Stochastic collocation approach for evaluation of journal bearings dynamic coefficients

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.

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Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

Journal of Tribology ◽

10.1115/1.4037730 ◽

2017 ◽

Vol 140 (2) ◽

Cited By ~ 3

Author(s):

Mohammad Miraskari ◽

Farzad Hemmati ◽

Mohamed S. Gadala

Keyword(s):

Journal Bearing ◽

Nonlinear Coefficient ◽

Journal Bearings ◽

Flexible Rotor ◽

Dynamic Coefficients ◽

Flexible Rotors ◽

Rotor Bearing ◽

Bearing Force ◽

Derivatives Of ◽

Bearing System

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.

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Mathematical Model and Analysis of the Water-Lubricated Hydrostatic Journal Bearings considering the Translational and Tilting Motions

Mathematical Problems in Engineering ◽

10.1155/2014/353769 ◽

2014 ◽

Vol 2014 ◽

pp. 1-15 ◽

Cited By ~ 1

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.

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Linear stability analysis of finite length journal bearings in laminar and turbulent regimes

Proceedings of the Institution of Mechanical Engineers Part J Journal of Engineering Tribology ◽

10.1177/1350650117691697 ◽

2017 ◽

Vol 231 (10) ◽

pp. 1254-1267 ◽

Cited By ~ 8

Author(s):

Mohammad Miraskari ◽

Farzad Hemmati ◽

MY Alqaradawi ◽

Mohamed S Gadala

Keyword(s):

Linear Stability ◽

Finite Length ◽

Journal Bearings ◽

Operating Conditions ◽

Stable Region ◽

Dynamic Coefficients ◽

Rotor Bearing ◽

High Reynolds ◽

Turbulent Models ◽

Laminar And Turbulent Regimes

Dynamic coefficients of a finite length journal bearing are numerically calculated under laminar and turbulent regimes based on Ng–Pan–Elrod and Constantinescu models. Linear stability charts of a flexible rotor supported on laminar and turbulent journal bearings are found by calculating the threshold speed of instability associated to the start of instable oil whirl phenomenon. Local journal trajectories of the rotor-bearing system were found at different operating conditions solely based on the calculated dynamic coefficients in laminar and turbulent flow. Results show no difference between laminar and turbulent models at low loading while significant change of the size of the stable region was observed by increasing the Reynolds number in turbulent models. Stable margins based on the laminar flow at relatively low Sommerfeld numbers [Formula: see text] were shown to fall inside the unstable region and hence rendering the laminar stability curves obsolete at high Reynolds numbers. Ng-Pan turbulent model was found to be generally more conservative and hence is recommended for rotor-bearing design.

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Nonlinear Dynamic Oil-Film Forces in Infinite-Short Journal Bearings

ASME/STLE 2011 Joint Tribology Conference ◽

10.1115/ijtc2011-61045 ◽

2011 ◽

Cited By ~ 1

Author(s):

Lihua Yang ◽

Weimin Wang ◽

Lie Yu

Keyword(s):

Nonlinear Dynamic ◽

Reynolds Equation ◽

Journal Bearing ◽

Analytic Solutions ◽

Journal Bearings ◽

Oil Film ◽

Dynamic Coefficients ◽

Representation Model ◽

Linear And Nonlinear

In this paper, the analytic solutions of oil-film forces in infinite-short cylindrical journal bearing are calculated by solving its corresponding Reynolds equation. On this base, the linear and nonlinear dynamic coefficients of the bearing are predicted. By comparing the dynamic oil-film forces approximately represented by dynamic coefficients with the analytic solutions, the accuracy of this representation model is investigated. The results show that more orders of dynamic coefficients are included in representation model, the obtained approximate oil-film forces are more close to their analytic solutions. This can be a reference to illustrate the feasibility and applicability of representing oil-film forces by applying the dynamic coefficients of bearings.

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