Numerical and experimental identification of the static characteristics of a combined Journal-Magnetic bearing: Smart Integrated Bearing

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1 Numerical and experimental identification of the static characteristics of a combined Journal-Magnetic bearing: Smart Integrated Bearing M El-Hakim*, A S Dimitri**, T Saqr*, J Mahfoud***, A Adly**, A El- Shafei** * RITEC, Cairo, Egypt ** Cairo University, Giza, Egypt *** Université de Lyon, INSA-Lyon, LaMCoS UMR5259, Villeurbanne, France ABSTRACT This work is part of a research program aiming at developing a new concept of smart bearings; the Smart Integrated Bearing (SIB). SIB consists of a journal bearing and an Electro-Magnetic Actuator (EMA), for which load carrying capacity is assumed by the journal bearing and the controllability by the EMA. The work intends to define a simple (force/current) model of the EMA, which is necessary to obtain a linear action line. To identify the model, a test rig was designed and manufactured. Investigations are performed to determine the influence of oil, the hysteresis effects and the linearity domain. 1 INTRODUCTION The concept of smart machines was discussed since the nineteen nineties [1]. The basic idea is to have a machine capable of responding to the varying operating conditions and the environment while improving the performance as well as providing information on its status and predicting suitable actions. Many steps have contributed to a smart machine [2-8], but actually more development is still needed to achieve this ideal concept of smart machine. In an effort in this direction, the authors have worked towards the concept of a smart machine, by developing a smart bearing. In this concept, an integrated journal Bearing (JB)/Active Magnetic Bearing (AMB) has been introduced [9, 10]. The purpose is to reap the advantages of large load carrying capacity of JB [11] along with the controllability advantages of AMB [12] while eliminating both their respective disadvantages. This concept, which we like to call a Smart Integrated Bearing (SIB), requires actually a paradigm shift in thinking about bearings. The SIB requires oil in an AMB, and adds controllability to the JB, both issues that require a leap forward in both the JB and AMB communities. This paradigm shift, particularly adding oil to an AMB, is the purpose of this investigation. It is required to study the effect of oil on the characteristics of the AMB both numerically and experimentally, before applying the SIB concept to rotating machinery. Thus, the purpose of this paper is to develop a numerical model for the SIB with oil and comparing it to an AMB in air. Moreover, it is required to

2 experimentally establish this concept and to determine the material characteristics of the SIB. In this paper, the newly proposed SIB is investigated. A mathematical magnetic model based on magnetic circuit theory, assuming negligible eddy current effects and conservative flux. The magnetic actuator is defined using a finite element model to numerically simulate the non-linear saturation zone. Experimentally, it is required to identify the material magnetic properties and the effect of the presence of oil on the actuator magnetic characteristics. A design was made of the SIB considering the loading conditions and the dimensions of a test rig which is a model for an industrial rotor. The experimental set-up and testing procedure are described showing the used test rig and its instrumentation. The obtained numerical and experimental results are illustrated and compared, showing the influence of the presence of oil, material relative permeability, and hysteresis. It is clearly seen that the oil has minor effects on magnetic properties and actually provides favorable forces in the linear zone. 2 NOMENCLATURE B: magnetic flux density (T) Φ: magnetic flux (Tm) μ o: permeability (Tm/A), permeability of free space: 4π x 10-7 μ r: relative permeability H: magnetomotance (A/m) l: magnetic flux iron path length (m) l g: magnetic gap (m) F: force (N) J: current density (A/m 2 ) I: current (A) α: pole inclination angle N: coils number of turns A g: magnetic pole area (m 2 ) 3 MAGNETIC ACTUATOR MODELING A mathematical model for the EMA is derived based on the magnetic circuit theory using Maxwell equations (1) assuming negligible eddy currents and flux conservation [13]. Magnetomotance: H Conservation of flux:. B 0 J Magnetomotance is the equation relating the amount of magnetic field generated to the ampere turns and current passing through the windings. Assuming that: path dl is parallel to H, path can be broken into n segments where H is constant, J is uniform in the coils. Assuming constant permeability in each segment B i=μ ih i, the ampere loop law in lumped form is obtained as in equation (2). n n Bili Ni I i (2) i1 i i1 (1)

3 The conservation of flux is applied since all the magnetic field should pass in a closed loop path starting from one magnet pole and ending with the other pole, where B is assumed to be uniform and perpendicular to the area as in equation (3). n B da 0 i (3) i1 Ai Applying these principals on the magnetic actuator having the geometry shown in figure 1, the magnetic field could be expressed by equation (4). 0NI B 2l g l r, gap r, iron (4) Figure 1: Magnetic Actuator Geometry The magnetic force could be obtained by the integration over the closed path of the magnetic flux where the magnetic field is perpendicular to the surface of the iron is expressed by the equation. For lumped model, the force equation (5) becomes, n 1 2 (5) F 2 0 i1 B i A i Substituting from equation (4) into the magnetic force equation (5) for the given geometry and taking into consideration the poles inclination angle α, the total magnetic force F could be finally obtained analytically using equation (6). 2 0 N Ag cos 2 F I 2 2l g l (6) r, gap r, iron

