scholarly journals Estimation of Random Friction Forces on the Microbearing Cooperating Surfaces

2019 ◽  
Vol 26 (2) ◽  
pp. 167-174
Author(s):  
Krzysztof Wierzcholski ◽  
Andrzej Miszczak
Keyword(s):  
Dynamic Viscosity ◽  
Apparent Viscosity ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Superficial Layer ◽  
Mathematical Form ◽  
Friction Forces ◽  
Random Roughness ◽  
Load Carrying ◽  
Gap Height

Abstract Presented paper concerns a new mathematical form of stochastic theory of hydrodynamic friction forces occurring on the real cooperating surfaces in computer micro bearing fan and computer microbearing in hard disc driver HDD. This paper presents particularly a new-review of stochastic analytical considerations realized by the authors for friction forces estimation during hydrodynamic lubrication performed on the ground of the measurements of the gap height between two roughness surfaces. After numerous experimental measurements directly follows that the random unsymmetrical increments and decrements of the gap height of computer microbearings have important influence on the load carrying capacities and finally on the friction forces and wear of cooperating surfaces. The main topic demonstrates the influence of the variations of expectancy values and standard deviation of the computer microbearing gap height on the friction forces occurring in the HDD and microbearing fan. Moreover, it is observed the evident connection between the apparent dynamic viscosity and the features of the microbearing superficial surface. Hence after abovementioned remarks follows the corollary that the influence of the microbearing gap height stochastic variations connected with the surface roughness tend moreover indirect from the apparent viscosity into the friction forces variations. The synthetic, complex elaboration of obtained results indicates finally the influence of the random roughness in micro and nano level of microbearing surfaces on the friction forces distribution. A new results contained in this paper are obtained taking into account 3D variations of dynamic viscosity of the non-Newtonian lubricant, particularly variations crosswise the film thickness and influences of surface superficial layer features on the lubricant apparent viscosity.

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.

DETERMINATION OF RANDOM FRICTION FORCES ON THE BIOLOGICAL SURFACES OF A HUMAN HIP JOINT WITH A PHOSPHOLIPID BILAYER

Tribologia ◽  
2019 ◽  
Vol 284 (2) ◽  
pp. 131-142
Author(s):  
Krzysztof Wierzcholski
Keyword(s):  
Hip Joint ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Phospholipid Bilayer ◽  
Mathematical Form ◽  
Friction Forces ◽  
Biological Surfaces ◽  
Gap Height ◽  
The Impact ◽  
Human Joint

The paper presented concerns a new mathematical form of the stochastic theory of hydrodynamic friction forces occurring on real human hip joint surfaces with a phospholipids bilayer. This paper particularly presents a new review of stochastic analytical considerations realized by the authors for friction forces estimation during hydrodynamic lubrication of biological surfaces performed on the basis of the gap height measurements in the human hip joint. After numerous experimental measurements, it directly follows that the random unsymmetrical increments and decrements of the gap height of human joints have an important influence on the load carrying capacities and finally on the friction forces and wear of cooperating cartilage surfaces. The main topic demonstrates the impact of the variations of expectancy values and the standard deviation of the human joint gap height on the friction forces occurring in the human joint. Moreover, an evident connection is observed between the apparent dynamic viscosity and the features of the cartilage surface coated by the phospholipid cells. Hence, after the abovementioned remarks, follows the corollary that the influence of the gap height stochastic variations and random surfaces coated by the PL cells tend indirectly from the apparent viscosity into the friction force variations. The synthetic, complex elaborations of the results obtained indicate the influence of the random roughness and stochastic growth of living biological cartilage surfaces on the friction forces distribution.

ON RANDOM EXPECTED VALUES VARIATIONS OF TRIBOLOGY PARAMETERS IN HUMAN HIP JOINT SURFACES

Tribologia ◽  
2021 ◽  
Vol 297 (3) ◽  
pp. 45-56
Author(s):  
Krzysztof Wierzcholski ◽  
Jacek Gospodarczyk
Keyword(s):  
Friction Coefficient ◽  
Synovial Fluid ◽  
Carrying Capacity ◽  
Dynamic Viscosity ◽  
Fluid Dynamic ◽  
Load Carrying Capacity ◽  
Friction Forces ◽  
Load Carrying ◽  
Gap Height ◽  
Human Joint

This paper presents recent progress in the knowledge concerning the stochastic theory of bio- hydrodynamic lubrication with a phospholipids bilayer. On the basis of experimental measurements and analytical solutions, the research concerns the determination of the random expectancy values of load carrying capacity, the friction coefficient, and synovial fluid dynamic variations. After numerous measurements, it directly follows that the random density function of the gap height in the human joint usually indicates a disorderly increases and decreases in the height. Such irregular gap height variations have an important influence on the random synovial bio-fluid dynamic viscosity. This finally leads to the friction coefficient and cartilage wear changes of cooperating bio- surfaces. The main topic of this paper relates to the expectancy values of the tribology parameters localized inside the variable stochastic standard deviation intervals of the human joint gap height. The results obtained finally indicate the influence of the random roughness and growth of living biological cartilage surfaces on the expectancy values of the synovial fluid dynamic viscosity, load carrying capacity and friction forces in human hip joints.

