Lubrication Problems Research Articles

Rolling Bearing Condition Monitoring Technique Based on Cage Rotation Analysis and Acoustic Emission

The objective of this paper is to present an approach for the detection of change in rolling element bearings (REB) operating conditions that can lead to premature failure. The developed technique is based on the measurement of the kinematics of the bearing cage. The rotational motion of the cage is driven by the traction forces produced in the contacts of the rolling elements with the races. It is known that the cage angular frequency relative to shaft angular frequency is dependent of the bearing load, the bearing speed and the lubrication condition, as these factors are determinant for the lubricant film thickness and the associated traction forces. As an important part of REB failures are caused by misalignment or lubrication problems, any evidence of these conditions should be interpreted as an incipient fault. In this paper a novel method for the determination of the instantaneous angular speed (IAS) of the cage is developed. The method is evaluated in a deep grove ball bearing test rig equipped with the cage IAS sensor, as well as custom acoustic emission (AE) transducer and a piezoelectric accelerometer. The cage IAS is analyzed under different bearing loads and shaft speed, showing the dependence of the cage angular speed with the calculated lubricant film thickness. Typical bearing faulty operating conditions (mixed lubrication regime, lubricant depletion and misalignment) are recreated and it is shown that the cage IAS is dependent on the lubrication regime and is sensitive to misalignment. The AE signal is used as a lubrication regime evaluator as well. Experimental results show that the proposed technique can be used as a condition monitoring tool to detect abnormal REB conditions that can lead to premature failure.

An Extended Reynolds Equation for Non-Newtonian Lubrication With the Upper Convected Maxwell Model

Abstract The upper convected Maxwell (UCM) model is one of the ways to describe lubricant’s viscoelasticity. In this paper, a new modified Reynolds equation for the UCM model is derived. This equation may be called extended as compared to its analogs because it incorporates the complete structure of the upper convected derivative without the explicit omitting of any term or using the perturbation technique. Then, a numerical scheme for solving the viscoelastic lubrication problems with the employment of the derived equation is described. A mixed Euler–Lagrange approach is used here: the constitutive rheological equations are resolved by a semi-Lagrangian technique and the extended Reynolds equation is discretized by the finite volume method. A constant surface slope problem is considered as a test case. Excellent agreement is achieved between the numerical solution at low Deborah number and one of the approximate solutions. The results of simulations with different types of time derivative used in Maxwell model both for two- and three-dimensional cases are also discussed.

Investigation of machinability in milling of Inconel 718 with solid Sialon ceramic tool using supercritical carbon dioxide (scCO2)-based cooling conditions

Milling of hard-to-machining materials is still a challenge since the high cutting temperature caused by the cooling lubrication problems and the property of materials. This paper proposes the use of supercritical carbon dioxide (scCO 2 ), supercritical carbon dioxide based minimum quantity lubrication cutting fluid (scCO 2 -MQL), and supercritical carbon dioxide based minimum quantity lubrication with oil droplets cutting fluid (scCO 2 -OoW) as the eco-friendly cooling-lubrication methods for milling of Inconel 718 superalloy. The cutting forces, cutting temperatures, surface roughness, surface topographies, subsurface characteristics and tool wear were performed to quantify the effect of various cooling methods. The results indicated that the application of scCO 2 -based cooling conditions was an effective cooling and lubrication technology for the ceramic tool since it could reduce the cutting force and temperature and improve the surface finish with lower peaks and valleys dispersion compared with other cooling conditions. Compared with the scCO 2 -MQL, only scCO 2 and dry milling conditions, the topographies of machined surface under the scCO 2 -OoW condition have been significantly improved. Furthermore, the scCO 2 -OoW cooling technique has facilitated the removal of debris adhering to the ceramic tool and improved lubrication of the cutting zone.

About a cavitation model including bubbles in thin film lubrication taking convection into account

In lubrication problems, which concern thin film flow, cavitation has been considered as a fundamental element to correctly describe the characteristics of lubricated mechanisms. This cavitation model consists of a coupled problem between the compressible Reynolds PDE (that describes the flow) and the Rayleigh-Plesset ODE (that describes micro-bubbles evolution). Very few theoretical results exist in the mathematical literature about such couple problems. A complete form including bubbles convection is studied here. Local times existence results are proved based on the semi group theory. Stability theorems are obtained in a particular case.

