Based upon a Gecim-Winer fluid flow model, a curvilinear squeeze film bearing is considered. The equations of motion are given in a specific coordinates system. After general considerations on the Gecim-Winer fluid flow these equations are used to derive the Reynolds equation. The solution of this equation is obtained by a method of successive approximation. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of the Gecim-Winer fluid flow in gaps of two simple bearings: radial and spherical are presented.
In the paper, the model of a DeHaven fluid and some other models of non-Newtonian fluids, in which the shear strain rates are known functions of the powers of shear stresses, are considered. It was demonstrated that these models for small values of material constants can be presented in a form similar to the form of a DeHaven fluid. This common form, called a unified model of the DeHaven fluid, was used to consider a curvilinear squeeze film bearing. The equations of motion of the unified model, given in a specific coordinate system are used to derive the Reynolds equation. The solution to the Reynolds equation is obtained by a method of successive approximations. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of flows of the unified DeHaven fluid in gaps of two simple squeeze film bearings are presented.
The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated with a lubricant being a viscoplastic fluid of a Herschel-Bulkley type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Herschel-Bulkley lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze films in a step bearing (modeled by two parallel disks) is discussed in detail.
Based upon a Prandtl fluid flow model, a curvilinear squeeze film bearing is considered. The equations of motion are given in a specific coordinate system. After general considerations on the Prandtl fluid flow these equations are used to derive the Reynolds equation. The solution of this equation is obtained by a method of successive approximation. As a result one obtains formulae expressing the pressure distribution and load-carrying capacity. The numerical examples of the Prandtl fluid flow in gaps of two simple bearings are presented.
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The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated by a lubricant being a viscoplastic fluid of a simple Casson type is considered. After general considerations on the flow of the viscoplastic fluid (lubricant) in a bearing clearance and in a porous layer the modified Reynolds equation for the curvilinear squeeze film bearing with a Casson lubricant is given. The solution of this equation is obtained by a method of successive approximation. As a result one obtains a formula expressing the pressure distribution. The example of squeeze film in a step bearing (modeled by two parallel disks) is discussed in detail.
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The influence of inertia and wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated by a viscoplastic fluid of a Bingham type is considered. The general consideration on the flow of the viscoplastic fluid in a bearing clearance and in a porous layer are presented. Using the Morgan-Cameron approximation and an averaged inertia method the modified Reynolds equation for the curvilinear thrust bearing is given. The solution of this equation for the case of the squeeze film bearing is presented. As a result one obtains a formula expressing the pressure distribution. The example of a squeeze film between parallel disks is discussed in detail.
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The influence of a wall porosity on the pressure distribution in a curvilinear squeeze film bearing lubricated by a viscoplastic fluid of a Bingham type is considered. The general consideration on the flow of viscoplastic fluid in a bearing clearance and in a porous layer are presented. The modified Reynolds equation for the curvilinear thrust bearing is given. The solution of this equation for the case of the squeeze film bearing is presented. As a result one obtains a formula expressing the pressure distribution. The example of a squeeze film between parallel disks is discussed in detail.
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The flow of a synovial fluid modelled as a couple-stress fluid in a squeeze film biological bearing with a permeable layer is considered. The biobearing is modelled by two rotational surfaces and the permeable layer is adhered to the curved impermeable surface. The flow in a squeeze film biobearing is considered with inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. The flow of a couple-stress fluid in permeable layer satisfies the modified Darcy's law. As an example the biological bearing modelled by two parallel surfaces is discussed.
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The flow of a power-law lubricant in a squeeze film bearing is considered. The bearing is modelled by two curvilinear rough surfaces. The flow in the bearing clearance is considered without inertia. Using the Christensen stochastic model of a surface roughness the closed-form solution is obtained. A step bearing and a spherical bearing are discussed as examples. It is shown that the power-law exponent and the roughness considerably influence the bearing performance.
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The flow of a power-law lubricant in a squeeze film bearing with one porous wall is considered. The bearing is modelled by two curvilinear rough surfaces and the porous wall is adheres to the curved non-porous surface. The flow in the bearing clearance is considered without inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. Using the Christensen stochastic model of a surface roughness a closed-form solution is obtained. A step bearing and a spherical bearing are discussed as examples. It is shown that the power-law exponent and the roughness influence the bearing performance considerably.
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The flow of a power-law lubricant in a squeeze film bearing is considered. The bearing is modelled by two curvilinear rough surfaces. The flow in the bearing clearance is considered with inertia effects. Using the Christensen stochastic model of a surface roughness a closed-form solution is obtained. A step bearing and a spherical bearing are discussed as examples. It is shown that the power-law exponent and the roughness considerably influence the bearing performance.
