Pressure-dependence of dielectric relaxation time in poly(propylene glycol) and its application to high-pressure viscosity estimation

Dielectric permittivity and loss of poly(propylene glycol) with different molecular weights (400–3000) and terminal groups (OH and CH₃) have been measured in the frequency range of 100 Hz to 1.5 MHz. Measurements were conducted over the temperature range 202–293 K under atmospheric pressure and 283–320 K under pressure up to 600 MPa. Two relaxation processes, one with strong absorption in the high-frequency region (α-relaxation) and the other a weak process in the low-frequency region (α′-relaxation), were observed for the OH-terminated samples having molecular weights above 2000 and for all the CH₃-terminated samples. Most of the experimental data under high pressure showed a nonlinear decrease in the logarithm of the frequency of maximum dielectric loss with increasing pressure. The pressure-dependence of the dielectric relaxation time of the α-process was analyzed by several models based on the free-volume concept. The regression results of dielectric relaxation time as a function of pressure were applied to the estimation of high-pressure viscosity. The predicted viscosity showed relatively good agreement with viscosity data obtained from a falling-sphere viscometer.     

Analysis of high shear rate viscosity data for engine oils

Reduced Variable Methods are proposed for the analysis of high shear rate viscosity data. It is shown that the correct reduction methods reduce all measurements to a single master curve. Once established this curve can be used to predict data at any temperature provided the kinematic viscosity is known. The principles are discussed by which numerical models can be established to give universal parameters characteristic of the viscosity index (vi) improver. Such a model could then be used to calculate the high shear rate viscosity of any blend. One simple model proposed by Cross is discussed. The meaning of the parameters used in the model are compared to the basic principles set out in the previous section. It is shown that for complete characterisation of the vi improver it is necessary to have some method for the estimation of the limiting high shear rate viscosity, η_∞. It is not possible to obtain η_∞ by curve fitting data covering the experimentally accessible range of shear rates. Methods are proposed by which η_∞ may be estimated with reasonable reliability. Experimental results are shown on model oils made with commercially important vi improvers     

Inverse approach for estimating rheological characteristics of adsorption layer in thin film EHL contacts

A modified Reynolds equation is derived for thin film elastohydrodynamic lubrication (TFEHL) by means of the viscous adsorption theory. This TFEHL theory can be used to explain the deviation between the measured film thickness and that predicted from the convenient elastohydrodynamic lubrication (EHL) theory under very thin film conditions. Results show that the thinner the film, the greater the ratio of the adsorption layer to the total film thickness becomes, and the greater the value of the pressure–viscosity index (z′). An inverse approach is proposed to estimate the pressure distribution based upon the film thickness measurement and to determine the pressure–viscosity index of oil film, and the thickness (δ) and the viscosity ratio (η^*) of the adsorption layer in TFEHL circular contacts. Based on TFEHL theory, the inverse approach can reduce z′ error, and provides a reasonably smooth curve of pressure profile by implementing the measurement error in the film thickness. This algorithm not only estimates the pressure, but also calibrates the film shape. Consequently, it predicts z′, η^*, and δ with very good accuracy. It can also be used to evaluate the lubrication performance from a film thickness map obtained from an optical EHL tester. Results show that the estimated value of z′ is in very good agreement with the experimental data.     

Evaluation of molybdate ester as a synergist for arylamine antioxidant in lubricants

An oil-soluble additive molybdate ester (ME) was synthesized. The antioxidation properties of p,p′-dioctyldiphenylamine (DODPA)- and ME-containing poly-α-olefin (PO)-derived lubricants were evaluated by differential scanning calorimetry (DSC) to measure and hot oil oxidation (HOO) tests. DSC test measures incipient oxidation temperature (IOT) and oxidation induction time (OIT) of the lubricant at high temperatures and the oxidation stability of oil viscosity increase is measured by HOO test. DSC test shows that IOT and OIT of DODPA-containing PO were improved significantly by ME addition. HOO test indicates that when combining with DODPA antioxidants, ME can also effectively reduce the increase in viscosity of the mineral oil 150 SN. These results suggest that the ME shows a good oxidative synergism with DODPA antioxidant. In addition, the changes occurring to DODPA in 150 SN oxidation with and without ME were observed by GC/MS analysis. The proposed mechanism of the inhibition involves a synergy between ME and DODPA.     

