Structural design and performance analysis of a new type of axial magnetic bearings with multi-ring redundant structure in circular direction

Abstract

With the continuous development of magnetic bearings in aerospace and military, reactor turbine power generation, flywheel energy storage and other fields, the request for the reliability of magnetic bearing system becomes higher. In order to improve the reliability of the magnetic bearing, a novel axial magnetic bearing with multi rings in peripheral direction (AMB-MRC) is proposed. By studying the influence of rings number and current direction through coils on bearing capacity, as well as the method of redundant reconstruction and the property after reconstruction, the corresponding design criteria are proposed. The redundancy, bearing capacity and eddy current loss of the AMB-MRC compared with the existing AMB-MRR with 2 rings. The results show that the bearing capacity of proposed novel bearing is nearly equal to AMB-MRR with 2 rings when their volume is the same, but the redundancy of proposed novel bearing is better in improving the reliability of the magnetic bearing system.

Keywords

AMB-MRC bearing capacity redundancy temperature field eddy current loss

1. Introduction

With the properties of no contact, no mechanical abrasion and no lubrication, the magnetic bearing which can make the rotor be suspended by the controllable electromagnetic force, has a typical application in high-tech fields, such as turbine machinery, energy storage flywheel, machining with ultra-high speed and precision, aerospace, etc. For the advantages above all, the magnetic bearing has become one of the top choices in selecting supporting equipment for rotating machinery with high speed and high precision [1, 2, 3].

With the continuous development of magnetic bearings in aerospace and military, reactor turbine power generation, flywheel energy storage, artificial heart pumps and other fields, the requirement for the reliability of magnetic bearing system becomes higher. So how to improve the reliability of magnetic bearing system is the key problem to applying the magnetic bearing technology on advanced manufacturing equipment and national defense core equipment. At present, the fault tolerance method of the magnetic bearing has been carried out by the domestic and foreign scholars to improve the reliability of magnetic bearing system, and the redundant design of key components is the research focus. Lyons et al. designed magnetic bearing redundant structure with multiple spare controllers used to control the aero engine [4]. Maslen and Meeker proposed a theory of bias current linearization [5]. Storace proposed a redundant method of radial magnetic bearing where two pole pairs at 180 deg radial separation combined to create a single control axis. The stator core is segmented with nonmagnetic sections in order to minimize the magnetic coupling between adjacent pole pairs. Meanwhile, he also proposed a kind of concentric two ring axial magnetic bearing the redundant structure [6]. The British scholar Schroder did redundant design about power amplifier failure and coil failure. Research of the decentralized control and centralized control on radial magnetic bearing system, and the control performance of the decentralized control and centralized control is compared [7]. Wu et al. had a research on the 8-pole radial magnetic bearing with coupling by the method of bias current linearization. Then a fault-tolerant control method was proposed based on the controller reconstruction and the simulation on the states before and after the reconstruction was studied. The simulation results showed that this method had good performance of fault-tolerant [8]. In general, the main research includes:

Fault tolerant control for sensor faults [9, 10, 11, 12, 13, 14, 15, 16, 17]. It is proposed that the redundant technology of sensor is one of the effective ways to improve the reliability of magnetic bearing. The fault diagnosis and fault tolerant control of sensor in magnetic bearing system are also studied.

Redundant controllers for controller fault [18, 19, 20, 21, 22]. The typical fault forms of the magnetic bearing controller are described. Besides, the design of the redundant controller, including the redundant scheme of the digital controller, diagnosis and processing of fault and control algorithm design is also studied.

Fault tolerant control for actuators [23, 24, 25, 26, 27, 28, 29, 30, 31, 32]. Analytical redundancy structure design and fault-tolerant control of the magnetic suspension bearing actuator, including power amplifier and coil fault are studied.

As far as the present research situation, redundant structure design of the magnetic bearing is the primary method to improve the reliability of magnetic bearing. However, most of the current research on the redundancy of magnetic bearings is mainly directed to radial bearings. There are no other redundancy schemes in axial magnetic bearing except for the redundancy scheme proposed by Storace in 1995 for axial magnetic bearings with two-ring redundant structure in concentric direction. In this paper, a new type structure of axial magnetic bearings with multi-ring redundant structure in circular direction is proposed. The redundancy, bearing capacity and eddy current loss are compared with the traditional axial magnetic bearing without redundancy and axial magnetic bearings with two-ring redundant structure in concentric direction.

