Standard Lubrication Research Articles

Higher order lubrication model between slip walls

A higher order lubrication model between slip walls is proposed for predicting the flow fields that cannot be described by the standard lubrication models based on the thin-gap approximation. The analysis shows that when considering the non-negligible pressure gradient in the surface-normal direction, the local pressure can be separated into (i) the base contribution by the modified Reynolds lubrication equation and (ii) the higher order component varying in both longitudinal and wall-normal directions, which takes the form proportional to the longitudinal derivative of the local velocity of the Couette–Poiseuille flow. For both (i) and (ii), the effect of the slip boundaries appears as the apparent displacements of the no-slip solid walls, and for (i) additional terms (to the no-slip case) also appear. The validity of the higher order slip-wall lubrication model is established by comparing the analytical prediction of the pressure with the fully resolved numerical results in a relatively wide region between a no-slip corrugated wall and a flat plate with varying slip length: the contribution of the higher order term is identified as the decreased lubrication pressure due to velocity slip. The model also successfully predicts the trend of pressure change between the varying slip case and a more realistic system with constant slip length for a channel, where the thin-gap approximation does not hold.

An experimental method for determining the service life and reliability of the CNC lathe main spindle bearing assembly

The main spindle bearing assembly (MSBA) plays an important role in the quality and service life of CNC machine tools and industrial equipment. The MSBA is usually evaluated based on the allowable wear or the stiffness independently combined with the vibration characteristics. Therefore, it is very important to determine the service life of MSBA when the wear reaches the allowable value, and the stiffness is reduced to the allowable value. This paper studies the simultaneous relationship of wear, stiffness, and vibration characteristics of MSBA in a CNC lathe. The results show that the service life of MSBA is different when evaluated based on each criterion (wear or stiffness). The stiffness of the MSBA is reduced to the allowable limit [J] = 200 N/μm with a Root Mean Square (RMS) value of about 5.75 mm/s2. The wear of the MSBA reaches the allowable limit [δa] = 5 μm with an RMS value of about 4.5 mm/s2. The life of MSBA calculated according to the stiffness criterion is about 1.18 times higher than that calculated based on the wear criterion. The average life of MSBA with standard lubrication according to the wear criterion reaches ∼15,799 h and RMS reaches ∼2.4508 mm/s2.

РЕЗУЛЬТАТЫ ИССЛЕДОВАНИЯ ВЛИЯНИЯ УСЛОВИЙ ФУНКЦИОНИРОВАНИЯ ТУРБОКОМПРЕССОРА НА ЕГО РАБОТОСПОСОБНОСТЬ

The operability of the bearing assembly, which ensures the operation of the turbocharger at different speeds of its rotor, determines the reliability of the turbocharger as a whole. In this regard, the condition of the turbocharger bearing assembly determines the performance of the entire turbocharger. The purpose of the research is to justify the parameter that determines the performance of the turbocharger and a comparative assessment of changes in the state of turbochargers with a standard lubrication system and when using individual bearing assembly lubrication systems. The main factors affecting the state of the turbocharger bearing assembly, and hence the length of the rotor rotation by inertia after the engine stops, are considered to be: the increase in the clearance in the bearing assembly, the speed of rotation of the turbocharger rotor before the engine stops, and the time of pressure drop in the bearing assembly to zero after the engine stops. To obtain dependences describing the effect of the gap in the turbocharger bearing, the time of pressure drop in its lubrication system after the engine stops, and the change in the duration of rotation of the turbocharger rotor by inertia in dynamics, we conducted experimental studies. The experiment involved vehicles with a standard lubrication system and with an individual lubrication system for the turbocharger bearing assembly. The data was sample along the main diagonal of the matrix of experimental indicators. The dependences of the effect of the gap and the time of pressure drop in the bearing assembly on the duration of rotation of the rotor of the turbocharger by inertia after stopping the engine, at the speed of rotation of the rotor before stopping the engine 10000, 25000 and 40000 min-1 are obtained. A comparative analysis of this indicator is given for turbochargers with a standard and individual lubrication system of the bearing assembly, which shows that the duration of rotation of the rotor by inertia increases from 45 s (standard lubrication mode) to 90 s (with an individual lubrication system). This gives us reason to believe that the wear rate of the bearing will decrease by half during operation

Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis

We extend the lubrication approximation for a viscous flow in two-dimensional channels with arbitrary shape functions and moderate aspect ratio. The higher-order model is obtained following an asymptotic analysis. Velocity and pressure profiles for the approximated model are given analytically and involve the derivatives of the shape functions of the walls up to the second order. Comparisons with full-scale simulations are given and show good agreement as well as improvements from the classical standard lubrication approximation.

Self-similar finite-time singularity formation in degenerate parabolic equations arising in thin-film flows

A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, , where h is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at . We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.

Analytical solution for the lubrication force between two spheres in a bi-viscous fluid

An analytical solution for the calculation of the normal lubrication force acting between two moving spheres embedded in a shear-thinning fluid represented by a bi-viscous model is provided. The resulting force between the suspended spheres exhibits a consistent transition between the Newtonian constant-viscosity limits and it reduces to the well-known standard Newtonian lubrication theory for viscosity-ratio approaching one. Effects of several physical parameters of the theory are analyzed under relevant physical conditions, i.e., for a prototypical case of two non-colloidal spheres immersed in a non-Newtonian fluid with rheology parameterized by a bi-viscosity model. Topological results for high/low-viscosity regions in the gap between spheres are also analyzed in detail showing a rich phenomenology. The presented model enables the extension of lubrication dynamics for suspensions interacting with non-Newtonian matrices and provides a clean theoretical framework for new numerical computations of flow of dense complex particulate systems.

Usefulness of oil lubrication during colonoscopy: A comparative study with the conventional technique

BackgroundThe different forms of lubrication are among the most simple, accessible, and economic techniques that have been implemented for improving the diagnostic performance of colonoscopy. AimTo determine whether the use of oil improved the number of complete colonoscopies, facilitated the procedure, reduced pain, or improved the study's diagnostic performance, compared with the conventional lubrication technique. Patients and methodsOne hundred and seventy-five patients referred for colonoscopy were alternately allocated to receive treatment with the standard lubrication method with chlorhexidine gel (group 1) or lubrication with corn oil administered through the working channel (group II). The number of complete colonoscopies, the length of time needed to reach the cecum, the degree of difficulty estimated by the endoscopist and the assistant, the level of pain at the end of the study estimated by the patient, and the endoscopic findings were all determined. ResultsEighty-eight patients made up group I and 87 made up group II. No statistically significant differences were found between the two groups in relation to general characteristics, the number of complete colonoscopies (93 vs. 97%, respectively), the time needed to reach the cecum (8:00 vs. 8:41min, respectively), the level of pain at the end of the study, or the detection of polyps. The degree of difficulty was slightly lower in group II, but with no statistical significance. ConclusionsLubrication with oil during colonoscopy did not improve the number of complete colonoscopies, did not facilitate the study, nor did it reduce pain or increase the diagnostic performance of the study, when compared with the conventional technique.

TWO-STROKE ENGINE BEHAVIOR (SMALL CHAINSAW) OPERATING WITH NON-COMMERCIAL FUEL BLENDS AND DIVERSE LUBRICATION

The paper presents results for experimental tests in a two-stroke internal combustions engine operating on commercial fuel (gasoline and ethanol blends), with different proportions in mineral oil for lubrication purposes. Appropriate instrumentation was used to carry out the measurement of the quantities of interest, namely fuel consumption (g/s), angular velocity (rpm) and emissions (CO2 and NOx). The methodology was based on regulations from INMETRO (motor vehicles energy conversion efficiency) and ABNT (testing of internal combustion engines). Results obtained are analyzed and discussed for the fuel consumption versus angular velocity (g/s x rpm) for each combination fuel blend and lubricating oil (quantities). Main findings are that fuel consumption increases non linearly as angular velocity increases and as lubrication lowers, while emissions decreases as angular velocity increases. Lowest fuel consumption and emissions occurred, respectively, for A25/L1:25 and A25/L1:50 (commercial fuel and standard lubrication).

Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects

We investigate the injection of inviscid gas into the narrow liquid-filled gap between a rigid base plate and an overlying elastic sheet. After an early-time transient in which the gas deflects the sheet into a large blister, the viscous liquid displaced by the expanding bubble starts to accumulate in a wedge which advances as the elastic sheet peels away from the base. We analyse theoretically the subsequent interaction between viscous forces, elastic (bending or tension) forces and capillary forces. Asymptotic expressions are derived for the speed of spreading of the bubble, which reveal that the effect of the capillary pressure drop at the bubble tip is to suck down the sheet over the liquid wedge and thereby reduce the speed. We show that the system passes through three different asymptotic regimes in sequence. At early times, capillary effects are weak and hence the spreading of the bubble is controlled dominantly by the viscous-peeling process at the wedge tip. The capillary forces grow in importance with time, and at late times they dominate viscous effects and balance with elastic forces, leading to quasi-static spreading. Finally, at very late times, the capillary suction generates a narrow bottleneck at the wedge tip, which pushes a large ridge of liquid ahead of it. These results hold in the framework of standard lubrication theory as well as with an improved lubrication model, which takes into account films of wetting liquid deposited behind the advancing bubble tip. The predictions of the model are shown to be in excellent agreement with the Navier–Stokes simulations and experimental results from Part 1 of this work.

Resource-efficient Ball Screw by Adaptive Lubrication

In this paper, the development of a methodology for reducing the energy demand and increasing the life time of ball screws by minimizing the friction torque with adaptive lubrication of the ball screw nut is presented.Therefore, a simulation model of the feed axis has been developed and fitted metrologically at an especially designed test stand with an adaptive lubrication system for the ball screw nut. The model allows the calculation of the optimum friction torque of the feed axis and thus determines the need for lubricants in case a deviation to the measured friction torque of the feed axis should arise.The comparison of tests dealing with the life time of ball screws with standard lubrication and new adaptive lubrication aims at proving the increase of the life time. This endeavor will result in characteristic lubrication strategies for a resource-efficient operation of ball screws during constant operating conditions.

Meniscal Tear Film Fluid Dynamics Near Marx’s Line

Extensive studies have explored the dynamics of the ocular surface fluid, though theoretical investigations are typically limited to the use of the lubrication approximation, which is not guaranteed to be uniformly valid a-priori throughout the tear meniscus. However, resolving tear film behaviour within the meniscus and especially its apices is required to characterise the flow dynamics where the tear film is especially thin, and thus most susceptible to evaporatively induced hyperosmolarity and subsequent epithelial damage. Hence, we have explored the accuracy of the standard lubrication approximation for the tear film by explicit comparisons with the 2D Navier-Stokes model, considering both stationary and moving eyelids. Our results demonstrate that the lubrication model is qualitatively accurate except in the vicinity of the eyelids. In particular, and in contrast to lubrication theory, the solution of the full Navier-Stokes equations predict a distinct absence of fluid flow, and thus convective mixing in the region adjacent to the tear film contact line. These observations not only support emergent hypotheses concerning the formation of Marx's line, a region of epithelial cell staining adjacent to the contact line on the eyelid, but also enhance our understanding of the pathophysiological consequences of the flow profile near the tear film contact line.

