Theoretical Study on Static Performance of Herringbone Grooved Aerodynamics Foil Bearing

2020 ◽  
Author(s):  
ZeDa Dong ◽  
Cheng Cheng ◽  
Fangcheng Xu
Keyword(s):  
Power Consumption ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Structural Parameters ◽  
Operational Parameters ◽  
Film Pressure ◽  
Friction Power ◽  
Foil Bearings ◽  
Bearing Load ◽  
Herringbone Grooves

Abstract In this paper, the mathematical model of herringbone grooved aerodynamic foil bearings is established, and the finite difference method is used to obtain the discretized form of Reynolds equation. The static characteristics of bearings, such as film pressure, film temperature, are obtained by solving the Reynolds equation and energy equation. The bearing load capacity and friction power consumption are obtained by calculating the film thickness and film pressure distribution in the bearing gap. The influence of the bearing operational parameters, such as eccentricity and rotation speed, and the bearing structural parameters, such as groove width, groove depth ratio, groove number and helix angle, on the bearing load capacity and friction power consumption of bearings are analyzed. The methods of improving bearing load capacity and reducing friction power consumption are obtained. Simultaneously, by comparing the bearing load capacity and friction power consumption of herringbone grooved gas foil bearings and gas foil bearings (GFBs) without herringbone grooves, the influence of herringbone grooves on the bearing performance is obtained.

Experimental analysis of influence of double-layer bump foils on aerodynamic thrust foil bearings performance

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fangcheng Xu ◽  
Zeda Dong ◽  
Jianhua Chu ◽  
Haoming Wang ◽  
Yongliang Wang
Keyword(s):  
Power Consumption ◽  
Double Layer ◽  
External Force ◽  
Performance Optimization ◽  
Load Capacity ◽  
Foil Thickness ◽  
Selection Scheme ◽  
Content Type ◽  
Friction Power ◽  
Foil Bearings

Purpose Gas thrust foil bearings (GTFBs) are used to balance the axial load of engines. However, in some working conditions of large axial force, such as the use of single impeller air compressor, the load capacity of GTFBs is still insufficient. To solve this problem, the load capacity can be improved by increasing the stiffness of bump foil. The purpose of this paper is to explore a scheme to effectively improve the performance of thrust foil bearings. In the paper, the stiffness of bump foil is improved by increasing the thickness of bump foil and using double-layer bump foil. Design/methodology/approach The foil deformation of GTFBs supported by three different types of bump foils, the relationship between friction power consumption and external force and the difference of limited load capacity were measured by experimental method. Findings The variation of the foil deformation, bearing stiffness, friction power consumption with the external force at different speeds and limited load capacity are obtained. Based on experimental results, the selection scheme of bump foil thickness is obtained. Originality/value This paper provides a feasible method for the performance optimization of GTFBs.

A General Solution of Reynolds’ Equation for a Full Finite Journal Bearing

1967 ◽  
Vol 89 (2) ◽  
pp. 203-210 ◽  
Author(s):  
R. R. Donaldson
Keyword(s):  
Fourier Series ◽  
Series Solution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Load Capacity ◽  
Separation Of Variables ◽  
Hill Equation ◽  
Eigenvalues And Eigenvectors ◽  
General Series ◽  
Bearing Load

Reynolds’ equation for a full finite journal bearing lubricated by an incompressible fluid is solved by separation of variables to yield a general series solution. A resulting Hill equation is solved by Fourier series methods, and accurate eigenvalues and eigenvectors are calculated with a digital computer. The finite Sommerfeld problem is solved as an example, and precise values for the bearing load capacity are presented. Comparisons are made with the methods and numerical results of other authors.

Static Characteristics of Gas Foil Thrust Bearing Based on Gas Rarefaction Model

2015 ◽  
Author(s):  
Jiajia Yan ◽  
Guanghui Zhang ◽  
Zhansheng Liu ◽  
Fan Yang
Keyword(s):  
Film Thickness ◽  
Optimization Design ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Rarefied Gas ◽  
Load Capacity ◽  
Structural Parameters ◽  
Lubricating Film ◽  
Lift Off ◽  
Foil Thrust Bearing

A modified Reynolds equation for bump type gas foil thrust bearing was established with consideration of the gas rarefaction coefficient. Under rarefied gas lubrication, the Knudsen number which was affected by the film thickness and pressure was introduced to the Reynolds equation. The coupled modified Reynolds and lubricating film thickness equations were solved using Newton-Raphson Iterative Method and Finite Difference Method. By calculating the load capacity for increasing rotor speeds, the lift-off speed under certain static load was obtained. Parametric studies for a series of structural parameters and assembled clearances were carried out for bearing optimization design. The results indicate that with gas rarefaction effect, the axial load capacity would be decreased, and the lift-off speed would be improved. The rarefied gas has a more remarkable impact under a lower rotating speed and a smaller foil compliance coefficient. When the assembled clearance of the thrust bearing rotor system lies in a small value, the lift-off speed increases dramatically as the assembled clearance decreases further. Therefore, the axial clearance should be controlled carefully in assembling the foil thrust bearing. It’s worth noting that the linear uniform bump foil stiffness model is not exact for large foil compliance ∼0.5, especially for lift-off speed analysis, due to ignoring the interaction between bumps and bending stiffness of the foil.