2. Performance of circular multi ring redundant axial magnetic bearings

2.1 Structural design

Magnetic bearing showed in Fig. 1 is called axial magnetic bearings with multi-ring redundant structure in circular direction [33], shortened for AMB-MRC. AMB-MRC is composed of 2 stators, a rotor and coil. The stators are made of electrical iron. There are several coil rings in each stator in the circular direction.

Table 1
Initial conditions for the design of AMB-MRC

External diameter (mm)	90
Maximum magnetic flux density designed (T)	1.2
Air gap (mm)	0.3
Current density (A/mm2)	5

Figure 1.

Structure of AMB-MRC.

Figure 2.

Schematic diagram of two redundant structure parameters.

Magnetic bearing showed in Fig. 2 is called axial magnetic bearings with multi-ring redundant structure in radial direction, shortened for AMB-MRR. In order to facilitate the comparison, structure parameters of AMB-MRC and AMB-MRR are optimized based on the initial conditions (shown in Table 1) under the condition of same volume. The optimized results are shown in Table 2.

Table 2

Structure parameters of AMB-MRC and AMB-MRR

	R0 (mm)	R1 (mm)	R2 (mm)	R3 (mm)	R4 (mm)	R5 (mm)	R6 (mm)	R7 (mm)	N
AMB-MRC-3	45	43.49	36.92	33.08	26.21	25			90
AMB-MRC-4	45	43.88	37.08	32.92	26.12	25			89
AMB-MRC-5	45	43.97	37.24	32.76	26.03	25			88
AMB-MRC-6	45	44.04	37.43	32.57	25.96	25			86
AMB-MRR-1	45	42.83	28.56	25					177
AMB-MRR-2	45	43.82	36.89	33.94	27.01	25			90
AMB-MRR-3	45	44.19	39.43	37.77	33.21	30.96	26.40	25	61

Where AMB-MRC-k means the number of rings of AMB-MRC is k, here k can be 3, 4, 5 and 6; AMB-MRR-j means the number of rings of AMB-MRR is j, here j can be 1, 2 and 3; N means number of coil turns. R0 $\sim$ R7 are shown in Fig. 2.

2.2 Bearing capacity analysis of AMB-MRC and AMB-MRR

2.2.1 Bearing capacity analysis of AMB-MRC

Finite element model is established according to the different stator structures and the optimization results of redundant structure in circular direction, and the simulation analysis is studied by ANSYS Workbench. Firstly, in the same kind of redundant structure, the value and direction of the current through the adjacent coils are the same. Then the electrifying mode is changed and the current is increased gradually. Meanwhile, the simulation results of electromagnetic force and the corresponding magnetic flux density B are recorded until the value of B is equal to the maximum magnetic flux density B ${}_{\max}$ . Finally, the other kinds of redundant structure are studied and repeat the above steps. The mechanical properties of axial magnetic bearing with circular redundant structure of different rings are analyzed.

Figure 3.

The magnetic field distribution of AMB-MRC in the same current.

For AMB-MRC, the magnetic flux density in internal magnetic pole weakens and the magnetic flux density in the junction of adjacent external magnetic poles strengthens due to coupling effect between adjacent poles when the direction of current in the adjacent coils is the same. The magnetic flux density in the junction of adjacent external magnetic poles, internal and external magnetic poles is smaller but very uniform. Therefore, bearing capacity of AMB-MRC is smaller when the direction of current in the adjacent coils is the same and the value of current is smaller. The magnetic flux density in internal magnetic pole is weakened, so magnetic saturation phenomenon is not easy to be occurred. With the increasing of the current, the bearing capacity will rise sharply (as shown in Fig. 3). When the value of current is a constant, the coupling effect of adjacent poles will gradually increase with the increasing of number of the rings, making the magnetic flux density corresponding smaller. Therefore, bearing capacity of bearing with higher number of rings is smaller than that of bearing with lower number of rings when the value of current is a constant. However, when the magnetic flux density of bearing with higher number of rings is equal to the magnetic flux density of bearing with lower number of rings, the former has higher bearing capacity (as shown in Fig. 4a and b).

