IDENTIFICATION OF DYNAMIC COEFFICIENTS IN A JOURNAL BEARING FROM EXPERIMENTAL UNBALANCE RESPONSES AND INVERSE PROBLEM

2017 ◽  
Author(s):  
Carlos Alberto Bavastri ◽  
Alcemir Miliavacca
Keyword(s):  
Inverse Problem ◽  
Journal Bearing ◽  
Dynamic Coefficients

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.

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

2017 ◽  
Vol 140 (2) ◽  
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.

Stability Analysis of a Hydrodynamic Journal Bearing With Rotating Herringbone Grooves

2003 ◽  
Vol 125 (2) ◽  
pp. 291-300 ◽  
Author(s):  
G. H. Jang ◽  
J. W. Yoon
Keyword(s):  
Journal Bearing ◽  
Equations Of Motion ◽  
Fourier Series Expansion ◽  
Algebraic Equations ◽  
High Rotational Speed ◽  
Dynamic Coefficients ◽  
Stiffness Coefficients ◽  
Hydrodynamic Journal Bearing ◽  
The Stability ◽  
Herringbone Grooves

This paper presents an analytical method to investigate the stability of a hydrodynamic journal bearing with rotating herringbone grooves. The dynamic coefficients of the hydrodynamic journal bearing are calculated using the FEM and the perturbation method. The linear equations of motion can be represented as a parametrically excited system because the dynamic coefficients have time-varying components due to the rotating grooves, even in the steady state. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving Hill’s infinite determinant of these algebraic equations. The validity of this research is proved by the comparison of the stability chart with the time response of the whirl radius obtained from the equations of motion. This research shows that the instability of the hydrodynamic journal bearing with rotating herringbone grooves increases with increasing eccentricity and with decreasing groove number, which play the major roles in increasing the average and variation of stiffness coefficients, respectively. It also shows that a high rotational speed is another source of instability by increasing the stiffness coefficients without changing the damping coefficients.

Optimization of Journal Bearing Profile for Higher Dynamic Stability Limits

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Rodrigo Nicoletti
Keyword(s):  
Journal Bearing ◽  
Optimization Procedure ◽  
Control Points ◽  
Time Domain Simulation ◽  
Rotating System ◽  
Stability Margins ◽  
Dynamic Coefficients ◽  
The Stability ◽  
Stability Limits ◽  
Improve Stability

This work presents an optimization procedure to find bearing profiles that improve stability margins of rotor-bearing systems. The profile is defined by control points and cubic splines. Stability margins are estimated using bearing dynamic coefficients, and obtained solutions are analyzed as a function of the number of control points and of the Sommerfeld number at optimization. Results show the feasibility of finding shapes for the bearing that significantly improve the stability margins. Some of the obtained solutions overcome the stability margins of conventional bearings, such as the journal bearing and preloaded bearings with 0.5 and 0.67 preload. A time domain simulation of a flexible shaft rotating system supported by such bearings corroborates the results.

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

2011 ◽  
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.

Determination of Dynamic Coefficients in a Hydrodynamic Journal Bearing Based on the 3-D Navier-Stokes Equations and Considering Cavitation Effects

2012 ◽  
Author(s):  
Changhu Xing ◽  
Minel J. Braun
Keyword(s):  
Pressure Distribution ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Maximum Magnitude ◽  
Navier Stokes Equations ◽  
Dynamic Coefficients ◽  
Finite Perturbation ◽  
Hydrodynamic Journal Bearing

Dynamic coefficients are very important for the stability of a hydrodynamic journal bearing and therefore for its design. In order to determine the stiffness, damping and added mass coefficients of the hydrodynamic bearing, the finite perturbation method around its stabilization position was employed. Based on the Reynolds equation with Gumbel cavitation algorithm, the maximum magnitude of the perturbation was judged by comparing results from finite perturbation (numerical way) to those from infinitesimal perturbation (additional analytical equations need to be derived based on order analysis), as well as theoretical analysis. Using the determined perturbation amplitude, the full three-dimensional Navier-Stokes equations in CFD-ACE+ were used to evaluate coefficients from an actual lubricant and compare to those obtained with Reynolds equation. Finally, a homogeneous gaseous cavitation algorithm is coupled with the Navier-Stokes equation to establish the pressure distribution in the bearing. When gas concentration was varied, the pressure distribution as well as the dynamic coefficients changed significantly.