Pressure–Viscosity Coefficients for Polyalkylene Glycol Oils and Other Ester or Ionic Lubricants

We present in this article new viscosity and density data for polypropylene glycol monomethyl ether, which completes a series of articles where we have published dynamic viscosity data of poly(propylene glycol) dimethyl ethers, dipentaerythritol esters, and pentaerythritol esters. New dynamic viscosity measurements up to 60 MPa at five temperatures in the range of 303.15–373.15 K, and density values at temperatures ranging from 298.15 to 398.15 K up to 60 MPa are reported in addition to other physical properties that affect the behavior of the fluids in elastohydrodynamic lubrication regime, such as the viscosity index value, VI, the universal pressure–viscosity coefficient, α _film, and the temperature–viscosity coefficient, β. The experimental measurements were performed using a rotational automated viscometer Anton Paar Stabinger SVM3000, a rolling-ball viscometer Ruska 1602-830 for high pressures, and an automated Anton Paar DMA HPM vibrating-tube densimeter. Together with these data, we also present a comparison of the film-generating capability for the fluids above mentioned as well as for other five ionic liquids. We analyze the dependence of the molecular structure on the lubrication properties of these oils, which can help the lubricant engineers to develop products with enhanced performance.     

High-performance base fluids for environmentally adapted lubricants

Future lubricants have to be more environmentally adapted, have a higher level of performance, and lower total life cycle cost (LCC) than presently used lubricants. To be able to formulate those lubricants, the properties of the base fluids have to be well known. Base fluid properties that influence the formulated lubricant performance could be divided into three different groups. These groups are: physical, chemical, and film formation properties. In this study, properties from all of these groups are investigated to improve the understanding on thier influence on base fluid overall performance.There are more or less environmentally adapted base fluids available for formulation of lubricants. They could be divided into different groups, mineral, semi–synthetic, and synthetic fluids. Synthetic fluids could be of different types: polyalpha olefins (PAO), synthetic ester, polyglycols, and others. The most interesting group for formulation of environmentally adapted lubricants are the synthetic esters. In this study, the properties for a large number of environmentally adapted ester base fluids are studied in detail. The tested properties relate to the macroscopic/molecular behavior and include: viscosity–temperature—pressure effects, η(p,T), thermal conductivity, λ(p,T), and heat capacity per unit volume, ρc_p(p,T). The film formation capability in elasto-hydrodynamic contacts is also studied. Different connections between the molecular structure and the performance of the fluids are discussed. As an example, it is found that a large number of carboxylate groups in the ester molecule improve the thermal properties, and thereby a thicker lubricating film could be maintained in highly loaded, high-slip contacts.     

Frictional behaviour of non-Newtonian lubricants

This investigation is concerned with the prediction of the frictional behavior of non-Newtonian fluids in a statically loaded journal bearing. The pressure distribution, friction and bearing load capacity are obtained for various values of the flow behaviour index, n. For the pseudoplastic fluids (n<1) the load carrying capacity and the friction forces are decreased, while shear thickening fluids (n>1) exhibited increases in the friction forces and load. The coefficient of friction was found to decrease as the value of n is increased, provided the dimensionless load exceeded a certain value     

A new method for determining the mechanical stability of lubricating greases

Mechanical stability is of central importance when dealing with the long-term service-length of grease-lubricated roller bearings. Poor stability will lead to consistency degradation of the grease, because of mechanical forces between the rolling parts of the bearing. The result can be leakage of grease through seals, or at worst a total failure of the bearing. The present investigation was initiated because present-day methods for prediction of mechanical stability show weak correlation with real service-length. The aim of the project was to develop a useful alternative. In order to fulfil this, both field tests and laboratory tests were carried out. In the field tests, nine different commercial greases were examined in the wheel bearings of five ore waggons, used for transporting ore by railroad from the Kiruna Mine in northern Sweden to Narvik in northern Norway for shipping to foreign markets. The test ore waggons travelled a distance of about 300,000 km during a period of 3 years. Small samples of greases were taken, on eight different occasions, for consistency testing. After the end of the test period, the damage on the bearings was also studied. In the laboratory tests, new undestroyed greases of the same brand as in the field tests were examined using conventional methods, such as the V2F, the Roll Stability Test and the Grease Worker. Comparisons between the field tests and these laboratory tests indicate poor correlation. In addition to these conventional methods, the relevance of the shear strength of the greases to the prediction of the mechanical stability was also tested. The shear stress τ_L depends on the applied pressure p, thus τ_L=τ₀+γ·p where τ₀ is the shear stress at atmospheric pressure. γ is a property of the lubricant in the same way as viscosity or density. It was found that γ correlates well with the mechanical stability in service. Increased γ values lead to a decrease in the mechanical stability. One reasonable explanation is that high γ values correspond to high shear stresses in the grease, and thus severe conditions for the thickener.     