Figure 4.

The mechanical properties comparison of AMB-MRC in the same direction current.

The magnetic flux density in internal magnetic pole strengthens and the magnetic flux density in the junction of adjacent external magnetic poles nearly decreases to zero because the direction of magnetic field generated by adjacent poles is inverse. As magnetic flux density of internal magnetic pole differs widely with that of external magnetic pole, it results in a higher bearing capacity of AMB-MRC when the direction of current in the adjacent coils is inverse. However, the magnetic flux density in the internal magnetic pole is relatively large, so magnetic saturation phenomenon is easy to be occurred. For AMB-MRC, with the increasing of current, the increasing amount of bearing capacity when the direction of current of adjacent poles is inverseis smaller than that when the direction of current of adjacent poles is the same (as shown in Fig. 5).

Figure 5.

The magnetic field distribution of AMB-MRC in the reverse current.

From Fig. 6, under this condition the initial bearing capacity is large. With the increase of the current, the magnetic flux density increases rapidly. When the current reaches about 4 A, the magnetic flux density in the magnetic pole has reached the designed maximum flux density B ${}_{\max}$ , and the bearing capacity is 461 N. Because of the magnetic saturation phenomenon, bearing capacity will not improve greatly although the current is still increasing.

Figure 6.

The mechanical properties comparison of AMB-MRC in the reverse current.

The number of rings in this kind of structure may be odd or even. When the direction of current in adjacent coils needs to be opposite, the bearing with the even number of rings can meet this demand, while the bearing with the even number of rings cannot. For example, when the number of rings is three, direction of current in two of the three coils has to be the same. Due to the effect of magnetic field coupling, distribution of the magnetic flux density in magnetic poles is non-uniform (as shown in Fig. 7). As the bearing capacity generated by each of the magnetic poles is different, it will result in rotator having a trend to reverse. It increases the difficulty of control. And the carrying capacity of the current is almost no difference between the current and the inverse-cis- or inverse-cis-inverse. When the direction of current in the adjacent coils is inverse, it is better not to use the odd number of ring in order to avoid the phenomenon of uneven distribution of the magnetic field.

Figure 7.

Magnetic field distribution of AMB-MRC-N (N represent odd number).

Comparing the mechanical properties under different electrifying mode and different number of rings, it can provide the basis for the choice according to different working environment. In order to obtain greater bearing capacity and avoid the magnetic saturation phenomenon, the direction of current in adjacent coils should be the same; while the hardware is limited but certain bearing capacity is still needed, the direction of current in adjacent coils may be inverse reducing power consumption. It is conducive to the safe operation of bearings. So in the actual working conditions we should choose different electrifying modes according to the actual requirements.

In general, with the increasing of number of rings bearing capacity decreased gradually, but the decline range is not wide. At the same time the magnetic coupling is also increasing, when magnetic flux density reaches to the designed maximum B ${}_{\text{max}}$ , carrying capacity for the bearing whose number of rings is six is maximum. But under that condition, the requirement for the hardware is the highest. The mechanical properties of bearing whose number of rings is six are the best incomprehensive consideration.

2.2.2 Bearing capacity analysis of AMB-MRR

Storace studied the structure and magnetic field distribution of AMB-MRR in 1995. On the basis of it, when the number of rings increases, the magnetic induction on the magnetic pole and the bearing capacity of the changes have been studied. The magnetic flux density of AMB-MRR at each magnetic pole is shown in Fig. 8.

Figure 8.

Comparison of magnetic flux density in magnetic poles of AMB-MRR when the value of the current is the same.

