Analysis of nonlinear viscoelastic lubrication using Giesekus constitutive equation

2020 ◽  
pp. 135065012094428 ◽  
Author(s):  
Ali Abbaspur ◽  
Mahmood Norouzi ◽  
Pooria Akbarzadeh ◽  
Seyyed Amirreza Vaziri
Keyword(s):  
Pressure Distribution ◽  
Normal Stress ◽  
Carrying Capacity ◽  
Viscoelastic Model ◽  
Normal Stress Difference ◽  
Load Carrying Capacity ◽  
Stress Difference ◽  
Mobility Factor ◽  
Nonlinear Viscoelastic ◽  
Load Carrying

Recent research has shown that adding polymeric materials to mineral oils and consequently changing the behavior of Newtonian lubricants into viscoelastic materials will enhance the lubrication performance. Therefore, in order to examine theoretically the actual behavior of such lubricants, a suitable viscoelastic model must be considered. Hence, in this paper, the solution of fluid film lubrication is presented analytically using the Giesekus viscoelastic model. This constitutive model is based on the concept of configuration-dependent molecular mobility and is suitable for predicting the nonlinear viscoelastic properties. Indeed, it can describe the power-law regions for viscosity, the normal-stress coefficients, the elongational viscosity, and also the complex viscosity. In order to linearize the momentum and constitutive equations and obtain the generalized Reynolds equation, the perturbation method is used and the mobility factor is considered as the perturbation parameter. Here, the effects of mobility factor, outlet-to-inlet height ratio, and Weissenberg number on fluid film pressure distribution, velocity profiles, load capacity, friction coefficient, and first normal stress difference are investigated in detail. Due to the normal stress difference in viscoelastic fluids, using a viscoelastic fluid in contrast a Newtonian fluid can significantly increase the load-carrying capacity of bearing. Another result is with increasing the value of mobility factor, the fluid viscosity decreases and consequently the pressure distribution decreases simultaneously while the lateral normal stress in the y-direction increases. The term pressure distribution is more negligible than the term lateral normal stress and as a result by increasing the mobility factor the load-carrying capacity increases too. It is also observed that, when the Weissenberg numbers tend to infinity regardless of the mobility factor, the friction coefficient tends towards a constant value and rubber-like elasticity is responses.

Numerical Simulation of a First Normal Stress Difference-Based Model for Shear-Induced Crystallization of Polyethylene

2011 ◽  
Vol 266 ◽  
pp. 130-134
Author(s):  
Jin Yan Wang ◽  
Jing Bo Chen ◽  
Chang Yu Shen
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Normal Stress ◽  
Viscoelastic Model ◽  
Normal Stress Difference ◽  
Simple Shear Flow ◽  
Stress Difference ◽  
Avrami Model ◽  
First Normal Stress Difference ◽  
Induced Crystallization

The paper presents a numerical simulation for the isothermal flow-induced crystallization of polyethylene under a simple shear flow. The effect of flow on crystllization is considered through the simple mathematical relationship between the additional number of nuclei induced by shear treatment and the first normal stress difference. Leonov viscoelastic model and Avrami model are used to describe the normal stress difference and the crystallization kinetics, respectively. It is found that the short-term shear treatment has a large effect on the crystallization dynamics of polyethylene , but the effect of the intensity of the shear flow is not infinite ,which shows a saturation phenomenon, namely, the accelerated degree of crystallization tending to level off when the shear rate or shear time is large enough.

An Approximate Solution for the Infinitely Long, Gas Lubricated Slider Bearing

1965 ◽  
Vol 87 (4) ◽  
pp. 1085-1086
Author(s):  
H. J. Sneck
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Load Carrying ◽  
Numerical Design ◽  
The One ◽  
Design Calculations

The only exact solution for the infinitely long, gas-lubricated slider bearing is the one obtained by Harrison [1] for the plane wedge isothermal film. The resultant formulas for the pressure distribution and load-carrying capacity are complicated and therefore quite cumbersome in numerical design calculations. In the analysis to follow, a simplified, approximate solution is developed which can be applied to any infinitely long slider geometry.

Performance characteristics of rectangular aerostatic thrust bearing by conformal mapping

2018 ◽  
Vol 70 (8) ◽  
pp. 1457-1475
Author(s):  
Shang-Han Gao ◽  
Sheng-Long Nong
Keyword(s):  
Conformal Mapping ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Thrust Bearing ◽  
Performance Characteristics ◽  
Load Carrying Capacity ◽  
Möbius Transform ◽  
Content Type ◽  
Air Supply ◽  
Load Carrying

Purpose This paper aims to analyze the pressure distribution of rectangular aerostatic thrust bearing with a single air supply inlet using the complex potential theory and conformal mapping. Design/methodology/approach The Möbius transform is used to map the interior of a rectangle onto the interior of a unit circle, from which the pressure distribution and load carrying capacity are obtained. The calculation results are verified by finite difference method. Findings The constructed Möbius formula is very effective for the performance characteristics researches for the rectangular thrust bearing with a single air supply inlet. In addition, it is also noted that to obtain the optimized load carrying capacity, the square thrust bearing can be adopted. Originality/value The Möbius transform is found suitable to describe the pressure distribution of the rectangular thrust bearing with a single air supply inlet.