A method to obtain the linear dynamic coefficients for journal bearing in vertical rotors

2019 ◽  
Vol 72 (1) ◽  
pp. 38-45 ◽  
Author(s):  
Changmin Chen ◽  
Jianping Jing ◽  
Jiqing Cong
Keyword(s):  
Coordinate System ◽  
Linear Models ◽  
Journal Bearing ◽  
Leading Edge ◽  
Content Type ◽  
Linear Dynamic ◽  
Dynamic Coefficients ◽  
Vertical Rotor ◽  
Rotor Bearing ◽  
Stiffness And Damping

Purpose The infinitesimal perturbation (IP) method is commonly used in calculating stiffness and damping of journal bearing in horizon rotor systems. The boundary condition (BC) for the perturbed pressure is assumed being zero at leading edge of film, although it is usually not zero because of nonzero pressure gradient. This assumption is sufficiently accurate for most purpose in horizon rotors. However, for journal bearing in vertical rotor-bearing systems, the BC with the assumption in IP method will bring in significant errors in calculating linear dynamic coefficients. This paper aims to propose a method to obtain the dynamic coefficients of journal bearing in vertical rotors. Design/methodology/approach The stiffness and damping are approached based on IP method and the modified BC of perturbed pressure. As it is difficult to predict perturbed pressure at leading edge at a fixed coordinate system using IP method, a dynamic coordinate system is introduced in this method, of which the origin on circumferential direction is defined as the leading edge of film. Findings The effectiveness and accuracy of proposed IP method in dynamic coordinate (IPMDC) system are verified by comparing the obtained results with analytical solutions. The comparison shows that the results from IPMDC present a good agreement with the analytic solutions. Originality/value The proposed method can be applied in obtaining linear dynamic coefficients of journal bearing in vertical rotors with high precisions. Instead of the usual nonlinear analysis of vertical rotors, this method provides a feasibility of predicting the instability threshold of vertical rotor-bearing systems via linear models.

Identification of Dynamic Coefficients of a Five-Pad Tilting Pad Journal Bearing up to Highest Surface Speeds

2020 ◽  
Author(s):  
Philipp Zemella ◽  
Thomas Hagemann ◽  
Bastian Pfau ◽  
Hubert Schwarze
Keyword(s):  
Flow Rate ◽  
Time Domain ◽  
Static Load ◽  
Journal Bearing ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Tilting Pad ◽  
Oil Flow ◽  
Tilting Pad Journal Bearing ◽  
The Impact

Abstract Tilting-pad journal bearings are widely used in turbomachinery industry due to their positive dynamic properties at high rotor speeds. However, the exact description of this dynamic behavior is still part of current research. This paper presents measurement results for a five-pad tilting-pad journal bearing in load between pivot configuration. The bearing is characterized by a nominal diameter of 100 mm, a length of 90 mm, and a pivot offset of 0.6. Investigations include results for surface speeds between 25 and 120 m/s and specific bearing loads ranging from 0.0 to 3.0 MPa. Results of theoretical predictions are commonly derived from perturbation of stationary operation under static load. Therefore, experimental results for stationary operation including pad deflection under static load are presented first to characterize the investigated bearing. Measured results indicate considerable non-laminar flow in the upper region of the investigated range of rotor speeds. Second, dynamic excitation test are performed with excitation frequencies up to 400 Hz to evaluate dynamic coefficients of a stiffness (K) and damping (C) KC-model, and additionally, a KCM-model using additional virtual mass (M) coefficients. KCM-coefficients are obtained by fitting frequency dependent KC-characteristics to the KCM-model structure using least square approach. The wide range of rotating and excitation frequencies leads to subsynchronous as well as supersynchronous vibrations. Excitation forces are applied with multi-sinus and single-sinus characteristics. The latter one allows evaluation of KC-coefficients at the particular frequency ratio in the time domain. Here, frequency and time domain evaluation algorithms for dynamic coefficients are used in order to assess their special properties and quality. The impact of surface speed, bearing load, and oil flow rate on measured and predicted KCM-coefficients is investigated. Measured and predicted results can be well fitted to a KCM-model and show a significant influence of the ratio between fluid film and pivot support stiffness on the speed dependent characteristic of bearing stiffness coefficients. However, the impact of this ratio on damping coefficients is considerably lower. Further investigations on the impact of oil flow rates indicate that a significant decrease of direct damping coefficients exists below a certain level of starvation. Above this limit, direct damping coefficients are nearly independent of oil flow rate. Results are analyzed in detail and demands on improvements for predictions are derived.

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