Wyniki wyszukiwania - Biblioteka Nauki

1

The effect of a surface roughness on load carrying capacity in slide journal bearing lubriceted with oil of non-newtonian properties

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Miszczak A.

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2019

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tom Vol. 49, iss. 3

497--526

EN

The Author presents the method that taking account an influence of surface roughness on both flow and operating parameters of a slide journal bearing in the paper. For this purpose, the expected value for the gap height function should be determined. The expected value is then the most probable value of the height of the lubrication gap. There are presented the results of analytical and numerical calculations of flow and operating parameters in slide journal bearings. Numerical calculations were performed using the finite difference method as well as own calculation procedures and the Mathcad 15 software.

PL

W prezentowanej pracy Autor przedstawia metodę uwzględniania wpływu chropowatości powierzchni na parametry przepływowe i eksploatacyjne łożysk ślizgowych. W tym celu wyznacza się wartość oczekiwaną dla funkcji wysokości szczeliny. Wartość oczekiwana jest wtedy najbardziej prawdopodobną wartością wysokości szczeliny smarnej. W pracy przedstawione są wyniki obliczeń analitycznych i numerycznych parametrów przepływowych i eksploatacyjnych w poprzecznych łożyskach ślizgowych. Obliczenia numeryczne wykonano wykorzystując metodę różnic skończonych, własne procedury obliczeniowe i oprogramowanie Mathcad 15.

2

An Analysis of Hydrodynamic Pressure Distribution and Load Carrying Capacity of a Conical Slide Bearing Lubricated with Non-Newtonian Second Grade Flui

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Miszczak A. , Czaban A.

Tribologia

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2019

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tom nr 2

83--95

EN

In this paper, the authors present the equations of the hydrodynamic lubrication theory for conical slide bearings lubricated with the oil with properties described by the Rivlin-Ericksen model. It is assumed, that the considered lubricating oil shows non-Newtonian properties, i.e. it is an oil for which, apart from the classic dependence of oil viscosity on pressure, temperature and operating time, there is also a change in dynamic viscosity values caused by the changes of shear rate. The method of a small parameter was used to solve the conservation of momentum, stream continuity, and energy conservation equations. The small parameter method consists in presenting the sought functions (pressure, temperature, components of the velocity vector) in the form of a uniformly convergent series expansion in powers of a constant small parameter. These functions are substituted into the system of basic equations, and then the series are multiplied by the Cauchy method. By a comparison of the coefficients with the same powers of a small parameter, we obtain systems of partial differential equations, from which the subsequent approximations of unknowns of the sought functions are determined. The small parameter method separates the non-linear system of partial differential equations and creates several linear systems of equations. The aim of this work is to derive the equations describing and allowing the determination of the temperature distribution, hydrodynamic pressure distribution, velocity vector components, load carrying capacity, friction force and friction coefficient in the gap of conical slide bearing, lubricated with the oil of the properties described by the Rivlin-Ericksen model, taking into account its viscosity changes due to time of operation.

PL

W artykule autorzy przedstawiają równania hydrodynamicznej teorii smarowania olejem o modelu Rivlina-Ericksena stożkowego łożyska ślizgowego. Olej ten charakteryzuje się nienewtonowskimi właściwościami, czyli jest to olej, dla którego, oprócz klasycznych zależności lepkości oleju od ciśnienia, temperatury i czasu eksploatacji, występuje dodatkowo zmiana lepkości dynamicznej od szybkości ścinania. Do rozwiązania równań zachowania pędu, ciągłości strugi i zachowania energii wykorzystano metodę małego parametru. Metoda ta polega na przedstawieniu poszukiwanych funkcji (ciśnienia, temperatury, składowych wektora prędkości) w formie jednostajnie zbieżnego szeregu potęgowego rozwiniętego względem stałego małego parametru. Funkcje te podstawia się do układu równań podstawowych, a następnie wymnaża te szeregi metodą Cauchy’ego. Porównując współczynniki przy jednakowych potęgach małego parametru, otrzymuje się układy równań różniczkowych cząstkowych, z których wyznacza się kolejne przybliżenia niewiadomych, poszukiwanych funkcji. Metoda małego parametru rozprzęga nieliniowy układ równań różniczkowych cząstkowych, tworząc kilka liniowych układów równań. Celem niniejszej pracy jest wyprowadzenie równań umożliwiających wyznaczenie rozkładu temperatury, rozkładu ciśnienia hydrodynamicznego, składowych wektora prędkości, siły nośnej, siły tarcia i współczynnika tarcia w szczelinie poprzecznego łożyska ślizgowego smarowanego olejem o modelu Rivlina-Ericksena z uwzględnieniem zmian lepkości od czasu eksploatacji oleju.

3

Estimation of random friction forces on the microbearing cooperating surfaces

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Wierzcholski K. , Miszczak A.

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tom Vol. 26, No. 2

167--174

EN

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.

4

Operating parameters of a slide bearing with parabolic-shaped slide surfaces with consideration of the stochastic changes in the lubrication gap height

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Miszczak A. , Wierzcholski K.

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tom Vol. 26, No. 4

171--178

EN

In this article, the authors present the equations of the hydrodynamic theory for a slide bearing with parabolicshaped 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 nonNewton (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.