AN ANALYSIS OF HYDRODYNAMIC PRESSURE DISTRIBUTION AND LOAD CARRYING CAPACITY OF A CONICAL SLIDE BEARING LUBRICATED WITH NON -NEWTONIAN SECOND GRADE FLUI

Tribologia ◽  
2019 ◽  
Vol 284 (2) ◽  
pp. 83-95
Author(s):  
Andrzej Miszczak ◽  
Adam Czaban
Keyword(s):  
Partial Differential Equations ◽  
Small Parameter ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Velocity Vector ◽  
Hydrodynamic Pressure ◽  
Parameter Method ◽  
Load Carrying Capacity ◽  
Small Parameter Method ◽  
Load Carrying

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.

Effects of piezo-viscous–coupled stress lubricant on the squeeze film performance of parallel triangular plates

2019 ◽  
Vol 234 (9) ◽  
pp. 1514-1521 ◽  
Author(s):  
H Aminkhani ◽  
M Daliri
Keyword(s):  
Pressure Distribution ◽  
Carrying Capacity ◽  
Couple Stress ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Film Performance ◽  
Pressure Dependency ◽  
Load Carrying ◽  
Viscosity Variation ◽  
Coupled Stress

The paper shows the combined effects of couple stress fluids and lubricant viscosity variation with pressure in squeeze film performance of parallel triangular plates. By solving Reynolds equation and using perturbation method, the pressure distribution is obtained with consideration of viscosity variation with pressure. Also, with integrating pressure in the film region, load-carrying capacity is derived. A fourth-order Rang–Kutta is used to solve the nonlinear differential equation between lubricant film thickness and time. Various cases of couple stress, iso-viscous and piezo-viscous contributions are analyzed. According to the results, it is found that using couple stress fluid as a lubricant and considering viscosity–pressure dependency will increase characteristics of the squeeze film such as load-carrying capacity, pressure distribution, and triangular plates moving time, significantly as compared to the classical Newtonian iso-viscous lubricant.

Squeeze-Film Behavior for Porous Annular Disks

1970 ◽  
Vol 92 (4) ◽  
pp. 593-596 ◽  
Author(s):  
Hai Wu
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Carrying Capacity ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Load Carrying ◽  
Annular Disks

An analysis is made of the squeeze-film behavior between two annular disks when one disk has a porous facing. The problem is solved analytically. Results are presented for pressure distribution, load-carrying capacity, and film thickness as functions of time.

scholarly journals Thrust Porous Bearing with Rough Surfaces Lubricated by a Rotem-Shinnar Fluid

2016 ◽  
Vol 10 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Anna Walicka ◽  
Edward Walicki
Keyword(s):  
Pressure Distribution ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Equations Of Motion ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Porous Bearing ◽  
Load Carrying ◽  
Plastic Fluid

Abstract In the paper the influence of both bearing surfaces roughness and porosity of one bearing surface on the pressure distribution and load-carrying capacity of a thrust bearing surfaces is discussed. The equations of motion of a pseudo-plastic fluid of Rotem-Shinnar, are used to derive the Reynolds equation. After general considerations on the flow in a bearing clearance and in a porous layer using the Morgan-Cameron approximation and Christensen theory of hydrodynamic lubrication the modified Reynolds equation is obtained. The analytical solutions of this equation for the cases of squeeze film bearing and externally pressurized bearing are presented. As a result one obtains the formulae expressing pressure distribution and load-carrying capacity. Thrust radial bearing with squeezed film is considered as a numerical example.

The Impact of Linear Deformations on Stationary Hydrostatic Thrust Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 874-877 ◽  
Author(s):  
Noah D. Manring ◽  
Robert E. Johnson ◽  
Harish P. Cherukuri
Keyword(s):  
Pressure Distribution ◽  
Closed Form ◽  
Flow Rate ◽  
Carrying Capacity ◽  
Thrust Bearing ◽  
Load Carrying Capacity ◽  
Thrust Bearings ◽  
Load Carrying ◽  
Number Flow ◽  
The Impact

In this work, the operating sensitivity of the hydrostatic thrust bearing with respect to pressure-induced deformations will be studied in a stationary setting. Using the classical lubrication equations for low Reynold’s number flow, closed-form expressions are generated for describing the pressure distribution, the flow rate, and the load carrying capacity of the bearing. These expressions are developed to consider deformations of the bearing that result in either concave or convex shapes relative to a flat thrust surface. The impact of both shapes is compared, and the sensitivity of the flow rate and the load carrying capacity of the bearing with respect to the magnitude of the deformation is discussed. In summary, it is shown that all deformations increase the flow rate of the bearing and that concave deformations increase the load carrying capacity while convex deformations decrease this same quantity relative to a non-deformed bearing condition.

An Analysis of the Squeeze Film Between Porous Rectangular Plates

1972 ◽  
Vol 94 (1) ◽  
pp. 64-68 ◽  
Author(s):  
Hai Wu
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Laplace Equation ◽  
Carrying Capacity ◽  
Reynolds Equation ◽  
Squeeze Film ◽  
Load Carrying Capacity ◽  
Rectangular Plates ◽  
Load Carrying ◽  
In Series

The squeeze film between two rectangular plates when one has a porous facing is studied theoretically. The problem is described by the modified Reynolds equation in the film region and the Laplace equation in the porous region. Results are presented for pressure distribution, load-carrying capacity, and film thickness as functions of time in series form. The effect of the porous facing on the squeeze film behavior is discussed and found to be important.

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