CFD simulation of magnetorheological fluid journal bearings

https://doi.org/10.1016/j.simpat.2011.01.001Get rights and content

Abstract

Magnetorheological fluid journal bearing can be controlled by a steady magnetic field doing that very effective for attenuating and controlling the performance of the rotor bearing systems.

An integrated simulation study, of a magnetorheological (MRF) fluid journal bearing, via computational fluid dynamics (CFD) and finite element method (FEM) is presented in this paper. The journal bearing characteristics such as, eccentricity, attitude angle, oil flow and friction coefficients are calculated and presented as functions of the magnetic field, and L/D bearing ratios.

A specific procedure in order to simulate an MRF bearing operated in high eccentricity ratios is also presented and the meshing requirements are discussed.

Introduction

Magnetorheological fluid (MRF) is a manageable fluid that exhibits drastic changes in rheological properties adjustable and interchangeable to the applied magnetic field strength. The fluid is potentially advantageous to be employed in many applications. MRF is a kind of controllable or smart fluids whose rheological properties can be dramatically and reversibly varied by the application of an external magnetic field in a very short period of time. The MRF has the property of a normal viscosity in the absence of an external magnetic field, but in the presence of a strong magnetic field immediately solidifies to a grease state.

The MRF’s are one of the most active ‘‘smart materials’’ of the current range. Most researches in the application of the MRF’sare focused on structural vibration control and flow power system. Stanway et al. [1] and Wang and Meng [2] made a survey study in the state of the MRF’s and the application of the MRF’s in several mechanical engineering systems. There are many papers dealing with the application of the magnetorheological fluids for controllable dampers [3], [4], [5], [6], [7] for seismic response control of frame structures [8] and vibration control of large structures [9]. The rapid, reversible and dramatic changes in its rheological properties provide a possibility of control in flow power systems [10], [11].

Congenital smart fluids to magnetorheological are the electrorheological fluids (ERF), which also exhibit drastic changes in rheological properties and interchangeable depending on the applied electric field strength. There are also, dozens of papers published which deal with the application of ER fluid in bearings for rotational machinery.

Vance and Ying [12] developed and demonstrated the dynamic behavior of the rotor systems supported on the multi-disk ER fluid damper. Dimarogonas and Kollias [13], [14] studied stability of a rotor system supported by journal bearings with ER fluid theoretically and compared the capability of three kinds of ER fluid damper for controlling the rotor vibration.

Nikolajsen and Hoque [15] presented a multi-disk ER fluid damper operating in shear flow mode and studied the effectiveness of the multi-disk ER fluid damper in controlling the vibration of rotor systems when passing through the critical speeds.

Nikolakopoulos and Papadopoulos [16] studied the dynamic characteristics of a controllable journal bearing lubricated with the ER fluid.

Based on the Bingham fluid theory, Tichy [17], Docier and Tichy [18] analyzed the dynamic characteristics of fluid film force and the existing conditions and manner of core in the ER fluid squeeze-film damper and journal bearings. Recently, Gertzos et al. [19] presented a CFD analysis in which for Bingham lubricated journal-bearing performance characteristics, such as relative eccentricity, attitude angle, pressure distribution, friction coefficient, lubricant flow rate, and the angle of maximum pressure, are derived and presented for several length over diameter (L/D) bearing ratios and dimensionless shear numbers of the Bingham fluid. The above diagrams presented in the form of Raimondi and Boyd charts, and can easily be used in the design and analysis of journal bearings lubricated with Bingham fluids.

From the above literature it is obvious that the ER fluids give the possibility of controllable journal bearings. However, in comparison with the properties of the ER fluid, an MRF inherently has higher yield strength; therefore it is capable of generating a greater fluid force. Furthermore, the MRF is activated by the application of an external magnetic field, which is easily produced by a simple, low-voltage electromagnetic coil and avoids probably arcing problems.

Furthermore in the field of magnetorheological fluid lubricated journal bearings the published works are limited.

Zhu [20] presented an MRF squeeze-film damper operating in the squeeze film mode and showed that the MRF squeeze-film damper can effectively control the vibration of a rotor system, but an unbalanced magnetic pull force existing in the journal due to the eccentricity of the journal with respect to the damper housing may pull the journal to the damper housing and lock up the damper like a rigid support when the applied current in the coil is over a certain value.

