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.

Dynamics of a motorized spindle supported on water-lubricated bearings

2016 ◽  
Vol 231 (3) ◽  
pp. 459-472 ◽  
Author(s):  
Huihui Feng ◽  
Shuyun Jiang
Keyword(s):  
Reynolds Equation ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Motorized Spindle ◽  
Dynamic Coefficients ◽  
Numerical Predictions ◽  
Tilting Angle ◽  
Dynamic Performances ◽  
Experimental Values ◽  
Rotor Dynamic

The purpose of this paper is to investigate the dynamic performances of a motorized spindle supported on water-lubricated bearings. A modified transfer matrix method considering both of the translational and tilting dynamic coefficients of the bearings is established. The turbulent Reynolds equation is adopted and numerically solved by the perturbation method and the finite difference method, and the dynamic characteristics of the water-lubricated journal bearings are obtained; the effects of the eccentricity ratio, tilting angle, and the rotational speed on the dynamic coefficients of the water-lubricated journal bearings are analyzed. The critical speed, the dynamic stiffness of spindle nose, and unbalance response of the motorized spindle are investigated. Finally, a comparative study of rotor dynamic behaviors between the 32- and the eight-coefficient bearing models is conducted. The numerical predictions obtained by the 32-coefficient bearing models correlate well with the experimental values available in the literature.

Characteristics of Micro Gas Journal Bearings Based on Effective Viscosity

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Haijun Zhang ◽  
Changsheng Zhu ◽  
Qin Yang
Keyword(s):  
Knudsen Number ◽  
Effective Viscosity ◽  
Reynolds Equation ◽  
Load Capacity ◽  
Journal Bearings ◽  
Eccentricity Ratio ◽  
Rarefied Flow ◽  
Attitude Angle ◽  
Modified Reynolds Equation ◽  
Bearing Number

According to the first order slip velocity boundary, a modified Reynolds equation for micro gas journal bearings is presented with consideration of effective viscosity under a rarefied flow condition. A modified Reynolds equation is attained and solved using the finite difference method. The nondimensional pressure, load capacity, and attitude angle for micro gas journal bearings under different reference Knudsen numbers (the ratio of ambient molecular mean free path to the average radial clearance), bearing numbers, and eccentricity ratios are obtained. The numerical analysis demonstrates that the slip model with effective viscosity is in a better agreement with the FK model derived by Fukui and Kaneko than that without effective viscosity. When the bearing number is constant, the pressure and load capacity decrease, and the attitude angle changes inversely with the increasing reference Knudsen number. The larger the eccentricity ratio, the larger change in attitude angle from effective viscosity. When eccentricity ratio is less than 0.6, the attitude angle changes softly, and the effect of effective viscosity is unobvious. When the eccentricity ratio is constant, the influence of effective viscosity on nondimensional load capacity and attitude angle becomes larger with the increasing bearing number, and the influence is more prominent with a larger reference Knudsen number.

Analysis of static and dynamic characteristics of spiral-grooved gas journal bearings in high speed

2019 ◽  
Vol 233 (19-20) ◽  
pp. 6774-6792 ◽  
Author(s):  
Laiyun Song ◽  
Kai Cheng ◽  
Hui Ding ◽  
Shijin Chen ◽  
Qiang Gao
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Load Capacity ◽  
Structural Parameters ◽  
Dynamic Stiffness ◽  
Journal Bearings ◽  
Linear Perturbation ◽  
Static And Dynamic Characteristics ◽  
Gas Bearings ◽  
Spiral Grooves

The spiral grooves structures could promote load capacity and improve stability of the gas journal bearings working in high-speed condition. In this study, the unsteady Reynolds equation is solved by linear perturbation method and finite difference method in which the mesh of the groove region is specially treated. The static and dynamic characteristics of spiral grooves journal gas bearings are investigated in different working conditions and the pumping effect caused by spiral-groove structure is revealed and analyzed. Further, the influences of groove structural parameters on the dynamic stiffness and damping coefficients are studied and discussed, which provides guidelines for the design of the journal gas bearings with spiral grooves.

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.

Theoretical Condition for the Cxy=Cyx Relation in Fluid Film Journal Bearings

1989 ◽  
Vol 111 (3) ◽  
pp. 426-429 ◽  
Author(s):  
T. Kato ◽  
Y. Hori
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Fluid Film ◽  
Finite Width ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Cross Terms ◽  
Linear Damping ◽  
Theoretical Condition

A computer program for calculating dynamic coefficients of journal bearings is necessary in designing fluid film journal bearings and an accuracy of the program is sometimes checked by the relation that the cross terms of linear damping coefficients of journal bearings are equal to each other, namely “Cxy = Cyx”. However, the condition for this relation has not been clear. This paper shows that the relation “Cxy = Cyx” holds in any type of finite width journal bearing when these are calculated under the following condition: (I) The governing Reynolds equation is linear in pressure or regarded as linear in numerical calculations; (II) Film thickness is given by h = c (1 + κcosθ); and (III) Boundary condition is homogeneous such as p=0 or dp/dn=0, where n denotes a normal to the boundary.

