An Analytical Model for the Basic Design Calculations of Journal Bearings

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
R. K. Naffin ◽  
L. Chang
Keyword(s):  
Analytical Model ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Basic Design ◽  
Reasonable Accuracy ◽  
Design Calculations

This paper presents an analytical model for the basic design calculations of plain journal bearings. The model yields reasonable accuracy as compared with published numerical solutions under the same conditions. The principles and procedures of the formulations are presented along with accuracy analyses.

Introduction

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Fluid Flow ◽  
Engineering Design ◽  
Ocean Waves ◽  
Basic Design ◽  
Natural Phenomena ◽  
Turbofan Engine ◽  
Expansion Waves ◽  
Supersonic Aircraft ◽  
Bodily Fluids ◽  
Design Calculations

In this chapter the wide array of engineering devices, from the kitchen tap (a valve) to supersonic aircraft, the basic design of which depends upon considerations of the flow of gases and liquids, is shown. Much the same is true of most natural phenomena from the atmosphere and our weather to ocean waves, and the movement of sperm and other bodily fluids. In this textbook a number of the concepts, principles, and procedures which underlie the analysis of any problem involving fluid flow or a fluid at rest are introduced. In this Introduction, examples have been selected for which, by the end of the book, the student should be in a position to make practically useful engineering-design calculations. These include a dam, a rocket motor, a supersonic aerofoil with shock and expansion waves, a turbojet engine, a turbofan engine, and the blading of a gas turbine.

The Effect of Journal Bearing Misalignment on Load and Cavitation for Non-Newtonian Lubricants

1986 ◽  
Vol 108 (4) ◽  
pp. 645-654 ◽  
Author(s):  
R. H. Buckholz ◽  
J. F. Lin
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Surface Boundary ◽  
Film Rupture ◽  
Aspect Ratios ◽  
Free Surface Boundary Condition ◽  
Load Carrying ◽  
Boundary Location ◽  
Surface Boundary Condition

An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.

A Study of Transient Response of Flexible Rotors in High Speed Turbomachinery

1992 ◽  
Author(s):  
V. Pavelic ◽  
R. S. Amano
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Analytical Model ◽  
High Speed ◽  
Angular Speed ◽  
Journal Bearings ◽  
Hydrodynamic Characteristics ◽  
Flexible Assembly ◽  
Lagrange’S Equation ◽  
Equations Of Motions

In many applications the design operating range of the turbomachinery may be well above the rotor first critical speed which leads to the problem of insuring that the turbomachinery performs with a stable, low-level amplitude of vibration. Under certain conditions of high speed and loading the rotor system can start orbiting in its bearing at a rate which is less than the rotor angular speed, and this phenomena is commonly known as whirling or whipping action. This whipping action may produce additional undesirable dynamic loads on the overall flexible assembly and eventually destroy the rotor. Some of this action is also transient in nature. Whirling is a self-exited vibration caused mainly by the fluid bearings and by the internal friction damping of the rotor. To understand this occurrence, a general dynamic mathematical model was derived considering also the complete viscous characteristic of hydrodynamic journal bearings. The general equations of motions of the system are obtained from Lagrange’s equation of motion. The system kinetic, potential, and dissipation functions are determined based on the generalized coordinates of the system. The journal displacements are related to the overall dynamics of the rotor using deformable bearings. The loads acting at the journals of the shaft are integrated from the fluid film pressure distribution in the journal bearings using mobility method. A unique mathematical model is formulated and solved. This model includes the elastic and inertial properties of the flexible rotor, the elastic, damping and inertial properties of supports and the hydrodynamic characteristics of the journal bearings. The equations of motions result in a system of nonlinear second order differential equations which are solved by using finite difference method. The solution of the equations of motions is used to plot maps of motion of journal centers. A computer program was implemented to aid in the solution of the system of equations and to verify analytical model. The computer program used test data available in literature and the results were compared to be very good. The analytical model and results obtained in this study can be of great help to designers of high speed turbomachinery.

