Investigations in Hydrostatic Planar Bearings Compensated by Tapered-Spool Restrictors II: Load Capacity and Static Stiffness

2015 ◽  
Vol 32 (1) ◽  
pp. 71-82
Author(s):  
Y. Kang ◽  
H.-C. Cheng ◽  
C.-W. Lee ◽  
S.-Y. Hu
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Effective Area ◽  
Design Parameters ◽  
Static Characteristics ◽  
Static Stiffness ◽  
Single Action ◽  
Hydrostatic Bearing ◽  
Closed Type ◽  
Maximum Stiffness

ABSTRACTThis study including two parts investigates the influence of design parameters of tapered-spool restrictors and hydrostatic planar bearing on static characteristics of load capacity and static stiffness. The former part provides guides for the design of single-action and double-action tapered-spool restrictors. This part provides design guides for planar hydrostatic bearing and for matching up with tapered-spool restrictor. The equations of flow continuity are utilized to determine the film thickness for open-type planar bearing and worktable displacement for closed-type planar bearing with respect to the recess pressure, respectively. The load capacity can be obtained by multiplying recess pressure by effective area of bearing pad. Furthermore, the static stiffness can be obtained by differentiating the recess pressure with respect to film thickness or worktable displacement. The finding results give that the usage range of recess pressure, and the availability ranges of design parameters of restrictor and bearing parameters. Which are found for getting the maximum stiffness.

Investigations in Hydrostatic Planar Bearings Compensated by Tapered-Spool Restrictors I: Flow Rate

2015 ◽  
Vol 32 (1) ◽  
pp. 63-69
Author(s):  
Y. Kang ◽  
H.-C. Cheng ◽  
C.-W. Lee ◽  
S.-Y. Hu
Keyword(s):  
Flow Rate ◽  
Analytical Method ◽  
Pressure Difference ◽  
Load Capacity ◽  
Design Parameters ◽  
Static Characteristics ◽  
Static Stiffness ◽  
Flow Rates ◽  
Single Action ◽  
Hydrostatic Bearing

ABSTRACTThis paper is former part of serial studies to investigate the influence of design parameters of tapered-spool type restrictors on static characteristics of hydrostatic bearing. The flow rates passing restrictors can determine the static characteristics of hydrostatic bearings. In this part an analytical method which includes formulas and solving is utilized to simulate dimensionless flow rate in both single-action and double-action tapered-spool restrictors. The numerical results illustrate the variations of flow rates with respect to the change of pressure and pressure difference, respectively. The findings give that the design parameters of tapered-spool restrictors and the useful range of recess pressure. The following part will depend on this paper results to study load capacity and static stiffness of hydrostatic bearing compensated by tapered-spool restrictor.

Design for static stiffness of hydrostatic bearings: double-action variable compensation of membrane-type restrictors and self-compensation

2014 ◽  
Vol 66 (2) ◽  
pp. 322-334 ◽  
Author(s):  
Yuan Kang ◽  
De-Xing Peng ◽  
Yu-Hong Hung ◽  
Sheng-Yan Hu ◽  
Chorng-Shyan Lin
Keyword(s):  
Load Capacity ◽  
Pressure Ratio ◽  
Design Parameters ◽  
Static Stiffness ◽  
Content Type ◽  
Hydrostatic Bearings ◽  
Closed Type ◽  
Maximum Stiffness ◽  
Membrane Type

Purpose – This article is the fourth part of a serial studies about constant and variable compensations of the closed-type hydrostatic plane-pad bearing, which is presented for the double-action membrane-type restrictor and self-type compensation. The paper aims to discuss these issues. Design/methodology/approach – The load capacity and static stiffness in thrust direction of the planar bearing is determined by the flow continuity equation which belongs to the same approaches as shown in previous parts of this serial studies. Findings – The results reveal that the appropriate range of recess pressure ratio and design parameters of bearing and restrictor for the infinite or maximum stiffness can be obtained. Also, the influence of design parameters on negative stiffness that should be avoided in bearing design is revealed in detail. Originality/value – The determination of design parameters of a double-action membrane-type restrictor can be yielded from finding results of this study for maximum stiffness in design of hydrostatic bearings.

