Two Flow Models for Designing Hydrostatic Bearings With Porous Material

2019 ◽  
Author(s):  
M. Böhle ◽  
Y. Gu ◽  
A. Schimpf
Keyword(s):  
Porous Material ◽  
Laplace Equation ◽  
Power Loss ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Darcy Law ◽  
Axially Symmetric ◽  
Present Contribution ◽  
Hydrostatic Bearings ◽  
Improved Model

Abstract The numerical prediction of load capacity, stiffness, power loss of hydrostatic journal bearings must be performed for technical applications. In this contribution hydrostatic bearings consisting of porous material are considered. Porous hydrostatic bearings have the advantage that no pressure erosion occurs and that the flow medium can be led homogenously to the gap between shaft and bearing. It is still a problem to design such bearings because the flow in the porous material must be taken into account. There is a simple flow model (SFM) available to calculate quickly the load capacity, stiffness, power loss. This model which is based on the assumption that the flow inside the porous material is axially symmetric works well provided that the eccentricity is small (dimensionless eccentricity e/h0 < 0.5). For large eccentricities — larger than e/h0 > 0.5 the axially symmetric assumption is too strong violated and the results for load capacity, stiffness become inaccurate. Therefore an improved model was developed which is described in the present contribution. This improved model couples the Reynolds equation for hydrodynamic lubrication (REHL) with Darcy Law as it had already been done for the aforementioned fast working SFM. The improved model is not based on the axially symmetric assumption but models the flow completely inside the porous material, i.e. Darcys Law is applied for the porous material without making any assumptions. By the application of the new model, its short name is Full Darcy’s Law (FDL) Model, bearings with high eccentricities can be designed. The application of Darcys Law leads to a Laplace equation for the static pressure distribution in the porous material which is coupled with the REHL. It is described how the resulting equation system is solved by a finite difference method. In this contribution the fast working SFM is described shortly again. The main emphasis lies on the introduction of the FDL-model which needs more computer resources for designing a porous bearing than the SFM. It is explained in detail how the coupling between Darcy Law (Laplace equation) and the REHL is realized. A comparison between the results of both models is shown and the differences are interpreted. Additionally, CFD results are used in order to validate the results of the FDL-model.

Numerical Investigation of the Flow in Hydrostatic Journal Bearings With Porous Material

2018 ◽  
Author(s):  
M. Böhle
Keyword(s):  
Porous Material ◽  
Numerical Method ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Volume Flow Rate ◽  
Load Capacity ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Volume Flow ◽  
Present Contribution

The numerical prediction of load capacity, stiffness, power loss etc. of hydrostatic journal bearings must be performed for technical applications. CFD offers one possibility but is time consuming. In the present contribution a fast working numerical method is introduced based on the numerical solution of the Reynolds equation for hydrodynamic lubrication (REHL). It is applied in order to examine the flow inside three-dimensional journal bearings. The emphasis lies on the treatment of journal bearings with porous material. By the application of porous material the lubricant can be fed uniformly around the shaft and therefore improves the reliability of the journal bearing. The contribution gives a short outline of the possibilities and limitations of the application of the REHL. A detailed description of a finite difference method is given by which the REHL is solved. It is described in detail how the load capacity, stiffness, volume flow rate etc. of classical hydrodynamic journal bearings and journal bearings with porous material can be treated by the REHL whereby the emphasis lies on the treatment of journal bearings with porous material. Darcy’s law is implemented in the numerical method in order to take into account the pressure loss of the porous material which is the flow restrictor of the journal bearing. Many results are shown and discussed. Pressure distributions, load capacity, volume flow rates through the porous material, direction of force for a hydrodynamic and porous bearing etc. are shown and discussed in dependence of the eccentricity of the shaft.