Wang and Gordaninejad [4] combine a fluid mechanics-based approach and the Herschel–Bulkley constitutive equation to develop a theoretical model for predicting the behavior of field-controllable, magnetorheological, and electrorheological (ER) fluid dampers.

Hesselbach and Abel-Keilhack [21] investigated the influence of the magnetic field on the bearing gap of hydrostatic bearings with MRF’s. They found that, in a closed loop control, a nearly infinite stiffness, only limited by the resolution of the measuring system, can be achieved. The results showed that the concept of a hydrostatic bearing with MRF’s can overcome the drawbacks (stiffness and response time) of conventional hydrostatic bearing.

Kim et al. [22], presented a controllable semi-active smart fluid damper (SFD) using magnetorheological fluids, focusing on its design and modeling. It offers a comprehensive design method and an innovative experimental identification and modeling technique for MR-SFDs. They constructed a prototype MR-SFD and investigated how some of the critical design parameters affect the performance of the MR-SFD. Additionally they characterized the damper’s dynamic behavior experimentally using a novel excitation method that adopts active magnetic bearing (AMB) units. In modeling the dynamic behavior of the MR-SFD, they employed the describing function method. The describing function analysis effectively captured the non-linear dynamic behavior of the MR-SFD. Carmignani et al. [23] presented an analytical, numerical and experimental study off a magnetorheological squeeze-film damper. Numerical simulations were carried out in order to evaluate the dynamic behaviour of the damped rotor as a function of the current supplied to the adjustable device. A linear model that depicts the main characteristics of the system has been developed as a useful tool in damper and control design. They tested different fluids, and an optimal fluid has been singled out. The tests conducted on the selected fluid shown that it is possible to have the optimum conditions for each steady rotational speed.

Urreta et al. [24] summarizes the work carried out in the development of hydrodynamic lubricated journal bearings with magnetic fluids. Two different fluids have been analyzed, one ferrofluid from FERROTEC APG s10n and one magnetorheological fluid from LORD Corp., MRF122-2ED. Theoretical analysis has been carried out with numerical solutions of Reynolds equation, based on apparent viscosity modulation for ferrofluid and Bingham model for magnetorheological fluid. The authors in order to validate their model, designed, manufactured and set up a test bench, where their preliminary results shown that magnetic fluids can be used to develop active journal bearings.

The design of a magnetorheological squeeze-film damper is presented and discussed by Forte et al. [25]. A numerical simulation has been carried out in order to evaluate the dynamic behavior of the damped rotor as a function of the magnetic field strength. The authors made a test rig of a slender shaft supported by two oilite bearings and an unbalanced disk. The damper was interfaced with the shaft through a rolling bearing and the electric coils generate the magnetic field whose field lines cross the magnetorheological film.

In this paper a simulation study via computational fluid dynamics is presented for a magnetorheological fluid lubricated journal bearing. Both, magnetic and rheological fields are solved. The aim of this paper is: (i) the presentation of a coupled model which solves the magnetic and rheological field giving a tool for the design of the MRF lubricated bearings, (ii) the accurated calculation of the bearing attitude angle, eccentricity, friction coefficients and oil flow even for high eccentricities versus the magnetic field and (iii) the numerical techniques to get accurate results in high eccentricities.

The paper is organized as follows: The problem definition and computation approach are first presented early in Section 2, followed by an analytical validation of the model, in Section 3. Simulation results are then presented and discussed in Section 6, and the main findings are finally summarized and discussed in Section 7.

Section snippets

Geometrical model

In the present work, the bearing is considered to be rigid, and the flow steady and isothermal. The geometry of the bearing follows the model that is shown in Fig. 1; here, Ob is the bearing centre, Oj the journal centre, Rb the bearing radius, Rj the journal radius, e the bearing eccentricity, φ the attitude angle, and L the bearing length. The external load W is assumed vertical (i.e. along the y-axis) and constant and a magnetic field H is applied between rotor and the bearing.