ОДИН ПРОСТОЙ СЛУЧАЙ ЛИНЕЙНОГО КОНТАКТА ТЕЛ С ДВУХСЛОЙНЫМИ ПОКРЫТИЯМИ С УЧЕТОМ СМАЗКИ

The main goal of this paper is to consider formulation and solution of a lubrication problem based on the expressions for elastic surface displacements derived asymptotically from an exact solution for a loaded double coated elastic substrate which are valid within a certain region of the problem input parameters. Therefore, a new relatively simple numerical model of the behavior of lubrication parameters in a line lightly loaded contact of double coated elastic cylinders has been developed. For simplicity materials and coatings of both cylinders are considered identical. The main part of the elastic displacements of the contact surfaces is represented by simple Winkler like contributions. The problem is reduced to a numerical solution of a system of two transcendent equations. The formulas for lubrication parameters such as distributions of contact pressure, gap, lubrication film thickness, shear stress, coefficient of friction, and contact energy loss were derived and used for specific calculations. Generally, compared to lubrication parameters in the contact of rigid solids without coatings the effect of the double coating resulted in reduced (up to 60% or more) contact pressure, increased contact area and film thickness as well as some reduction of frictional forces and energy losses. Some specific results for the obtained solutions are provided.

Two-dimensional generalized non-Newtonian EHL lubrication: Shear rate-based solution versus shear stress-based solution

Lubricant behaves non-Newtonian at high shear stress and high shear rate. The non-Newtonian shear behavior of oil such as shear-thinning, viscoelasticity, and limiting shear stress could have influences on almost all characteristics of an elastohydrodynamic lubrication (EHL) contact, that is, the central film thickness, the coefficient of friction, and the temperature rise in the lubricating film. For example, for lubricants of large molecular weight or of polymer blended ones, there can be inlet shear-thinning, which would reduce the EHL film thickness. For the EHL traction in a rolling/sliding EHL contact, it cannot be reasonably predicted without the consideration of non-Newtonian rheology. In EHL numerical studies, the non-Newtonian properties and the constitutive equations are expressed by the concept of generalized viscosity [Formula: see text], which can be either a function of shear rate [Formula: see text] or a function of shear stress [Formula: see text]. In this way, a non-Newtonian lubrication problem could be solved as a generalized Newtonian problem based on solvers for a Newtonian EHL problem. According to the function of the generalized viscosity [Formula: see text], numerical solutions can be classified into shear rate-based ones and shear stress-based ones. In this work, these two kinds of numerical solutions are revisited. And their efficiency is compared for a two-dimensional (2D) non-Newtonian point contact EHL problem (here 2D means non-Newtonian flow in both the x and y directions). Results show that the shear rate-based numerical solution has a higher efficiency than the shear stress-based one. The shear rate-based 2D generalized Newtonian method is more suitable to analyze multiple EHL contacts in angular contact ball bearings and gears with complex 2D flow and/or transient EHL lubrication problems.

Access to computers

In one of Duncan Dowson’s talks on the early attempts to solve the elastohydrodynamic lubrication problem, he commented that progress only became possible when he and Gordon Higginson were granted private access to the University computer at weekends. And how these words brought back memories! For John Tripp and I could never have solved our numerical problem without the courtesy of the Norwalk State Technical College allowing us access to its computer out of term. That was in 1964. In this century, such a story is hard to believe, when every researcher has on his own desk, for his own use, a computer more powerful than either of the two referred to above. It seems worth recalling how computing has changed in my scientific lifetime.

Some Aspects of Plane Poiseuille Flow of a Polar Fluid through a Porous Layer with Brinkman Effects

Polar fluid through a porous structure is considered in an attempt to derive expressions for its effective viscosity under Poiseuille flow. Expressions for the velocity field and micro-rotation are obtained and compared with the corresponding expressions for flow in free space in order to illustrate the effects of the porous medium parameters on the traversing fluid. This work might be of applicability in the study of lubrication problems in configurations involving porous linings, and in the study of the effects of viscosity changes on oil well yield.

