Solution of the Elastohydrodynamic Finite Journal Bearing Problem

1973 ◽  
Vol 95 (3) ◽  
pp. 342-351 ◽  
Author(s):  
K. P. Oh ◽  
K. H. Huebner
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Iteration Scheme ◽  
Bearing Material ◽  
Constant Property ◽  
Elasticity Equations ◽  
Minimum Film Thickness ◽  
Three Dimensional Elasticity

Finite-element techniques are applied to solve the elastohydrodynamic finite journal bearing problem. Reynolds’ equation for the fluid film and the three-dimensional elasticity equations for the bearing housing are solved simultaneously using a unique iteration scheme. The analysis yields the pressure distribution and the displacement distribution which satisfy the elastohydrodynamic requirements of realistic three-dimensional bearing geometries. From these distributions, important information such as the stresses in the bearing material and the minimum film thickness in the lubricant can be calculated. In the calculations it is assumed that the bearing operates with a constant-property lubricant and a linearly elastic bearing material. The solution procedure is applied to a typical problem and numerical results are presented.

Elastohydrodynamic Studies of Three-Lobe Journal Bearings with Non-Newtonian Lubricants

1991 ◽  
Vol 205 (6) ◽  
pp. 379-388 ◽  
Author(s):  
K C Goyal ◽  
R Sinhasan
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Performance Characteristics ◽  
Continuity Equations ◽  
Viscosity Term ◽  
Elasticity Equations ◽  
Wide Range ◽  
Deformation Coefficient ◽  
Three Dimensional Elasticity

A computer aided elastohydrodynamic study of the three-lobe journal bearing with non-Newtonian lubricants is presented for the static and dynamic performance characteristics. The three-dimensional momentum and continuity equations in cylindrical coordinates governing the flow of Newtonian lubricants in the clearance space of a three-lobe journal bearing have been solved using the finite element method. The non-Newtonian effect is introduced by modifying the viscosity term for the model iteratively. Three-dimensional elasticity equations are solved to obtain deformations in the bearing shell. Static and dynamic performance characteristics are presented for a wide range of values of non-dimensional load, deformation coefficient and non-linearity factor.

Debris Effects on EHL Contact

2000 ◽  
Vol 122 (4) ◽  
pp. 711-720 ◽  
Author(s):  
Young S. Kang ◽  
Farshid Sadeghi ◽  
Xiaolan Ai
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Force Balance ◽  
Time Dependent ◽  
Elasticity Equations ◽  
Minimum Film Thickness ◽  
Bounding Surfaces ◽  
Force Balance Equation ◽  
Ehl Contact

A model was developed to study the effects of a rigid debris on elastohydrodynamic lubrication of rolling/sliding contacts. In order to achieve the objectives the time dependent Reynolds equation was modified to include the effects of an ellipsoidal shaped debris. The modified time dependent Reynolds and elasticity equations were simultaneously solved to determine the pressure and film thickness in EHL contacts. The debris force balance equation was solved to determine the debris velocity. The model was then used to obtain results for a variety of loads, speeds, and debris sizes. The results indicate that the debris has a significant effect on the pressure distribution and causes a dent on the rolling/sliding bounding surfaces. Depending on the size and location of the debris the pressure generated within the contact can be high enough to plastically deform the bounding surfaces. Debris smaller than the minimum film thickness do not enter the contact and only large and more spherical debris move toward the contact. [S0742-4787(11)00501-7]

Elasticity solution for thick laminated anisotropic cylindrical panels under dynamic load

2002 ◽  
Vol 216 (3) ◽  
pp. 315-322 ◽  
Author(s):  
A Alibiglu ◽  
M Shakeri ◽  
M R Eslami
Keyword(s):  
Differential Equations ◽  
Dynamic Load ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Cylindrical Panel ◽  
Great Length ◽  
Elasticity Equations ◽  
Shell Panel ◽  
Asymmetric Load ◽  
Three Dimensional Elasticity

The dynamic response of an axisymmetric arbitrary laminated anisotropic cylindrical panel subjected to asymmetric load is studied on the basis of three-dimensional elasticity equations. The shell panel has a great length and is simply supported at both edges. The highly coupled partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) with variable coefficients by means of trigonometric function expansion in circumferential directions. The resulting OPEs are solved by Galerkin's finite element method. Numerical examples are presented for 45°/-45° and 45°/-45°/45° laminations under dynamic load. Finally, the results are compared with published results.

