Control of a smart electro-magnetic actuator journal integrated bearing to a common equilibrium position: A simulation study

https://doi.org/10.1016/j.ymssp.2020.107556Get rights and content

Highlights

Abstract

The integration of plain journal bearings (JBs) and active magnetic bearings (AMBs) has previously been introduced as an innovative bearing concept in rotating machinery, known as smart electro-magnetic actuator journal integrated bearings (SEMAJIBs). The integrated bearing system tends to exploit the advantages and eliminate the deficiencies of each individual bearing technology. However, the integration of the two bearing technologies introduces new design and control challenges, such as operating the two bearings at a common equilibrium position. The mismatch between the equilibrium positions of the two bearings consumes both bearing load capacities leading to a load sharing problem. A novel experimentally validated control scheme has been adopted in this study to eliminate this problem and to ensure the availability of the integrated bearing load capacities. The scheme introduces a low frequency periodic biasing that enables the controller to detect non-zero static force in the AMB by sensing rotor motion at the bias carrier frequency. Consequently, the AMB controller can modify its magnetic center to match the JB equilibrium position resulting in zero static force in the AMB. Additionally, the control scheme permits the conventional control of AMBs to overcome JBs instabilities. The effectiveness of the control scheme has been demonstrated through numerical simulations using a Jeffcott rotor model supported on a pair of SEMAJIBs, for both stable and unstable operating regimes of the rotor.

Introduction

The dynamic characteristics and performance of rotating machinery are significantly affected by the adopted bearing technology. Mechanical bearing technologies, such as plain journal bearings (JBs), represent mature and robust technologies in rotating machinery. However, plain JBs are usually associated with rotor instabilities that limit their performance [1]. During the last few decades, active vibration control methods have been investigated extensively to eliminate JB instabilities using piezoactuators [2] or separate active magnetic bearings (AMBs) [3], [4], [5], [6], [7]. Regarding active vibration control using AMBs, the integration of plain JBs and AMBs in a single integrated bearing unit was not explored.

The integration of the mature JB and AMB technologies has previously been introduced as an innovative integrated bearing concept [8], [9], [10], known as smart electro-magnetic actuator journal integrated bearings (SEMAJIBs). The excellent load carrying and damping characteristics of JBs combined with the controllability of AMBs provide SEMAJIBs with promising capabilities [11]. Additionally, each bearing type tends to eliminate the limitations of the other bearing. For instance, the controllability of AMBs can be used to overcome the instabilities of plain JBs, namely, oil whip and oil whirl [12], [13]. Moreover, the high load carrying ability of plain JBs leads to small-sized AMBs which act as magnetic actuators for control and partial load sharing purposes. The development of SEMAJIBs included investigating the effect of oil on the characteristics of the AMB [10], investigating multiple controllers for the instability control [11], [12], [13], and investigating the load sharing between the controllers [13], [14]. A test rig was designed and constructed for experimentally verifying the different controllers [15]. Controlling both the first mode oil whip and the second mode oil whip was demonstrated both theoretically and experimentally [16]. Unbalance control was also investigated [17], [18], as well as the use of the SEMAJIB as a smart bearing for turbomachinery control and smart condition based corrective maintenance (SCBCM) [17], [18]. Compared to advanced JB types with enhanced stability characteristics, such as tilting pad JBs, the developed SEMAJIBs not only provide stable operation but also a smart tool for sensing, diagnostics, and corrective maintenance. Further development of the SEMAJIB technology may include the adoption of JB types with better stability characteristics compared to plain JBs, such as multi-lobe JBs.

The integration of the two bearing technologies introduces new design and control challenges, such as operating the two bearings at a common equilibrium position. Hydrodynamic lubrication in JB principally relies on the existence of an eccentricity between the center of the rotating journal and the geometric center of the stationary bearing. For the integrated bearing system, the magnetic center of the AMB typically coincides with the geometric center of the stationary bearing. Additionally, the rotating journal of the JB is also the rotor of the AMB. Consequently, the equilibrium positions of the rotating journal in case of JB and the rotor in case of AMB do not coincide. This mismatch produces opposing forces acting on the journal/rotor from both bearings at static equilibrium which partially consumes both bearings’ load capacities. Hence, the AMB applies an undesirable static force on the rotor rather than using its full capacity in controlling plain JB instabilities. Elimination of the AMB static force requires the control of the AMB to shift its equilibrium position to coincide with the JB equilibrium position. The JB equilibrium position depends strongly on rotor speed and loading conditions (see, for instance, Fig. 4 below). One apparently possible approach is to measure and record this position with the AMB turned off. Then, the AMB would be turned on and its equilibrium position set to match the predetermined JB equilibrium position resulting in zero static force in the AMB. However, as the rotor speed and/or loading conditions change, the JB equilibrium position changes and the load sharing problem reappears. Consequently, the AMB would repeatedly need to be turned off to determine the new JB equilibrium position for any change in rotor speed and/or loading conditions. This approach will result in an impractical operation of the SEMAJIB, especially for unstable operating regimes of the rotor.

On the other hand, a novel experimentally validated control scheme was introduced in [19] to drive the AMB static force to zero while permitting the control of the AMB to cooperate with an adjacent mechanical support without prior knowledge of the common equilibrium position. Generally, in AMB, the currents applied to the opposing pair of magnets are symmetric about a common fixed value, i.e., a constant bias. The basic principle of the control scheme developed in [19] relies on a low frequency periodic biasing scheme which enables the AMB controller to detect non-zero static force by sensing rotor motion at the bias carrier frequency. Consequently, the AMB controller will be able to modify its magnetic center to match the JB equilibrium position, thus eliminating the consumed bearing load capacities due to the opposing forces from JB and AMB. The numerical and experimental results verified the theoretical concept of the control scheme using a simple single degree of freedom system.