Generating fractal rough surfaces with the spectral representation method

The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. The characteristics of fractal rough surfaces simulated by the spectral representation method and the conventional Fast Fourier transform filtering method are compared. Furthermore, the fractal rough surfaces simulated by these two methods are compared in the simulation of contact and lubrication problems. Next, the influence of low and high cutoff frequencies on the normality of the simulated Gaussian fractal rough surfaces is investigated with roll-off power spectral density and single power-law power spectral density. Finally, a simple approximation method to generate non-Gaussian fractal rough surfaces is proposed by combining the spectral representation method and the Johnson translator system. Based on the simulation results, the current work gives recommendations on using the spectral representation method and the Fast Fourier transform filtering method to generate fractal surfaces and suggestions on selecting the low cutoff frequency of the power-law power spectral density. Furthermore, the results show that the proposed approximation method can be a choice to generate non-Gaussian fractal surfaces when the accuracy requirements are not high. The MATLAB codes for generating Gaussian and non-Gaussian fractal rough surfaces are provided.

Implications of the third-grade nanomaterials lubrication problem in terms of radiative heat flux: A Keller box analysis

Steady flow of non-Newtonian nanofluid impinging on a vertical lubricated surface is numerically investigated. The rheological behaviour of the base fluid is characterized by the constitutive equation of third-grade fluid and the power-law fluid model is used for lubricant. Higher-order chemical reaction and nonlinear radiative heat flux are also taken into account. The governing nonlinear partial differential equations are simplified using the Prandtl boundary layer theory and similarity transformations. An efficient and accurate implicit finite difference method is applied to approximate the resulting nonlinear coupled differential equations with complicated boundary conditions for several values of parameters of interest. The velocity, temperature, nanoparticles concentration profiles Nusselt number, and streamlines are illustrated through graphs for full slip and no–slip case as well as assisting and opposing flow cases. The temperature and concentration profiles are also described for linear and non-linear thermal radiation and for different order chemical reactions. The numerical results are compared with the existing literature and found good agreement. It is found that heat and mass transfer rates reduces over the lubricated surface compared with the rough surface.

A Sparse Matrix-Based Method for Rapid Solving the Reynolds Equation

Abstract Due to the repeated iteration, the numerical method represented by the finite-difference method has the disadvantages of low computational efficiency and long time-consuming in solving the Reynolds equation. This paper proposed a new sparse matrix-based method to solve the difference Reynolds equation by replacing the pressure iterative process with the sparse matrix solver. Compared with the traditional iterative methods, this new method's computational efficiency is about two orders of magnitude higher, and it shows high accuracy in different degrees-of-freedom. Two cases of aerostatic lubrication and elastohydrodynamic lubrication are used to illustrate the effectiveness of this method. This method can support the rapid analysis of fluid lubrication problems and lay the foundation for developing the lubrication calculation library.

On the MAOR method for a class of hydrodynamic lubrication problems

In this paper, for solving horizontal linear complementarity problems arising from finite-difference discretizations of hydrodynamic lubrication, the modulus-based accelerated overrelaxation iteration method (MAOR) is analyzed. The convergence range of the relaxation parameters is given, shown to be the generalization of the case of successive overrelaxation. Numerical examples show the efficiency of the MAOR method with the proposed theoretical results.

Molecular dynamics study on the adsorption synergy of MWCNTs/MoS2 nanofluids and its influence of internal-cooling grinding surface integrity

The combination of nanofluids and internal-cooling grinding was applied in machining super-alloy to solve the problem of insufficient heat transfer and lubrication, thereby improving the surface integrity. In this paper, molecular dynamics method was utilized to calculate the interaction energy and mean square displacement (MSD), and the adsorption or dispersion behavior of nanoparticles (MWCNTs, MoS2) and ionic liquid ([EMIm]BF4) in the base fluid (H2O) was revealing. The centroid distance and the dynamic images indicated that the dispersion distance of 4 wt% [EMIm]BF4-MWCNTs reaches 105.37 Å, which is the optimal ratio. In the adsorption of MWCNTs and MoS2, it was observed that the two kinds of nanoparticles formed a pressure-bearing sandwich structure, which can synergistically enhance heat transfer and lubrication. Raman spectroscopy affirmed the modification effect of ionic liquids. Nanoparticle size and contact angle tests indicated that the optimized nanofluid has excellent dispersion and film-forming properties. In addition, nanofluids were applied to the grinding process through a pressurized internal-cooling grinding wheel. Compared with the conventional coolant, the grinding temperature of the optimized nanofluid is reduced by 9.28% and 12.89%, and the surface roughness on the workpiece is reduced by 21.34% and 23.73%, which effectively lessens the furrow and burrs.

