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The common approach for the flow factor calculation is based on using the Reynolds equation to simulate the micro-level flow. However, for structured surfaces the fluid flow cannot be represented correctly, due to the assumptions made when deriving the Reynolds equation. In this work, a novel method using the Navier-Stokes equations for the calcula...
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... two sliding surfaces 1 and 2 exhibit local height changes h 1 (x, y) and h 2 (x, y), which are measured from the mean level of each surface. Figure 1 is showing a 2D cross section through the 3D geometry with geometric definitions and visualization of the flow rate calculation. Pressure and velocity boundary conditions are described in Section 3.2. In the lubrication gap generated from these two surfaces, the nominal gap height h * , is defined as the difference between the mean levels of the two surfaces h 1,0 and h 2,0 ...
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... In Figure 4, the oil film with a global length , width and pitch angle is visible. It was assumed that the surface was smooth, and the roughness of a surface was not included in this simulation model, unlike [30,31], who used flow factors to describe the real surface topography. Within this study, the performance of the texture geometry parameters themselves should be analyzed in detail and the effects of surface roughness should be neglected. ...
The modification of surface geometries to reduce friction is an omnipresent topic of research. In nature, different low-friction surfaces, such as fish skins, exist. To transfer this knowledge to technical applications, for example, to journal or plain bearings, many numerical and experimental studies of textured surfaces have been performed. In this work, the influence of the geometric parameters (texture length , width , angle and start position of a wedge-shaped texture on three different convergent oil film gaps was analyzed in full-film lubrication and compared with untextured oil film gaps. With the aid of a CFD (computational fluid dynamics) model, a comprehensive variation study was conducted, and the best-performing wedge-shaped texture was determined. The results show that an open texture at the inlet provides the largest improvement. Furthermore, it can be observed that the optimal relative texture width and absolute inlet height for the three investigated oil film gaps are similar. In contrast to the volume flow of the untextured geometry, the volume flow of the textured one is significantly higher, especially that perpendicular to the movement direction.
... In the average flow model, a separate deterministic sub-model is required for determining the flow factors, which will provide a general effect exhibited by surface roughness when using the average flow model. However, this model is unable to give specific details regarding the elevated pressure areas where roughness peaks of the opposite surface contact with each other [10][11][12][13]. Later, deterministic models were introduced for robust In the worst circumstances of lubrication where different surface features take part to support the external load, local experimentation is nearly impossible or very expensive, even though expensive ML experimentation can only yield a general trend of contact performance and behaviors. ...
... In the average flow model, a separate deterministic sub-model is required for determining the flow factors, which will provide a general effect exhibited by surface roughness when using the average flow model. However, this model is unable to give specific details regarding the elevated pressure areas where roughness peaks of the opposite surface contact with each other [10][11][12][13]. Later, deterministic models were introduced for robust design calculations, whereby local variation in tribological parameters can be predicted. ...
Solid asperity interactions are common and inevitable under severe loading conditions for any lubricated contact. Heavy-duty machine components (gears, bearings, etc.) generally operate under Mixed Lubrication (ML), where uneven surface features contact each other when the generated fluid pressure is not enough to support the external load. The Reynolds equation is commonly used to simulate smooth lubricated contacts numerically. In rough lubricated interfaces where opposite surface asperities make contact, the Reynolds equation alone cannot accurately predict pressure using the traditional numerical simulation method. In this paper, lubrication–contact interface conditions (LCICs) have been implemented and extended to solve the multiple asperity contact problem using the full-multigrid approach. The developed novel algorithm has significantly accelerated the solution process and improved the accuracy and efficiency of pressure calculation for fluid–solid sub-interactions that can occur in ML regions. The results of the finite difference method (FDM) results have been compared with those of computational fluid dynamics (CFD) simulation to validate the newly developed model. Hence, the proposed optimized solution method will provide valuable insight to researchers and industry engineers interested in simulating the ML problem where the effect of the fluid–solid interface can be captured effectively to improve reliability in the calculation of the life expectancy of the lubricated parts.
