Thermohydrodynamic Performance of Thrust Bearings With Circular Tilted Pads Under the Presence of Air Gas Bubbles and Centrifugal Forces

1989 ◽  
Vol 111 (3) ◽  
pp. 510-517 ◽  
Author(s):  
L. A. Abdel-Latif ◽  
E. M. Bakr ◽  
M. I. Ghobrial
Keyword(s):  
Gas Bubbles ◽  
Lubricating Oil ◽  
Compressible Medium ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Thrust Bearings ◽  
Characteristic Values ◽  
The Finite Difference Method ◽  
Temperature And Pressure ◽  
Bearing Characteristic

This paper deals with the analysis of thrust bearings with tilted circular pads running under thermohydrodynamic conditions. During operation, a considerable quantity of air/gas bubbles is dispersed inside the lubricating oil and build a compressible medium. The important lubricant properties, namely viscosity and density are altered substantially due to bubble presence as well as temperature rise. The influence of the centrifugal forces become significant as the speed and load become higher. Such type of bearings has been herein investigated taking into account both influencing phenomena. The geometric and loading parameters are varied to show the combined effect on the bearing characteristic values. The governing equations of the THD theory are solved numerically using the finite difference method. The surface tension of bubbles and the change of bubble content with temperature and pressure are included in the governing equations as are the centrifugal forces.

Analysis of Heavily Loaded Tilted Pads Thrust Bearings With Large Dimensions Under TEHD Conditions

1988 ◽  
Vol 110 (3) ◽  
pp. 467-476 ◽  
Author(s):  
L. A. Abdel-Latif
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Iterative Scheme ◽  
Equation System ◽  
Successive Approximation Method ◽  
Heavy Load ◽  
Thrust Bearings ◽  
Characteristic Values ◽  
Heavy Loads ◽  
Bearing Characteristic

Huge thrust bearings with centrally pivoted and tilted pads operating under heavy loads are analzyed using the (thermoelastohydrodynamic) TEHD-theory. The Reynolds equation, the energy equation of the oil film, and the heat conduction equation of the bearing, all are coupled with the deflection equation and solved simultaneously in order to determine the bearing characteristic values. The first three equations are transformed by means of finite difference method and the last equation is solved using the method of Ritz-Galerkin. Based on successive approximation method a new iterative scheme is presented to apply the heavy load incrementally which provides a successful convergence of the equation system. In order to find the equilibrium state of the pad, another iterative scheme based on a controlled change of the pad tilts is applied. The tilts are changed as a function of the offset of the hydrodynamic resultant force from the pivot location. It is proved that the new scheme is quite efficient in successful convergence of the equation system and in saving CPU time.

scholarly journals Transient free convection in an inclined square porous cavity filled with a nanofluid using LTNE and Buongiorno’s models

2018 ◽  
Vol 240 ◽  
pp. 03014
Author(s):  
Mikhail Sheremet ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Inclination Angle ◽  
Equilibrium Temperature ◽  
Brownian Diffusion ◽  
Governing Equations ◽  
Nanofluid Flow ◽  
Porous Cavity ◽  
Flow And Heat Transfer ◽  
The Finite Difference Method ◽  
Porous Enclosure

The combined effect of Brownian diffusion, thermophoresis and cavity inclination angle on natural convective heat transfer in an inclined porous enclosure has been studied numerically. Fluid containing nanoparticles of low concentration circulates inside the cavity under the effect of the buoyancy force. Governing equations with corresponding boundary conditions formulated using the non-dimensional stream function and vorticity variables have been solved by the finite difference method. An influence of the cavity inclination angle, Darcy and Nield numbers on nanofluid flow and heat transfer has been investigated. It has been found that high Nield numbers illustrate more equilibrium temperature distribution inside the porous cavity.

scholarly journals Feasibility of a Quasi-Static Approach in Assessing Side-Wind Hazards for Running Vehicles