Enhancing the lifetime of MoS2-lubricated ball bearings

Solid lubricated ball bearings can be a choice, if standard lubrication cannot be used, as for example because of surroundings like high temperature or vacuum. Law enforcements as well can be a reason for choosing such bearings. Although molybdenum disulfide (MoS2) as one kind of solid lubrication for ball bearings has been known for 60 years, a universal valid lifetime prediction has not been developed yet. This paper presents an overview of the possible approaches to get an idea of the lifetime for such systems. Options to enhance the life by redesigning the cage are shown, among others by the use of mulitbody simulation. Furthermore first results of investigating the materials, coatings and the transfer of additional lubrication from the cage to the primary contact between rolling body and raceway are presented.

Study of Iron Nanopowders into Fluids of Industrial Lubrication

The machines and equipment has required increasing performance of lubricating fluids and coolants which plays important role on reducing friction with the metal parts and heat extraction. Viscosity and thermal conductivity are the most important properties of lubricants, in relation to the friction between the fluid molecules. This paper presents two useful models to predict this properties and their relation with the particles volume fraction and temperature in the nanofluid formed by adition of iron or particles produced by friction. Nanofluids are innovative heat transfer fluids with superior potential for enhancing the heat transfer performance of conventional fluids. In this paper the Unit Cell Model (UCM) which considers the Brownian movement experienced by the nanoparticles are adapt to predict the increment of thermal conductivity of iron nanopowders and standard lubrication oil. The viscosity of the nanofluids was adapt from a model usually suitable for predict the effective viscosity of emulsions. Model results indicated a strong effect of the particle size and volume fractions on the increment of thermal conductivity.

Aeration in Lubrication With Application to Drag Torque Reduction

The aeration of an oil film flowing between the faces of two closely spaced circular plates (one stationary, and one rotating) is examined experimentally, numerically, and with an improved lubrication model. The gap between the plates is small compared to their radii, making lubrication theory appropriate for modeling the flow. However, standard lubrication boundary conditions suggested by Reynolds (1886, "On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil," Philos. Trans. R. Soc. London, 177, pp. 157-234) of p = 0 and pn = 0 (Dirichlet and Neumann conditions on pressure) at the gas-liquid interface do not allow for the inclusion of a contact line model, a phenomenon that is important in the inception of aeration. Hence, the standard theory does not adequately predict the experimentally observed onset of aeration. In the present work, we modify the Neumann boundary condition to include both interfacial tension effects and the dynamics of the interface contact angle. The resulting one-dimensional Cartesian two-phase model is formulated to incorporate the prescribed contact line condition and tracks the interface shape and its motion. This model is then implemented in an axisymmetric, two-dimensional model of the rotating disk flow and used to predict the onset of aeration for varying surface tension and static contact angles. The results of the modified lubrication model are compared with experimental observations and with a numerical computation of the aerating flow using a volume of fluid method.

Marine ice sheet dynamics. Part 2. A Stokes flow contact problem

We develop an asymptotic theory for marine ice sheets from a first-principles Stokes flow contact problem, in which different boundary conditions apply to areas where ice is in contact with bedrock and inviscid sea water, along with suitable inequalities on normal stress and boundary location constraining contact and non-contact zones. Under suitable assumptions about basal slip in the contact areas, the boundary-layer structure for this problem replicates the boundary layers previously identified for marine ice sheets from depth-integrated models and confirms the results of these previous models: the interior of the grounded ice sheet can be modelled as a standard free-surface lubrication flow, while coupling with the membrane-like floating ice shelf leads to two boundary conditions on this lubrication flow model at the contact line. These boundary conditions determine ice thickness and ice flux at the contact line and allow the lubrication flow model with a contact line to be solved as a moving boundary problem. In addition, we find that the continuous transition of vertical velocity from grounded to floating ice requires the presence of two previously unidentified boundary layers. One of these takes the form of a viscous beam, in which a wave-like surface feature leads to a continuous transition in surface slope from grounded to floating ice, while the other provides boundary conditions on this viscous beam at the contact line.