Hydrodynamic Pressure of Thrust Step Bearings

2009 ◽  
Author(s):  
Shuangbiao Liu ◽  
W. Wayne Chen ◽  
Diann Y. Hua
Keyword(s):  
Analytical Solution ◽  
Coordinate System ◽  
Laplace Equation ◽  
Analytical Solutions ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Hydrodynamic Pressure ◽  
Finite Width ◽  
Cylindrical Coordinate ◽  
Lubrication Models

Step bearings are frequently used in industry for better load capacity. Analytical solutions to the Rayleigh step bearing and a rectangular slider with a finite width are available in literature, but none for a fan-shaped thrust step bearing. This study starts with a known solution to the Laplace equation in a cylindrical coordinate system, which is in the form of infinite summation. An analytical solution to pressure is derived in this paper for hydrodynamic lubrication problems encountered in the fan-shaped step bearing. The presented solutions can be useful for designers to maximize bearing performance as well as for researchers to benchmark numerical lubrication models.

Numerical Investigation of Static and Dynamic Characteristics of Water Hydrostatic Porous Thrust Bearings

2011 ◽  
Vol 5 (6) ◽  
pp. 773-779 ◽  
Author(s):  
Yuki Nishitani ◽  
◽  
Shigeka Yoshimoto ◽  
Kei Somaya
Keyword(s):  
Porous Material ◽  
Dynamic Characteristics ◽  
Machine Tools ◽  
Measuring Equipment ◽  
Load Capacity ◽  
Damping Coefficient ◽  
Static And Dynamic Characteristics ◽  
Thrust Bearings ◽  
Hydrostatic Bearings ◽  
Aerostatic Bearings

A moving table supported by aerostatic bearings can achieve excellent accuracy of motion because of its noncontact support and, hence, it is used in various precision machine tools and measuring equipment. However, because of low viscosity of air, the damping coefficient of aerostatic bearings is not very high, causing vibration with nanometer-order amplitudes. The accuracy of machine tools and measuring equipment could deteriorate because of this vibration. It is expected that water hydrostatic bearings would have a higher damping coefficient than aerostatic bearings due to the higher viscosity of water. In addition, water, like air, does not pollute the environment. In this paper, the static and dynamic characteristics of water hydrostatic thrust bearings using porous material were numerically investigated and comparedwith conventional pocket hydrostatic bearings with a capillary restrictor. Hydrostatic porous bearings can be easily constructed because the porous material becomes a viscous restrictor itself. It was consequently found that water hydrostatic porous thrust bearings have higher maximum load capacity and slightly lower stiffness than water bearings with a capillary restrictor.

Load Influence on Hydrostatic Oil Film Journal Bearing Stiffness Characteristics

2020 ◽  
Author(s):  
Leonid Moroz ◽  
Leonid Romanenko ◽  
Roman Kochurov ◽  
Evgen Kashtanov
Keyword(s):  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Fluid Pressure ◽  
Performance Characteristics ◽  
Published Data ◽  
Geometrical Parameters ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Stiffness Characteristics

Abstract Hydrostatic bearings are widely used in industry, including aerospace and energy sectors. Hydrodynamic lubrication mechanism has been well studied analytically and experimentally and various types of bearings were developed to provide increasing operating speed, load capacity, stability and efficiency for modern rotating machines. Hydrostatically lubricated bearings have principal difference (in comparison with hydrodynamic bearings) and their characteristics have been an area of continued research. The goal of this work is to develop a robust algorithm, which can predict hydrodynamical characteristics and dynamic stiffness and damping coefficients of hybrid and hydrostatic bearings with increased accuracy and which can be used for engineering/design purposes. The developed approach is based on Reynold’s equations, where the unknown parameters are the rotor position and fluid pressure in recess pockets. Finite difference method in combination with the successive over-relaxation algorithm is used for a numerical solution of Reynold’s equations. Newton’s method is applied to solve the generated system of equations. Applying the developed approach, the effect of load influence on the hydrodynamical and the dynamic stiffness characteristics has been studied. Several hydrostatic bearing designs which are based on the published data were considered to compare the results calculated applying the approach with the experimental and theoretical data given in the literature. Performed study shows when journal eccentricity can’t be neglected while simulating hydrostatic bearing characteristics. Simulations also allow for analysis of how different design/geometrical parameters and initial conditions (supply pressure) influence bearing performance characteristics. The developed approach can be utilized as a practical tool which allows for the prediction of performance characteristics of hydrostatic bearing with increased accuracy.

