An Alternative Hydrodynamic Force Model for Finite Bearings

2009 ◽  
Author(s):  
Yaser Bastani ◽  
Marcio de Queiroz
Keyword(s):  
Reynolds Equation ◽  
Hydrodynamic Force ◽  
Journal Bearings ◽  
Closed Form Expression ◽  
Force Model ◽  
Eccentricity Ratio ◽  
Form Expression ◽  
Order Polynomial ◽  
Polynomial Models ◽  
Bearing System

A method for determining a closed-form expression for the hydrodynamic forces in finite plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely-long (IL) or infinitely-short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. The models are shown to outperform the standard limiting approximations in the steady-state analysis of the bearing system under static loading.

A New Analytic Approximation for the Hydrodynamic Forces in Finite-Length Journal Bearings

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Yaser Bastani ◽  
Marcio de Queiroz
Keyword(s):  
Finite Length ◽  
Reynolds Equation ◽  
Computational Study ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Closed Form Expression ◽  
Impedance Method ◽  
Analytic Approximation ◽  
State Behavior ◽  
Order Polynomial

A new method for determining a closed-form expression for the hydrodynamic forces in finite-length plain journal bearings is introduced. The method is based on applying correction functions to the force models of the infinitely long (IL) or infinitely short (IS) bearing approximation. The correction functions are derived by modeling the ratio between the forces from the numerical integration of the two-dimensional Reynolds equation and the forces from either the IL or IS bearing approximation. Low-order polynomial models, dependent on the eccentricity ratio and aspect ratio, are used for the correction functions. A comparative computational study is presented for the steady-state behavior of the bearing system under static and unbalance loads. The results show the proposed models outperforming the standard limiting approximations as well as a model based on the finite-length impedance method.

Influence of the Lubrication Model on the Dynamic Response of Mechanical Systems

2013 ◽  
Author(s):  
Paulo Flores
Keyword(s):  
Dynamic Response ◽  
Reynolds Equation ◽  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Dynamic Responses ◽  
Force Model ◽  
Revolute Joints

The main objective of this work is to present a study on the use of different hydrodynamic force models on the dynamic response of mechanical systems with lubricated revolute joints. For this purpose, the fundamental issues related to the classical theory of lubrication for dynamically loaded journal-bearings are revised, which is used to evaluate the Reynolds’ equation for dynamic regime. The hydrodynamic forces that develop at the lubricated revolute joints are determined and included into the dynamic equations of motion. In this study, three different approaches are considered to evaluate the hydrodynamic forces, namely the Pinkus and Sternlicht approach for long journal-bearings and the Frêne et al. models for both long and short journal-bearings. Results for a mechanical system with a lubricated revolute joint are presented and used to discuss the main assumptions and procedures adopted in this work. From the computational simulations performed, it can be observed that the hydrodynamic force model play a crucial role in predicting the dynamic behavior of mechanical systems and originate some uncertainties in their dynamic responses.

Dynamic Behavior of Pure Squeeze Films in Narrow Porous Bearings

1974 ◽  
Vol 96 (3) ◽  
pp. 361-364 ◽  
Author(s):  
P. R. K. Murti
Keyword(s):  
Dynamic Behavior ◽  
Cyclic Load ◽  
Journal Bearing ◽  
Load Capacity ◽  
Squeeze Film ◽  
Closed Form Expression ◽  
Cyclic Loads ◽  
Eccentricity Ratio ◽  
Form Expression ◽  
Bearing Material

The dynamic behavior of squeeze film in a narrow porous journal bearing under a cyclic load is analyzed. A thin-walled bearing with a nonrotating journal is considered and a closed form expression for the pressure distribution is derived. The locus of the journal center is found by numerical methods and it is established with an example that actual contact between the journal and bearing can be avoided by appropriate design of the bearing. Consequently, it is proved that pure squeeze films have a load capacity only under cyclic loads. The analysis also reveals that the permeability of the bearing material and the wall thickness of the bearing influence significantly the operating eccentricity ratio.

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.

Dynamic characteristics of water-lubricated journal bearings

2019 ◽  
Vol 20 (4) ◽  
pp. 404
Author(s):  
Qiang Li ◽  
Shuo Zhang ◽  
Yujun Wang ◽  
Weiwei Xu ◽  
Zengli Wang ◽  
...  
Keyword(s):  
Dynamic Characteristics ◽  
Hydrodynamic Force ◽  
Hydrodynamic Forces ◽  
Journal Bearings ◽  
Dynamic Responses ◽  
Force Model ◽  
Ecological Awareness ◽  
Mesh Movement ◽  
Linear And Nonlinear ◽  
Structured Mesh

The increasing ecological awareness and stringent requirements for environmental protection have led to the development of water lubricated journal bearings. For the investigation of water-lubricated journal bearings, a new structured mesh movement algorithm for the CFD model is developed and based on this method, the nonlinear transient hydrodynamic force model is established. Then, with consideration of velocity perturbation, a method to determine dynamic coefficients and linear hydrodynamic forces is promoted. After validation of static equilibrium position and stiffness coefficients, a comparative linear and nonlinear hydrodynamic force analysis of multiple grooves water-lubricated journal bearings (MGWJBs) is conducted. The calculation results indicate that the structured mesh movement algorithm is suitable for the dynamic characteristics investigation of water-lubricated journal bearings. And the comparative study shows that there is a considerable difference between the linear and nonlinear hydrodynamic forces of MGWJBs. Further investigation should be carried to evaluate the dynamic responses of rotor supported by MGWJBs under difference force models.