The viscosity of dimethyl ether

Dimethyl ether (DME) has been recognised as an excellent fuel for diesel engines for over one decade now. Engines fuelled by DME emit virtually no particulate matter even at low NO_x levels. This is only possible in the case of diesel oil operation if expensive and efficient lowering particles and NO_x traps are installed.The most significant problem encountered when engines are fuelled with DME is that the injection equipment breaks down prematurely due to extensive wear. This tribology issue can be explained by the very low lubricity and viscosity of DME. Recently, laboratory methods have appeared capable of measuring these properties of DME. The development of this is rendered difficult because DME has to be pressurised to remain in the liquid state and it dissolves most of the commercially available elastomers.This paper deals fundamentally with the measurement of the viscosity of DME and extends the discussion to the difficulty of viscosity establishing of very thin fluids. The main issue here is that it is not easy to calibrate the viscometers in the very low viscosity range corresponding to about one-fifth of that of water. The result is that the low viscosity is measured at high Reynolds numbers so that the outcome has to be corrected by various factors. The validity of these can be discussed especially when they exceed a few percent of the apparent viscosity.The volatile fuel viscometer (VFVM) developed at DTU is presented. By enclosing a standard glass capillary viscometer in a glass tube it is possible to measure the viscosity of fluids at pressures below 15 bars. The kinematic viscosity of DME was established at 0.184 cSt @ 25 °C at the vapour pressure of the fluid at that temperature. The measurements were made at reasonable Reynolds numbers so the correction factors are negligible indicating a high accuracy of the method.Other pressurised viscometers have appeared since the development of the VFVM. These predict a 5–19% higher viscosity for DME than the VFVM. It seems that the causes for these differences are a too high Reynolds number and/or an influence of the gas used for pressurisation in these methods. The results of the VFVM are consolidated by measurements of the viscosities of propane and butane: these agree with the outcome of measurements using a quartz crystal microbalance (QCM) a method that is supposedly less sensible than the Reynolds number.     

Synthesis and Characterization of Alkyl-Bridged Bicycloheptanes as Traction Fluids

The traction fluid is a critical component of a toroidal-continuously variable transmission (T-CVT). As the medium that transmits power through the toroids, the traction fluid needs to provide a high traction coefficient and retain low dynamic viscosity at cold temperatures; this is a challenging combination of properties. A comparison of a variety of fluids shows a broad correlation between the traction coefficient and the fluid's low temperature viscosity, or pour point. This work investigated a series of novel compounds as traction fluids through chemical synthesis and the measurement of their relevant physical properties. Specifically, four new alkyl-bridged bicycloheptane fluids have been synthesized and refined to high purity. Their traction coefficients, measured with a ball-on-disc traction apparatus, are comparable to those of commercial fluids over the relevant range of temperature and pressure. Their dynamic viscosities at low temperature, however, are higher than the viscosity of commercial fluids and exceed the value of 3 × 10 ⁴ cP at ?40°C. These bridged bicycloheptanes also exhibit a correlation between their low-temperature viscosity and traction coefficient. The reasons for this correlation are discussed, and the effect of the molecular structure on viscosity and traction coefficient is investigated. This analysis finds semi-quantitative relationships between fluid properties and the molecule's volume, stiffness, and ring structure.     