The effect of mass transfer on steady two-dimensional rimming flow

Motivated by applications in rapidly rotating machinery, the standard lubrication model of two-dimensional thin-film flow on the inside of a rotating circular cylinder is adapted in a simple manner to incorporate the effect of mass flux into the free surface of the film. A numerical attack, validated against published results for the zero-mass-flux case, is used to study the case of constant mass fraction with non-zero injection into and extraction from the film, this representing the steady-state operating condition in an aero-engine. It is found that increasing mass flux inhibits the formation of the steep fronts on the film surface, thus reducing the chances of droplets being stripped away from the film when there is a core flow present, and that recirculation zones may be suppressed by an increase in the Bond number, thus reducing the chances of oil degradation in rapidly rotating machinery.

Ultralow Friction of Mesogenic Fluid Mixtures in Tribological Reciprocating Systems

Tribological systems that are lubricated with mesogenic fluids may exhibit ultralow friction coefficients. This effect, which has not yet been well examined, has been reproducibly observed in a reciprocating friction system after a certain running-in period in different mixtures with two reference lubricants. Aim of the present work was to study the tribological behavior of different mesogenic fluids as pure lubricants and in mixtures with standard lubrication oils. Surface analysis was performed to correlate the tribological characteristics with surface features. A basic approach is described to explain the several effects, which lead to the observed results. A better understanding of the tribological behavior is essential for the development of efficient production methods and for the qualification of mesogenic lubricants for possible future applications.

Cavitation in an oscillatory squeeze film rheometer

The effect of cavitation on plate force is considered in an oscillatory squeeze film rheometer. A model is developed for a Newtonian fluid assuming a central circular void based on standard lubrication theory. Account is taken of the drop in force due to plate skewness and also the reduction in plate motion due to compliance of the test apparatus. The simple model derived is suitable when considering random oscillations where relatively small voids are predicted. For a sinusoidal input with relatively large amplitude, a bigger void is generated which prolongs the effect of cavitation. Account of this effect is taken in an extended model but to achieve adequate correspondence between simulated and experimental values of plate force it was necessary to introduce a factor reducing the flow rate from the liquid region into the void. A modified spectral technique is used for experimental analysis of nonlinear squeeze film dynamics.

Elastohydrodynamics of the Eyelid Wiper

This paper presents an elastohydrodynamic model of the human eyelid wiper. Standard lubrication theory is applied to the fluid layer between the eyelid wiper and ocular surface. The role of the lubrication film is to reduce the shear stresses by preventing solid to solid contact between the eyelid wiper and ocular surface. For the lubrication film to be effective, it is required that the orientation of the eyelid wiper changes between the opening and closing phases of a blink. In order to model this, the hydrodynamic model is coupled with an elastic mattress model for the soft tissue of the eyelid wiper and ocular surface. This leads to a one-dimensional non-linear partial differential equation governing the fluid pressure in the lubrication film. In order to solve the differential equation, a loading condition or constraint equation must be specified. The resulting system is then solved numerically. The model allows predictions of the tear film flux from under the upper eyelid, as well as normal and shear stresses acting on the ocular surface. These factors are important in relation to dry eye syndrome, deformation of the cornea and contact lens design. It is found that the pressure and shear stress under the eyelid act across a length of approximately 0.1 mm which is consistent with clinical observations. It order to achieve a flow of tears from under the upper eyelid during a blink, the model requires that the normal force the eyelid applies to the ocular surface during the closing phase of the blink is significantly higher than during the opening phase of the blink.

Surface tension driven fingering of a viscoplastic film

We investigate surface-tension-driven fingering of a thin layer of viscoplastic fluid. Using standard lubrication theory we derive an equation for the flow of the film which includes effects of surface tension and yield stress. We obtain traveling-wave solutions to model the advance of a steadily propagating front and then apply a linear stability analysis to model finger growth and to determine the effect of the yield stress. Qualitative agreement is demonstrated between the numerical results and experiments.