3D HYDRODYNAMIC PRESSURE IN GAP HEIGHT DIRECTION FOR CYLINDRICAL BEARING VISCOELASTIC LUBRICATION

2013 ◽  
Vol 20 (1) ◽  
pp. 367-374
Author(s):  
Krzysztof Wierzcholski
Keyword(s):  
Hydrodynamic Pressure ◽  
Gap Height

scholarly journals An EHL Extension of the Unsteady FBNS Algorithm

2021 ◽  
Author(s):  
Erik Hansen ◽  
Altay Kaçan ◽  
Bettina Frohnapfel ◽  
Andrea Codrignani
Keyword(s):  
Elastic Deformation ◽  
Hydrodynamic Pressure ◽  
Detailed Comparison ◽  
Elastic Deformations ◽  
Surface Textures ◽  
Discretization Schemes ◽  
Grid Points ◽  
Gap Height ◽  
Further Development ◽  
Ball On Disc

Abstract Many engineering applications rely on lubricated gaps where the hydrodynamic pressure distribution is influenced by cavitation phenomena and elastic deformations. To obtain details about the conditions within the lubricated gap, solvers are required that can model cavitation and elastic deformation effects efficiently when a large amount of discretization cells is employed. The presented unsteady EHL-FBNS solver can compute the solution of such large problems that require the consideration of both mass-conserving cavitation and elastic deformation. The execution time of the presented algorithm scales almost with N log(N) where N is the number of computational grid points. A detailed description of the algorithm and the discretized equations is presented. The MATLAB© code is provided in the supplements along with a maintained version on GitHub to encourage its usage and further development. The output of the solver is compared to and validated with simulated and experimental results from the literature to provide a detailed comparison of different discretization schemes of the Couette term in presence of gap height discontinuities. As a final result, the most favourable scheme is identified for the unsteady study of surface textures in ball-on-disc tribometers under severe EHL conditions.

scholarly journals A New Progress in Random Hydrodynamic Lubrication for Movable Non-Rotational Curvilinear Biosurfaces with Phospholipid Bilayers

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Krzysztof Wierzcholski ◽  
Keyword(s):  
Dynamic Viscosity ◽  
Hydrodynamic Lubrication ◽  
Wrist Joint ◽  
Biological Fluid ◽  
Hydrodynamic Pressure ◽  
Superficial Layer ◽  
Estimation Methods ◽  
Friction Forces ◽  
Biological Surfaces ◽  
Gap Height

This paper aims to highlight the result of a new progression of mathematical estimation methods of stochastic bio-hydrodynamic lubrication parameters for arbitrary, curvilinear, non-rotational, co-operating, living biological surfaces coated with phospholipid bi-layers. Movable, non-rotational, co-operating surfaces occur in various biological friction nods like the collar bone, the blade bone, the jump joint, and the wrist joint. Specifically, the author presents a synthetic and comprehensive estimation of stochastic bio-hydrodynamic lubrication parameters for co-operating, rotational cartilage bio-surfaces with phospholipid bi-layers occurring in human spherical hip joints and cylindrical elbow joints. The method of research discussed in this paper focuses on a review of stochastic analytical considerations performed by the author. This research is based on the measurements of the gap height between two movable, non-rotational bio-surfaces. The gap is restricted between two co-operating biological surfaces. After several experiments, it could be inferred that there are symmetric as well as asymmetric random increments and decrements in the gap height. Such changes are applicable to the hydrodynamic pressure, load-carrying capacity, friction forces, and wear of the co-operating biological surfaces in human friction nods and contacts. The prime purpose of this paper is to demonstrate the influence of variations in the expected values and standard deviation of the gap height on the hydrodynamic lubrication parameters that occur during the friction process. It can thus be concluded that the apparent dynamic viscosity of biological lubricant varies in the ultra-thin gap height direction, depending on the susceptibility of the superficial layer of the lubricated bio-surface. The results presented in this paper are obtained considering the 3D variations in the dynamic viscosity of the biological fluid, particularly the random variations crosswise the film thickness in non-Newtonian biological fluid properties.

scholarly journals Operating Parameters of a Slide Bearing with Parabolic-Shaped Slide Surfaces with Consideration of the Stochastic Changes in the Lubrication Gap Height

