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1

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

Miszczak Andrzej, Czaban Adam

Tribologia

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2019

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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.

2

Carrying capacity and friction forces in a transverse journal bearing, lubricated with non-Newtonian oil

Miszczak A., Sikora G.

Journal of KONES

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2017

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Vol. 24, No. 3

203--210

EN

In this article, the authors present the results of numerical calculations. Calculations concern dimensionless carrying capacity and friction forces in a transverse journal bearing, lubricated by the oil of non-Newtonian properties. For analytical-numerical considerations a model of apparent viscosity changes based on exploitation time, pressure, temperature, shear rate was assumed The non-Newtonian properties of lubricating oil were characterized by increasing viscosity with increasing shear rate and described as an additional part in the constitutive equationβ3·tr(A1 2)A1. Analytical-numerical calculations were performed for smooth, non-porous plain bearing with full angle of wrap. Non-isothermal, laminar and fixed flow of lubricant in the lubrication gap of the journal bearing was assumed. Numerical calculations of hydrodynamic pressure distribution were made for Reynolds boundary conditions. The finite difference method was used to determine the Reynolds equation and the successive approximation method by taking into account the influence of pressure, temperature and non-Newtonian properties on the change of apparent viscosity. The results of the calculations are presented in the form of graphs and tables illustrating the influence of relative eccentricity and pressure, temperature and non-Newtonian properties on changes in the dimensionless load and friction force. Analysis of the obtained results illustrates the high-pressure effect on the increase of the carrying capacity and friction force for high relative eccentricities. A similar situation is by considering the non-Newtonian properties.

3

CFD analysis of the hydrodynamic lubrication of a misaligned, slide conical bearing

Czaban A.

Tribologia

|

2016

|

nr 4

41--53

EN

The lateral loads carried by hydrodynamic bearings, and also their uneven distribution, introduce an additional axial misalignment between the shaft and sleeve. The machining and mounting errors also result in improper initial alignment of bearing shaft or sleeve. Furthermore, due to vibrations, misalignment of shaft fluctuates during the operation of the bearing. This has an impact on the operating parameters of the bearing, and, in extreme cases, where the maximum allowable value of the misalignment is exceeded, the bearing can be damaged. The aim of this work is to investigate the effect of misalignment on the hydrodynamic pressure distribution in the conical sliding bearing lubrication gap and on the bearing load carrying capacity and friction force values. This paper shows the result of a CFD simulation of hydrodynamic conical bearings lubrication with the assumption that the bearings are misaligned, i.e. where the rotation axis of bearing shaft is not parallel to the axis of the cone of the bearing sleeve. The commercial CFD software ANSYS Fluent was used in this research. It was assumed that the flow of lubricating oil is laminar, without slipping on bearing surfaces, and that the oil has non-Newtonian properties.

PL

Nierównomierny rozkład sił obciążających łożysko ślizgowe, a co za tym idzie – deformacja wału powodują powstawanie nierównoległości pomiędzy osią czopa a osią panewki łożyska. Dodatkowo błędy procesu obróbki lub pomiędzy osią czopa i osią panewki. Położenie osi czopa nie jest stałe podczas pracy łożyska i zmienia się np. w związku z jego drganiami. Celem tej pracy jest zbadanie wpływu nierównoległości osi obrotu czopa w stosunku do osi panewki na rozkład ciśnienia hydrodynamicznego, wartości sił nośnych i na wartość momentu tarcia w stożkowym łożysku ślizgowym. W niniejszej pracy zaprezentowano wyniki symulacji CFD dla stożkowego łożyska ślizgowego przy założeniu, że przepływ oleju w szczelinie smarnej jest laminarny. Założono, że olej jest płynem o właściwościach nienewtonowskich, a zależność naprężeń od szybkości ścinania jest opisana relacją Ostwalda de Waele. Symulacje przeprowadzono dzięki wykorzystaniu komercyjnego oprogramowania CFD Ansys Fluent.

4

Generalized Newtonian fluids as lubricants in the hydrodynamic conical bearings : a CFD analysis

Czaban A.

Journal of KONES

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2016

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Vol. 23, No. 2

89--95

EN

Additives, ageing or wear and impurities can cause, that relationship between shear stress and shear rate in a lubricating oil is or becomes non-linear, and due to this, a significant change in the values of operating parameters of slide hydrodynamic bearings may occur. It is important to take into account such dependence during design and simulations of slide bearings. The calculations, which consider the non-linear properties of the lubricating oil, can be carried out by adopting the generalized Newtonian fluid models. This paper shows the result of CFD simulation of slide conical bearings hydrodynamic lubrication, assuming that the lubricating oil behaves as a generalized Newtonian fluid. The hydrodynamic pressure distributions, load carrying capacities and friction torques were calculated for bearings lubricated with different types of generalized Newtonian fluids and the obtained data were compared. In the study, the following models of fluids were adopted: the Power-law fluid (Ostwald-de Waele), the Cross fluid and the Carreau fluid. The coefficients of mentioned relationships were determined by fitting the curves described by each model to the experimental data using the least squares approximation method. The calculations of hydrodynamic pressure distributions, load carrying capacities and friction torques were carried out using the commercial CFD software Ansys Fluent from the Ansys Workbench 2 platform.

