Structure study and performance analysis on the new laminated core type axial redundant magnetic bearing

Abstract

The continuous development of magnetic bearing in areas of aerospace, military, turbine power generation and flywheel energy storage has raised higher requirement for the reliability of magnetic bearing system. However, the integrated armco iron structure adopted by traditional concentric axial redundant magnetic bearing stator causes more eddy current loss and temperature rise when working and is not reliable. For the purpose of reducing eddy current loss and improving the reliability of magnetic bearing, this paper proposes a laminated core type axial redundant magnetic bearing. The comparison of dual-ring axial redundant magnetic bearing and laminated core type axial redundant magnetic bearing regarding their carrying capacity and temperature rise performance showed that the latter was better in an obvious way.

Keywords

Axial magnetic bearing laminated core redundancy temperature field eddy current loss

1 Introduction

A magnetic bearing is a high performance bearing that uses controllable electromagnetic force to suspend the rotor. Considering it causes less physical deterioration, energy consumption, noises and has long life, working with no lubrication and oil pollution, it has been listed into the preferred bearings for high-speed and high-precision rotary machinery [1–3].

The continuous development of magnetic bearing in flywheel energy storage, aerospace and artificial heart pump has raised higher requirement for the reliability of magnetic bearing system. So, how we can improve the reliability of magnetic bearing system is the key for application of magnetic bearing technology in advanced manufacturing equipment and core defense equipment. Currently, domestic and overseas scholars have conducted a series of studies on magnetic bearing in order to improve the reliability of magnetic bearing system. For the purpose of controlling aircraft engine, Lyons J.P. et al. designed a redundant structure for magnetic bearing with several back-up controllers [4]. Maslen E.Ha and C. Meeker David developed bias current linearization theory [5]. Storace A.F. proposed a redundant structure for concentric dual-ring axial magnetic bearing and a redundant method for radial magnetic bearing [6]. P. Schroder, a British scholar, developed a redundant design for faults of power amplifier and coil [7]. Wu Buzhou et al. studied how coupled eight-polar radial magnetic bearing uses bias current linearization and proposed a fault tolerance method for analyzing reconstruction of controller and further studied the simulation before and after reconstruction [8]. To date, major studies at home and abroad include: (1) On fault tolerance control of sensor [9–17], which studied the fault diagnosis and fault tolerance control of sensor of magnetic bearing system and believed that redundant technology of sensor is one of the effective ways in improving reliability of magnetic bearing; (2) On redundant controller that has faults [18–22], which analyzed familiar faults happened to magnetic bearing controller and studied design of redundant controller; (3) On fault tolerance control of actuator [23–32], which studied analytical redundant structure and fault tolerance control when power amplifier and coil fail.

As far as the current studies are concerned, introducing redundant design to magnetic bearing structure is a preferred method to improve the reliability of magnetic bearing. However, current studies on redundant magnetic bearing usually point to radial bearing and axial redundancy can hardly be found except for the redundancy scheme proposed by Storace A.F. in 1995 for concentric dual-ring axial magnetic bearing, and in addition to this, traditional concentric axial magnetic bearing stator uses integrated armco iron structure, which can give rise to higher eddy current loss and temperature rise when working and temperature rise in magnetic rotor system may exert great influence on the normal operation of the whole magnetic bearing and further damage the reliability of the system.

In this paper, the new-type axial redundant magnetic bearing is studied aiming at the redundancy and temperature rise of traditional concentric dual-loop axial magnetic bearing. Its stator core is stacked with silicon steel sheet that replaces the integral structure of stator of traditional concentric dual-loop axial magnetic bearing so as to greatly reduce the eddy current loss and temperature rise. Meanwhile, the dual-coil structure is employed to ensure that the laminated core type axial redundant magnetic bearing has the redundant capacity.

2 Physical design and mechanical property analysis of concentric-structure and laminated-structure axial redundant magnetic bearings

2.1 Structure of traditional concentric dual-loop axial redundant magnetic bearing

The structure of traditional concentric dual-loop axial magnetic bearing redundant structure is shown in Fig. 1. See Table 1 for the main dimension parameters.

2.2 Calculation of electromagnetic force of integral dual-loop redundant axial magnetic bearing

Modeling is built according to the structure parameters of integral dual-loop axial magnetic bearing in Table 1 and a finite element calculation of the electromagnetic field is made in ANSYS Workbench.