Stability analysis of a rigid rotor supported by two-lobe hydrodynamic journal bearings operating with a non-Newtonian lubricant

2018 ◽  
Vol 233 (6) ◽  
pp. 884-898 ◽  
Author(s):  
Saurabh K Yadav ◽  
Arvind K Rajput ◽  
Nathi Ram ◽  
Satish C Sharma
Keyword(s):  
Reynolds Equation ◽  
Pressure Field ◽  
Equation Of Motion ◽  
Journal Bearings ◽  
Rigid Rotor ◽  
Linear Finite Element ◽  
Runge Kutta Method ◽  
The Stability ◽  
Ellipticity Ratio ◽  
Bearing System

In the present work, an investigation has been performed on a rigid rotor supported by two-lobe journal bearings operating with a non-Newtonian lubricant. The governing Reynolds equation for pressure field is solved by using non-linear finite element method. Further to study the dynamic stability of the bearing system, governing equation of motion for the rotor position is solved by fourth order Runge–Kutta method. Bifurcation and Poincaré maps of two-lobe bearings are presented for different values of the non-Newtonian parameter and bearing ellipticity ratio. The numerical results illustrate that the ellipticity of a bearing with a dilatant lubricant improve the stability of the rotordynamic system.

A Comparative Thermal Analysis of Slot-Entry and Hole-Entry Hybrid Journal Bearings Lubricated With Non-Newtonian Lubricant

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
H. C. Garg ◽  
Vijay Kumar ◽  
H. B. Sharda
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Journal Bearing ◽  
Flow Equation ◽  
Journal Bearings ◽  
Constant Flow ◽  
Viscosity Variation ◽  
Bearing System ◽  
Flow Valve ◽  
Newtonian Behavior

The effect of viscosity variation due to temperature rise and non-Newtonian behavior of the lubricant on the performance of hole-entry and slot-entry hybrid journal bearings system is the focus of this investigation. The performance characteristics of nonrecessed hybrid journal bearings operating with different flow controlling devices, i.e., constant flow valve, capillary, orifice, and slot restrictors, have been compared. Finite element method has been used to solve the Reynolds equation governing the flow of lubricant in the bearing clearance space along with the restrictor flow equation, energy equation and conduction equation using suitable iterative technique. The non-Newtonian lubricant has been assumed to follow the cubic shear stress law. The results indicate that variation in viscosity due to rise in temperature and non-Newtonian behavior of the lubricant affects the performance of nonrecessed hybrid journal bearing system quite significantly. The results further indicate that bearing performance can be improved by selecting a particular bearing configuration in conjunction with a suitable compensating device.

Linearized ph Stability Theory for Translatory Half-Speed Whirl of Long, Self-Acting Gas-Lubricated Journal Bearings

1963 ◽  
Vol 85 (4) ◽  
pp. 611-618 ◽  
Author(s):  
J. S. Ausman
Keyword(s):  
Stability Theory ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Journal Bearings ◽  
Ph Stability ◽  
Time Dependent ◽  
Rotor Speed ◽  
Eccentricity Ratio ◽  
Bearing Sleeve ◽  
Threshold Point

The linearized ph approximation to the time dependent Reynolds equation is solved simultaneously with the equations of motion for a rotating journal shaft supported by a rigidly mounted bearing sleeve. Given the two bearing parameters Λ=6μωR2paC2 and Ω=MCω2πpaDL a critical operating eccentricity ratio is determined below which the bearing is unstable and above which the bearing is stable. Whirl frequency at the threshold point is computed to be equal to or slightly less than one-half rotor speed.

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.

Influence of dimple location and depth on the performance characteristics of the hydrodynamic journal bearing system

2020 ◽  
Vol 234 (9) ◽  
pp. 1500-1513
Author(s):  
Niranjan Singh ◽  
RK Awasthi
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Dynamic Performance ◽  
Performance Characteristics ◽  
Eccentricity Ratio ◽  
Bearing Surface ◽  
Surface Textures ◽  
Hydrodynamic Journal Bearing ◽  
Theoretical Results ◽  
Bearing System

This paper concerns with theoretical investigation to predict the influence of cylindrical textures on the static and dynamic performance characteristics of hydrodynamic journal bearing system and the performance is compared with smooth surface bearing. The Reynolds equation governing the fluid–film between the journal and the bearing surface is solved numerically with the assistance of finite element method and the performance characteristics are evaluated as a function of eccentricity ratio, dimple depth and its location. In this study, four journal bearing configurations viz: smooth (non-textured), full-textured, partially textured-I, and partially textured-II are considered for the evaluation of theoretical results. The simulated results indicate that the influence of surface textures is more significant when the textures were created in upstream zone of 126°–286° and dimple aspect ratio nearly 1.0.

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