The Comparison of Four Pressure-Thermal Models of Oil Film Bearing With the Non-Newtonian and Temperature-Viscosity Effects

2016 ◽  
Author(s):  
Feng Liang ◽  
Quanyong Xu ◽  
Xudong Lan ◽  
Ming Zhou
Keyword(s):  
Temperature Field ◽  
Numerical Model ◽  
High Speed ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Oil Film ◽  
Viscosity Effects

The thermohydrodynamic analysis of oil film bearing is essential for high speed oil film bearing. The temperature field is coupled with the pressure field. The numerical model can be built or chosen according to the complexity of the objects and requirement of the accuracy. In this paper, four pressure-thermal (P-T) models are proposed, which are zero-dimensional temperature field coupled with Reynolds equation (0D P-T model), two-dimensional temperature field coupled with Reynolds equation (2D P-T model), two-dimensional temperature with third dimensional correction coupled with Dawson equation (2sD P-T model), three-dimensional temperature field coupled with Dawson equation (3D P-T model). The non-Newtonian and temperature-viscosity effects of the lubrication oil are considered in all the four models. Two types of cylindrical journal bearing, the bearing with/without axial grooves, are applied for the simulation. All the simulated cases are compared with the solutions of the CFX. The results show that the 0D P-T model fails to predict the behavior of high speed bearing; The 2D and 2sD P-T model have an acceptable accuracy to predict the performance of the bearing without grooves, but are not able to simulate the P-T field of the bearing with grooves because of the under-developed thermal boundary layer; The 2sD P-T model shows a great improvement when calculating the pressure field compared with the 2D P-T model; the 3D P-T model coincides well with the CFX at any condition. The comparison of these four models provides a reference to help designer choose a proper numerical model for a certain project.

Investigation of the Failure of Heavily Loaded Journal Bearings

1994 ◽  
Vol 208 (3) ◽  
pp. 167-171
Author(s):  
D Ashman
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Elastohydrodynamic Lubrication ◽  
Failure Criteria ◽  
Operating Conditions ◽  
Minimum Film Thickness ◽  
Hydrodynamic Solution ◽  
Metrological Study ◽  
Theoretical Minimum

This paper gives details of a combined theoretical and experimental investigation of a plain journal bearing under heavily loaded conditions together with a metrological study of the bearing geometry. It was found that under high loading conditions a simplified analytical expression relating the Sommerfeld number to the non-dimensional minimum film thickness, using a hydrodynamic solution of the isoviscous form of the Reynolds equation, could be developed. An alternative theoretical solution based on elastohydrodynamic lubrication was also considered. In addition, experimental work determined a variety of operating conditions that produced metal-to-metal contact. These operating conditions were then compared with the theoretical minimum film thickness calculations and bearing manufacturing data. This process was used to determine combined failure criteria based on operating conditions and machining capability.

Three-Dimensional Analysis of an Elastic Plate-Cylinder Intersection by the Boundary-Point-Least-Squares Technique

1977 ◽  
Vol 99 (1) ◽  
pp. 17-25 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Boundary Point ◽  
Shell Theory ◽  
Three Dimensional ◽  
Middle Part ◽  
Elasticity Equations ◽  
Three Dimensional Elasticity ◽  
Tension Loading ◽  
Theoretical Results

The boundary-point-least-squares technique is applied to the axisymmetric three-dimensional elasticity problem of a hollow circular cylinder normally intersecting with a perforated flat plate. The geometry of the intersection is partitioned into three parts. Boundary conditions on the middle part and continuity conditions between adjacent parts are satisfied using the numerical boundary-point-least-squares technique while the governing elasticity equations and all other boundary conditions are satisfied exactly. Sample theoretical results are presented for the case of axisymmetric radial tension loading on the plate. The results compare favorably with previously published experimental data and provide supplementary data to theoretical results obtained using existing shell theory solutions.

scholarly journals Partial-mixed special finite element for the analysis of multilayer composites and FGM

2012 ◽  
Author(s):  
Orlando Andrianarison ◽  
Ayech Benjeddou
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Single Layer ◽  
Static Problem ◽  
Functionally Graded ◽  
Elasticity Equations ◽  
Graded Material ◽  
Transverse Stresses ◽  
Three Dimensional Elasticity

A partial-mixed special finite element (FE) is proposed for the static analysis of multilayer composite and functionally graded material plates. Using the Hamiltonian formalism, the three-dimensional elasticity equations are first reformulated so that a partial-mixed variational formulation, retaining as primary variables the translational displacements augmented with the transverse stresses only, is obtained; this allows, in particular, a straightforward fulfilment of the multilayer interfaces continuity conditions. After an only in-plane FE discretisation, the static problem is then reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved analytically, through the layer thickness, using the symplectic formalism; the multilayer solution is finally reached via the state-space method and the propagator matrix concept. The performance, in convergence and accuracy, of the proposed approach, applied to representative examples, is shown to be very satisfactory.

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