(1) Before losing efficacy

In normal operation of the two sets of coils, the concentric dual-loop axial redundant magnetic bearing has two electrification modes, that is, the same dual-loop current direction and opposite dual-loop current directions. The corresponding intensity distribution of magnetic induction is as shown in the Fig. 2.

With simulation analysis, it is known that for the two sets of coils for concentric dual-loop axial magnetic bearing, when the adjacent coils are electrified with the same-direction current, the magnetic field on inner-outer-loop pole will be strengthened, and the magnetic field of the consequent pole will be weakened. The great enhancement extent of inner-outer-loop magnetic field leads to a dramatical increase of the bearing carrying capacity. However, the magnetic field distribution of the whole stator pole is uneven with a relatively large differentiation, and the B value within the area of center pole is almost zero, that is, the area of consequent pole doesn’t work. Therefore, in the design process, the area of consequent pole can be designed intentionally, the smaller, the better. When the currents of adjacent coils are opposite, the magnetic field on inner-outer-loop pole weakens, and the magnetic field of consequent pole is strengthened. But the weakening degree of inner-outer-loop magnetic field is greater than the strengthened magnetic field of consequent pole, causing a sharp drop of the bearing carrying capacity. However, the magnetic field distribution of the integral integrated stator magnetic field is relatively even with a relatively small differentiation.

(2) After losing efficacy

When one set of coils loses efficacy, the simulation results of the electromagnetic field of concentric dual-loop axial redundant magnetic bearing are as shown in Fig. 3. As shown in the figure, When a set of coils losing efficacy, the B value distribution on the inner and outer poles and on the intermediate pole is not uniform, a pole appear easily lead in saturated condition.

2.3 Structure of laminated core type axial redundant magnetic bearing

From the above-mentioned simulation analysis, when the concentric dual-ring redundant axial magnetic bearing is electrified with the same-direction current, the area of consequent pole doesn’t work. Based on this, we design the laminated coretype axial magnetic bearing with the area of consequent pole removed. In this way, we can effectively utilize the pole area and coil space area in the case of a certain integral structure.

The laminated coretype axial redundant magnetic bearing, adopts a single-loop/two-set coil structure. Two sets of coils are placed inside and outside with the structure as shown in Fig. 4. See Table 2 for structure parameters. For the convenience of comparison, the volumes of concentric dual-loop axial redundant magnetic bearing and laminated coretype axial redundant magnetic bearing are set as the same.

2.4 Calculation of electromagnetic force of laminated coretype axial redundant magnetic bearing

Modeling is built according to the structure parameters of laminated coretype axial redundant magnetic bearing in Table 2 and a finite element calculation of the electromagnetic field is made in ANSYS Workbench.

(1) Before losing efficacy

In normal operation of the two sets of coils, as there is no consequent pole between the two sets of coil, there is only one electrifying mode for the coils of laminated coretype axial redundant magnetic bearing. When the two sets of coils are electrified with the same-direction current (I = 3 A), the calculation result is as shown in Fig. 5.

(2) After losing efficacy

When one set out of the two sets of coils for laminated coretype axial redundant magnetic bearing loses efficacy, the finite element calculation of the electromagnetic field shall be made in ANSYS Workbench. The results are as shown in Fig. 6.

When a set of coils loses efficacy, the magnetic flux density on both inner and outer poles decrease, and the declining degree is similar. Due to the structure characteristic, the magnetic flux density on the inner and outer poles are still not uniform, the magnetic flux density on the inner magnetic pole is greater than that on the outer pole. However, the magnetic flux density on each magnetic pole after the failure of the dual-loop axial redundant magnetic bearing are more uniform, which means the allowed compensate currents of lamination structure is larger than that of concentric structure, as well as the electromagnetic force after reconstruction under the premise of that one set of coils loses efficacy.

2.5 Comparative analysis of electromagnetic force

From the above calculation results, subject to the fact that the carrying capacity after redundancy compensation of coil failure can basically recover to the original capacity, a comparison is made on the electromagnetic force of integral dual-loop axial redundant magnetic bearing and laminated core type axial redundant magnetic bearing before and after failure as shown in Table 3. With the analysis of the above-mentioned two types of structures from the perspective of redundancy, it is found that if partial coils of axial magnetic bearing lose efficacy, the carrying capacity will lower at the moment so that certain performance margin can be reserved for coils in advance during design. When failure occurs, the carrying capacity can be improved through increasing coil current to ensure that the electromagnetic force generating from the redundant structure after failure in the electrification of compensating current will not change in comparison of that before failure, which is the design condition based on redundancy.