Stokes Roughness Effects on Hydrodynamic Lubrication. Part II—Effects Under Slip Flow Boundary Conditions

1986 ◽  
Vol 108 (2) ◽  
pp. 159-166 ◽  
Author(s):  
Y. Mitsuya
Keyword(s):  
Flow Regime ◽  
Carrying Capacity ◽  
Stokes Equations ◽  
Hydrodynamic Lubrication ◽  
Slip Flow ◽  
Load Carrying Capacity ◽  
Roughness Effects ◽  
Random Roughness ◽  
Load Carrying ◽  
Flow Effects

Stokes roughness effects on hydrodynamic lubrication are studied in the slip flow regime. Slip flow boundary conditions for Navier-Stokes equations are derived, assuming that the fluid on a surface slips due to the molecular mean free path along the surface, even if the surface is rough. The perturbation method for Navier-Stokes equations, which was derived in Part I of this report, is then applied. Slip flow effects on load carrying capacity and frictional force are numerically clarified for both Stokes and Reynolds roughnesses. In the slip flow regime, second-order quantities induced by Stokes effects, such as flow rate, load carrying capacity, and frictional force are in proportion to the wavenumber squared. This phenomenon relative to the quantities being proportional is also the same as that in the continuum flow regime. As a result of velocity slippage, the load carrying capacity in Stokes roughness is found to decrease more than in Reynolds roughness for incompressible films, while the relationship is reversed for compressible films having a high compressibility number. The simulation of random roughness, which is generated by numerical means, clarifies one important result: the average slip flow effects associated with random Stokes roughness become similar to the slip flow effects in deterministic sinusoidal Stokes roughness, whose wavelength and height are statistically equivalent to those of random roughness. Although attention should be given to the fact that Stokes effects on random roughness demonstrate considerable scattering with the continuum flow, such scattering diminishes with the slip flow.

SURFACE RANDOM PARAMETERS FOR ENDOPROSTHESIS LUBRICATION

Tribologia ◽  
2016 ◽  
Vol 265 (1) ◽  
pp. 117-127
Author(s):  
Krzysztof WIERZCHOLSKI
Keyword(s):  
Bone Fractures ◽  
Humanoid Robots ◽  
Superficial Layer ◽  
Knee Joints ◽  
The European Union ◽  
Friction Forces ◽  
Non Invasive ◽  
Cartilage Cells ◽  
Gap Height ◽  
One Year

Within the last ten years in the European Union the number of bone fractures caused by the osteoarthritis increased twofold. More than 100000 hip or knee joints in total have been implanted in Germany during one year. Within ten years, 5% of them have failed by aseptic loosening. The non-invasive determination of friction forces and the control of their values during lubrication of cartilage cells on the superficial layer of human joint surfaces before implantation have a significant but not sufficient influence on the observation of the early abrasive wear of cartilage joint and the development of osteoporosis. From this fact was drawn the inspiration for the performed investigations referring the endoprosthesis surface parameters, because knowledge of the roughness of prosthesis surfaces and friction forces and their control methods makes it possible to provide the necessary random standard deviation of gap height and finally information about implantation possibility. This paper has been prepared based on the objective knowledge gained from the author’s experimental and theoretical experiences to represent the methodology and goal of the idea described in the study and to make possible a wider discussion on this subject for further developments during the realization of various bioengineering projects in the field of hydrodynamic artificial human and humanoid robots joints.

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.

Geometrical Structure for Endoprosthesis Surface Lubrication and Wear Prognosis

2016 ◽  
Vol 251 ◽  
pp. 206-211 ◽  
Author(s):  
Krzysztof Wierzcholski
Keyword(s):  
Bone Fractures ◽  
Superficial Layer ◽  
Knee Joints ◽  
The European Union ◽  
Friction Forces ◽  
Non Invasive ◽  
Cartilage Cells ◽  
Gap Height ◽  
One Year ◽  
And Control

It can be stated that over the last ten years in the European Union, the number of bone fractures caused by osteoarthritis has increased twofold. More than 100,000 hip or knee joints in total were implanted in Germany during one year. Within ten years, 5% of them have failed by aseptic loosening.The non-invasive determination of friction forces and control of their values during lubrication of cartilage cells on the superficial layer of human joint surfaces before implantation has a significant but not sufficient impact on the observation of the early abrasive wear of the cartilage joint and development of osteoporosis. From this fact was drawn the inspiration for the performed investigations related to the endoprosthesis surface parameters because knowledge of the roughness of prosthesis surfaces and friction forces and their control methods permits provision of a necessary standard deviation of the gap height and finally information about the implantation possibility. This paper has been prepared based on the objective of European Project UE Grant IRSES,612593, 2013-2016 to represent the methodology and goal of the idea described in and make a wider discussion possible on this subject for further developments during the realization.

Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces

1969 ◽  
Vol 184 (1) ◽  
pp. 1013-1026 ◽  
Author(s):  
H. Christensen
Keyword(s):  
Surface Roughness ◽  
Stochastic Models ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Stochastic Theory ◽  
Type Equation ◽  
Mathematical Form ◽  
Slider Bearing ◽  
Operating Characteristics ◽  
Different Types

This paper deals with hydrodynamic aspects of rough bearing surfaces. On the basis of stochastic theory two different forms of Reynolds-type equation corresponding to two different types of surface roughnesses are developed. It is shown that the mathematical form of these equations is similar but not identical to the form of the Reynolds equation governing the behaviour of smooth, deterministic bearing surfaces. To illustrate the functional effects of surface roughness the influence on the operating characteristics of a plane pad, no side leakage slider bearing is analysed. It is shown that surface roughness may considerably influence the operating characteristics of bearings and that the direction of the influence depends upon the type of roughness assumed. The effects are not, however, critically dependent upon the detailed form of the distribution function of the roughness heights.

scholarly journals Two-scale homogenization of hydrodynamic lubrication in a mechanical seal with isotropic roughness based on the Elrod cavitation algorithm

2021 ◽  
pp. 135065012110176
Author(s):  
Yanxiang Han ◽  
Qingen Meng ◽  
Gregory de Boer
Keyword(s):  
Surface Topography ◽  
Carrying Capacity ◽  
Hydrodynamic Lubrication ◽  
Tribological Performance ◽  
Stribeck Curve ◽  
Polar Coordinate System ◽  
Load Carrying Capacity ◽  
Mechanical Seal ◽  
Macro Scale ◽  
Load Carrying

A two-scale homogenization method for modelling the hydrodynamic lubrication of mechanical seals with isotropic roughness was developed and presented the influence of surface topography coupled into the lubricating domain. A linearization approach was derived to link the effects of surface topography across disparate scales. Solutions were calculated in a polar coordinate system derived based on the Elrod cavitation algorithm and were determined using homogenization of periodic simulations describing the lubrication of a series of surface topographical features. Solutions obtained for the hydrodynamic lubrication regime showed that the two-scale homogenization approach agreed well with lubrication theory in the case without topography. Varying topography amplitude demonstrated that the presence of surface topography improved tribological performance for a mechanical seal in terms of increasing load-carrying capacity and reducing friction coefficient in the radial direction. A Stribeck curve analysis was conducted, which indicated that including surface topography led to an increase in load-carrying capacity and a reduction in friction. A study of macro-scale surface waviness showed that the micro-scale variations observed were smaller in magnitude but cannot be obtained without the two-scale method and cause significant changes in the tribological performance.

scholarly journals Elastic hydrodynamic lubrication analysis for a sine movable tooth drive

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881410 ◽  
Author(s):  
Lizhong Xu ◽  
Wentao Song
Keyword(s):  
Film Thickness ◽  
Hydrodynamic Lubrication ◽  
Normal Operation ◽  
Speed Ratio ◽  
Input Shaft ◽  
Load Carrying ◽  
Radial Dimension ◽  
Lubrication Condition ◽  
Shaft Rotation Angle ◽  
Large Speed

The sine movable tooth drive has small radial dimension such that the heat, caused by friction, becomes an important factor in deciding its load-carrying ability. It is important to determine the amount of tooth lubrication in order to reduce the heat caused by the friction. This study provides equations for the meshing performance and provides the forces for the sine movable tooth drive. Using these equations, the minimum oil film thickness for the drive system is investigated. Results show that the minimum film thickness between the movable tooth and input shaft or shell changes periodically along the input shaft rotation angle. A large movable tooth radius and a movable tooth rotation radius could increase the film thickness between the movable tooth and the input shaft or the shell. In addition, a large speed ratio could increase the film thickness between the movable tooth and the input shaft, but this would also decrease the film thickness between the movable tooth and the shell. A large sine amplitude could increase the film thickness between the movable tooth and the input shaft, but this does not change the film thickness between the movable tooth and the shell. Under normal operation speeds, the hydrodynamic lubrication condition occurs between the movable tooth and the input shaft, and the partial membrane hydrodynamic state occurs between the movable tooth and the shell.

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