Static analysis of hydrostatic conical bearings using flow resistance network method

2014 ◽  
Vol 66 (3) ◽  
pp. 411-423 ◽  
Author(s):  
Shun-Te Hsiao ◽  
Yuan Kang ◽  
Shyh-Ming Jong ◽  
Hsing-Han Lee ◽  
De-Xing Peng ◽  
...  
Keyword(s):  
Flow Resistance ◽  
Load Capacity ◽  
Design Parameters ◽  
Width Ratio ◽  
Static Stiffness ◽  
Content Type ◽  
Single Action ◽  
Network Method ◽  
Conical Bearing ◽  
Land Width

Purpose – This paper aims to study the static characteristics of the hydrostatic conical journal bearings by utilizing single-action membrane restrictors to compensate the working pressures of recesses. Design/methodology/approach – The flow resistance network method is used to analyze the influences of load capacity and static stiffness of bearing with the design parameters, including the number of recesses, radial eccentricity ratio, axial displacement ratio, restriction constant, membrane compliance, length-diameter ratio, circumferential land width ratio, axial land width ratio and half of cone angle. Findings – This study shows the infinite stiffness of the oil produced in the first and second recesses while single-action membrane restriction constant of 2 and 3, respectively, as well as in the fourth recess while single-action membrane restriction constant of 0.01 and 0.1, respectively. Research limitations/implications – This article provides the hydrostatic conical bearings in static and unbiased states for analyses of design parameters. The analyses ignore dynamic pressure effect and do not use the Reynolds equation, and assuming that each oil recesses pressure is constant. Practical implications – The influences of the design parameters including the number of recesses, membrane restriction, membrane compliance, length-diameter ratio, half of con-angle, circumferential land width ratio, and axial land width ratio are discussed to the load capacity and static stiffness of conical bearing. Originality/value – Based on the characteristics of the conical bearing through analysis, this article suggests the front bearing with hard membrane restrictor (capillary) and the back bearing with soft membrane restrictor are the most appropriate for axial stiffness.

Design for static stiffness of hydrostatic bearings: double-action variable compensation of spool-type restrictors

2014 ◽  
Vol 66 (1) ◽  
pp. 83-99 ◽  
Author(s):  
Yuan Kang ◽  
Ding-Wen Yang ◽  
Sheng-Yan Hu ◽  
Yu-Hong Hung ◽  
De-Xing Peng ◽  
...  
Keyword(s):  
Pressure Ratio ◽  
Parameter Determination ◽  
Design Parameters ◽  
Static Stiffness ◽  
Content Type ◽  
Thrust Bearings ◽  
Continuity Equations ◽  
Hydrostatic Bearings ◽  
Closed Type ◽  
Maximum Stiffness

Purpose – This paper is the third part of a serial studies for constant and variable compensations of the closed-type hydrostatic thrust bearings which has face-to-face recesses couple. The static stiffness of closed-type hydrostatic thrust bearings can then be obtained from the differentiation of recess pressure with respect to worktable displacement. The paper aims to discuss these issues. Design/methodology/approach – In this paper, the double-action restrictors of cylindrical-spool-type and tapered-spool-type are taken into consideration for variable compensation of hydrostatic bearings. Findings – The static stiffness in thrust direction of hydrostatic bearing is determined by the flow continuity equations that are formulated by film flow and compensation flow for each recess, respectively. The type selection and parameter determination of the double-action spool-type restrictors can be obtained from finding results of this study for maximum stiffness in design of hydrostatic bearings. Originality/value – This study reveals that the appropriate range of recess pressure ratio and design parameters of restrictors for the maximum stiffness can be obtained, the avoidance of negative stiffness is also provided.

scholarly journals A Simulation Study for the Design of Membrane Restrictor in an Opposed-Pad Hydrostatic Bearing to Achieve High Static Stiffness

Lubricants ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 71
Author(s):  
Ta-Hua Lai ◽  
Shih-Chieh Lin
Keyword(s):  
Optimal Design ◽  
Design Procedure ◽  
Effective Area ◽  
Design Parameters ◽  
Static Stiffness ◽  
Load Range ◽  
Hydrostatic Bearing ◽  
Optimal Value ◽  
Bearing Stiffness ◽  
Design Restriction

The effects of a membrane restrictor’s design parameters on the performance of a hydrostatic opposed-pad bearing are presented in this article. Compared to the single-pad bearing, the opposed-pad bearing can perform much better in terms of static stiffness over a wider load range. It is also found that, for small bearing eccentricity, the optimal design restriction ratio of 0.25 still results in high bearing stiffness even if the dimensionless stiffness of membrane is not the optimal value of 1.33. Furthermore, decreasing the ratio of the upper effective area to the lower effective area generally increases the applicable working range of the bearing. Additionally, for high loading demands, the chance for further improvement of bearing performance by employing different design parameter for each pad is examined. Finally, a design procedure for designing the membrane restrictor for an opposed-pad bearing to achieve high static stiffness is given.