From the table the following findings are obtained:

(1) Under the circumstance of the same volume and current value, before and after losing efficacy, the mechanical property of laminated coretype axial redundant magnetic bearing is superior to integral dual-loop axial redundant magnetic bearing.

(2) When one set of coils loses efficacy, the electromagnetic force can be compensated through current compensation. After that, the mechanical property of laminated coretype axial redundant magnetic bearing is still superior to the integral dual-loop axial redundant magnetic bearing.

3 Analysis of the temperature field of axial redundant magnetic bearing

The analysis of thermal property of laminated coretype axial redundant magnetic bearing focuses on the calculation of the heat generation rate of heat source and distribution of temperature field. In the analysis on the temperature field of magnetic bearing, only the heat emission of copper loss and iron loss is considered [33].

3.1 Copper loss of laminated coretype axial redundant magnetic bearing

The computational formula of copper loss of laminated coretype axial redundant magnetic bearing is [3] $\begin{eqnarray}\displaystyle P_{cu}=I_{\max }^{2}r=I_{\max }^{2}\frac{{\rho}L}{S}, & & \displaystyle\end{eqnarray}$ (1) Where r is the resistance of coils; $\rho$ is the resistivity of coils; L is the total length of coils; S is the cross sectional area of lead.

3.2 Iron loss of laminated coretype axial redundant magnetic bearing

The iron loss of laminated coretype axial redundant magnetic bearing is mainly composed of magnetic hysteresis loss and eddy current loss. wherein, the magnetic hysteresis loss meets the following relational expressions [3,34] $\begin{eqnarray}\displaystyle {\Delta}P_{C}={\sigma}_{C}\left(\frac{f}{100}\frac{B_{a}}{10^{4}}\right)^{{\beta}}V_{\mathit{FE}}{\gamma}_{\mathit{FE}}, & & \displaystyle \nonumber\end{eqnarray}$ $\begin{eqnarray}\displaystyle B_{a}=\frac{{\mu}_{0}\mathit{NI}_{m}}{2x}, & & \displaystyle\end{eqnarray}$ (2) u _o: permeability of vacuum. N: turns per coil I _m: AC amplitude of coil current. x: air gap size.

Where B _a is the amplitude of alternating magnetic induction intensity; f is the frequency of high-frequency current output by the switch amplifier, according to the test, f = 20 kHz [35]; V _FE is the volume of core; 𝛾_FE is the proportion of materials, as for armco iron, assume 7.78 × 103; for silicon steel sheets, assume 7.65 × 103. σ_c is the coefficient of magnetic hysteresis loss, for silicon steel sheets, σ_c = 0.2; when Ba < 1, 𝛽 = 1.6.

As to the axial magnetic bearing of a concentric structure, the eddy current loss is [3,34] $\begin{eqnarray}\displaystyle {\Delta}P_{w}={\sigma}_{w}\left(\frac{f}{100}B_{a}\right)^{2}V_{\mathit{FE}}{\gamma}_{\mathit{FE}}, & & \displaystyle \nonumber\end{eqnarray}$ $\begin{eqnarray}\displaystyle B_{a}=\frac{{\mu}_{0}\mathit{NI}_{m}}{2x}, & & \displaystyle\end{eqnarray}$ (3) In the formula: σ_w is the coefficient of eddy-current loss, for armco iron, σ_w = 2; for silicon steel sheet, σ_w = 0.4;

It is observed from Formula (2) and (3) that, the magnetic hysteresis loss is far less than eddy current loss, less by 4 orders of magnitude at least. Therefore, magnetic hysteresis loss can be ignored in the calculation process of iron loss. $I_{\rm m}=0.138{\rm A}.$

3.3 Heat generation rate of laminated coretype axial redundant magnetic bearing

According to the definition of heat generation rate [36] $\begin{eqnarray}\displaystyle q=\frac{Q}{V}, & & \displaystyle\end{eqnarray}$ (4) Where Q is the heat source, that is, calorific value of the entir system; V is the volume of heat source. For coils, Q refers to the calorific value caused by copper loss during the operation of coils; as for bearing stator and rotor, Q refers to the calorific value caused by iron loss arising from the operation of stator and rotor of axial bearing.

3.4 Finite element calculation of the temperature field of laminated coretype axial magnetic bearing

The heat generation rate on different parts of each bearing is calculated according to formulas (1), (3) and (4) as shown in Table 4. The formulas (1), (3) and (4) are applicable to the pre-improved concentric-structure axial magnetic bearing and the laminated axial magnetic bearing improved.