Spin-Up From Rest of a Two-Layer Liquid in a Cylinder

1994 ◽  
Vol 116 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Kwan Yeop Kim ◽  
Jae Min Hyun
Keyword(s):  
Analytical Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Bottom Layer ◽  
Meridional Flow ◽  
Individual Layer ◽  
Ekman Number ◽  
Radial Profiles ◽  
The Individual

A numerical and analytical study is made of spin-up from rest of a two-layer liquid in a rapidly rotating cylinder. The overall system Ekman number is small. The density of the top layer is smaller than that of the bottom layer (ρ1/ρ2<1.0), but the ratio of the individual layer kinematic viscosities is arbitrary (v1/v2<1.0 or v1/v2>1.0). The highlights of the analytical model, which is based on amended formulations of the Wedemeyer-Gerber-Homicz flow configurations, are briefly recapitulated. Comprehensive numerical solutions are secured to the time-dependent Navier–Stokes equations. The numerical solutions are validated by comparing the maximum interface displacements with the available experimental data as well as the analytical model predictions. Descriptions are made of the prominent characteristics of the interface shape for the two regimes of v1/v2<1.0 and v1/v2 > 1.0. Details of the azimuthal and meridional flow structures are illustrated by exploiting the numerical solutions. The computed meridional flows are compatible with the basic assumptions embedded in the development of the analytical model. Sequential plots of the radial profiles of azimuthal velocities are presented. These show that the global spin-up process is substantially accomplished over (En−1/2Ω−1), where En denotes the value of the smaller Ekman number of the two layers. The numerical study gives credence to the reliability and accuracy of the simplified analytical model.

On The Fluid-Solid Interaction in Reference to Thermoelastohydrodynamic Analysis of Journal Bearings

1991 ◽  
Vol 113 (2) ◽  
pp. 398-404 ◽  
Author(s):  
M. M. Khonsari ◽  
S. H. Wang
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Collective Effect ◽  
Thermoelastic Deformation ◽  
Simulation Results ◽  
Thermal Dilation ◽  
Fluid Solid Interaction

Thermohydrodynamic analysis of journal bearings is extended to include provisions for the shaft thermal dilation as well as the bush thermoelastic deformation. Numerical solutions using a combination of the finite difference and finite element methods are presented. Comparison of the simulation results with those obtained experimentally yielded satisfactory agreement. It was found that while the shaft and bush thermal expansion and the bush elastic deformation are individually important, the collective effect of these factors must be considered for meaningful end results.

Hydrostatic Gas Journal Bearings for Micro-Turbomachinery

2004 ◽  
Vol 127 (2) ◽  
pp. 157-164 ◽  
Author(s):  
L. X. Liu ◽  
C. J. Teo ◽  
A. H. Epstein ◽  
Z. S. Spakovszky
Keyword(s):  
Natural Frequency ◽  
Analytical Model ◽  
High Speed ◽  
Experimental Testing ◽  
Fluid Dynamic ◽  
Damping Ratio ◽  
Journal Bearings ◽  
Fiber Optic Sensor ◽  
Gas Bearings ◽  
Aspect Ratios

Several years ago an effort was undertaken at MIT to develop high-speed rotating MEMS (Micro Electro-Mechanical Systems) using computer chip fabrication technology. To enable high-power density the micro-turbomachinery must be run at tip speeds of order 500m∕s, comparable to conventional scale turbomachinery. The high rotating speeds (of order 2 million rpm), the relatively low bearing aspect ratios (L∕D<0.1) due to fabrication constraints, and the laminar flow regime in the bearing gap place the micro-bearing designs to an exotic spot in the design space for hydrostatic gas bearings. This paper presents a new analytical model for axially fed gas journal bearings and reports the experimental testing of micro gas bearings to characterize and to investigate their rotordynamic behavior. The analytical model is capable of dealing with all the elements of, (1) micro-devices, (2) dynamic response characteristics of hydrostatic gas bearings, (3) evaluation of stiffness, natural frequency and damping, (4) evaluation of instability boundaries, and (5) evaluation of effects of imbalance and bearing anisotropy. First, a newly developed analytical model for hydrostatic gas journal bearings is introduced. The model consists of two parts, a fluid dynamic model for axially fed gas journal bearings and a rotordynamic model for micro-devices. Next, the model is used to predict the natural frequency, damping ratio and the instability boundary for the test devices. Experiments are conducted using a high-resolution fiber optic sensor to measure rotor speed, and a data reduction scheme is implemented to obtain imbalance-driven whirl response curves. The model predictions are validated against experimental data and show good agreement with the measured natural frequencies and damping ratios. Last, the new model is successfully used to establish bearing operating protocols and guidelines for high-speed operation.