Soft-tribology: Lubrication in a compliant PDMS–PDMS contact

We investigate the influence of surface roughness and hydrophobicity on the lubrication of a soft contact, consisting of a poly(dimethylsiloxane) (PDMS) sphere and a flat PDMS disk. The full Stribeck curves, showing boundary, mixed and elasto-hydrodynamic (EHL) lubrication, are presented for varying surface roughness and hydrophobicity. It is found that neither surface roughness nor hydrophobicity influence the friction coefficient (μ) within the EHL regime. However, increasing surface roughness decreases μ in the boundary regime, while extending the limits of the boundary and mixed lubrication regimes to larger values of the product of velocity and lubricant viscosity (Uη). The transition from the mixed lubrication to EHL regime is found to take place at lower values of the film thickness parameter Λ for increasingly rough surfaces. We found Λ=0.7 in the case of a root mean square (r.m.s.) surface roughness of 3.6 μm, suggesting that the effective surface roughness in a compliant compressed tribological contact is lower than that at ambient pressures. Rendering the PDMS surface hydrophilic promotes full-film lubrication and dramatically lowers μ in the boundary regime by more than an order of magnitude. This influence of surface wetting is also displayed when examining a range of lubricants using hydrophobic tribopairs, where the boundary μ decreases with decreasing lubricant–substrate contact angle. Implications of these measurements are discussed in terms of the creation of model surfaces for biotribological applications.     

Mechanical analysis of the scratching of metals and polymers with conical indenters at moderate and large strains

Scratch test provides a convenient mean to study the surface mechanical properties and the tribological performances of materials. The representative strain of the material in this test increases with the attack angle β of the indenter and so for a conical indenter increases as its apical angle 2θ decreases. But the mechanical analysis of this test by analytic models is very intricate. First we perform a preliminary discussion of the various aspects of the problem by considering the plane strain scratching of materials by wedges. After we present the conditions of the numerical simulations of the scratch test with conical indenters with a three-dimensional (3D) finite element code. These simulations provide the scratch geometry (contact surface, elastic recovery), the plastic strain map and the volume average plastic strain, the scratch hardness and the force ratio, the apparent friction coefficient μ₀=F_t/W. So we compare the behaviour of polymeric and metallic materials in scratch test at low and large strain and relate their difference in scratching resistance to their rheological properties. Polymers develop more higher elastic strains than metals a phenomenon which is characterised at low strain by the yield stress to Young's modulus ratio ε_e=σ_y/E. For θ=70.3° where pure ploughing occurs we study the scratching of elastic perfectly plastic solids with various values of ε_e under zero friction. Some comparisons with the behaviour in indentation are performed and we study the influence of friction in the scratching of workhardened steel with the same cone. At high strain the main rheological difference is the workhardening behaviour: it is described by a power law for metals and an exponential law for polymers. For θ decreasing from 70.3 to 20° we compare the behaviour of a cold worked steel to the behavour of polycarbonate, a thermoplastic polymer: a transition from ploughing to ploughing–cutting occurs only for steel.     

Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y₀ and tangent modulus E_T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point (ε_c, σ_c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ_c at the specific true strain ε_C lead to the same loading and unloading indentation curve. We show that the true strain ε_c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ_c/ε_c is directly related to the elastic modulus of the indented material and the tip geometry.     

Pressure-viscosity effect on the solutions of a lubricated thick elastic bonded strip

Utilizing the numerical method developed by the author for isoviscous, fully flooded, elastohydrodynamic lubrication of a rigid cylinder rolling or sliding on an elastic strip (layer) which is attached to a rigid substrate (bonded strip), the influence on the pressure-viscosity coefficient, α, upon solutions is investigated. The present solutions are obtained for contacts operating in the transition region betweeen isoviscous-elastic and piezoviscous-elastic regimes where a pressure spike can be expected in some sense.New sets of results are presented for central and minimum film thicknesses in dimensionless form when the bonded strip is thick (0γ1, where γ = a/t is the ratio of the half contact width to strip thickness). It is shown that the film thickness depends not only on the values of α but also is influenced by Poisson's ratio, v.     

Heterogeneous tensile test on elastoplastic metallic sheets: Comparison between FEM simulations and full-field strain measurements

The aim of this work is to propose a non-standard tensile test suitable for the identification of material parameters using full-field strain measurements and finite element analysis. The shape of the sample to be used in this new test must verify three criteria: (i) large heterogeneity of the strain in the gauge area, (ii) large strain-paths diversity and (iii) a good sensitivity of the strain field to the material parameters. After identifying the mechanical parameters of a dual-phase steel sheet using σ–ε and r–α curves, samples of different shapes were studied in order to choose the one that presents the best compromise between the three criteria. The comparison between simulated and measured fields shows a qualitative accordance. Taking into account the difference between these fields in the expression of the cost-function to minimize is expected to improve the quality of the identified material parameters.     

