Theoretical Research on Aerostatic Rectangular Guideways with Finite Difference Method

2007 ◽  
Vol 339 ◽  
pp. 371-376 ◽  
Author(s):  
Xiao Feng Zhang ◽  
Bin Lin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Difference Method ◽  
Load Capacity ◽  
Theoretical Research ◽  
Orifice Diameter ◽  
Supply Pressure ◽  
Design And Manufacture

The load capacity and stiffness of the aerostatic rectangular guideways, which apply annular orifice restrictor and porous restrictor respectively, were analyzed with finite difference method in this paper. A program for solving the pressure distribution, load capacity and stiffness is programmed with VB. The calculated results show that the rise of supply pressure is good for improving the load capacity and stiffness of guideways. The decrease of the orifice diameter in annular orifice restriction and the permeability in porous restriction is advantageous to improve the stiffness of guideways, but both the corresponding bearing clearance and load capacity decrease. In both the annular restriction and porous restriction, the best film thickness which make the stiffness maximum exists under the definite supply pressure and parameter of the restrictor. Under the same supply pressure, the load capacity and stiffness of porous restriction is higher than the orifice restriction. Meanwhile, the design and manufacture of porous restrictor is simple. The porous restrictor is the perfect restrictor of aerostatic guideways.

Sloshing and Swirling in Partially Loaded Prismatic Chamfered Tanks

2017 ◽  
Author(s):  
Gustavo M. Karuka ◽  
Makoto Arai ◽  
Hideyuki Ando
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Pressure Distribution ◽  
Natural Frequency ◽  
Difference Method ◽  
Simulation Data ◽  
Tank Model ◽  
Breadth Ratio ◽  
Sloshing Pressure

In this study a sloshing experiment using a partially filled membrane tank model was carried out and compared with numerical simulation. The pressure was measured at 10 points and a load cell measured the longitudinal and transversal forces, under regular and irregular excitation. A 3D finite difference method based solver was used for the numerical simulation. When the prismatic tank length to breadth ratio is near 1, swirling, i.e., liquid free surface’s rotating motion in the tank might occur when the tank is excited near its natural frequency, especially for medium and low tank filling levels. According to the experimental and simulation data, the magnitude of the forces and impact pressures in this situation can be significant and therefore cannot be neglected. Tank designs might use different length to breadth ratios (Lt/Bt) depending on the ship size and number of tanks, so the problem is worth being investigated. The Lt/Bt and the occurrence of swirling was then investigated. The pressure distribution when the swirling occurs is then compared with the 1st mode sloshing pressure distribution, and considerations about the tank safety are inferred.

scholarly journals Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 388-394 ◽  
Author(s):  
F. J. Dietzen ◽  
R. Nordmann
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Flow Field ◽  
Pressure Distribution ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Finite Difference Techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence model (k-ε-model) are solved by a finite-difference method. A motion of the shaft around the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotordynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs [1] and with experimental results.

Combined Influence of Misalignment and Orifice Diameter on the Static Performances of Hydrostatic, Water-Lubricated Journal Bearings

2014 ◽  
Vol 607 ◽  
pp. 608-611
Author(s):  
Hui Hui Feng ◽  
Chun Dong Xu ◽  
Feng Feng Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Film Thickness ◽  
Power Loss ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Orifice Diameter ◽  
Rigid Rotor ◽  
Static Performance

The water-lubricated bearings have gained an increasing focus to overcome the disadvantages of the oil film bearings and gas bearings. In this paper, the influences of orifice diameter in aligned and misaligned conditions on the static performance of two hydrostatic, four-recess, water-lubricated journal bearings used to support a rigid rotor, are investigated. The steady Reynolds equation for the journal bearing for the turbulent bulk flow and the film thickness expression considering tilting angles are used and numerically solved by finite difference method. Results demonstrate that the static performances, such as the quality, power loss and temperature rise are affected by the tilting angles, orifice diameter to some degree.

Numerical Analysis of the Lubrication Performances for Ultra-Thin Gas Film Lubrication of Magnetic Head/Disk With a New Finite Difference Method

Tribology ◽  
2005 ◽  
Author(s):  
Ping Huang ◽  
Hongzhi Wang ◽  
Langui Xu ◽  
Yonggang Meng ◽  
Shizhu Wen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Film Thickness ◽  
Difference Method ◽  
Magnetic Head ◽  
Balance Position ◽  
Pressure Distributions ◽  
Load Carrying ◽  
Squeeze Effect ◽  
Film Lubrication

In the present paper, a new iterative algorithm of finite difference method to numerically solve the lubrication problems of magnetic head/disks under ultra thin gas film thickness is introduced. Pressure distributions are calculated when a slider deviates slowly or abruptly from the balance position due to perturbations. The results show that when the slider moves in the film thickness direction, the pressure always tends to force the slider back to the balance position. Steady flying simulations show that the pitch angle is the sensitive parameter to the load carrying capacity of the slider, which should be carefully controlled in design. Squeeze effect is apparent when abrupt movements or rotations happen, which can avoid, to some extent, fatal damages due to vibration or uncertain interferences.

