Experimental identification of linear oil-film coefficients using least-mean-square method in time domain

doi:10.1016/j.jsv.2004.12.011

Journal of Sound and Vibration

Volume 287, Issues 4–5, 4 November 2005, Pages 809-825

https://doi.org/10.1016/j.jsv.2004.12.011 Get rights and content

Abstract

In general sense, under small perturbation the stability of rotor-bearing system can be determined by linear oil-film coefficients of hydrodynamic bearing and oil-film forces can also be expressed by these coefficients. This paper proposes an experimental method to identify these coefficients and presents their characteristics under various operational conditions. A delicate test rig is constructed and experimental data are acquired under various testing conditions. From the experimental data, the relative velocity of the journal and the oil-film forces can be obtained by using a differentiator. The coefficients are identified using least-mean-square method in time domain. Some identified results are compared with the theoretical data. The experimental results indicate that the linear oil-film dynamic coefficients are sensitive to the excitation amplitude. The intensity of sensitivity is varied for different coefficients. From the investigation, it can be concluded that the linear oil-film force model will be invalid once the condition of small perturbation is not satisfied.

Introduction

Journal bearings have been widely used in high-speed rotating machinery. Since dynamic characteristics of oil-film bearing affect the unbalance responses and stability of machines, obtaining reliable bearing oil-film coefficients becomes particularly important. However, there exist so many factors influencing on the dynamic characteristics of oil-film bearing (such as pressure boundary conditions, temperature boundary conditions, cavitations, etc.) that it is not easy to calculate oil-film coefficients accurately. Thus both experimental and theoretical investigations on oil-film coefficients of journal bearing are indispensable.

Since it is impossible to measure the linear oil-film coefficients directly, many experimental techniques have been developed to identify these bearing parameters. All of these techniques are featured by excitation of journal or rotor mass, measurement of the corresponding input force, and the associated response of the journal or rotor mass. An economical and convenient experimental method to estimate these dynamic coefficients is based on the impulse responses [1], [2], [3], [4]. An impulse excitation covers a wide range of frequency characteristics, which increases the reliability of estimated coefficients. Tieu and Qiu proposed a method to determine the oil-film coefficients from two or more sets of unbalance responses [5]. They utilized the synchronous unbalance responses to simplify the calculation of coefficients. This method is convenient to estimate the coefficients of journal bearing on-line. Kostrzewsky and Flack used sinusoidal excitation to recognize oil-film coefficients [6], [7]. Their method can produce high-energy and high signal-to-noise ratio responses in the specified frequency. This method has been widely applied in experimental studies, including this paper.

Notably, not so many successful studies on measuring bearing oil-film coefficients are available up to now. Agreement between experimental results and theoretical predictions has been observed only in some specific conditions. This paper is to identify the linear coefficients under various operating conditions and study the influence of perturbation amplitude on these coefficients. The experimental study is performed on a deliberate test rig. The diameter of the test bearing is 152 mm. First, the relative velocity and oil-film forces of this bearing are obtained from the experimental data using a differentiating FIR filter. A least-mean-square method in time domain is then introduced, and eight linear oil-film dynamic coefficients are identified and evaluated. Detailed experimental procedures and data processing techniques are presented. Finally, some measurement results are compared with the theoretical data. The influence of excitation amplitude on these identified oil-film coefficients is also discussed.

Section snippets

Mathematical model

Based on the linear theory, the oil-film force increment of journal bearing is the linear algebraic function of displacements $(x, y)$ and velocities $(\dot{x}, \dot{y})$ with respect to the journal's static equilibrium position $(x_{0}, y_{0})$ , it can be written as $[\begin{matrix} Δ {\tilde{f}}_{X} \\ Δ {\tilde{f}}_{Y} \end{matrix}] = k_{1} [\begin{matrix} x - x_{0} \\ y - y_{0} \end{matrix}] + d_{1} [\begin{matrix} \dot{x} \\ \dot{y} \end{matrix}] = [\begin{matrix} k_{XX} & k_{XY} \\ k_{YX} & k_{YY} \end{matrix}] [\begin{matrix} x - x_{0} \\ y - y_{0} \end{matrix}] + [\begin{matrix} d_{XX} & d_{XY} \\ d_{YX} & d_{YY} \end{matrix}] [\begin{matrix} \dot{x} \\ \dot{y} \end{matrix}],$ where $Δ {\tilde{f}}_{X}, Δ {\tilde{f}}_{Y}$ are the oil-film force increments in the horizontal and vertical directions. $k_{1}$ and $d_{1}$ are the linear stiffness and damping coefficient matrices. They have their respective