Analysis on the steady state performance of a multi pad externally adjustable fluid film bearing

2019 ◽  
Vol 71 (6) ◽  
pp. 803-809 ◽  
Author(s):  
Girish Hariharan ◽  
Raghuvir Pai
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Fluid Film ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Content Type ◽  
Bearing Load ◽  
Performance Capability ◽  
Film Profile

Purpose This study aims to investigate the performance characteristics of an externally adjustable bearing with multiple pads in steady state conditions. The proposed adjustable bearing geometry can effectively control the hydrodynamic operation in bearing clearances by adjusting the pads in radial and tilt directions. These pad adjustments have a significant role in improving the bearing characteristics such as load capacity, attitude angle, side leakage, friction variable and Sommerfeld number, which will be analysed in this paper. Design/methodology/approach The adjustable bearing is designed with circumferentially spaced four bearing pads subjected to similar radial and tilt adjustments. Tilt angles are applied along the leading edges of bearing pads. A modified film thickness equation is used to incorporate the pad adjustments and accurately predict the variation in film profile. Finite difference approximation is adopted to solve the Reynolds equation and discretize the fluid film domain. Findings For negative radial and tilt adjustments, higher hydrodynamic pressures are generated in bearing clearances, which increases the bearing load capacity at different eccentricity ratios. From comparative analysis for different pad adjustments, superior bearing performance is observed for bearing pads under negative radial and negative tilt adjustments. Originality/value This research presents a detailed theoretical approach to analyse the performance capability of a four pad adjustable bearing geometry, which is not available in literatures. Improved bearing performances with negative pad adjustments can attract bearing designers to implement the proposed adjustability-bearing concept in rotating machineries.

Bump Foil Damping Using a Simplified Model

2006 ◽  
Vol 128 (3) ◽  
pp. 542-550 ◽  
Author(s):  
Erik E. Swanson
Keyword(s):  
Load Capacity ◽  
Analytical Techniques ◽  
Model Parameters ◽  
Enabling Technology ◽  
Good Match ◽  
Foil Bearings ◽  
Load Dependence ◽  
Study Results ◽  
Bearing Load ◽  
Damping Model

Foil bearings are a key enabling technology for advanced and oil-free rotating machinery. In certain applications, they provide a level of performance that is difficult or impossible to match with other technologies. A number of reasonably successful analytical techniques to predict bearing load capacity, power loss, and stiffness have been developed. Prediction of damping, however, has remained problematic. This work presents a fresh look at the damping problem. Using a simplified representation of a bump foil, this work considers explicitly adding the load dependence of the friction force. This approach is shown to provide a good match to previous experimental data. Parametric study results for the various model parameters are presented to examine the characteristics of this model. It is concluded that the load-dependent frictional force is important to consider for a bump foil damping model.

Analysis of Gas Lubricated Compliant Thrust Bearings

1983 ◽  
Vol 105 (4) ◽  
pp. 638-646 ◽  
Author(s):  
H. Heshmat ◽  
J. A. Walowit ◽  
O. Pinkus
Keyword(s):  
Load Capacity ◽  
Structural Parameters ◽  
Analytical Investigation ◽  
Operational Parameters ◽  
Thrust Bearings ◽  
Foil Bearing ◽  
Operational Variables ◽  
The Common ◽  
Intermediate Value ◽  
Bearing Behavior

This work is concerned with an evaluation of the performance of a gas thrust bearing using what amounts to a spring supported compliant foil as the bearing surface. To enhance the load capacity of such a device, the leading portion of the foil is given an appropriate converging geometry. The paper offers an analytical investigation of the elastohydrodynamics of the compliant foil bearing, and the effects that the various structural and operational variables have on bearing behavior. Following the solution of the relevant differential equation, the geometry of the thrust sector is first optimized, then solutions are provided for a range of relevant geometrical and operational parameters. The parametric study shows that the optimum geometry for a bearing with the common OD to ID ratio of 2 is β=45deg,b=0.5,h¯1>10 In addition to the geometric parameters, there are also the structural parameters of the foil. The load capacity is shown to increase as the compliance of the bearing rises. While at moderate Λ’s high values of compliance yield the highest load capacity, at high Λ, the optimum compliance is some intermediate value, in our case, α* = 1. Since the stiffness of the bearing is a function of both the structural and hydrodynamic film stiffnesses, high loads tend to flatten the values of K for the softer bearings, leaving essentially the structural stiffness as the dominating spring constant.

