both treated using the finite element method with full account of all elastohydrodynamic couplings. Results of friction measurements are also reported and compared to theoretical predictions for lubricated contact of a rubber ball sliding against a steel disc under high loads.

Rough Soft-EHL with Non-Newtonian Lubricant

This paper presents the effect of surface roughness on soft elastohydrodynamic lubrication in circular contact with non-Newtonian lubricant. The time independent modified Reynolds equation, elastic equation and lubricant viscosity equation were formulated for compressible fluid. Perturbation method, Newton-Raphson method, finite different method and full adaptive multigrid method were implemented to obtain the film pressure, film thickness profiles and friction coefficient in the contact region at various the amplitude of surface roughness, surface speed of sphere, modulus of elasticity and radius of sphere. The simulation results showed that the film thickness in contact region depended on the profile of surface roughness. The minimum film thickness decreased but maximum film pressure and friction coefficient increase when the amplitude of surface roughness and modulus of elasticity increased. For increasing surface speeds, the minimum film thickness and friction coefficient increase but maximum film pressure decreases. When radius of sphere increases, the minimum film thickness increases but maximum film pressure and friction coefficient decrease.

Numerical Study on the Transient Adjustment of Wafer’s Posture in Chemical Mechanical Planarization

Chemical mechanical planarization(CMP) is one of the key techniques in integrated circuit manufacture. Wafer carrier is a very important component of CMP system. For studying the effect of position of ball joint on the ability of transient adjustment of wafer carrier orientation in planarization process, mixed soft elastohydrodynamic lubrication model is adopted to analyze the flow and contact behaviors over the pad surface, and the transient change of wafer orientation is simulated combining the transient motion equations of carrier. The simulation results indicate that the higher the height of the ball joint, the faster the orientation adjustment of wafer. The disadvantage of higher ball joint height is that the maximum nominal contact pressure is increased. The increasing of friction moment is of benefit to maintain the wafer in a balance posture, but non-uniformity of contact pressure distribution is increased. Therefore, the reasonable design of carrier structure is very important for the performance of CMP. The analysis of dynamic characteristics of carrier using the transient mixed lubrication model proposed can offer helpful theoretical guidance to the design of carrier.