When number of rings is three, the layout of magnetic poles is also N-S-N-S when the direction of current in adjacent coils is the same. But the degree of coupling is smaller than that of the bearing whose number of rings is two. Compared with magnetic intensity of bearing whose ring number is two, the magnetic intensity in internal ring and the external ring has reduced due to the coupling effect. Magnetic intensity of the middle part between internal ring and the external ring only reduces a little rather than fall to zero. When the direction of current in adjacent coils is inverse, layout of magnetic poles is N-S-S-N. The magnetic intensity in each pole is weakened, and the decreasing range is similar making magnetic flux density of the 4 poles not large but very uniform. When the current in coils is small, the initial bearing capacity is small because the magnetic flux density in the poles is not large. Meanwhile, the magnetic saturation phenomenon is not easy to occur. With the increasing of the current, the bearing capacity of AMB-MRR with 3 rings will be greatly improved as long as the hardware can meet the demand. There are two other kinds of electrifying mode for AMB-MRR with 3 rings – anticlockwise-clockwise-clockwise and clockwise-clockwise-anticlockwise. The degree of coupling under these conditions is between strong coupling when the direction of current is the same and weak coupling when the direction of current is reverse. The varying law of bearing capacity is as same as the degree of coupling shown in Fig. 8b. So in actual projects, layout form of NSSN is chose as the general form in order to obtain greater bearing capacity before the magnetic saturation phenomenon occurs. Compared with the same redundant structure with 3 rings under the N-S-S-N layout form, bearing capacity of 2 rings is larger than that of 3 rings because of the larger magnetic flux density in 2 ring structure when the current through coils is small. The mechanical properties of AMB-MRR with 2 rings are better.

2.3 Comparison of the bearing capacity of AMB-MRC with traditional AMB-MRR in the same volume

Simulation of the traditional AMB-MRR in the same volume is studied by the Ansys Workbench. When the magnetic flux density reaches the designed maximum value, the bearing capacity is shown in Table 3. Bearing capacity of AMB-MRC in the same volume is shown in Table 4.

Table 3
Bearing capacity of AMB-MRR

Number of rings		Magnetic flux density (T)	Current (A)	Magnetic force (N)
1		1.2	3	512.75
2	The same	1.2	3	295.84
	Inverse	1.2	6	567.65
3	The same	1.2	3	212.91
	Inverse	1.2	9	425.23

Table 4

Bearing capacity of AMB-MRC

Number of rings		Magnetic flux density (T)	Current (A)	Magnetic force (N)
3	The same	1.2	7	537.22
	Inverse	1.2	4	341.20
4	The same	1.2	7	501.67
	Inverse	1.2	4	351.75
5	The same	1.2	7	475.36
	Inverse	1.2	4	330.61
6	The same	1.2	7.5	523.85
	Inverse	1.2	4	338.66

Comparing Tables 3 and 4, when the magnetic flux density reaches the designed B ${}_{\text{max}}$ for two kinds of redundant structure, the bearing capacity of the mhas no obvious difference. But it needs a higher hardware demand for traditional AMB-MRR.

2.4 Comparison of redundancy performance

In view of the above two types of redundancy from the point of view, when part of the coils of AMB fall in failure, the bearing capacity will decline. To achieve the fault-tolerant operation under the condition of that the bearing capacity is constant before and after failure, only increasing the number of rings is not enough and other measures must be adopted. As the bearing capacity of the magnetic bearing can be improved by increasing the current in the coils, so certain performance margin of coils can be took into account in the design. When failure occurs, the bearing capacity can be improved by increasing the current in the non-failure coils to guarantee that bearing capacity after failure is equal to that before failure. It is called the design condition based on redundancy.

According to standard that bearing capacity after failure is not less than the initial capacity, AMB-MRC with six rings and AMB-MRR with 2 rings having the best mechanical performance are analyzed. When the initial current is 3 A, bearing capacity of AMB-MRC with six rings after failure by compensating current are compared with bearing capacity before failure, and the simulation results are shown in Table 5; bearing capacity of AMB-MRR with 2 rings after failure by compensating current are compared with bearing capacity before failure, shown in Table 6.