Theoretical Study on Static Performance of Double-Bump Foil Bearings

2021 ◽  
Author(s):  
Fangcheng Xu ◽  
Jianhua Chu ◽  
Wenlin Luan ◽  
Guang Zhao
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Static Characteristics ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Static Performance ◽  
Initial Clearance

Abstract In this paper, single-bump foil models with different thickness and double-bump foil models with different initial clearances are established. The structural stiffness and equivalent viscous damping of double-bump foil and single-bump foil are analyzed by finite element simulation. The results show that the double-layer bump foil has variable stiffness and the displacement of the upper bump is greater than the initial gap when the two-layer bumps contact. A model for obtaining static characteristics of aerodynamic compliant foil thrust bearing is established on the basis of the stiffness characteristics of the double-bump foil. This paper solves gas Reynolds equation, the gas film thickness equation and the foil stiffness characteristic equation via the finite element method and the finite difference method. The static characteristics of the thrust bearings including the bearing pressure distribution, the gas film thickness and the friction power consumption have been obtained. The static characteristics of two kinds of foils have been compared and analyzed, and the effect of initial clearance on the static performance of double-bump foil bearings is studied. The results show that the double-bump foil structure can effectively improve the load capacity of thrust bearing. In addition, the static performance of double-bump foil thrust bearings is between the performance of the single-bump foil bearing and the double-bump foil bearing whose foil’s clearance is zero. The smaller the initial clearance is, the easier it will be to form a stable double-bump foil supporting structure.

Hydrodynamic Analysis of Hydrostatic Bearings With Runner Misalignment and Pad Damage

2013 ◽  
Author(s):  
Timothy Dimond ◽  
David Barnes
Keyword(s):  
Film Thickness ◽  
Analytical Solutions ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Element Solution ◽  
Flow Loop ◽  
Hydrodynamic Analysis ◽  
Hydrostatic Bearing ◽  
Hydrostatic Bearings ◽  
Minimum Film Thickness

Hydrostatic bearings are used in applications where surface speeds are low, or viscosities are insufficient to develop significant load capacity due to shear flow. They are also used in jacking applications for initial liftoff of rotors under low or no rotation conditions, especially for heavy rotors where significant babbitt damage would otherwise occur. Traditional hydrostatic bearing analyses assume isothermal lubricating flows. Analytical solutions also assume that the pressure in the pocket of the hydrostatic bearing is constant. This assumption is only approximately correct for low and zero operating speeds. Analytical solutions also assume that the runner and pad surfaces are parallel. The analytical solutions are not capable of capturing damage or misalignment effects. This paper describes a hydrodynamic analysis of a hydrostatic thrust bearing. The solution is based on a finite element solution to the generalized Reynolds equation. The finite element solution is applied in both the pocket and pad regions of the hydrostatic bearings. The analysis includes a flow loop balance that considers the effects of pressure losses in the lubricant supply piping, allowing for modeling of saturation effects in bearing load capacity. The flow loop balance for the lubrication supply is coupled with the bearing solution. This allows for pad loads to vary as a function of circumferential position in thrust bearings. The analysis was applied to the operation of a hydrostatic thrust bearing system for the HUSIR radio telescope at the Massachusetts Institute of Technology. Simplified models of pad damage and runner misalignment were considered in the analysis. The minimum film thickness and pressure profile was calculated. Runner misalignment reduced minimum film thickness by up to 80% when compared to a parallel runner under identical loading conditions. Runner damage equivalent to twice the nominal film thickness reduced the minimum film thickness by approximately 10%.