Computational Efficiency Improvement of Dimple Textured Hydrodynamic Journal Bearing Using Progressive Mesh Densification Method

Abstract There is a considerable amount of study carried out on textured hydrodynamic bearings. The numerical solution of textured bearings is a matter of concern for the researchers. There are several methods used to estimate the performance parameters of textured bearings. However, progressive mesh densification (PMD) method is not yet used for textured bearings while it has been used for mixed elastohydrodynamic lubrication (EHL) and thermo-EHL problems. In the present analysis, the PMD method is implemented to estimate the performance parameters of the textured journal bearing. It is compared with the multigrid and the fixed mesh methods and found to be very effective in improving computational efficiency.

Why homogenization should be the averaging method of choice in hydrodynamic lubrication

For the computation of the hydrodynamic pressure distribution in fluid film lubrication problems, averaging techniques are frequently used for applications with rough or textured surfaces to reduce the computational cost. The present work shows the excellent suitability of homogenization for this purpose. For comparison, the most frequently applied averaging method is used: the average flow model by Patir and Cheng. The two models are briefly summarized to show the similarity of the formulations, resulting in the same implementation effort. By means of two textured applications, the superiority of the homogenization method is demonstrated and errors inherent in the average flow model are quantified. Homogenization provides averaged pressure distributions with a significantly higher accuracy and allows for efficiently restoring local information to resolve pressure peaks by computing a higher-order solution. The latter is an accurate approximation of the solution of the original Reynolds equation and can be obtained with negligible additional computational cost. Further important advantages of the homogenization method such as its extensibility to simultaneously account for roughness and textures are pointed out.

Formulation to Calculate Isothermal, Non-Newtonian Elastohydrodynamic Lubrication Problems Using a Pressure Gradient Coordinate System and Its Verification by an Experimental Grease

This paper presents a formulation of point contact elastohydrodynamic lubrication analysis for an isothermal, non-Newtonian flow. A coordinate system of the pressure gradient was employed herein. A Couette flow and a Poiseuille flow were considered along the directions of the zero and non-zero pressure gradients, respectively. The Poiseuille flow velocity was assumed to be represented by a 4th-order polynomial of z along the film thickness direction. The Couette flow velocity was assumed to be represented by a linear function of z. Subsequently, the modified Reynolds equation, which contains an equivalent viscosity, was obtained. Using Bauer’s rheological model, the formulation presented in this study was applied to a grease that has been previously experimented upon. The results of previous studies were compared with those of the present study and a reasonable agreement was noted. The distribution of the equivalent viscosity showed a notable difference from that of Newtonian flow. The formulation can be incorporated easily to the usual elastohydrodynamic lubrication calculation procedure for Newtonian flow. The method can be easily applied to other non-Newtonian rheological models. The equivalent viscosity can be calculated using the one-parameter Newton-Raphson’s method; as a result, the calculation can be performed within a reasonable time.

Performance analysis of two-dimensional section of partially textured piston ring with cavitation boundary conditions

The lubrication problems for cavitation are solved using the Elrod algorithm/its modifications, which are extremely nonlinear in nature due to binary switch function, lead to convergence issues, consequently, prone to numerical instabilities. In the present study, a continuous switch function is used to avoid these issues, which has not been explored yet for investigating performance behaviours (minimum film thickness, friction force, and power-loss) of piston ring/cylinder liner pair. The modified Reynolds equation is discretized using the Finite Difference Method (FDM). The algebraic equations have been solved by employing the Elrod and Vijayaraghavan-Keith algorithm with a modified switch function proposed by Fesanghary-Khonsari, which satisfies the mass-conservative cavitation. On the other hand, the total computational domain plays a significant role in predicting accurate numerical results. Therefore, in the present investigation, a piston ring segment of 3 mm × 1.20 mm has been investigated, which comprises larger computational domains ever considered in previous studies. The textures are cylindrical and situated at both ends of the piston ring, leaving the center portion untextured in the axial direction. The minimum film thickness change with time (squeeze film action) and lubricant’s (SAE 20W-40 engine oil) viscosity change with operating temperature have been incorporated in the spectrum of this study. The textured piston ring demonstrated an increase up to 7.2% of the minimum film thickness, friction reduction up to 30%, and reduction in power-loss up to 11% compared to the conventional (un-textured) piston ring.

