scholarly journals Virial Approximation for Load and Loss in High-Speed Journal Bearings Using Pressurized Gases

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 27 ◽  
Author(s):  
Ssu-Ying Chien ◽  
Mark Cramer
Keyword(s):  
High Speed ◽  
Single Phase ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Ideal Gas ◽  
Small Density ◽  
Density Expansions ◽  
Steady Laminar ◽  
The Ideal

We consider steady, laminar, compressible lubrication flows in a high-speed two-dimensional journal bearing governed by the appropriate Reynolds equation. The thermodynamic states correspond to pressurized gases and are in the single-phase regime. Simple explicit formulas for the load capacity, power loss, and attitude angle are derived by applying the virial (or small density) expansions of pressure and shear viscosity to results developed in previous studies. The present virial approximation was compared to the exact numerical solutions to the Reynolds equation. It was shown that the results based on our virial expansions are quite accurate at thermodynamic states corresponding to dense and supercritical gases. The first virial correction is seen to significantly improve predictions based on the ideal gas theory.

scholarly journals Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui-Hui Feng ◽  
Chun-Dong Xu ◽  
Jie Wan
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Coefficients ◽  
Pressure Fields ◽  
Dynamic Performances ◽  
Rotary Speed

The water-lubricated bearings have been paid attention for their advantages to reduce the power loss and temperature rise and increase load capacity at high speed. To fully study the complete dynamic coefficients of two water-lubricated, hydrostatic journal bearings used to support a rigid rotor, a four-degree-of-freedom model considering the translational and tilting motion is presented. The effects of tilting ratio, rotary speed, and eccentricity ratio on the static and dynamic performances of the bearings are investigated. The bulk turbulent Reynolds equation is adopted. The finite difference method and a linear perturbation method are used to calculate the zeroth- and first-order pressure fields to obtain the static and dynamic coefficients. The results suggest that when the tilting ratio is smaller than 0.4 or the eccentricity ratio is smaller than 0.1, the static and dynamic characteristics are relatively insensitive to the tilting and eccentricity ratios; however, for larger tilting or eccentricity ratios, the tilting and eccentric effects should be fully considered. Meanwhile, the rotary speed significantly affects the performance of the hydrostatic, water-lubricated bearings.

Analysis of Hybrid (Hydrodynamic/Hydrostatic) Journal Bearing

2013 ◽  
Vol 650 ◽  
pp. 385-390 ◽  
Author(s):  
Vijay Kumar Dwivedi ◽  
Satish Chand ◽  
K.N. Pandey
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Gas Turbines ◽  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Natural Boundary Condition ◽  
Dimensional Solution

The Hybrid (hydrodynamic/ hydrostatic) journal bearing system has found wide spread application in high speed rotating machines such as compressors, gas turbines, steam turbines, etc. The present studies include solution of Reynolds equation for hydrodynamic journal bearing with infinitely long approximation (ILA), infinitely short bearing approximation (ISA) and finite journal bearing approximation. Further Finite Journal bearing approximation considers two dimensional solution of Reynolds equation with natural boundary condition, which cannot be solved by analytical method. So, here the solutions for finite journal bearing have been done with finite difference method (a MATLAB® code is prepared for finite difference method) to get bearing performance parameters such as load capacity, Sommerfeld no., etc.

The Load Capacity of Short Journal Bearings With Oscillating Effective Speed

1964 ◽  
Vol 86 (2) ◽  
pp. 348-353 ◽  
Author(s):  
B. K. Gupta ◽  
R. M. Phelan
Keyword(s):  
Significant Contribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Journal Bearings ◽  
Squeeze Film ◽  
Major Conclusion ◽  
Angular Velocities ◽  
Effective Speed

The development of the Reynolds equation for the general case of dynamically loaded journal bearings is extended to include the concept of an effective speed that combines in one term the angular velocities of the journal, bearing, and load. Numerical solutions for the short-bearing approximation are presented for the case of an oscillating effective speed and a load that is constant or varying sinusoidally. Results are compared with available experimental data. The major conclusion is that for those cases involving an oscillating effective speed and a reversing load, the only significant contribution to load capacity comes from the squeeze film and the wedge film can safely be ignored when designing such bearings.