Coefficients identification

The oil-film force increment can also be written as $Δ f_{i} (k) = k_{i, 1} x_{1} (k) + k_{i, 2} y_{1} (k) + k_{i, 3} {\dot{x}}_{1} (k) + k_{i, 4} {\dot{y}}_{1} (k) (for i = X or Y; k = 1 - n),$ where $Δ f_{i} (k)$ is the oil-film force increment; $n$ is the size of data obtained from each channel; $k_{i, 1}$ and $k_{i, 2}$ are linear stiffness coefficients; $k_{i, 3}$ and $k_{i, 4}$ are linear damping coefficients. It is assumed that ${\tilde{f}}_{i} (k)$ is the measured dynamic oil-film force (oil-film force increment) obtained from Eq. (2). The least-mean-square between $Δ f_{i} (k)$ and ${\tilde{f}}_{i} (k)$ can be calculated as

Conclusions

The following conclusions can be drawn from the above experimental study:

1.
The least-mean-square method in time domain is a fast and effective algorithm to identify the linear coefficients of journal bearings. The identified coefficients are repeatable and stable under conditions of small load parameter.
2.
The experiments show that linear coefficients increase with the growth of the load parameter. This is in agreement with the theoretical calculation.
3.
Because the velocity is acquired through a FIR

Acknowledgements

The supports from the National Natural Science Foundation of China (Grant No. 90210007 and 50335030) and China 863 High Tech Project (2002AA412410) are gratefully acknowledged.

References (10)

Z.L. Qiu et al.
Identification of sixteen dynamic coefficients of two journal bearings from impulse responses
Wear
(1997)
Y.Y. Zhang et al.
Identification of linearized oil-film coefficients in a flexible rotor-bearing system, part Imodel and simulation
Journal of Sound and Vibration
(1992)
Y.Y. Zhang et al.
Identification of linearized oil-film coefficients in a flexible rotor-bearing system, part IIexperiment
Journal of Sound and Vibration
(1992)
A.K. Tieu et al.
Identification of sixteen dynamic coefficients of two journal bearings from experimental unbalance responses
Wear
(1994)
G. D Jiang et al.
Identification of oil film coefficients of large journal bearings on a full scale journal bearing test rig
Tribology International
(1997)

There are more references available in the full text version of this article.

Cited by (24)