5

Analysis of the load carrying capacities and the friction force in the gap of the slide journal bearing lubricated with a non-Newtonian oil described by a power-law model

Miszczak A.

Journal of KONES

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2016

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Vol. 23, No. 3

327--335

EN

In this paper, the author presents the results of numerical calculations of load carrying capacities and friction forces in the gap of the slide journal bearing lubricated with an oil on the non-Newtonian's properties. In the studies, the power-law model has been assumed to describe the relationship between the stress tensors and shear rate tensors. The analytical and numerical calculations have been performed for the plain bearing, non-porous with a full wrap angle. It has been assumed isothermal, laminar and steady flow of lubricant in the gap of a slide bearing. Numerical calculations have been performed for the Gumbel’s boundary conditions and dimensionless lengths of the bearings like L=b/R =2;1.5;1; ½ and ¼. The flow-rate index and coefficient of consistency have been adopted based on the results of experimental studies of changes of dynamic viscosity in terms of a shear rate. It has been assumed that the apparent viscosity depends only on the shear rate. Dynamic viscosity of the engine oil, used in a gasoline engine with a capacity of 1800 cm3, has been tested on the Haake Mars III rheometer. The analytical solutions presented in the paper were based on more general derivations carried out by Professor K. Wierzcholski in his article: ‘Non-linear hydrodynamic lubrication in conjugated fields’ (publication in printing). In this paper, the key quantities such as components of vector of the velocity, hydrodynamic pressure and temperature were presented in the form of convergent power series. The values of load carrying capacities and friction forces were determined and compared for the event where the oil has properties of Newtonian and non-Newtonian. Calculations have been made for the dimensionless quantities.

6

CFD analysis of non-Newtonian and non-isothermal lubrication of hydrodynamic conical bearing

Czaban A.

Journal of KONES

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2014

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Vol. 21, No. 4

49--56

EN

In this work is shown the result of CFD simulation of hydrodynamic conical bearing lubrication with consideration of non-isothermal oil flow in a bearing lubrication gap and also with assumption, that oil has non- Newtonian properties. The determination of hydrodynamic pressure distribution in bearing gap was carried out by using the commercial CFD software ANSYS Academic Research for fluid flow phenomenon (Fluent). Calculations were performed for bearings without misalignment, i.e. where the cone generating line of bearing shaft is parallel to the cone generating line of bearing sleeve. The Ostwald-de Waele model for non-Newtonian fluids was adopted in this simulation. The coefficients of Ostwald-de Waele relationship were determined by application of the least squares approximation method and fitting curves described by this model to the experimental data, obtained for some motor oils, presented in previous work. The calculated hydrodynamic pressure distributions were compared with the data obtained for corresponding bearings, but assuming that the flow in the bearing lubrication gap is isothermal. Some other simplifying assumptions are: a steady-state operating conditions of a bearing, incompressible flow of lubricating oil, no slip on bearing surfaces, pressure on the side surfaces of bearing gap is equal to atmospheric pressure. This paper presents results for bearings with different rotational speeds and of different bearing gap heights.

7

CFD analysis of hydrodynamic lubrication of slide conical bearing with consideration of the bearing shaft and sleeve surface roughness

Czaban A

Journal of KONES

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2014

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Vol. 21, No. 3

35--40

EN

In this work is shown the result of CFD simulation of hydrodynamic conical bearing lubrication with consideration of the effect of the bearing shaft and sleeve surface roughness. The oil flow in a bearing lubrication gap largely depend on the condition of the cooperating surfaces of a bearing. Surface irregularities are formed already at the manufacturing process and furthermore the quality of the surface may change during operation of a bearing. In this work, as a parameter describing surface condition, the Ks roughness height parameter was taken (i.e. sand-grain roughness height). The hydrodynamic pressure distribution in lubrication gaps of investigated bearings were calculated by using the commercial CFD software ANSYS Academic Research for fluid flow phenomenon (Fluent). Calculations were conducted for bearings without misalignment. The Ostwald-de Waele model for non-Newtonian fluids was adopted in this simulation. The coefficients of Ostwald-de Waele relationship were determined by application of the least squares approximation method and fitting curves described by this model to the experimental data, obtained for some motor oils, presented in previous work. The calculated hydrodynamic pressure distributions were compared with the data obtained for corresponding bearings, but assuming that bearings have smooth surfaces and there is no slip on surfaces. This paper presents results for bearings with different rotational speeds and of different bearing gap heights.

8

CFD analysis of pressure distribution in slide conical bearing lubricated with non-Newtonian oil

Czaban A.

Journal of KONES

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2013

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Vol. 20, No. 3

117--124

9

Experimental values of temperature distribution in a sliding bearing sleeve lubricated with non-Newtonian oils

Miszczak A.

Polish Maritime Research

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2005

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nr 3

16-26

EN

This paper presents results of experimental investigations of temperature distributions on inner surface of a sleeve of transverse sliding bearing lubricated with non-Newtonian oils. The measurements were performed by means of Pt100 miniature sensors placed close to internal surface of the sleeve. To measure sleeve temperature distributions use was made of a test stand installed at Gdynia Maritime University. Delo 1000 Marine 30 oil, SAE 15W40 basic oil, and aferro-oil made of the SAE 15W40 basic oil were used as a lubricating medium. During measuring temperature distributions for the ferro-oil different intensity values of external magnetic field generated by electromagnets were applied.