Dynamic Behaviors of a Circular Worktable Mounted on Closed-Type Hydrostatic Thrust Bearing Compensated by Constant Compensations

2012 ◽  
Vol 29 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Y. Kang ◽  
H.-C. Chou ◽  
Y.-P. Wang ◽  
C.-H. Chen ◽  
H. C. Weng
Keyword(s):  
Dynamic Characteristics ◽  
Thrust Bearing ◽  
Dynamic Responses ◽  
Design Parameters ◽  
Dynamic Behaviors ◽  
Hydrostatic Bearing ◽  
Runge Kutta Method ◽  
Closed Type ◽  
External Loads ◽  
Flow Pump

AbstractThis study investigates the influences of constant compensations which are produced by capillary or constant flow pump on the dynamic characteristics of a circular worktable supported by a closed-type hydrostatic thrust bearing. The dynamic behaviors of this worktable are analyzed by using Runge-Kutta method to solve the coupled motion equation of worktable and pressure equations of hydrostatic film flow. For various supply pressure parameters, external loads, and varieties of design parameters, the dynamic responses of worktable subjected to both external excitations of harmonic force and step force are simulated, respectively. The results reveal the influences of both constant compensations on the dynamic characteristics of hydrostatic bearing by the different responses of worktable and make the appropriate parameters of design can be found for the worktable-bearing system. The accomplishments of this study will help the designers who deal with the hydrostatic- bearing compensated by constant restrictions to select the design parameters to approach the optimum condition.

Identification of design parameters for spool-type restrictors

2019 ◽  
Vol 234 (1) ◽  
pp. 63-72
Author(s):  
Sheng-Yen Hu ◽  
Yuan Kang ◽  
Hsin-Ming Fu ◽  
Chao-Ping Huang
Keyword(s):  
Flow Rate ◽  
Total Error ◽  
Design Parameters ◽  
Experimental Equipment ◽  
Flow Rates ◽  
Open Type ◽  
Single Action ◽  
Hydrostatic Bearing ◽  
Average Temperature ◽  
Identification Method

This study presents the identification method of design parameters for single-action cylindrical spool-type restrictors of hydrostatic bearing. These parameters include restriction parameter, spool displacement parameter, and spring preload. The flow rates, inlet pressures, and outlet pressures are measured to be utilized for parameter identification of single-action cylindrical spool-type restrictors by using experimental equipment. This equipment-like an open-type planar hydrostatic bearing supports a worktable for changing recess pressure by changing apply load. Then, design parameters can be identified from the measurements of the inlet pressure, the recess pressure, average temperature, and the flow rate for each restrictor by using minimizing total error square between measured and identified quantities of flow rates. An identification method with experiments for single-action cylindrical spool-type restrictors of hydrostatic bearing is presented and designed. Also, the influences of design parameters on flow rate of single-action cylindrical spool-type restrictors are studied by experiments. The experimental equipment used in this study is our design, which can be used for all types of restrictors and hydrostatic bearings. This identification method for design parameters of the single-action cylindrical spool-type restrictors is reliable, valid, and accurate. The identification of design parameters is necessary for design change and calibration of single-action cylindrical spool-type.

Numerical and experimental studies on the thermal and static characteristics of multi-leaf foil thrust bearing

2021 ◽  
pp. 135065012110110
Author(s):  
Yu Guo ◽  
Yu Hou ◽  
Qi Zhao ◽  
Xionghao Ren ◽  
Shuangtao Chen ◽  
...  
Keyword(s):  
High Speed ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Failure Process ◽  
Experimental Studies ◽  
Elastic Model ◽  
Static Characteristics ◽  
Bearing Load ◽  
Foil Thrust Bearing ◽  
Cooling Air

Foil bearing is considered to be a promising supporting technology in high-speed centrifugal machinery. Due to the high-speed shearing effect in the viscous lubricant film, heat generation could not be ignored. In this paper, a thermo-elastic model of the multi-leaf foil thrust bearing is proposed to predict its thermal and static characteristics. In the model, modified Reynolds equation, energy equation, and Kirchhoff equation are solved in a coupling way. The contact area between the foil and welding plate is taken into account. Besides, the effect of cooling air on the bearing temperature is investigated. The ultimate load capacity and transient overload failure process of the bearing is analyzed and discussed. The effect of rotation speed on the bearing temperature is more obvious than that of the bearing load. The bearing temperature drops obviously by introducing the cooling air, and the cooling effect is improved with the supply pressure. The transient overload failure of the bearing occurs when the bearing load exceeds the ultimate value.

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