Heat generation of ball bearing for rocket-engine turbopump in low-temperature gas hydrogen

Cryogenic fluid such as liquid hydrogen, liquid oxygen, and liquid methane is used for rocket propellant because of their performance. Cryogenic fluid turbopump equipped in rocket-engine is started to rotate after precooling bearings is completed. The ball bearing used for the turbopump have worse lubricating performance because the lubricant is not liquid material such as oil which coagulate at cryogenic temperature but solid material. Polytetrafluoroethylene (PTFE) is used for the lubricant in Japanese rocket engines [1]. One of the glass transition temperature of PTFE is around 100 K, and it is considered that the strength of PTFE become weak discontinuously above 100 K and poor lubrication problem would occur in bearings. Ball bearings for turbopump which need to perform high stiffness at high rotation speed don’t meet the performance suddenly when they have any slight damages. Therefore, bearings should be precooled before the engine start so that poor lubrication problems would not occur. However, there is little knowledge of the ball bearing performance in the environment of gas coolant. If ball bearings for turbopumps have good performance in the environment, turbopump can be started to rotate under the insufficient precool environment. It contributes reduction of time and propellant for the precool, and improvement of rocket performance and diversification of space transportation mission are expected. In this study, bearing rotational tests in gas coolant are conducted in the several conditions of the rotational speed and the thrust load in order to clarify the bearing performance for rocket engines in gas coolant.

Friction Force During Lubricated Steady Sliding of a Rigid Cylinder on a Viscoelastic Substrate

We study the friction force during lubricated sliding of a rigid cylindrical indenter against a viscoelastic substrate in the iso-viscous visco-elasto-hydrodynamic lubrication (VEHL) regime. The substrate is represented by a foundation model. The solution is controlled by three dimensionless parameters. The first of these, λ, measures the time for the indenter to move one contact zone relative to the viscoelastic relaxation time; the second is the ratio of the long time to short time compliance of the substrate, $$c_{\infty } /c_{0}$$ ; the third parameter, β, is the ratio of average fluid flow rate to the sliding velocity. Although our solution works well for the full range of parameters, we focus on the “Hertz” regime (β >>1) where practically all the fluid in the contact region is squeezed out. This regime is quite common in soft contact lubrication problems and presents significant numerical difficulties. Our analysis gives insight into why these numerical difficulties arise. The friction force can be decomposed into two parts, one due to viscoelastic dissipation and the other from hydrodynamics. Although these two are generally coupled, in the Hertz limit, an important result is that the viscoelastic portion of the friction force can be well approximated by the solution of the corresponding “dry” sliding problem, in which there is no lubricating fluid layer. This provides a simple way to decouple the hydrodynamic portion of the friction force from the viscoelasticity of the substrate. We study how hydrodynamic pressure and film thickness vary with the controlling dimensionless parameters. Scaling laws for these relationships are given in closed form.

Lubricated Friction and the Hersey Number.

Most frictional contacts are lubricated in some way, but is has proven difficult to measure and predict lubrication layer thicknesses and assess how they influence friction at the same time. Here we study the problem of rigid-isoviscous lubrication between a plate and a sphere, both experimentally and theoretically. The liquid layer thickness is measured by a novel method using inductive sensing, while the friction is measured simultaneously. The measured values of the layer thickness and friction on the disk are well described by the hydrodynamic description of liquid flowing through a contact area. This allows us to propose a modified version of the Hersey number that compares viscous to normal forces and allows us to rescale data for different geometries and systems. The modification overcomes the shortcomings of the commonly used Hersey number, adds the effects of the geometry of the configuration on the friction, and successfully predicts the lubrication layer thickness.