Limiting Stiffness and Damping Coefficients of Foil Bearing

2005 ◽  
Author(s):  
Jerzy T. Sawicki ◽  
T. V. V. L. N. Rao
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Necessary Conditions ◽  
Load Capacity ◽  
Damping Coefficients ◽  
Foil Bearing ◽  
Infinitesimal Perturbation ◽  
Stiffness And Damping ◽  
Limiting Values ◽  
Gas Journal Bearing

The limiting values of load capacity, stiffness and damping coefficients for a foil bearing are presented. The necessary conditions for high bearing numbers (journal operating at high speed) are obtained by simplifying the compressible Reynolds equation. Linearized stiffness and damping coefficients are obtained using infinitesimal perturbation method. Results of load capacity, stiffness and damping coefficients, for foil bearing are compared with those obtained for a rigid gas journal bearing. The limiting values of dynamic characteristics for a foil bearing are constant for all eccentricity ratios.

A Dynamic Analysis of a Dual Clearance Squeeze Film Damper

2010 ◽  
Author(s):  
L. Moraru ◽  
T. G. Keith ◽  
F. Dimofte ◽  
S. Cioc ◽  
N. Ene ◽  
...  
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Squeeze Film ◽  
Squeeze Film Damper ◽  
Squeeze Film Dampers ◽  
Abnormal Operating Conditions ◽  
Oil Films

Squeeze film dampers (SFD) are devices utilized to control the shafts of high-speed rotating machinery. A dual squeeze film damper (DSFD) consists of two squeeze film bearings that are separated by a sleeve, which is released when the rotor experiences abnormal operating conditions. In this part of our study of DSFD we analyze the case when both the inner and the outer oil films are active. We present computed and measured unbalance responses of a shaft supported in DSFD. The oil forces which are utilized in the calculation of the unbalance response are obtained from numerical solutions of the Reynolds equation. A finite-difference algorithm is utilized for solving the pressure equation within the calculation of the dynamic response of the shaft.

On the Analytical Evaluation of the Lubricant Pressure in the Finite Journal Bearing

2012 ◽  
Author(s):  
Athanasios Chasalevris ◽  
Dimitris Sfyris
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Closed Form Expression ◽  
Linear Ordinary Differential Equations ◽  
Definition Of

The Reynolds equation for the pressure distribution of the lubricant in a journal bearing with finite length is solved analytically. Using the method of the separation of variables in an additive and in a multiplicative form, a set of particular solutions of the Reynolds equation is added in the general solution of the homogenous Reynolds equation and a closed form expression for the definition of the lubricant pressure is presented. The Reynolds equation is split in four linear ordinary differential equations of second order with non constant coefficients and together with the boundary conditions they form four Sturm-Liouville problems with the three of them to have direct forms of solution and one of them to be confronted using the method of power series. The mathematical procedure is presented up to the point that the application of the boundaries for the pressure distribution yields the final definition of the solution with the calculation of the constants. The current work gives in detail the mathematical path with which the analytical solution is derived, and it ends with the pressure evaluation and a comparison with past numerical solutions and an approximate analytical solution for a finite bearing. Also the parameters of primary interest to the bearing designer, such as load capacity, attitude angle, and stiffness and damping coefficients are evaluated and compared with numerical results.

Effects of Power—Law, Non-Newtonian Lubricants on Load Capacity and Friction for Plane Slider Bearings

1986 ◽  
Vol 108 (1) ◽  
pp. 86-91 ◽  
Author(s):  
R. H. Buckholz
Keyword(s):  
Power Law ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Lagrange Equation ◽  
Load Capacity ◽  
Approximate Solutions ◽  
Finite Width ◽  
Aspect Ratios ◽  
Modified Reynolds Equation ◽  
Power Law Index