2019 ◽  
Vol 26 (4) ◽  
pp. 171-178
Author(s):  
Andrzej Miszczak ◽  
Krzysztof Wierzcholski
Keyword(s):  
Conservation Law ◽  
Hydrodynamic Pressure ◽  
Stochastic Equations ◽  
Hydrodynamic Theory ◽  
Lubricating Oil ◽  
Method Of Successive Approximations ◽  
Operating Parameters ◽  
Oil Viscosity ◽  
Slide Bearing ◽  
Gap Height

AbstractIn this article, the authors present the equations of the hydrodynamic theory for a slide bearing with parabolic-shaped slide surfaces. The lubricating oil is characterized by non-Newtonian properties, i.e. an oil for which, apart from the classic oil viscosity dependence on pressure and temperature, also an effect of the shear rate is taken into account. The first order constitutive equation was adopted for considerations, where the apparent viscosity was described by the Cross equation. The analytical solution uses stochastic equations of the momentum conservation law, the stream continuity and the energy conservation law. The solution takes into account the expected values of the hydrodynamic pressure EX[p(ϕ,ζ)], of the temperature EX[T(ϕ,y,ζ)], of the velocity value of lubricating oil EX[vi(ϕ,y,ζ)], of the viscosity of lubricating oil EX[ηT(ϕ,y,ζ)] and of the lubrication gap height EX[εT(ϕ,ζ)]. It was assumed, that the oil is incompressible and the changes in its density and thermal conductivity were omitted. A flow of lubricating oil was laminar and non-isothermal. The research concerned the parabolic slide bearing of finite length, with a smooth sleeve surface, with a full wrap angle. The aim of this work is to derive the stochastic equations, that allow to determine the temperature distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction force and friction coefficient, in the parabolic sliding bearing, lubricated with non-Newton (Cross) oil, including the stochastic changes in the lubrication gap height. The paper presents the results of analytical and numerical calculation of flow and operating parameters in parabolic sliding bearings, taking into account the stochastic height of the lubrication gap. Numerical calculations were performed using the method of successive approximations and finite differences, with own calculation procedures and the Mathcad 15 software.

Temperature and Adhesion Influence on the Microbearings Operating Parameters

2013 ◽  
Vol 199 ◽  
pp. 176-181 ◽  
Author(s):  
Krzysztof Wierzcholski ◽  
Andrzej Miszczak
Keyword(s):  
Dynamic Viscosity ◽  
Hydrodynamic Pressure ◽  
Hydrodynamic Theory ◽  
Adhesion Forces ◽  
Oil Viscosity ◽  
Friction Forces ◽  
Oil Flow ◽  
Velocity Changes ◽  
Gap Height ◽  
Viscosity Changes

In presented paper are elaborated the preliminary problems of thermo-hydrodynamic theory of lubrication for dependences between temperature, adhesive forces, and oil dynamic viscosity, in micro-scale inside super thin cylindrical boundary layer arising between two cooperating grooved cylindrical surfaces. In cylindrical micro-bearings are visible the large gradients of temperature changes and adhesion changes in very thin gap height direction. Hence the oil dynamic viscosity changes significantly in gap height direction. This fact implies the visible oil flow velocity changes and friction forces and the hydrodynamic pressure changes during the micro-bearing exploitation. Up to now the influence of adhesion forces simultaneously with temperature on oil viscosity changes and next on hydrodynamic pressure and load carrying capacity changes in cylindrical micro-bearing gap were not considered in analytical and numerical way.

scholarly journals Droplet impact onto a spring-supported plate: analysis and simulations

2021 ◽  
Vol 128 (1) ◽  
Author(s):  
Michael J. Negus ◽  
Matthew R. Moore ◽  
James M. Oliver ◽  
Radu Cimpeanu
Keyword(s):  
High Speed ◽  
Flexible Substrate ◽  
Practical Importance ◽  
Hybrid Approach ◽  
Hydrodynamic Pressure ◽  
Analytical Framework ◽  
Canonical System ◽  
Linear Process ◽  
Plate Motion ◽  
The Impact