Comparative study on the wear behaviour of different conventional and cross-linked polyethylenes for total hip replacement

In this study, five different types of conventional and cross-linked polyethylene (XLPE) (γ-sterilised PE GUR1020, EtO-sterilised PE GUR1020, γ-sterilised PE GUR1050, EtO-sterilised XLPE GUR1020, EtO-sterilised XLPE GUR1050) acetabular cups were tested on a hip joint simulator run for 5 million cycles in order to compare the relative long-term wear resistance in relation to material properties (PE grade, conventional or cross-linked) and sterilisation method (EtO treatment or γ-irradiation).Gravimetric measurements revealed significant differences between the wear behaviours of the five sets of acetabular cups. Weight loss was found to decrease along the series: γ-sterilised PE GUR1020>EtO-sterilised PE GUR1020>γ-sterilised PE GUR1050>EtO-sterilised XLPE GUR1050>EtO-sterilised XLPE GUR1020. The wear results were discussed in relation to the crystallinity degree of the cups which was determined by micro-Raman spectroscopy coupled to partial least-squares analysis. Within both conventional and cross-linked PE series, it appeared that higher crystallinity samples (i.e. γ-sterilised PE GUR1020 and EtO-sterilised XLPE GUR1050, respectively) were characterised by higher wear rates. The higher weight loss observed for PE GUR1020 was explained in relation to its lower molecular weight with respect to PE GUR1050. Raman analysis showed that wear testing did not significantly modify the crystallinity degree of any of the tested acetabular cups. The most worn cup, i.e. γ-sterilised PE GUR1020, appeared the most homogeneously polished upon wear testing, as confirmed by the lowest standard deviation associated to the crystallinity value recorded in the centre of the cup. The results of this investigation have clearly shown a dramatic wear reduction in favour of the cross-linked polyethylene.     

Lattice distortions in GaN on sapphire using the CBED–HOLZ technique

The convergent beam electron diffraction (CBED) methodology was developed to investigate the lattice distortions in wurtzite gallium nitride (GaN) from a single zone-axis pattern. The methodology enabled quantitative measurements of lattice distortions (α, β, γ and c) in transmission electron microscope (TEM) specimens of a GaN film grown on (0, 0, 0, 1) sapphire by metal-organic vapour-phase epitaxy. The CBED patterns were obtained at different distances from the GaN/sapphire interface. The results show that GaN is triclinic above the interface with an increased lattice parameter c. At 0.85 μm from the interface, α=90°, β=8905° and γ=11966°. The GaN lattice relaxes steadily back to hexagonal further away from the sapphire substrate. The GaN distortions are mainly confined to the initial stages of growth involving the growth and the coalescence of 3D GaN islands.     

Welding wave on the contact spot of solids

In this paper the theoretical model of adhesion between clean solid surfaces is presented. Material behaviour is described by hydrodynamic equations for viscous liquid and by the Gruneisen equation of state. This approach is quite suitable for quantitative analysis of mechanical processes running under high pressures. The model states that growth of a bonded area can occur in a regime of self-propagating welding wave (WW). WW originates at any active point where initial bonding takes place and further moves at velocity U_wwγ/η (γ is surface energy and η is viscosity of material). According to the model presented surface energy plays the key role in adhesion.     

A critical evaluation of film thickness‐derived pressure–viscosity coefficients

A single parameter, the pressure–viscosity coefficient, α, quantifies the pressure dependence of the viscosity of the liquid in elastohydrodynamic lubrication (EHL). Most published values of α have not been obtained from measurements of viscosity as a function of pressure. Rather, these effective pressure–viscosity coefficients have been derived from the measurement of the EHL film thickness, a more difficult procedure. In this article, five well‐characterized liquids that should be Newtonian in the EHL inlet are identified for which film‐derived coefficients have been reported. These coefficients are compared with coefficients derived from published viscosity correlations and new viscosity measurements. The film‐derived coefficients are found to not be an accurate representation of the piezoviscous response. The procedure of deriving a pressure–viscosity coefficient from a film thickness measurement does not offer an alternative to the simpler and easier viscometer measurement. Copyright © 2014 John Wiley & Sons, Ltd.     

Externally pressurized conical step bearing with visco-elastic lubricant

A solution for an externally pressurized conical step bearing with visco-elastic lubricant is obtained by using a regular perturbation technique. The effects of the parameters S (elastic number), H = h₁/h₂ (the ratio of film thickness) and sinα (α, the semi-vertical angle) on the pressure, the load capacity and the ratio of flow flux have been studied and are presented graphically. The effect of elasticity on improving bearing performance is very small.