A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
Load Capacity ◽  
Computational Effort ◽  
Radial Clearance ◽  
Foil Bearings ◽  
Mesh Model ◽  
Thermal Growth ◽  
Bearing Load ◽  
Cooling Air ◽  
Air Film ◽  
Generalized Reynolds Equation

A numerical model for 3D thermohydrodynamic analysis of bump-type foil bearings with a sparse mesh across the air film is described. The model accounts for heat convection into cooling air, thermal expansion of the bearing components, and material property variations due to temperature rise. Deflection of the compliant foil strip, described as a link-spring structure, is coupled to the solution of the generalized Reynolds equation and the energy equation to account for the effect of foil deformation on the film thickness. The variation in bump stiffness with the thermal growth of bumps is also considered in the model. The unique airflow in foil bearings created by the top foil detachment in the subambient region is analyzed for use in modifying the thermal boundary condition. The Lobatto point quadrature algorithm is used to represent the model on a sparse mesh and thereby reduce the computational effort. The calculated bearing temperatures are in remarkable agreement with both the published test data with the use of cooling air and that without the use of cooling air. The change of bearing radial clearance due to thermal growth of the bearing components was found to significantly affect the bearing load and to be a likely cause of the obvious drop in load capacity with a rise in ambient temperature.

A simplified FEM analysis on the static performance of aerostatic journal bearings with orifice restrictor

2020 ◽  
pp. 135065012095713
Author(s):  
Hailong Cui ◽  
Weiwei Gong ◽  
Yueqing Zheng ◽  
Yifei Li ◽  
Wei Wang ◽  
...  
Keyword(s):  
Elliptic Equation ◽  
Pressure Distribution ◽  
Load Capacity ◽  
Structural Parameters ◽  
Fem Analysis ◽  
Journal Bearings ◽  
Experimental Result ◽  
Maximum Relative Error ◽  
Film Pressure ◽  
Static Performance

This paper puts forward a simplified FEM based on MATLAB PDE tool to investigate the static performance of aerostatic journal bearings. The pressure distribution equation is transformed into a standard elliptic equation, the boundary conditions and coefficients of the transformed equation are also confirmed by contrasting it with the standard elliptic equation. Then the effects of bearings structural parameters and external supply pressure on the film pressure distribution, load capacity and static stiffness are studied. The film pressure distribution changes significantly with the eccentricity ratio, and an eccentricity range corresponding to the optimal stiffness is also confirmed. Finally, an experimental platform with reversal structure is applied to reduce the measurement error, the maximum relative error between the results of simulation and experimental result is 11.54%.

Modified Reynolds Equation for Aerostatic Porous Radial Bearings With Quadratic Forchheimer Pressure-Flow Assumption

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Rodrigo Nicoletti ◽  
Zilda C. Silveira ◽  
Benedito M. Purquerio
Keyword(s):  
Reynolds Equation ◽  
Load Capacity ◽  
Loading Capacity ◽  
Global Approach ◽  
Pressure Flow ◽  
Stiffness Coefficients ◽  
Porous Bearing ◽  
Bearing Load ◽  
Modified Reynolds Equation ◽  
Precision Machines

Aerostatic porous bearings are becoming important elements in precision machines due to their inherent characteristics. The mathematical modeling of such bearings depends on the pressure-flow assumptions that are adopted for the flow in the porous medium. In this work, one proposes a nondimensional modified Reynolds equations based on the quadratic Forchheimer assumption. In this quadratic approach, the nondimensional parameter Φ strongly affects the bearing load capacity, by defining the nonlinearity level of the system. For values of Φ>10, the results obtained with the modified Reynolds equation with quadratic Forchheimer assumption tend to those obtained with the linear Darcy model, thus showing that this is a more robust and global approach of the problem, and can be used for both pressure-flow assumptions (linear and quadratic). The threshold between linear and quadratic assumptions is numerically investigated for a bronze sintered porous bearing, and the effects of bearing geometry are discussed. Numerical results show that Φ strongly affects the bearing loading capacity and stiffness coefficients.

Effect of non-Newtonian lubrication of squeeze film conical bearing with the porous wall operating with Rabinowitsch fluid model

2018 ◽  
Vol 232 (10) ◽  
pp. 1293-1303 ◽  
Author(s):  
PS Rao ◽  
AK Rahul ◽  
S Agarwal
Keyword(s):  
Response Time ◽  
Reynolds Equation ◽  
Graphical Representation ◽  
Load Capacity ◽  
Porous Wall ◽  
Squeeze Film ◽  
Film Pressure ◽  
Pressure Load ◽  
Conical Bearing ◽  
Modified Reynolds Equation

In this article, a theoretical study is made to explore the effect of squeezing film in conical bearing for the permeable porous wall utilizing non-Newtonian lubricants. The Permeable medium impacts are characterized by modified Darcy’s law. The modified Reynolds equation representing the non-Newtonian properties following the cubic stress law condition is determined. After general contemplations on the flow in a bearing clearance and in a porous wall, the Cameron approximation is used to acquire modified Reynolds equation. The perturbation technique is used to solve the modified Reynolds equation and closed-form expressions are obtained for the fluid film pressure, load capacity, and response time. The results are illustrated by the graphical representation which shows that the introduction of porous on conical bearing with Rabinowitsch fluid, dilatant lubricant increases the film pressure, load capacity, and response time and decrease for pseudoplastic lubricant as compared to Newtonian fluid.

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