4 Rewriting equation (6), the iron relative permeability could be determined using equation (7) from the obtained experimental results of the force to current relation at the different gaps after setting the gap relative permeability μ r,gap to 1. r, iron N o 2 Acos( ) I F l 2 2l g (7) In order to verify the analytical calculations, a finite element magnetic model FEM is built using [14] which solves electromagnetic problems on two-dimensional planar and axisymmetric domains using Maxwell s equations. The FEM helps in modeling the non-linear characteristics such as saturation effects. Magnetostatic problems are problems in which the fields are time-invariant. In this case, the field intensity H and flux density B which follows equation (1) are subject to a constitutive relationship B = μh. If a material is nonlinear, the permeability, μ is actually a function of B as μ =B/H(B). The finite element solution is finding a field that satisfies equation (1) and the material relationship via a magnetic vector potential approach. The magnetic actuator finite element is meshed using triangular element. The iron core (stator, rotor) material is silicon iron sheets, the areas around the stator legs are copper wires includes the current intensity per unit area. Dirichlet boundary condition is applied for the magnetic problem where the value of potential on the boundary, is defined as A = 0. The numerical results are calculated by substituting into the model by the iron and oil permeability characteristics determined experimentally as will be shown later in the paper. In figure 2, a comparison is held between the two models for a gap of 0.5 mm. In the linear range, the analytical and FEM models are matching as long as the flux in the iron core did not reach the saturation. Therefore, this is the suitable range for linear control purposes. On the other hand, for higher values of current, the saturation effect could be observed in the FEM, as the force current trend changes, and a difference takes place between the analytical and FEM models due to the iron saturation. Figure 2: Analytical and FEM Results at 0.5 mm gap

5 In order to numerically investigate the effect of oil, the value of gap relative permeability has been changed in the FEM from 1 for air into 1.1 for oil. It is clear by comparing the (FEM Air and FEM Oil) in figure 2, that the oil presence has a negligible effect on the force values. In fact, it is found that the force is slightly increased in the linear range, then at higher values of current, this minor difference vanishes as the saturation becomes dominant. 4 EXPERIMENTAL SET-UP The experimental set-up used in this experiment consists of a shaft mounted on two load cells GTM type 1 kn each used to measure the force applied on the rotor. The shaft is also guided by two linear bearings used as guides preventing any lateral displacement for the shaft. In order to detect any displacement in the shaft during the experiment, two proximity probes of type Bently-Nevada 7200 transducer systems with 5 mm tip diameter are used. These probes are used to assure fixed air gap during the experiment. The current is supplied to the coil using GwInstek programmable DC power supply. The experimental setup is illustrated in figure 3. Figure 3: Experimental Setup The magnetic actuator is mounted in an aluminum housing consisting of a lower part and an upper cover. Aluminum is selected to eliminate magnetic flux losses through the housing. The magnetic actuator stator is fixed in the lower part of the housing and covered by the upper cover to avoid any displacement of the stator relative to the rotor and, thus, keeping constant gap during the test. In addition, the rotor is mounted on two load cells with neglected deflection. During the experiment, the gap is first adjusted using fillers, the shaft is moved using two screws mounted on the load cells. By turning the screws, the shaft moves up and down until the required gap is reached. Then, after fixing the required gap, the current is injected into the coils and the readings of the current and the force in the load cells are read respectively. The current is gradually increased up to the maximum possible value, and then decreased to investigate the saturation and hysteresis phenomena. Simultaneously, the proximity probe readings are monitored to make sure that the gap is fixed during the experiment. This procedure is repeated after flooding the stator in oil of type SAE RESULTS The experiments are first performed in air for three gaps: 0.6, 0.5, and 0.4 mm to define the force current relation. From the experimental results in air medium, the iron magnetic permeability and saturation characteristics are determined. The experiments are then repeated in case of oil, to investigate the effect of oil presence. The tested magnetic actuator parameters are listed in table (1).

6 Table (1): Magnetic Actuator Characteristics Parameter Value Average Flux Path Length (l) (m) Pole Area (A g) (m 2 ) Number of turns (N) 100 Pole inclination angle (α) ( ) 22.5 The obtained experimental results for 0.6, 0.5, and 0.4 gaps are plotted in figures 4, 5 and 6 respectively. Note that during the tests, the maximum reach current at 0.4 mm gap is less than the two other gaps, due to the greater forces values at the smaller gap. By analyzing the obtained results, it could be found that the model is fitting with the experimental results. The model is able to calculate the magnetic forces and as function of the current and the gap. The force is directly proportional to the square of the current passing through the coils and inversely proportional to the square of the gap between the stator and the rotor. In addition, the saturation effect could be observed at the current high values at the locations when the force curve trends change with the current at different gaps. The saturation currents I sat are found to be about 12, 10, and 8 A at the three gaps respectively, where the material saturation flux density B sat is reached. Figure (4): Magnetic Forces at 0.6 mm gap In case of merging the gap into oil, it could be observed experimentally that the presence of oil has a minor effect on changing the force to current relation. Actually, the force is slightly increased. Consequently, the same derived magetic model could be used in this case to simulate the magnetic actuator forces.