... A separate deterministic sub-model is required for determining the flow factors, which will provide a general effect exhibited by surface roughness when using the average flow model. However, this model is unable to give specific details regarding the elevated pressure areas where roughness peaks of the opposite surface contact with each other [10][11][12][13]. Later, deterministic models had been introduced for robust design calculation where local variation in tribological parameters can be predicted. ...
Solid asperity interactions are common and inevitable under severe loading conditions for any lubricated contact. Heavy-duty machine components (gear, bearings etc.) generally operate under Mixed Lubrication, where uneven surface features contact each other when generated fluid pressure is not enough to support the external load. The Reynolds equation is commonly used to simulate smooth lubricated contacts numerically. In rough lubricated interfaces where opposite surface asperities make contact, the Reynolds equation alone cannot accurately predict pressure using the traditional numerical simulation method. In this paper, Lubrication-Contact interface conditions (LCICs) have been implemented and extended to solve the multiple asperity contact problem using the full-multigrid approach. The developed novel algorithm has significantly accelerated the solution process and improved the accuracy and efficiency of pressure calculation for fluid-solid sub-interactions that can occur under ML regions. The Finite Difference Method (FDM) results have been compared with Computational Fluid Dynamics (CFD) simulation to validate the newly developed model. Hence, the proposed optimized solution method will provide valuable insight to researchers and industry engineers interested in simulating the ML problem where the effect of the fluid-solid interface can be captured effectively to improve reliability in the calculation of the life expectancy of the lubricated parts.
... The deterministic method that directly couples the measured microstructures is widely studied and a great deal of work has been done in this regard [2,3]. However, an accurate representation of real roughness imposes high requirements on the quality of mesh elements, while the stochastic method has less stringent requirements [4,5]. One of the most common stochastic methods is the average flow method proposed by Patir et al. [6]. ...
This paper introduces the grease average flow model considering non-Newtonian characteristics into the grease-mixed elastohydrodynamic lubrication (EHL) numerical analysis. On this basis, a method of grease EHL analysis is established with the roughness coupled indirectly. The effect of the rheological parameter on the variety law of the lubrication state is studied. The results show that the rheological parameter affects the lubrication state versus the dimensionless speed, material, and roughness. Finally, the film thickness and asperity load prediction formulas are derived based on the numerical simulation results, which are suitable for various greases obeying the Ostwald model.
... To consider the surface roughness effect in lubrication analysis, there are two basic methods [8]. ...
... Therefore, the Navier-Stokes equation is applied to calculate the microflow and subsequently the flow factor to depict the fluid impulse and microturbulence in greater detail [20], which is the basis for studying the influence of structured and textured surfaces. Pusterhofer et al. [8] described a method for calculating the flow factor utilizing the Navier-Stokes equation. They further explored the influence of microstructures on hydrodynamic lubrication performance in a deeper understanding. ...
In this paper, the application scope of the average flow model is extended to grease lubrication considering the non-Newtonian characteristics. First, flow factor expressions applicable to both Newtonian fluids and non-Newtonian fluids are derived. Then, a model problem is established by coupling the Reynolds governing equation, film thickness function and boundary conditions and solved for the flow factor. Fit the result into empirical relations for conveniently using in the grease lubrication analysis. Finally, the influence of several parameters on the flow factor is studied. The results demonstrate that the film thickness ratio, rheological index and surface elastic deformation have a significant effect on the flow factor, and the influence law is affected by the orientation of the surface roughness.
... Современные программные комплексы, позволяющие моделировать гидродинамические ПС, например ДВС, обладают возможностями для определения контактных давлений в подшипнике, величины износа поверхностей втулки и шейки вала и др. [28][29][30][31][32][33][34][35][36]. Однако на текущий момент не разработана последовательная методика, учитывающая комплекс различных параметров и режимов работы двигателя и позволяющая определить предотказное состояние ПС. ...