2019 ◽  
Vol 9 (16) ◽  
pp. 3377 ◽  
Author(s):  
Se-Jin Kim ◽  
Ho-Kyung Kim
Keyword(s):  
Valuable Insight ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Rolling Moment ◽  
Novel Approach ◽  
Reaction Forces ◽  
Static Approach ◽  
Tire Forces ◽  
Insight Into ◽  
Force Equilibrium

This study is an examination into the feasibility of a quasi-static approach to evaluating the reaction forces that impact tires. This information could lend valuable insight into efforts to limit overturning and side-slip accidents of vehicles exposed to strong side winds. The performance of the quasi-static approach was evaluated by comparing the calculated tire forces with those created using TruckSim, which is a dynamic vehicle analysis software. Governing equations were formulated for two types of vehicles that are susceptible to the force of wind, vans, and trailers, by considering a force equilibrium, a compatibility condition, and several assumptions. The quasi-static approach for trailers is a novel expansion of the conventional approach to a two-axle vehicle. Proposed enhancements to the quasi-static approach reflect the additional rolling moment of a trailer. The curvature and the cant of a curved road were accounted for via centrifugal forces. Both uniform and turbulent wind conditions were considered in questioning the feasibility of this novel approach.

Optimum Design of Fluid Film Bearing for HDD Spindle Considering the Tolerances

2010 ◽  
Author(s):  
Yuta Sunami ◽  
Masayuki Ochiai ◽  
Hiromu Hashimoto
Keyword(s):  
Optimum Design ◽  
High Speed ◽  
Low Noise ◽  
Production Costs ◽  
Fluid Film ◽  
Rotating Shaft ◽  
Fluid Film Bearings ◽  
Support Element ◽  
Characteristic Values ◽  
Bearing Characteristic

Fluid film bearings are widely used for high speed rotating machineries acting as rotating shaft support element. Especially, the bearings are widely applied to the OA equipments and IT devices. Optimization of bearing parameters is effective to improve the performance of the fluid film bearings since low noise and impact-proof characteristics are essential requirements for these equipments. On the other hand, bearings for miniaturized spindles are generally made by mass production process which will eventually requires reduction of production costs. In this paper, therefore small size HDD spindle using fluid film bearings is treated. Sensitivity analysis and optimum design that considered dimensional tolerances using the probabilistic techniques are conducted. As a result, the influence of bearing characteristic values on the occurrence of dimensional tolerances was clarified.

Untwist of Rotating Blades

1975 ◽  
Vol 97 (2) ◽  
pp. 180-187 ◽  
Author(s):  
M. Ohtsuka
Keyword(s):  
Cross Section ◽  
Virtual Work ◽  
Axial Flow ◽  
Arbitrary Cross Section ◽  
Principle Of Virtual Work ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Compressor Rotor ◽  
Flow Compressor ◽  
Good Agreement

This paper deals with the deformation and the stress of an axial flow compressor rotor blade under the loading of centrifugal forces. Coupled deformation of extension, bending, torsion and transverse shear of a pretwisted curved bar with arbitrary cross section is considered. Governing equations derived by means of the principle of virtual work are solved numerically by finite difference method. The warping functions used in the analysis were obtained by the use of finite element method. Measurement of the untwist angles and the stresses were carried out for the verification of the numerical analysis and they were found to be in good agreement.

scholarly journals Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Vibration Analysis ◽  
Mass Density ◽  
Functionally Graded ◽  
Governing Equations ◽  
Mass System ◽  
The Finite Difference Method

This paper presents an approach to the vibration analysis of axially functionally graded (AFG) non-prismatic Euler-Bernoulli beams using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, and mass density) of AFG beams vary along the longitudinal axis. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. In this paper, differential equations were formulated with finite differences, and additional points were introduced at the beam’s ends and at positions of discontinuity (supports, hinges, springs, concentrated mass, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends and to satisfy the boundary and continuity conditions. Moreover, grid points with variable spacing were also considered, the grid being uniform within beam segments. Vibration analysis of AFG non-prismatic Euler-Bernoulli beams was conducted with this model, and natural frequencies were determined. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFG non-prismatic Euler-Bernoulli beams, considering the damping. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was always increased through a grid refinement.