7 Figure (5): Magnetic Forces at 0.5 mm gap Figure (6): Magnetic Forces at 0.4 mm gap In order to characterize the actuator iron core magnetic properties, the material B- H curve is obtained from the experimental results. The curve is obtained by calculating the magnetic flux B and material permeability μ r,iron from the air experimental data using equations (4), and (7). The field intensity H is then obtained by the relation B = μ oμ r,iron H. The tested magnetic curve is plotted in figure (7). From the material curve, the material relative permeability in the linear zone is calculated from the slope and found to be 550. This value is important when equation (6) is used to model the actuator forces for purpose of control. In addition, the whole curve is inserted in the FEM to simulate the material linear and saturation zones.

8 Figure (7): Iron B-H curve The material hysterisis phenomena is also studied. The current is gradually increased and decreased during the test. Figure (8) illustrates the increasing and decreasing force curves for oil gap of 0.5 mm. It is clear that the increasing and decreasing curves are are almost identical especially in the linear zone of operation. Therefore, the material hysteresis effect could be neglected, which makes the actuator suitable for control due to the material linear behavior. Figure (8): Hysterisis effect at oil gap of 0.5 mm 6 CONCLUSIONS (1) Through this work, the concept of using a magnetic actuator in presence of oil accompanying journal bearing has proved validity. The oil has negligible effect on the magnetic force relation. In fact, the oil presence is favorable for the magnetic forces. (2) An analytical model and a finite element model have been developed for the magnetic actuator. Both show a satisfactory similarity with the experimental results. The analytical model could be efficiently used for purpose of control to model the relation between the force, current, and

9 gap. On the other hand, the finite element model showed the saturation effects and non-linear zone. (3) The actuator material magnetic characteristics have been identified by characterizing its relative permeability in the linear zone and limits of saturation. The iron B-H curve which characterizes the material is obtained from the experimental results. The hysteresis effect was also investigated and found to be negligible. This assures the linear behavior of the actuator material. Therefore, it could be efficiently used in linear control action. (4) Finally, this work is a step towards the definition of the Smart Integrated Bearing (SIB) aiming to develop a bearing able to provide a large load carrying capacity and controllability, by integrating journal bearing and magnetic actuator. 7 ACKNOWLEDGMENTS The authors are grateful to the support of the National Institute for Standards NIS. This research was funded by the Research, Development and Innovation Program (RDI), EU-Egypt Innovation Fund (/127781/M/ACT/EG). 8 REFERENCES [1] Schweitzer, G., 1998, "Magnetic bearings as a component of smart rotating machinery", Proceedings 5th International Conference on Rotor Dynamics IFToMM, Darmstadt, pp [2] Hathout, J.P., El-Shafei, A., Youssef, R., 1997, "Active control of multimode rotor-bearing systems using HSFDs", ASME Journal of Tribology, Vol. 119 Jan., pp [3] El-Shafei, A., 2002, "Active Control Algorithms for the control of rotor vibrations using hybrid squeeze film dampers", ASME Journal of Engineering for Gas Turbines and Power, Vol. 124, No. 3, pp [4] Kasarda, M.E.F., Mendoza H., Kirk R.G., Wicks A., 2004 "Reduction of subsynchronous vibrations in a single-disk rotor using an active magnetic damper", Mechanics Research Communications 31, pp [5] Carl R. Knospe, 2007, "Active magnetic bearings for machining applications", Control Engineering Practice 15, pp [6] Shuliang Lei, Alan Palazzolo, 2008, "Control of flexible rotor systems with active magnetic bearings", Journal of Sound and Vibration, Volume 314, Issues 1-2, 8 July, pp [7] A.S. Das, M.C. Nighil, J.K. Dutt, H. Irretier, 2008, "Vibration control and stability analysis of rotor-shaft system with electromagnetic exciters", Mechanism and Machine Theory, Volume 43, Issue 10, October, pp [8] Der Hagopian, J., Mahfoud, J., 2010, "Electromagnetic actuator design for the control of light structures", Smart Structures and Systems, Vol. 6, No.1. [9] El-Shafei, A., patent 7,836,601 [10] El-Shafei, A., and Dimitri, A.S., 2010, "Controlling Journal Bearing Instability Using Active Magnetic Bearing", ASME Journal of Engineering for Gas Turbine and Power, Vol. 132 Jan., No. 1. [11] El-Shafei, A., Tawfick, S.H., Raafat, M.S., Aziz, G.M., 2007, "Some Experiments on Oil whirl and Oil Whip", ASME Journal of Engineering for Gas Turbines and Power, Vol. 129, No. 1, pp [12] Schweitzer, Maslen, editors, 2009, "Magnetic Bearings".

10 [13] Maslen, E., 2000, "Magnetic Bearings", University of Virginia, Department of Mechanical, Aerospace, and Nuclear Engineering, Charlottesville, Virginia. [14] Quick Field version 5.9.