Table 5
Comparison of bearing capacity of AMB-MRC before and after failure

Number of	Current value when direction of	Bearing	Current value when direction of	Bearing
poles under	the current through the adjacent	capacity/N	the current through the adjacent	capacity/N
failure	coils is the same/A		coils is inverse/A

0	3	125.10	3	247.71
2	3.3	131.56	3.8	259.88
3	3.6	131.40	4.5	258.80
4	4.3	136.14	5.4	250.66

Table 6

Comparison of bearing capacity of AMB-MRR before and after failure

Number of poles under failure	Current value when direction of the current through	Bearing capacity/N
	the adjacent coils is the same/A
0	3	295.84
1 (inner)	5	321.78
1 (external)	5	295.95

From the data in Tables 5 and 6, bearing capacity in each kind of failure modes can be returned to the initial value through compensating the corresponding current, which means that the two structures have a certain redundancy. AMB-MRC can maintain normal operation by compensating coil current as long as there is no contiguous three coils or more falling in failure. However, AMB-MRR with two rings can only maintain the normal work under the condition of that one of the two rings falls in failure. Therefore, AMB-MRC is superior to AMB-MRR in redundancy which improves the reliability of the system.

3. Analysis of temperature field of AMB-MRC and AMB-MRR

The temperature characteristics of sensors in magnetic bearing system will be influenced by value and distribution of temperature in the work environment. The measurement accuracy of displacement will be influenced by the temperature characteristics and control accuracy will be influenced by measurement accuracy of displacement. So it is necessary to have an analysis of thermal characteristics of axial magnetic bearings since calorific condition will have a great impact on fault tolerance ability and the reliability. Thermal analysis of the axial magnetic bearing mainly concentrates on heat source, heat generating rate and temperature change. The heat source of the axial magnetic bearing is mainly the heating of the coils energized (copper loss) and the heating of the iron core (iron loss). When analyzing the temperature field of the magnetic suspension bearing, only the copper loss and the iron loss are considered. In order to analyze the temperature field of magnetic bearings, heat generation rate of the stator, rotor and the coil need to be calculated.

3.1 Heat generating rate of axial magnetic bearing

According to the definition of the heat generation rate,

$\displaystyle q=\frac{Q}{V}.$ (1)

Where $Q$ is the calorific value of heat source; Vis volume of heat source. For coils, $Q$ refers to the calorific value caused by copper loss generated during the work of the coil; for stator and rotor, $Q$ refers to the calorific value caused by iron loss generated during the work of stator and rotor.

Heat generating rate of each part is calculated. The results are shown in Table 7.

Table 7

The heat generation rate of AMB-MRC and AMB-MRR

	The heat generation rate of coils	The heat generation rate of stator and rotor
AMB-MRC with 6 rings	4.98 $\times$ 104	3.69 $\times$ 106
AMB-MRR with 2 rings	4.86 $\times$ 104	2.01 $\times$ 106

3.2 Simulation analysis of temperature field

According to the heat generating rate data calculated, temperature field analysis of AMB-MRR with 2 rings and AMB-MRC with six rings is carried out using ANSYS Workbench software under rotor speed of 7200 r/min. The result is shown in Table 8.

Table 8
The results of temperature field analysis of AMB-MRR with 2 rings and AMB-MRC with 6 rings

	AMB-MRR with 2 rings	AMB-MRR with 2 rings	AMB-MRC with 6 rings
	when direction of the current	when direction of the current	when direction of the current
	through the adjacent coils is	through the adjacent coils	through the adjacent coils
	the same	is inverse	is the same
Current (A)	3	3	3
Average temperature	107.67	107.67	181.525
of the stator
Average temperature	109.635	109.635	187.485
of the rotor
Average temperature	26.42	26.42	24.817
of the coils

It can be known from Table 8 that the maximum temperature of two kinds of redundant structures appeared in the rotors. Current direction has no effect on temperature field. Stator and rotor temperature of AMB-MRC is higher than the average temperature of stator and rotor in AMB-MRR.

For AMB-MRC, the presence of wall in the stator results in reversal of magnetization in the rotor in rotation. Magnetization frequency increases with the increasing of number of rings resulting in the increase of eddy current loss of rotor. For example in AMB-MRC with six rings, the sequence of magnetic poles in stator structure is N-S-N-S-N-S-N-S and the rotor will be magnetized repeatedly 6 times when rotating 360 degree. So the magnetization frequency is 6 times of the rotation frequency. In order to reduce the eddy current loss, the walls should be removed in the design of the redundant structure of the axial magnetic bearing to avoid magnetization of the rotor in the rotation process.