Hydrodynamic Lubrication of Pocket Bearings and Effect of Contouring the Inner and Outer Regions, and Optimum Design Data

1989 ◽  
Author(s):  
C. Bagci ◽  
C. J. McClure ◽  
S. K. Rajavenkateswaran
Keyword(s):  
Optimum Design ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Load Flow ◽  
Temperature Dependent Viscosity ◽  
Design Data ◽  
Planar Surfaces ◽  
Friction Factors ◽  
The Coefficient Of Friction ◽  
Dependent Viscosity

Abstract The article investigates pocket bearings with contoured profiles of exponential forms on both surfaces inside and outside of the step boundary forming hydro-dynamic action surfaces, and develops optimum design data yielding efficient slider bearings with small pockets with higher load capacities than conventional pocket bearings. In the case of a pocket bearings, in addition to the Reynolds equation used for the regions inside and outside the pocket, the continuity equation along the pocket boundary is satisfied to form the complete model of the bearing. The optimum design data includes dimensionless load-, flow-, temperature rise-, power loss-, stiffness-, and the coefficient of friction factors. Incompressible lubricant with temperature dependent viscosity is considered. Detailed study of conventional pocket bearings with planar surfaces is included. Some optimum exponential pocket bearings yield up to 561 percent increase in load capacity as compared to the conventional tapered bearings.

Modeling and experimental research on engaging characteristics of wet clutch

2019 ◽  
Vol 71 (1) ◽  
pp. 94-101 ◽  
Author(s):  
Yanzhong Wang ◽  
Yuan Li ◽  
Yang Liu ◽  
Wei Zhang
Keyword(s):  
Contact Surface ◽  
Hydrodynamic Lubrication ◽  
Load Capacity ◽  
Lubricating Oil ◽  
Centrifugal Effect ◽  
Element Analysis ◽  
Content Type ◽  
Clutch Engagement ◽  
Wet Clutch ◽  
Engagement Process

PurposeTo gain in-depth understandings of engaging characteristics, the purpose of this paper is to improve the model of wet clutches to predict the transmitted torque during the engagement process.Design/methodology/approachThe model of wet clutch during the engagement process took main factors into account, such as the centrifugal effect of lubricant, permeability of friction material, slippage factor of lubricant on contact surface and roughness of contact surface. Reynolds’ equation was derived to describe the hydrodynamic lubrication characteristics of lubricant film between the friction plate and the separated plate, and an elastic-plastic model of the rough surfaces contact based on the finite element analysis was used to indicate the loading force and friction torque of the contact surface.FindingsThe dynamic characteristics of wet clutch engagement time, relative speed, hydrodynamic lubrication of lubricating oil, rough surface contact load capacity and transfer torque can be obtained by the wet clutch engagement model. And the influence of the groove shape and depth on the engaging characteristics is also analyzed.Originality/valueThe mathematical model of the wet clutch during the engagement process can be used to predict the engaging characteristics of the wet clutch which could be useful to the design of the wet clutch.

Calculation of Cylindrical Worm Gear Drives of Different Tooth Profiles

1981 ◽  
Vol 103 (1) ◽  
pp. 73-82 ◽  
Author(s):  
H. Winter ◽  
H. Wilkesmann
Keyword(s):  
Coefficient Of Friction ◽  
Theoretical Basis ◽  
Power Loss ◽  
Influence Factor ◽  
Load Capacity ◽  
Worm Gear ◽  
Important Influence ◽  
Test Results ◽  
The Coefficient Of Friction ◽  
Gear Drives

The formulae of classical hydrodynamics are not suitable for the calculation of load capacity and power loss of worm gear drives. Thus a theoretical basis had to be developed for the comparison of different tooth profiles, materials of worm and worm wheel and lubricants. The data obtained were compared with test results. It proved that the coefficient of friction is an important influence factor.