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.

scholarly journals Analysis of the effect of oil inlet size on the static performance characteristics of non-Newtonian lubricated hole-entry hybrid journal bearings

2021 ◽  
Vol 37 ◽  
pp. 522-531
Author(s):  
Haiyin Cao ◽  
Yu Huang ◽  
Youmin Rong ◽  
Hao Wu ◽  
Minghui Guo
Keyword(s):  
Finite Element Method ◽  
High Speed ◽  
Reynolds Equation ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Power Law Model ◽  
The Finite Element Method ◽  
Solution Strategy ◽  
Nonuniform Mesh ◽  
Static Performance

Abstract In this study, the influence of inlet pocket size on the static performance of non-Newtonian lubricated hole-entry hybrid journal bearings is theoretically analyzed. The oil film of the bearing is discretized into a nonuniform mesh containing the geometric characteristics of the oil inlet pocket, and the inlet pocket is treated as a micro-oil recess. The Reynolds equation is solved by the finite element method based on Galerkin's techniques, and a new solution strategy to solve the recess/pocket pressure is proposed. The power-law model is used to introduce the non-Newtonian effect. The results show that the static performance characteristics of this type of bearing are greatly affected by the pocket size at both zero speed and high speed.

Lubrication of Porous Journal Bearings

1972 ◽  
Vol 94 (1) ◽  
pp. 69-73 ◽  
Author(s):  
C. Cusano
Keyword(s):  
Analytical Solution ◽  
Coefficient Of Friction ◽  
Load Capacity ◽  
Journal Bearings ◽  
Performance Characteristics ◽  
Eccentricity Ratio ◽  
Design Variables

An analytical solution for the performance characteristics of finite porous journal bearings is obtained. Results are presented which relate the eccentricity ratio and coefficient of friction as functions of load number for design variables of 0.0001, 0.001, 0.01, and 0.1. The load capacity obtained by using the finite bearing theory is compared to the load capacity obtained by using the short-bearing approximation and the infinite-bearing approximation.

scholarly journals Influence of Temperature Effect on the Static and Dynamic Performance of Gas-Lubricated Microbearings

Micromachines ◽  
2020 ◽  
Vol 11 (8) ◽  
pp. 716
Author(s):  
Liangliang Li ◽  
Zhufeng Liu ◽  
Chongyu Wang ◽  
Yonghui Xie
Keyword(s):  
High Speed ◽  
Load Capacity ◽  
Dynamic Performance ◽  
Operating Environment ◽  
Low Friction ◽  
Operating Stability ◽  
Comprehensive Performance ◽  
Different Temperatures ◽  
Dynamic Performances ◽  
The Difference

Gas-lubricated microbearings are widely applied in multiple fields due to their advantages of high-speed, low friction level and other features. The operating environment of microbearings is complex, and the difference of temperature has an important influence on their comprehensive performance. In this investigation, FEM (finite element method) is employed to investigate the static, dynamic and limit characteristics of microbearings lubricated by different kinds of gas at different temperatures. The results show that the rise of temperature leads to the decline of equivalent viscosity of gas, which weakens the load capacity of microbearings, and furthermore, affects the operating stability of microbearings. The dynamic performances of microbearings at different temperatures are very different, and the two dynamic limit characteristics are more sensitive to temperature when it changes.

Dynamic behaviors of a high-speed turbocharger rotor on elliptical floating-ring bearings

2019 ◽  
Vol 233 (12) ◽  
pp. 1785-1799 ◽  
Author(s):  
Congcong Zhang ◽  
Yongliang Wang ◽  
Rixiu Men ◽  
Hong He ◽  
Wei Chen
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Low Cost ◽  
Dynamic Behaviors ◽  
Oil Whirl ◽  
Excited Vibration ◽  
Dynamic Performances ◽  
Simulation Results ◽  
Bearing Design ◽  
Run Up

Floating-ring bearings are commonly used in automotive turbocharger applications due to their low cost and their suitability under extreme rotation speeds. This type of bearings, however, can become a source of noise due to oil whirl-induced sub-synchronous vibrations. The scope of this paper is to examine whether the concept of a floating-ring bearing with an elliptical clearance might be a solution to suppress sub-synchronous vibrations. A very time-efficient approximate solution for the Reynolds equation to the geometry of elliptical bearings is presented. The nonlinear dynamic behaviors of a turbocharger rotor supported by two concepts of elliptical floating-ring bearings are systematically investigated using run-up simulations. For the first concept of elliptical floating-ring bearings i.e. the outer bearing of the floating-ring bearing changed in the form of elliptical pattern (see Figure 1(b) in the article), some studies have pointed out that its steady-state and dynamic performances are superior to plain cylindrical floating-ring bearings but, the nonlinear run-up simulation results shown that this type of elliptical floating-ring bearings is not conducive to reduce the self-excited vibration levels. However, for the second type of elliptical floating-ring bearings i.e. both the inner and outer films of the floating-ring bearing changed in the form of elliptical pattern (see Figure 1(c) in the article), it is shown that the sub-synchronous vibrations have been considerably suppressed. Hence, the second noncircular floating-ring bearing design is an attractive measure to suppress self-excited vibrations.[Figure: see text]

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