AbstractThe high-speed impact of a droplet onto a flexible substrate is a highly non-linear process of practical importance, which poses formidable modelling challenges in the context of fluid–structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed analytical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot, and stiffness of the spring have on the motion of the solid, which undergo forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length and time scales.

scholarly journals A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 714
Author(s):  
Jiujiang Wang ◽  
Xin Liu ◽  
Yuanyu Yu ◽  
Yao Li ◽  
Ching-Hsiang Cheng ◽  
...  
Keyword(s):  
Analytical Modeling ◽  
Ultrasonic Transducer ◽  
Governing Equations ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Collapse Mode ◽  
Capacitive Micromachined Ultrasonic Transducer ◽  
Gap Height ◽  
Von Kármán ◽  
Analytical Expressions

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

scholarly journals Fast laser surface texturing of spherical samples to improve the frictional performance of elasto-hydrodynamic lubricated contacts

Friction ◽  
2021 ◽  
Author(s):  
G. Boidi ◽  
P. G. Grützmacher ◽  
A. Kadiric ◽  
F. J. Profito ◽  
I. F. Machado ◽  
...  
Keyword(s):  
Surface Texturing ◽  
Hydrodynamic Pressure ◽  
Friction Reduction ◽  
Laser Surface Texturing ◽  
Textured Surfaces ◽  
Engineering Applications ◽  
Lubricated Contacts ◽  
Fluid Uptake ◽  
Direct Laser ◽  
Frictional Performance

AbstractTextured surfaces offer the potential to promote friction and wear reduction by increasing the hydrodynamic pressure, fluid uptake, or acting as oil or debris reservoirs. However, texturing techniques often require additional manufacturing steps and costs, thus frequently being not economically feasible for real engineering applications. This experimental study aims at applying a fast laser texturing technique on curved surfaces for obtaining superior tribological performances. A femtosecond pulsed laser (Ti:Sapphire) and direct laser interference patterning (with a solid-state Nd:YAG laser) were used for manufacturing dimple and groove patterns on curved steel surfaces (ball samples). Tribological tests were carried out under elasto-hydrodynamic lubricated contact conditions varying slide-roll ratio using a ball-on-disk configuration. Furthermore, a specific interferometry technique for rough surfaces was used to measure the film thickness of smooth and textured surfaces. Smooth steel samples were used to obtain data for the reference surface. The results showed that dimples promoted friction reduction (up to 20%) compared to the reference smooth specimens, whereas grooves generally caused less beneficial or detrimental effects. In addition, dimples promoted the formation of full film lubrication conditions at lower speeds. This study demonstrates how fast texturing techniques could potentially be used for improving the tribological performance of bearings as well as other mechanical components utilised in several engineering applications.

scholarly journals Wellbore trajectory control tool seal system leakage analysis based on steady gap flow

2020 ◽  
Vol 12 (6) ◽  
pp. 168781402093046 ◽  
Author(s):  
Lei Shi ◽  
Keqiang Wang ◽  
Ding Feng ◽  
Hong Zhang ◽  
Peng Wang
Keyword(s):  
Prediction Method ◽  
Electronic System ◽  
Contact Length ◽  
Trajectory Control ◽  
Analysis Model ◽  
Rotating Shaft ◽  
Element Analysis ◽  
Gap Flow ◽  
Total Leakage ◽  
Gap Height

Lubricant leakage will inevitably occur during the working process of wellbore trajectory control tools. Even including the lubricant compensation system, serious leakage will still cause lacks lubrication of the internal mechanical structure as well as electronic system damaged by external infiltration fluid, especially when it comes to battery sub and other electronic equipment. Seal system leakage prediction method was presented based on the assumption of steady gap flow. It is assumed that there is a constant gap between the lip seal and the rotating shaft, the gap height is determined by oil film thickness, and the length of the gap was determined by the contact analysis using the Mooney–Rivlin constitutive model. The analysis results show that the contact length between the primary seal lip and the rotary shaft is about 0.1 mm under the condition of ensuring the contact between the deputy seal lip and the rotary shaft. The overall lubricant leakage finite element analysis model was established, and the relationship between the internal lubricant pressure of the tool and the total leakage was obtained. The results of analysis indicate that under the internal pressure of 0.03 MPa, the lubricant leakage is approximately 6 mL/h, which was verified by experiments.

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