The lubrication of a conventional, finite width plane bearing, using a power-law, non-Newtonian lubricant, is studied. The basic assumptions in this analysis are: thin fluid-film, no thermal effects, and a modified Reynolds’ equation for small bearing aspect ratios. Results from this study include bearing pressure, load, and friction formulas. Similar results for the not-so-small bearing aspect ratios are found via an Euler-Lagrange equation. This Euler-Lagrange equation is derived from the optimization integral for the modified Reynolds’ equation. Approximate solutions to the modified Reynolds’ equation and to the Euler-Lagrange equation are contrasted with numerical solutions for the modified Reynolds equation. Bearing aspect ratios in the range 0.1 to 0.6, clearance ratios in the range 1.2 to 4.0, and non-Newtonian power-law index in the range 0.4 to 1.0 are considered.

scholarly journals Validation of a Radial Compressor CFD Analysis

2020 ◽  
Vol 3 (1) ◽  
pp. 85-90
Author(s):  
Süleyman Emre Ak ◽  
Sertaç Çadırcı
Keyword(s):  
High Speed ◽  
Pressure Ratio ◽  
Ideal Gas ◽  
Cfd Analysis ◽  
Test Results ◽  
Radial Compressor ◽  
Computational Fluid Dynamics Cfd ◽  
Relative Errors ◽  
Mesh Convergence ◽  
The Ideal

In this study, a radial compressor flow at a high speed is investigated by Computational Fluid Dynamics (CFD) methods. The radial compressor of interest consists of a rotor, diffuser, and exit guide vanes and has an operational rotational speed of 21789 rpm. The geometry of the compressor and its test results such as compression ratio and adiabatic efficiency are available in literature. After extensive mesh convergence tests, steady-state CFD analysis has been performed for compressible and turbulent flow using the ideal gas approach. The main motivation of the study is the determine the appropriate CFD approach and boundary conditions of the problem that will fit best to the measurements. The CFD analysis revealed that the maximum relative errors for the adiabatic efficiency and the pressure ratio were 3.6 % and 1.3 %, respectively.

scholarly journals Performance Analysis of High-Speed Deep/Shallow Recessed Hybrid Bearing

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Lei Wang ◽  
Shuyun Jiang
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Load Capacity ◽  
Width Ratio ◽  
Drag Torque ◽  
Inertia Effects ◽  
Half Angle ◽  
Bearing Design ◽  
Hybrid Bearing

The present paper proposes a theoretical analysis of the performance of deep/shallow recessed hybrid bearing. It is intended that, on the basis of the numerical results drawn from this study, appropriate shallow recess depth and width can be determined for use in the bearing design process. By adopting bulk flow theory, the turbulent Reynolds equation and energy equation are modified and solved numerically including concentrated inertia effects at the recess edge with different depth and width of shallow recess. The results indicate that the load capacity, drag torque increases as the depth of shallow recess is shallower and the width ratio (half angle of deep recess versus half angle of shallow recess) is smaller. In contrast, the flow rate decreases as the depth of shallow recess is shallower and the width ratio is smaller. Nevertheless, the appropriate design of the depth and width of shallow recess might well induce the performance of high-speed deep/shallow recessed hybrid bearing.

Axial Flow Seal/Bearing Efficient Pressure Formulation for a Reynolds Equation Solution

2014 ◽  
Vol 630 ◽  
pp. 169-180
Author(s):  
Paul Allaire ◽  
Vladimir Yurko ◽  
Jian Ming Cao ◽  
Tim Dimond
Keyword(s):  
Finite Element ◽  
Approximate Solution ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Load Capacity ◽  
Axial Flow ◽  
Power Losses ◽  
Dimensional Finite Element ◽  
Pressure Formulation ◽  
Solution Parameters

Current fluid film seal/bearing pressure numerical solutions taking into account both circumferential and axial lubricant flows are not in wide spread use. The most common method is to solve a two dimensional finite element method of Reynolds equation. However, this type of solution often leads to a long computer solution times when employed in an advanced seal/bearing code. A new approximate solution of Reynolds equation for oil seal or bearing flows is proposed in this paper which includes the axial flow modeling. The objective is achieved by means of an axial approximation that can be used to develop a one dimensional centerline circumferential pressure finite element solution to Reynolds equation. Optimization of the parameters associated with the approximate solution parameters is shown. Example seal/bearing pressure and load capacity calculations are presented and the solution verified by comparison with a full finite element 2-D solution. Also, the method of calculating the axial and circumferential lubricant flows as well as axial and circumferential power losses are presented and validated.

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