Figure 9.

Stator structure of axial magnetic bearing with multi-ring redundant structure without walls.

Figure 10.

Comparison of bearing capacity of AMB-MRC without walls when direction of the current through the adjacent coils is the same.

It is known that the eddy current loss can be reduced by removing the sidewall. Since there is no sidewall, magnetic pole area is reduced and bearing capacity drops. But the rate of decline is not much, bearing capacity is an important indicator of magnetic bearing performance, the bearing capacity of the structure without sidewall is analyzed.

3.3 Structural design and stress analysis of AMB-MRC without walls

The design criterion of equal pole area is chosen for the design of the wall circumferential redundant axial magnetic bearing structure. The design of the stator ring section and the whole structure of the stator is shown in Fig. 9 [34].

Bearing capacity of the redundant axial magnetic bearings without walls is analyzed by ANSYS Workbench under the condition of that direction of current through the coils is inverse but the same current value. The results are in Figs 10 and 11.

Compared with the axial magnetic bearings with walls, current direction through the coils has a greater effect on coupling in axial magnetic bearings without walls. Area of the magnetic pole decreases as there are no walls which results in a certain degree of decline of bearing capacity, probably down about 5%, so, it results in obvious coupling between adjacent poles because of no walls. So the magnetic flux density is smaller compared with that of the structure with walls, and it is not easy for the phenomenon of magnetic saturation to occur. The bearing capacity can be improved by increasing current through coils.

Simulation analysis of temperature field of AMB-MRC with walls and without walls is carried out by the thermal analysis module of ANSYS Workbench. The results are shown in Table 9.

Table 9
Temperature field analysis results of AMB-MRC with 6 rings without walls and AMB-MRC with 6 rings with walls

	AMB-MRC with 6 rings without walls when	AMB-MRC with 6 rings with walls when
	direction of the current through the adjacent	direction of the current through the adjacent coils
	coils is the same	is the same
Current (A)	3	3
Average temperature	100.278	181.525
of the stator
Average temperature	103.89	187.485
of the rotor
Average temperature	24.817	24.817
of the coils

Figure 11.

Comparison of bearing capacity of AMB-MRC without walls when direction of the current through the adjacent coils is inverse.

The results show that the maximum temperature appears in the rotor, and the minimum temperature appears in the coils. Since there is no effect of remagnetization, the temperature of the stator and rotor in the sidewall structure is greatly reduced.

Table 10

Maximum temperature of stator and coils when magnetized

Rotating speed (r/min)	Maximum temperature of electric pure iron ( ${{}^{\circ}}$ C)
0	183.4
500	174.4
1000	156.7
1500	138.5
2000	125.6

Figure 12.

Experiment rig of simulating of the disk rotor when magnetized.

Considering the mechanical properties, redundancy and thermal properties comprehensively, the bearing capacity of structure without wall is smaller than that of structure with wall but the range of the decline is not large. But the overall temperature will not increase with the increasing of rotor speed as there is no remagnetization of the rotor which reduces the eddy current loss. Therefore, we can use AMB-MRC without walls to reduce the loss under the condition of losing part of bearing capacity.

4. Experimental measurement of temperature field of AMB-MRC with six rings

4.1 Experimental measurement of the temperature field of rotor under remagnetization

The theoretical analysis shows that the presence of wall in the stator results in reversal of magnetization in the rotor in rotation. Magnetization frequency increases with the increasing of number of rings resulting in the increase of eddy current loss of rotor. In order to prove the above theory, we experimentally verify the temperature field of the rotor and the rotor of the magnetized by simulating the experimental device which is magnetized by the disk rotor. Whether the rotor can be repeatedly magnetized can be controlled by changing the position of the core relative to the disc rotor. As shown in Fig. 12, when the current is flowing through the coil, the ends of the iron core will produce N pole and S pole. Different placement will make the disc rotor has been magnetized and not magnetized in two cases.