Characteristics of oil film nonlinearity in bearings and its effects in rotor balancing
2019, Journal of Sound and Vibration
Citation Excerpt :
The response to a rotating force applied to the journal is then a circular or elliptical orbit [7]. However, they are also used, of course, for simulating experimental behavior of rotating shafts, where orbits exhibit displacements that are not at all vanishing small, as presented by Ref. [8]. The higher are the amplitudes of the orbits the worst its behavior will be represented by the linear model.
Since unbalance is inherent to any rotating machine, and some effects like coupling misalignment and thermal bow, which are not taken into account in pre-balancing, can lead to changes in unbalance distribution, in-field rotor balancing is sometimes a necessary action. Traditionally, the influence coefficients method has been used as the main balancing procedure, and due to the low accessibility in assembled rotating machinery, generally only the journal displacements inside hydrodynamic bearings are available for the balancing procedure. However, influence coefficients method assumes linearity of rotor response and it is known that hydrodynamic bearings can sometimes present a strong nonlinear relationship between bearing forces and journal displacements, making balancing difficult or even impossible. Otherwise, the bearing housing vibrations are directly proportional to the bearing forces and are independent of the journal displacements, therefore avoiding problems related to oil film nonlinearities. This paper proposes the use of bearing housing accelerations as influence coefficients and verifies experimentally that balancing can be successful also in highly nonlinear oil film bearing conditions. First, the oil film nonlinear characteristics are introduced by means of a simple analytical model. Then, different behaviors have been experimentally investigated by means of a test rig rotor supported by three hydrodynamic bearings, designed to enhance oil film nonlinear effects. Nonlinear effects are quantified through deviations with respect to linear behavior and development of higher harmonics in the response of the oil film. It is shown that these effects can seriously affect the possibility of balancing with the use of influence coefficients. Finally, it has been verified experimentally that balancing with the use of bearing housing acceleration to calculate influence coefficients was successful, as expected.
Dynamic Coefficients of Finite Length Journal Bearing. Evaluation Using a Regular Perturbation Method
2019, International Journal of Mechanical Sciences
Citation Excerpt :
As commented in the Introduction Section, both, data and model predictions of the dynamic coefficients are sensitive to many design, processing, flow and fluid parameters and conditions, which difficult the comparison [25,26]. In this work we have chosen the data presented by Zhao et al. [21] for the comparison. To our best knowledge, this is the latest work that tests a plain-cylinder JB [26].
A set of simple expressions is deduced for static and dynamic parameters associated to hydrodynamic journal bearings (JB). The behavior of this system is governed by two dimensionless numbers, the aspect ratio, L/D, and the eccentricity ratio, η. In a previous work, we presented a regular perturbation method that extended the Ocvirk solution and successfully described isothermal JBs up to L/D and η of ∼1/2. Presently, we extend that methodology, modified using a smaller perturbation parameter, to obtain analytical expressions of the dynamic coefficients, as well as static variables like friction factor, load carrying capacity, lubricant flow rate and phase angle. The deduced expressions successfully describe the static and dynamic behavior of JBs up to L/D and η of ∼3/4.
Identification of oil-film coefficients for a rotor-journal bearing system based on equivalent load reconstruction
2016, Tribology International
Citation Excerpt :
However, as many factors (such as pressure boundary conditions, temperature boundary conditions, cavitations, etc.) have important influences on the system performances, and the contact between oil-film and rotor is complex and difficult to be simulated, it is really difficult to build a reasonable and accurate numerical or analytical model for rotor-bearing system. Even with the obtained models, researchers have reported that often the regression matrix of the estimation equation became ill-conditioned, and this led to scattering of the identified oil-film parameters [12]. Though the accurate model of the rotor-journal bearing system is difficult to be obtained, the separate rotor structure is simple and can be accurately modeled through finite element techniques.
In this paper, a laboratory method based on equivalent dynamic load reconstruction is proposed for the identification of oil-film coefficients. When modeling the rotor, the oil-film supports are considered as its dynamic load boundary conditions. Consequently, the identification of oil-film coefficients is first converted to the reconstruction of equivalent dynamic loads. Through Green's function method and regularization, the equivalent dynamic oil-film loads can be steadily and precisely reconstructed. Then, according to the mechanical relationships between the oil-film properties and the corresponding equivalent loads, the oil-film stiffness and damping coefficients are identified using least square scheme. A rotor structure with two journal bearings is investigated and the identification results of oil-film coefficients demonstrate the validity and accuracy of the proposed method.
Multi-frequency identification method in signal processing
2009, Digital Signal Processing: A Review Journal
Virtually vibration signals are always composed of many frequency components. Using the least squares method, a new multi-frequency identification algorithm has been proposed to identify the amplitude and phase of each component of a multi-frequency signal, and it will work well as long as the main frequency values are known. Based on this algorithm, two similar optimization procedures have been presented to obtain accurate frequency values for a sine-wave signal and a bi-tone signal, respectively. Assisted with band-pass filters and these optimization procedures, the multi-frequency identification algorithm can successfully identify the multi-frequency components of a signal. The multi-frequency identification method can be used to identify oil-film coefficients of journal bearing. And some reliable oil-film coefficients have been reached.
A Review on Application of Dynamic Parameters of Journal Bearing for Vibration and Condition Monitoring
2015, Journal of Mechanics
A novel iteration method for estimation of bearing dynamic coefficients in the rotor-bearing system
2021, International Journal of Hydromechatronics

View all citing articles on Scopus

View full text

Experimental identification of linear oil-film coefficients using least-mean-square method in time domain

Abstract

Introduction

Section snippets

Mathematical model

Coefficients identification

Conclusions

Acknowledgements

Wear

Journal of Sound and Vibration

Journal of Sound and Vibration

Wear

Identification of oil film coefficients of large journal bearings on a full scale journal bearing test rig

Tribology International