A Model for Flow Distribution in Manifolds

1971 ◽  
Vol 93 (1) ◽  
pp. 7-12 ◽  
Author(s):  
R. A. Bajura
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Analytical Model ◽  
Distribution Systems ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Flow Distribution ◽  
Analytical Investigation ◽  
Momentum Balance ◽  
Distribution Equation

An analytical investigation of the performance of flow distribution systems was conducted for both intake and exhaust manifolds. Primary emphasis was placed on configurations in which the lateral tubes formed sharp-edged junctions at right angles to the manifold axis. A mathematical model describing the flow behavior at a discreet branch point was formulated in terms of a momentum balance along the manifold. The model was extended to the case of continuous discharge or intake for a uniformly porous manifold. Numerical solutions of the governing flow distribution equation were obtained and compared with experimental data. Dimensionless parameters characterizing the performance of manifolds were formulated from the analytical model.

Dynamically Loaded Journal Bearings: Mobility Method of Solution

1965 ◽  
Vol 87 (3) ◽  
pp. 537-546 ◽  
Author(s):  
J. F. Booker
Keyword(s):  
Numerical Solutions ◽  
Journal Bearings ◽  
Dynamically Loaded ◽  
Method Of Solution ◽  
Mobility Method

An approach is presented for simplified analytical, graphical, and numerical solutions to extremely general problems of dynamically loaded bearings. A series of examples illustrates the application of the method to problems of varying complexity.

How Finite Element Calculations Improve Hyper Compressor Performance and Lifetime

2013 ◽  
Author(s):  
Nicole Retz ◽  
Andreas Allenspach
Keyword(s):  
Finite Element ◽  
Manufacturing Processes ◽  
Basic Design ◽  
Finite Element Calculations ◽  
Compressor Performance ◽  
Design Calculations

The basic design of actual hyper compressor was performed around 40 years ago, in a time when the use of computers was limited and most of the design calculations were made by hand. In our days most parts are significantly improved with the support of finite element calculations. In this paper the benefits of such an optimization will be highlighted by several examples like the compressor central valve, the flexible rod coupling or even the overall compressor vibrations. In addition the modeling of some for hyper compressors typical manufacturing processes like autofrettage will be discussed.

ANALYTICAL MODEL OF CONVECTIVE TEMPERATURE RECOVERY IN SHUT-IN WELL

2021 ◽  
Vol 7 (3) ◽  
pp. 25-40
Author(s):  
Ayrat Sh. Ramazanov ◽  
Denis F. Islamov
Keyword(s):  
Inverse Problems ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Fiber Optic Sensor ◽  
Reservoir Properties ◽  
Geophysical Research ◽  
Unsteady Temperature ◽  
Distributed Fiber Optic Sensor ◽  
Pressure Independent

Thermometry is the most informative method in the complex of field geophysical research. The method is applied at all stages of the well’s life. Modern technologies for recording the temperature in the well, for example, using a distributed fiber-optic sensor, allow continuous research, and in particular, to carry out temperature probing of the developed formations. Temperature sensing data can be used as an additional (alternative to pressure) independent source of information on reservoir properties. To assess the parametric sensitivity of the temperature field in the well and to solve inverse problems of thermometry, mathematical models are needed to describe the thermohydrodynamic processes both in the reservoir and in the well. This article is devoted to the development of an analytical model describing the change in temperature and pressure in the reservoir after a well shut-in, taking into account some approximations: zero compressibility of the reservoir, fluid and thermal conductivity. The pressure distribution in the reservoir is found from the solution of the piezoconductivity equation. And the temperature distribution from the heat flow equation. The method of characteristics was used for the solution. The results of comparison of analytical and numerical solutions for temperature changes in a shut-in well are presented. It follows from the results obtained that the temperature after well shut-in is sensitive to the size of the near-wellbore zone with altered permeability and to the distribution of permeability in the formation. The proposed analytical solution can be used in thermosimulators to solve inverse problems in order to estimate the parameters of the near-wellbore formation zone based on actual measurements of unsteady temperature in the wellbore of production wells, as well as for planning production geophysical studies using the thermometry method.

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