According to the relevant temperature fields of magnetic bearing and the used materials analyzed in Literatures [34] and [36], the heat conductivity coefficient and convective heat transfer coefficient of different materials obtained are as shown in Table 5.

According to the data in Table 4 and Table 5, the ANSYS Workbench can be used to make a calculation of the temperature field on each bearings before and after losing efficacy to get the different integral temperature field distributions before and after losing efficacy as shown in Fig. 7.

The average temperatures of different magnetic bearing stators, rotors and coils on one side before and after losing efficacy as well as those after current compensation are measured separately. See Table 6 for the results (reserving one decimal only).

From the data of temperature field in Table 6 it is known that in case of the same current before losing efficacy the average temperature of all parts of the laminated coretype axial redundant magnetic bearing is around 63% of the temperature of integral dual-loop axial redundant bearing. In case of the same current after losing efficacy, the average temperature of all parts of laminated core type axial redundant magnetic bearing is around 79% of the concentric dual-ring redundant bearing temperature. In the case of the same compensating current, the average temperature of all parts of laminated core type axial redundant magnetic bearing is around 78% of the temperature of integral dual-loop redundant bearing. Therefore, the conclusion is reached that the temperature rise of laminated core type axial redundant magnetic bearing will be superior to that of the integral dual-loop axial redundant magnetic bearing.

4 Redundancy verification experiment of laminated axial redundant magnetic bearing

In order to prove the simulation validity of laminated core type axial redundant magnetic bearing and the relevant carrying capacity, based on relevant redundancy theories, an experiment is conducted to verify the reconstruction feasibility and validity of laminated core type axial magnetic bearing redundant structure under the circumstance of failure of partial coils as well as the reconstruction with electrification of different magnitudes of compensating current after failure via a type of laminated core type axial magnetic bearing win a specific structure size.

4.1 About the experimental facility

The experimental facility includes: stator of laminated core type axial redundant magnetic bearing, rotor of laminated core type axial redundant magnetic bearing, counterweight plate, bearing bar, eddy current sensor, sensor protection ring, power amplifier, dsPACE system, etc. The pictures of real objects of the specific experimental facilities are as shown in Figs 8 and 9.

In Fig. 8, the laminated core type axial redundant magnetic bearing stator part is composed of 8 pieces of silicon steel sheets of equal volume and size equidistantly distributed on the circle. Inside the stator are twined with two sets of coils of the same turns and wire diameter. The space under the stator is connected with the bearing bar and counterweight plate; the lower end of counterweight plate is eddy current sensor fixed onto theholder of sensor used for detection of axial displacement of magnetic bearing stator. Here, the electric eddy current displacement sensor is placed below the counterweight plate to detect the displacement of counterweight plate so as to indirectly detect the axial displacement of magnetic bearing stator, but it is not placed above the stator to directly detect the stator displacement. As the magnetic field generated by electric eddy current displacement sensor may interfere the that from the laminated magnetic bearing, thus affecting the test accuracy, it should be taken into consideration.

In Fig. 9, from left to right are power amplifier, dsPACE system and DC Regulated Power Supply etc. The DC Regulated Power Supply provides stable voltage to eddy current sensor, that is input into stator coils after processing by power amplifier. The axial displacement signals collected by displacement sensor are input into the power amplifier after processing by dsPACE system, that is, the output signals of dsPACE system are the input signals of power amplifier. In this way, a closed-loop control circuit is formed to constantly detect and adjust the axial position of laminated axial magnetic bearing to achieve a balance.

4.2 Suspension experiment of laminated core type axial magnetic bearing

4.2.1 Normal axial suspension experiment

The laminated core type axial magnetic bearing is composed of two sets of coils in total. For each coil, one loop of single power amplifier is needed for independent control. Hence, two loops of power amplifier are needed for simultaneous control. The specific connection and corresponding control modes are as shown in Fig. 10.

As shown in Fig. 10, the outer set of coils is connected to power amplifier 1, and the inner set is connected to power amplifier 2. After coils and power amplifier are connected, dsPACE system is used to conduct online adjustment and control.The rotor can be made to achieve equilibrium and the suspension by regulating PID parameters. The control block diagram of simulink program is as shown in the following Fig. 11.