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.

Thermal Effects in Externally Pressurized Conical Bearings With Variable Viscosity

1988 ◽  
Vol 110 (2) ◽  
pp. 201-211 ◽  
Author(s):  
J. S. Kennedy ◽  
Prawal Sinha ◽  
Cz. M. Rodkiewicz
Keyword(s):  
Angular Velocity ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Film Thickness ◽  
Thermal Effects ◽  
Variable Viscosity ◽  
Load Capacity ◽  
Coupled Partial Differential Equations ◽  
Governing System ◽  
Conical Bearing

The influence of varying slider temperature on the characteristics of a conical bearing with constant film thickness rotating with a uniform angular velocity is examined. The fluid is considered to be incompressible and the viscosity is assumed to vary exponentially with temperature. The governing system of coupled partial differential equations in conical coordinates is solved numerically using finite difference method to yield the various bearing characteristics. The results show that maintaining the slider at temperature lower than that of the pad causes an increase in the load capacity of the bearing.

Effect of Turbulence and Offset Loading on the Performance of a Single Pad Externally Adjustable Fluid Film Bearing

2012 ◽  
Author(s):  
B. Satish Shenoy ◽  
Rammohan S. Pai B. ◽  
Raghuvir Pai B. ◽  
Shrikanth Rao D.
Keyword(s):  
Steady State ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Fluid Film ◽  
Wide Range ◽  
Steady State Performance

Paper deals with the effect of turbulence on steady state performance characteristics of an eccentrically loaded 120° single pad externally adjustable fluid film bearing. The bearing has an aspect ratio of one and operates over a wide range of eccentricity ratios and adjustments. Two load-offset positions (β/χ) of 0.45 and 0.55 are considered in the present analysis. Reynolds equation incorporated with the Linearized turbulence model of Ng and Pan is solved numerically using finite difference method. A comparative study predicts that, load capacity of a bearing operating with β/χ = 0.55 and Re = 16000 is superior for negative radial and tilt adjustment configuration of the pad.

scholarly journals Numerical analysis on the performance characteristics of a new gas journal bearing by using finite difference method

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110280
Author(s):  
Yuntang Li ◽  
Ruirui Li ◽  
Yueliang Ye ◽  
Xiaolu Li ◽  
Yuan Chen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Journal Bearing ◽  
Load Capacity ◽  
Linear Perturbation ◽  
Eccentricity Ratio ◽  
Dynamic Performances ◽  
The Stability ◽  
Gas Journal Bearing

This paper proposes a novel gas journal bearing in which orifices are different in diameter and distribute unevenly. Finite Difference Method (FDM) combined with Linear Perturbation Method (LPM) is used to solve the unsteady-state Reynolds equation of the flow field in the bearing clearance. Moreover, four types of bearing structures are used to discuss the effects of orifices different in diameter and uneven distribution on the bearing performance. The results demonstrate that the new bearing has better static and dynamic performances compared with those of traditional bearing in which orifices are equal in diameter and distribute evenly. Moreover, thin gas film thickness, high supply pressure, and large eccentricity ratio are hopeful for improving load capacity of the new bearing. Furthermore, the stability of the novel bearing is improved if eccentricity ratio is 0.25–0.3.

Gas Lubrication Analysis Method of Step-Dimpled Face Mechanical Seals

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Shaoxian Bai ◽  
Xudong Peng ◽  
Yefeng Li ◽  
Songen Sheng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shear Flow ◽  
Pressure Distribution ◽  
Difference Method ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Leakage Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations

In solving Reynolds equation with the conventional finite difference method, keeping the flow continuity has ofen been ignored, which will lead to an analysis error in the pressure distribution and leakage rate, especially for discontinuous clearance caused by step structures such as laser surface texturing sealing surfaces. In this paper, a finite difference method is introduced to satisfy the flow continuity to solve the Reynolds equation. Then, the pressure distribution for a typical rectangular step structure is obtained via two different methods: a numerical solution of the exact full Navier-Stokes equations, and a solution of the Reynolds equation solved by the previously mentioned method. A comparison between the two solution methods illustrates that, for both pressure flow and shear flow, the pressure distribution from the new difference method is in good agreement with that from the Navier-Stokes equations, and the new difference method can reflect the characteristic of the pressure sudden-change of the shear flow at the steps. Finally, the pressure distribution and leakage rate of a step-dimpled seal face are acquired with the presented method. The results show that the presented method allows gas-lubricating analysis of mechanical face seals with discontinuous clearance, and can keep the leakage rate continuous in the radial direction.

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