In this work, the effectiveness of the common equilibrium position (CEP) control scheme, developed in [19], will be further investigated using the advanced SEMAJIB system. The integrated bearing system is a multi-degree of freedom system with nonlinear and variable stiffness and damping coefficients that depend on many factors, such as rotor speed and position. Additionally, displacement of the rotating journal along the horizontal axis affects the stiffness and damping coefficients of the vertical axis, and vice versa. Moreover, magnetic forces of the AMB are affected by the displacement of the rotor in both horizontal and vertical directions. Hence, the dynamics of the integrated system are much more complicated than the single degree of freedom system studied in [19]. Additionally, integration of the common equilibrium position control approach with a plain JB stability control algorithm [11] will be investigated.

The next sections of this work are organized as follows: the mathematical model of the integrated bearing system is presented in Section II, the adopted CEP control scheme and its adaptation to the integrated bearing system will be detailed in Section III, while the numerical simulation results and their analysis will be discussed in Section IV. Finally, the conclusions will be summarized in Section V.

Section snippets

System modeling

The system under investigation is composed of a Jeffcott rotor supported on a pair of SEMAJIBs as shown in Fig. 1. The Jeffcott rotor is composed of a concentrated mass (i.e., unbalanced disk) centered on a massless flexible shaft. This model can be used to represent the first mode of an actual machine that operates above its first critical speed. In this work, the Jeffcott rotor model is used to capture the first mode of a test rig developed in the rotor-dynamics laboratory at Cairo University

Control methodology

In general, the control of AMBs employs a bias linearization strategy. This means that the opposing pair of magnets, in x-axis for instance, have currents controlled according to the following scheme,Ix,1t=Ib+ic,xtIx,2t=Ib-ic,xtwhere Ib is a constant bias current and ic,x is a symmetric perturbation applied to realize the AMB force. The magnitude of Ib is selected to be larger than i,cx. The control strategies of the AMB in x and y directions are similar. Thus, only the details of the control

Control of a stable SEMAJIB system to a common equilibrium position

The first set of results investigates the effectiveness of the control system to drive the SEMAJIB system to a common equilibrium position without JB instability control. The rotor is assumed to be running below its natural frequency at Ω2=0.5Ωn. At this speed, the initial stable journal static equilibrium position is 24.853μm in x direction and -11.535μm in y direction. This position is represented in Fig. 4 in a non-dimensional form at 0.31 in x direction and -0.144 in y direction. The

Conclusions

The integration of journal bearings and active magnetic bearings into a SEMAJIB system introduces new design and control challenges, such as operating the two bearings at a common equilibrium position. The mismatch between the equilibrium positions of both bearings produces opposing forces acting on the journal/rotor from both bearings at static equilibrium which partially consume bearings load capacities. A novel control scheme has been adopted to adjust the active magnetic bearing equilibrium

CRediT authorship contribution statement

Mohamed L. Shaltout: Conceptualization, Methodology, Software, Investigation, Writing - original draft. Antoine S. Dimitri: Conceptualization, Methodology, Software, Validation, Writing - review & editing. Eric H. Maslen: Conceptualization, Writing - review & editing, Supervision. Aly El-Shafei: Conceptualization, Writing - review & editing, Supervision, Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (28)

  • J. Tůma et al.

    Active vibrations control of journal bearings with the use of piezoactuators

    Mech. Syst. Signal Process.

    (2013)
  • M.E.F. Kasarda et al.

    Reduction of subsynchronous vibrations in a single-disk rotor using an active magnetic damper

    Mech. Res. Commun.

    (2004)
  • A. Bonfitto et al.

    Sensorless active magnetic dampers for the control of rotors

    Mechatronics

    (2017)
  • A. El-Shafei et al.

    Some experiments on oil whirl and oil whip

    J. Eng. Gas Turbines Power.

    (2007)
  • M.E.F. Kasarda et al.

    A magnetic damper for first mode vibration reduction in multimass flexible rotors

    J. Eng. Gas Turbines Power.

    (1990)
  • A.H. Pesch, J.T. Sawicki, Stabilizing hydrodynamic bearing oil whip with μ-synthesis control of an active magnetic...
  • A. Looser et al.

    An active magnetic damper concept for stabilization of gas bearings in high-speed permanent-magnet machines

    IEEE Trans. Ind. Electron.

    (2014)
  • A. El-Shafei, Integrated Journal Bearing, U.S. Patent No. 10,612,592 B2,...
  • A. El-Shafei, Methods of controlling the instability in fluid film bearings, U.S. Patent No. 7,836,601,...
  • M. El-Hakim, A.S. Dimitri, T. Saqr, J. Mahfoud, A. Adly, A. El-Shafei, Numerical and experimental identification of the...
  • A. El-Shafei et al.

    Controlling journal bearing instability using active magnetic bearings

    J. Eng. Gas Turbines Power.

    (2010)
  • A.S. Dimitri et al.

    Oil whip elimination using fuzzy logic controller

    J. Eng. Gas Turbines Power.

    (2015)
  • A.S. Dimitri et al.

    Magnetic actuator control of oil whip instability in bearings

    IEEE Trans. Magn.

    (2015)
  • Antoine Dimitri, Active Control of Smart Bearings, PhD Dissertation, Cairo University,...
  • Cited by (0)

    View full text