Governing equations and assumptions

The following

Magnetic field simulation meshing requirements

We use a standard element size of 1 mm in order to perform the basic meshing procedure. The need for high accuracy in our results within the magnetorheological fluid domain drives us to perform a secondary meshing in that particular area with a smaller element size.

The geometry is considered axisymmetric. In Fig. 7, the element’s colors depict the regions of different materials used for the analysis. The high mesh density in the region of the MRF is clearly depicted. We use the PLANE 53 element.

Numerical model validation

To validate the present computational approach, we test our tool for the case of: (i) a journal bearing operating with Bingham fluids and (ii) we validated our results regarding the magnetic field simulation with a squeeze-film damper lubricated with magnetorheological fluids. We compare our results in case (i) to those reported in [19] for a similar problem setup, see Fig. 10a, Fig. 10b, Fig. 11a, Fig. 11b, and for case (ii) to those reported in [25], see Fig. 12a, Fig. 12b.

In case (i) of

Performance characteristics

The relations below were used in order to obtain solution. The friction force is calculated in the equilibrium position by integrating the shear stress τ over the bearing (or journal) area:Ffri=AiτtdAi,i=jorbwhere i = j refers to the journal and i = b refers to the bearing and Ai is the total area of journal or bearing.

The friction coefficient is calculated by the relation:fi=FfriW

The load-carrying capacity that the bearing will support is found by integrating the pressure around the journal. The

Results

The magnetic analysis provides the magnitude of the magnetic field within the volume of the bearing. The main characteristics of the magnetorheological journal bearing are the bearing radius Rb, the radial clearance C and the length to diameter ratio and thus the length of the bearing L itself. The coil turns number and coil cable diameter have constant values throughout the coupled magnetic-CFD simulation. The rest of the geometric parameters are extracted in relation to the basic design

Conclusions

This paper has addressed the problem of magnetorheological fluid lubricated journal bearings operating. To this end, we developed a tool for solving the coupled magnetic-rheological flow problem.

For a selected number of bearing states, several L/D ratios, magnetic field variations, solutions were obtained in terms Sommerfeld number variation. The present results demonstrate that, in comparison to a normal bearing (lubrication with out magnetic field), the presence of magnetic filed can be

Acknowledgement

This work is supported by the research program “KARATHEODORIS 2009” funded by the Research Council of the University of Patras, Greece.

References (26)

  • C. Dorier et al.

    Behavior of a Bingham-like viscous fluid in lubrication flows

    J. Non Newtonian Fluid Mech.

    (1992)
  • K.P. Gertzos et al.

    CFD analysis of journal bearing hydrodynamic lubrication by Bingham lubricant

    Tribol. Int.

    (2008)
  • R. Stanway et al.

    Applications of electro-rheological fluids in vibration control: a survey

    Smart Mater. Struct.

    (1996)
  • J. Wang, G. Meng, Magnetorheological fluid devices: principles, characteristics and applications in mechanical...
  • Y.K. Ahn et al.

    On the design and development of a magneto-rheological mount

    Veh. Syst. Dyn.

    (1999)
  • X. Wang et al.

    Flow analysis and modeling of field-controllable, electro- and magneto-rheological fluid dampers

    J. Appl. Mech., Trans. ASME

    (2007)
  • N.K. Singh, Analysis of micro fluid car suspension system (MFCSS) and effect of this on comfort factor and life of...
  • N.D. Sims, R. Stanway, A.R. Johnson, D.J. Peel, W.A. Bullough, Smart fluid damping: shaping the force/velocity response...
  • N.D. Sims, N.M. Wereley, Modelling of smart fluid dampers, in: Proceedings of SPIE – The International Society for...
  • Y.L. Xu et al.

    Seismic response control of frame structures using magnetorheological/electrorheological dampers

    Earthquake Eng. Struct. Dyn.

    (2000)
  • W. Liu, Vibration control of large scale flexible structures using magnetorheological dampers, Ph.D. Thesis, Department...
  • K. Yoshida, T. Soga, M. Kawachi, K. Edamura, S. Yokota, Magneto-rheological valve-integrated cylinder and its...
  • J. Yoo, N.M. Wereley, Performance of a MR hydraulic power actuation system, in: Proceedings of SPIE – The International...
  • Cited by (0)

    View full text