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An attempt has been made to study and analyze the performance of a hydromagnetic squeeze film between conducting porous rough infinitely long rectangular plates with electrically conducting lubricant in the presence of a transverse magnetic field. The bearing surfaces are assumed to be transversely rough. The random roughness is characterized by a stochastic random variable with non zero mean, variance and skewness. The associated Reynolds' equation is then stochastically averaged with respect to the random roughness parameter. This equation is solved with appropriate boundary conditions to find the pressure distribution, which is then used to obtain the load carrying capacity. Lastly, the response time is calculated. The results are presented graphically as well as in a tabular form. It is seen that the bearing system gets affected adversely owing to transverse surface roughness. But variance (-ve) tends to increase the load carrying capacity. Also, the bearing system resists an enhanced performance due to hydromagnetization. In addition, the load carrying capacity increases considerably due to conductivity while it decreases with respect to the aspect ratio The combined effect of porosity, the aspect ratio and the standard deviation associated with roughness is substantially adverse. However, this negative effect can be compensated to some extent by hydromagnetization and conductivity in the case of negatively skewed roughness. It is also observed that the bearing with magnetic field can support a load even when there is absence of flow. This investigation makes it plain and clear that roughness must be given due consideration while designing the bearing system.
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The flow of a Newtonian lubricant in a bearing clearance is discussed. The bearing is modelled by two rotational surfaces and the porous layer is adhered to the curved impermeable surface. The effects of rotational inertia forces on the pressure distribution are examined. The flow in the bearing clearance is considered with inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. As an example the bearing modelled by two spherical surfaces was discussed in detail.
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The flow of a power-law lubricant in a squeeze film bearing with one porous pad is considered. The bearing is modelled by two curvilinear surfaces and the porous pad is adhered to the curved non-porous surface. The flow in the bearing clearance is considered with inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. Using the averaged inertia method the closed-form solution is obtained. A step bearing is discussed as an example.
PL
Rozważono przepływ potęgowego środka smarnego w wyciskanym filmie łożyska z porowatą wkładką. Łożysko jest modelowane dwiema krzywoliniowymi powierzchniami, a porowata wkładka przylega do zakrzywionej nieprzepuszczalnej powierzchni. Przepływ w szczelinie łożyska jest rozważony z uwzględnieniem bezwładności, a równania Naviera-Stokesa i Poissona rozwiązano wykorzystując przybliżenie Morgana-Camerona. Stosując metodę uśrednionej bezwładności uzyskano formuły określające ciśnienie i siłę nośną. Jako przykład rozważono łożysko płytkowe.
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The paper describes the squeeze film of the non-Newtonian fluids between two circular plates with slip boundary conditions, having as final result the pressure distribution and the load capacity.
PL
W artykule opisano wyciskaną warstwę cieczy nie-Newtonowskiej pomiędzy dwoma kolistymi dyskami, z uwzględnieniem warunków brzegowych ujmujących poślizg. Efektem rozważań jest opis rozkładu ciśnienia oraz nośności.
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The flow of a couple stress fluid in the clearance of a curvilinear bearing with a porous pad is considered. The porous pad is connected with the upper impermeable rotating surface which approaches the lower fixed bearing surface. The Reynolds and Poisson equations are uncoupled by using the Morgan-Cameron approximation and a closed-form solution is obtained. As an example the bearing formed by two disks is discussed.
PL
W pracy rozważono przepływ płynu z naprężeniami momentowymi w krzywoliniowej szczelinie łożyska z porowatą wkładką. Porowata wkładka powiązana jest z górną nieprzepuszczalną wirującą powierzchnią, która zbliża się do dolnej nieruchomej powierzchni łożyska. Do rozwiązania równań Poissona oraz Reynoldsa wykorzystano przybliżenie Morgana-Camerona. Jako przykład rozpatrzono łożysko utworzone przez dwie kołowe tarcze.
The flow of couple stress fluid in the clearance of a curvilinear channel with the porous pad was considered. The porous pad was connected with the upper impermeable rotating surface approaching the lower fixed channel surface. The Reynolds and Poisson equations were uncoupled using the Morgan-Cameran approximation and closed-form solution was obtained, As an example the channel formed by two disks was discussed.
Inertia effects in the flow of suspension modelled as a power-law fluid in a curvilinear squeeze film channel with the porous pad were considered. The analysis was based on the assumption that the porous pad consisted of a system of capillaries of very small radii, which allowed the use of the Darcy law and the Mor-gan-Cameron approximation for the flow in the porous pad. A spherical channel was discussed as an example.
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The flow of a synovial fluid in a squeeze film biological bearing is considered. The biobearing is modelled by two rotational surfaces and the porous layer is adheres to the curved non-porous surface. The flow in the biobearing clearance is considered with inertia and the Navier-Stokes and Poisson equations are uncoupled by using the Morgan-Cameron approximation. As an example the biobearing modelled by two disks and two spherical surfaces is discussed.
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The flow of a couple stress fluid in the clearance of a curvilinear thrust bearing with a porous pad is considered. The porous pad is connected with an upper impermeable rotating surface which approaches the lower fixed bearing surface. The Reynolds and Poisson equations are uncoupled by using the Morgan-Cameron approximation and a closed-form solution is obtained. Expressions for the pressure and capacity load of the bearing are given. As an example the bearing modelled by two disks and two spherical surfaces is discussed.
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