scholarly journals Kirchhoff-Love Plate Theory: First-Order Analysis, Second-Order Analysis, Plate Buckling Analysis, and Vibration Analysis Using the Finite Difference Method

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Finite Difference ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Second Order ◽  
Governing Equations ◽  
Order Analysis ◽  
First Order ◽  
Order Polynomial ◽  
The Finite Difference Method ◽  
Point Stencil

This paper presents an approach to the Kirchhoff-Love plate theory (KLPT) using the finite difference method (FDM). The KLPT covers the case of small deflections, and shear deformations are not considered. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected points of the structure. Generally in the case of KLPT, the finite difference approximations are derived based on the fourth-order polynomial hypothesis (FOPH) and second-order polynomial hypothesis (SOPH) for the deflection surface. The FOPH is made for the fourth and third derivative of the deflection surface while the SOPH is made for its second and first derivative; this leads to a 13-point stencil for the governing equation. In addition, the boundary conditions and not the governing equations are applied at the plate edges. In this paper, the FOPH was made for all of the derivatives of the deflection surface; this led to a 25-point stencil for the governing equation. Furthermore, additional nodes were introduced at plate edges and at positions of discontinuity (continuous supports/hinges, incorporated beams, stiffeners, brutal change of stiffness, etc.), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at the plate edges and to satisfy the boundary and continuity conditions. First-order analysis, second-order analysis, buckling analysis, and vibration analysis of plates were conducted with this model. Moreover, plates of varying thickness and plates with stiffeners were analyzed. Finally, a direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. In first-order, second-order, buckling, and vibration analyses of rectangular plates, the results obtained in this paper were in good agreement with those of well-established methods, and the accuracy was increased through a grid refinement.

The flow-difference feedback iteration method for aerostatic thrust bearings and its convergence characteristics

2019 ◽  
Vol 233 (11) ◽  
pp. 1743-1752
Author(s):  
Yazhe Li ◽  
Kai Zhou ◽  
Zhen Zhang
Keyword(s):  
Convergence Rate ◽  
Iteration Method ◽  
Grid Size ◽  
Good Convergence ◽  
Thrust Bearings ◽  
Initial Values ◽  
Flow Balance ◽  
Iteration Methods ◽  
The Finite Difference Method ◽  
Mesh Grid

The flow-difference feedback iteration method for aerostatic thrust bearings is proposed to the flow balance-based iteration, and two modification methods are further provided to improve the adaptability. The bearing capability calculated by the proposed method is validated by the experimental data. Moreover, the influence of convergence rate factors, iterative initial values, and mesh grids on the iteration ratio is investigated. Compared with the conventional iteration methods, the proposed method with appropriate convergence rate factors provides a higher convergence efficiency. In addition, good convergence behavior under different iterative initial values and the mesh grid size is shown, and the convergence rate is insensitive to the finite difference method parameters. A series of calculations are conducted to investigate the generality of the proposed methods.

Paper 5: Design of Lubricating-Oil Systems

1969 ◽  
Vol 184 (15) ◽  
pp. 41-52 ◽  
Author(s):  
R. E. Liddell ◽  
R. F. Rimmer ◽  
R. E. H. Orr
Keyword(s):  
Lubricating Oil ◽  
Thrust Bearings

Some aspects of the design of lubricating-oil systems for high-powered gearing are discussed and reference is made to the results of trials on thrust bearings, filters, centrifuges, drain tanks, and venting arrangements.

Free Rotation of an Elastic Rod With an End Mass

1986 ◽  
Vol 53 (4) ◽  
pp. 864-868 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Angular Momentum ◽  
Large Deformations ◽  
Free Rotation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Elastic Rod ◽  
Critical Rotation ◽  
Minimum Total Energy ◽  
Equilibrium Configurations ◽  
Flexible Antenna

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.

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