The article deals with the types of wear and failures of journal bearings. Based on the physics of failures, a method for determining the pre-failure state of plain bearings is proposed, including: determination of the limiting clearance in the bearing; determination of the limit value of oil viscosity; determination of the limiting value of the ovality of the shaft neck and liners; determination of the maximum area of chipping of the surface of the liners; determination of the limit value of the concentration of active abrasive particles in the lubricant. The solution of these problems is based on the calculation of the determination of the hydromechanical characteristics (HMC) of bearings using the hydrodynamic theory of lubrication, the determination of the zones of contact interaction between the elements of the rolling stock, the duration of the boundary lubrication regime, the amount of wear on the surfaces of the sleeve and the shaft neck. Calculation studies were carried out on the example of calculating the dynamics of the connecting rod bearing of the crankshaft of a heat engine. In particular, it is shown that with a diametrical clearance in the connecting rod bearing of 90–120 μm, the duration of the boundary regime of lubrication is more than 25%, which is the limiting value. Reducing the oil viscosity (measured at 100 С) below 9.5 mPa∙s is unacceptable, as it leads to an increase in the duration of the boundary lubrication regime by up to 42%. For the same reasons, the ellipticity of the liners more than 5 microns is unacceptable. A mass concentration of active abrasive particles in the oil of more than 0.1% leads to a sharp increase in the maximum wear rate of the bearing, and this concentration should be considered the limit in terms of its pre-failure state. The technique allows at the early stages of designing machines, which include hydrodynamic plain bearings, to determine the criteria for their pre-failure state.
... The flow in the rough lubrication gap is determined using the program OpenFoam® based on the Navier Stokes equations according to de Kraker [27,28]. More detailed information on the model set-up can be found in [32]. The calculated flows through the rough lubrication gap cutouts are compared with those of ideally smooth lubrication gaps and the flow factors are obtained. ...
Contact models are used, among others, to describe the asperity contact in lubricated contacts. In recent decades, a large number of contact models have been developed based on different approaches. In this article a selection of classical statistical contact models are compared with a deterministic FE model. The validation of the different approaches was carried out applying an indirect methodology. By comparing a numerically determined Stribeck curve, on which the characteristics of the contact model has a significant influence, and experimentally determined Stribeck curves, the applicability of the different contact models can be evaluated. The influence of elastic and elastoplastic material behaviour in the deterministic contact model on the asperity contact pressure curves and Stribeck curves, respectively, was examined during the investigations. The results show, that the elastic FEM contact model and the statistical model according to Greenwood and Tripp provide the best agreement with the experimental Stribeck data. This can be attributed to the fact that the roughness peaks are smoothed immediately in the early contact stage and the smoothed surface behaves almost elastically.
... There are progresses in both stochastic and deterministic solutions of mixed lubrication. For example, plastic deformation at asperity contacts has been taken into account [594−596], the computational fluid dynamics (CFD) that directly solves the Navier-Stokes equation has been introduced in analysis of roughness effect [597], and new algorithms have been developed to improve computational efficiency [598,599]. Robbe-Valloire [600] proposed a model for mixed lubrication between nominally flat rough surfaces, in which asperity contacts were classified into five different modes of deformation or lubrication, with contact forces in each mode evaluated via corresponding theories. ...
... In parallel to the popular numerical solver based on finite difference discretization, many researchers rely on the finite element method (FEM) to solve the equations involved in lubrication and solid contact [590,599,611], and CFD-based commercial software has become a popular tool in analysis of EHL, which could provide critical information for across-film distributions of velocity, temperature, and viscosity [597,612]. ...
The reach of tribology has expanded in diverse fields and tribology related research activities have seen immense growth during the last decade. This review takes stock of the recent advances in research pertaining to different aspects of tribology within the last 2 to 3 years. Different aspects of tribology that have been reviewed including lubrication, wear and surface engineering, biotribology, high temperature tribology, and computational tribology. This review attempts to highlight recent research and also presents future outlook pertaining to these aspects. It may however be noted that there are limitations of this review. One of the most important of these is that tribology being a highly multidisciplinary field, the research results are widely spread across various disciplines and there can be omissions because of this. Secondly, the topics dealt with in the field of tribology include only some of the salient topics (such as lubrication, wear, surface engineering, biotribology, high temperature tribology, and computational tribology) but there are many more aspects of tribology that have not been covered in this review. Despite these limitations it is hoped that such a review will bring the most recent salient research in focus and will be beneficial for the growing community of tribology researchers.
... The trend in the research towards patterned micro topographies calls for updated simulation strategies using the Navier-Stokes equations for solving the micro model. Based on the method of de Kraker [23,24], authors presented, in a previous publication, a novel approach for modeling surface topography effects in hydrodynamic lubrication [25]. ...