It is observed from the control block diagram of simulink programs that the sensor parameters in equilibrium position are set as 0.3. As it is required to make a magnification of 10 times, the equilibrium position is 3 mm. The initial current is 2A. The control switch can control the switch between two sets of coils and one set of coils. When kzkg inputs a the numerical value greater than or equal to zero, two sets of coils operate normally. When the numerical value less than zero is input in kzkg, the power amplifier below will disconnect while the upper power amplifier can operate normally to realize the experimental objective of redundancy reconstruction. When one set of coils operates, the numerical value of compensation can be also changed to realize the redundancy reconstruction test electrified with different compensating currents after losing efficacy.

In normal fluctuation, the initial position of the stator is set at the maximum displacement deviating from the equilibrium position. PID parameters are constantly regulated to the stator back to the equilibrium position quickly. The final regulated PID parameters are: K _P = 34, K _I = 5, K _D = 4; The fluctuation displacement curve of the stator is as shown in Fig. 12.

It is observed from Fig. 12, that the stator returns to the equilibrium position quickly in normal fluctuation, and after transitory oscillations, the rotor starts to stabilize at the equilibrium position at about 6 s, when the equilibrium position is set around 0.3 with a relatively good stability.

It can be seen from Fig. 13 that the corresponding power amplifier current curve of two sets of coils are consistent in normal flucatuation, about 2.5 A.

4.2.2 Restruction experiment of different compensating currents after coil failure

After the magnetic bearing stabilizes suspension, one set of coils loses efficacy at certain time, and the following two methods can be used to make the magnetic bearing system to reconstruct: 1. After losing efficacy, no compensating current is added, but the electromagnetic suspension of the pole pair is increased with the automatic adjustment of the feedback control system so as to reach a stable suspension state again; 2. After failure of one set of coils, certain current is compensated to the other set of coils to increase the electromagnetic suspension of the pole pair so as to reach a stable suspension state again.

Case 1: After the magnetic bearing stabilizes suspension, one set of coils is made to lose efficacy lat certain time without adding compensating current, so that the electromagnetic suspension of the pole pair is increased through an automatic adjustment of the feedback control system to reach a stable suspension state again. Under such circumstance, the displacement chang curve of the stator and current change of two sets of coils are as shown in Figs 14 and 15.

It can be seen from Figs 14 and 15 that, after failure of one set of coil, if no compensating current is added to the other set of coils, due to the sudden decrease of electromagnetic suspension, the stator of laminated core type axial magnetic bearing may drop close to 0.8 mm, approaching the protection plane without collision, after the regulation for about 12 s, it returns to the equilibrium position. In addition, the current of coils without failure has a relatively large fluctuations. The maximum value has exceeded 7A before dropping to a stable value. So far, it indicates that the reconstruction experiment of new laminated core type axial magnetic bearing after losing efficacy is successful.

Case 2: after the magnetic bearing stabilizes suspension, one set of coils is made to fail at certain time, and certain current compensated to the other set of coils to increase the electromagnetic suspension of the pole pair to reach a stable suspension state again. Under such circumstance, the displacement chang curve of the stator and current change of two sets of coils are as shown in Fig. 16(a–h).

With the above experimental results, the change curves of redundancy reconstruction process under different compensating currents are compared (Fig. 17):

(1) By compensating different currents, the laminated core type axial magnetic stator can finally return to the equilibrium position, stabilize and suspend.

(2) By compensating different currents, as the downward fluctuation range of laminated core type axial magnetic stator varies, the larger the compensating current, the lower the downward fluctuation range of the stator, and the smaller the current fluctuation.

(3) After failure of coils, proper current can be proactively compensated to the laminated core type axial magnetic bearing coils. Compared with no increase of compensating current after failure, the system can realize faster reconstruction.

5 Conclusions

(1) Under the condition of the same volume, the mechanical property of laminated core type axial redundant magnetic bearing before and after losing efficacy is superior to integral dual-loop axial redundant magnetic bearing.

(2) Under the condition of the same volume, the heating emission of laminated core type axial redundant magnetic bearing before and after failure is superior to integral dual-loop axial redundant magnetic bearing.

(3) With regard to the laminated core type axial redundancy magnetic bearing in case of failure, the larger the compensating current, the smaller the downward fluctuation range of stator, and the smaller the current fluctuation. Proper current can be proactively compensated to the failed laminated core type axial redundancy magnetic bearing, so that the system can realize faster reconstruction.

Footnotes

Acknowledgements

The authors gratefully acknowledge the support of this research by the National Natural Science Foundation of China grants on “Research on stabilization mechanism and control strategies of vehicular magnetic-levitated flywheel rotor in reconfiguration process of supporting structure” (No. 51575411).

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