Design of Multi-Recess Hydrostatic Journal Bearings for Minimum Total Power Loss

1974 ◽  
Vol 96 (1) ◽  
pp. 226-232 ◽  
Author(s):  
C. Cusano ◽  
T. F. Conry
Keyword(s):  
Rotational Speed ◽  
Power Loss ◽  
Load Capacity ◽  
Maximum Load ◽  
Journal Bearings ◽  
Design Criterion ◽  
Total Power ◽  
Eccentricity Ratio ◽  
Constant Ratio ◽  
Design Charts

The design problem is formulated for multi-recess hydrostatic journal bearings with a design criterion of minimum total power loss. The design is subject to the constraints of constant ratio of the recess area to the total bearing area and maximum load capacity for a given recess geometry. The L/D ratio, eccentricity ratio, ratio of recess area to total bearing area, and shaft rotational speed are considered as parameters. The analysis is based on the bearing model of Raimondi and Boyd [1]. This model is generally valid for low-to-moderate speeds and a ratio of recess area-to-total bearing area of approximately 0.5 or greater. Design charts are presented for bearings having a ratio of recess area-to-total bearing area of 0.6 and employing capillary and orifice restrictors, these being the most common types of compensating elements. A design example is given to illustrate the use of the design charts.

Effect of velocity slip in a narrow rough porous journal bearing

2003 ◽  
Vol 217 (1) ◽  
pp. 59-70 ◽  
Author(s):  
K Gururajan ◽  
J Prakash
Keyword(s):  
Porous Material ◽  
Coefficient Of Friction ◽  
Strong Interaction ◽  
Journal Bearing ◽  
Load Capacity ◽  
Tangential Velocity ◽  
Velocity Slip ◽  
Qualitative And Quantitative ◽  
Slip Effects ◽  
Thin Walled

The paper examines the effect of velocity slip in a thin-walled infinitely short rough porous journal bearing operating under steady conditions in a hydrodynamic regime. The analysis extends earlier work [1] in which the tangential velocity at the surface of the porous material was neglected. The problem is solved analytically together with associated boundary conditions. It is found that there exists a strong interaction between roughness and slip effects. A comparison with the case of an infinitely long journal bearing [2] shows that there are significant qualitative and quantitative differences in load capacity and coefficient of friction. However, the slip-induced variations in friction force are similar to those for an infinitely long journal bearing.

The Influence of Ambient Pressure on the Measured Load Capacity of Bump-Foil and Spiral-Groove Gas Thrust Bearings at Ambient Pressures up to 69 Bar on a Novel High-Pressure Gas Bearing Test Rig

2019 ◽  
Author(s):  
Jason Wilkes ◽  
Ryan Cater ◽  
Erik Swanson ◽  
Kevin Passmore ◽  
Jerry Brady
Keyword(s):  
Power Loss ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Ambient Pressure ◽  
Spiral Groove ◽  
Test Rig ◽  
Thrust Bearings ◽  
Order Of Magnitude ◽  
Foil Thrust Bearing ◽  
Thrust Load

Abstract This paper will show the influence of ambient pressure on the thrust capacity of bump-foil and spiral-groove gas thrust bearings. The bearings were operating in nitrogen at various pressures up to 69 bar, and were tested to failure. Failure was detected at various pressures by incrementally increasing the thrust load applied to the thrust bearing until the bearing was no longer thermally stable, or until contact was observed by a temperature spike measured by thermocouples within the bearing. These tests were performed on a novel thrust bearing test rig that was developed to allow thrust testing at pressures up to 207 bar cavity pressure at 260°C while rotating at speeds up to 120,000 rpm. The test rig floats on hydrostatic air bearings to allow for the direct measurement of applied thrust load through linkages that connect the stationary thrust loader to the rotor housing. Test results on a 65 mm (2.56 in) bump-foil thrust bearing at 100 krpm show a marked increase in load capacity with gas density, which has not previously been shown experimentally. Results also show that the load capacity of a similarly sized spiral-groove thrust bearing are relatively insensitive to pressure, and supported an order-of-magnitude less load than that observed for the bump-foil thrust bearing. These results are compared with analytical predictions, which agree reasonably with the experimental results. Predicted power loss is also presented for the bump-foil bearing; however, measured power loss was substantially higher.

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