... To make use of casted crankshafts in high-performance engines possible, different surface treatments are compared in this article with the goal of comparing and understanding wear and friction properties under application-near conditions. This task is carried out by a physical simulation on a rotational tribometer together with a virtual simulation, using a novel approach for modeling surface topography effects in hydrodynamic lubrication [25]. Besides finding an optimization potential for crankshaft surface topographies, this study allows for comparison and validation between physical and virtual simulation approaches. ...
... In the following, the most important information on the simulation models are given. Details can be found in [13] for the macro model and in [25] for the micro model. The EHD macro model is implemented in COMSOL Multiphysics by an FEM-Mesh with around 43,000 elements and uses the original geometry of the shaft specimen and the bearing shells mounted in the bearing shell holders. ...
Optimizing the surface topography of cast iron crankshafts offers the opportunity to use this material as an alternative to steel in high-performance combustion engines. In the past, this was not possible due to the higher wear on bearing shells and the higher friction losses in relation to forged steel shafts. In order to find an optimized shaft micro topography, the friction and wear behavior of steel and cast iron shafts with different surface treatments were compared to each other, using a combined physical (experimental) and a virtual (computational) simulation approach. The experiments were carried out with a rotary tribometer using a journal bearing test configuration with the possibility to test real-life bearing shells and shaft specimens, manufactured from real-life crankshafts. In the experiments, a polished steel shaft with low bearing wear was effective. The optimization of cast iron crankshafts by a novel surface treatment showed a significant reduction of bearing wear in relation to the classical surface finishing procedures of cast iron shafts. A computational simulation approach, considering the real-life micro topography by using the Navier–Stokes equations for the calculation of micro hydrodynamics, supports the assessment of fluid friction. The virtual simulation shows, in accordance to the experimental results, only a minor influence of the investigated shaft topographies on the fluid friction. Further optimization of shaft surfaces for journal bearing systems seems possible only by the usage of patterned micro topographies.
... [18] presented a CFD-FVM model for modelling surface effects under hydrodynamic lubrication. On the use of Reynolds models for fluid films, they stated: "for structured surfaces the fluid flow cannot be represented correctly, due to the assumptions made when deriving the Reynolds equation" [18]. Their model was based on Navier-Stokes equations, was applied to a 3D rough lubrication gap at the micro-scale, and was coupled with a Reynolds-based model working at a coarser scale. ...
... They noticed that Navier-Stokes equations allows for the simulation of surface induced effects and that, "used in the classical sense, the Reynolds equation takes into account only the macroscopic geometry . . . hydrodynamic effects because of the microscopic surface structure are not taken into account" [18]. Furthermore, the authors reported that "when the surface profile shows strong height changes, which can cause velocity changes in height direction . . . the Reynolds equation ...
... In [2], it has also been demonstrated that it is possible to derive the set of reduced equations for the classical lubrication approximation governing incompressible and iso-viscous flows from the full Navier-Stokes equations specialized for flows in thin gaps and applying dimensional analysis considerations. is no longer valid to describe the flow through the rough gap" [18]. The authors highlighted the advantage of Navier-Stokes equations in providing greater detail of the fluid dynamics fields with respect to Reynolds models for fluid films, thus enabling to assess the effects of structured and textured surfaces under hydrodynamic lubrication. ...
Rough and textured surfaces are of paramount importance for lubrication, both in nature and in technology. While surface roughness relevantly influences both friction and wear, artificial surface texturing improves the performance of slider bearings as an energy efficiency action. The simulation of hydrodynamic lubrication by taking into account complex surfaces as boundaries requires the use of computational fluid dynamics (CFD) software able to predict the pressure and the velocity profile through the thickness of the fluid and at any point within the 3D domain. In the present study, a CFD–smoothed particle hydrodynamics (SPH) code is applied to simulate hydrodynamic lubrication for a linear slider bearing in the presence of a 3D rough surface, showing the capabilities of CFD–SPH in modelling such complex interaction phenomena. Numerical assessments involve the load capacity, the 3D fields of the velocity vector, and the pressure 3D field (both within the fluid domain and at the fluid–plate interface).