Table 11
Maximum temperature of stator and coils when magnetized after the removal of influence of wind speed

Rotating speed (r/min)	Maximum temperature of electric pure iron ( ${{}^{\circ}}$ C)
0	183.4
500	191.5
1000	199.6
1500	205.3
2000	214.3

Figure 13.

Maximum temperature of stator and coils after thermal equilibrium under different rotating speeds.

In order to analysis the influence of remagnetization in the rotor on the temperature field, the input current should be direct current when doing experiment. The distance between the stator and the rotor is equal to 1 mm; the diameter of coil is 0.56 mm; the number of coil turns is 64; resistor is 0.5 $\Omega$ ; and rotor speed can be adjusted respectively for 0, 500 r/min, 1000 r/min, 1500 r/min and 2000 r/min by frequency converter. Under the above mentioned conditions, the temperature field of rotor and coil is analyzed.

Experiment principle: As shown in Fig. 12, the stator is placed on the opposite to rotor along the horizontal direction when the rotating rotor is driven by the motor in a certain speed. The sequence of pole in the rotor is N-S. Rotor is magnetized repeatedly one time during a period of rotating.

Experimental steps: (1) Adjust the rotation speed of the motor for 0, 500 r/min, 1000 r/min, 1500 r/min and 2000 r/min; Adjust air gap between the stator and rotor to be 1 mm and current through the coil to be 0.5 A. (2) The temperature data of the coil, the stator and the rotor is collected by infrared thermal imager at a certain distance once every 2 minutes. When the temperature is almost constant, it means that the thermal equilibrium is reached. At this point the motor should be shut down and the input of the current should be stopped. (3) The collected data is analyzed by Smart view software.

The maximum temperature of the stator and coil measured at five different speeds when the thermal equilibrium is reached is shown in Fig. 13. The maximum temperature of stator and coil as the revolving speed increases is shown in Table 10.

It can be seen from Fig. 13 and Table 10 that the maximum temperature of the stator and the coil gradually decreases with the gradual increase of speed. Heat transfer between the stator and coil and the surrounding air increases because of the rotor’s increasing speed resulting part of the heat exchanging to the air. It may have some disturbance on the analysis of the influence of rotor magnetization on temperature change. In order to eliminate the disturbance, the influence of the rotor speed on the heat transfer is found by the stator and coil temperature cooling curves at different speeds. The maximum temperature of the stator and coil after the removal of influence of wind speed is obtained that is shown in Table 11.

Table 12

Maximum temperature of stator and coils when not magnetized after the removal of influence of wind speed

Revolving speed (r/min)	Maximum temperature of stator and coils when not magnetized
0	183.4
500	186.7
1000	193.3
1500	201.6
2000	203.4

Figure 14.

Experiment rig of simulating of disk rotor when not magnetized.

It can be seen from the Tables 10 and 11 the maximum temperature of stator and coil will increase with the increase of speed after the removal of influence of wind speed on temperature of stator and coil. Due to the increase of the revolving speed the remagnetization frequency of the rotor will be increased. It makes the iron loss significantly increase which leads to the increase of the temperature in the stator and coil.

4.2 Experimental measurement of temperature field of rotor without repeated magnetization

Experimental device that simulatesthe rotorwithout repeated magnetization is shownin Fig. 14. When U-shaped core is placed opposite the rotor along the vertical direction, rotor driven by the motor is rotating in a certain speed. The sequence of pole is always N in the circle whose radius is R where having no remagnetizing.

The experiment was carried out by using the experimental device shown in Fig. 14. The position of the core is adjusted to appropriate position. Excluding the influence of wind speed on the temperature of stator and coil, the temperature variation of stator and coil is shown in Table 12 when the rotor is not magnetized.

It can be seen from the table that after removing of effect of wind speed the maximum temperature of the stator and coil has no significant change when the rotor has not been repeated magnetized with the increase of speed. Although the revolving speed increases, the iron loss will not increase because the rotor has not been repeated magnetization. Therefore, the temperature will not change significantly.

From the above experimental results, the existence of wall structure makes the rotor of the six rings redundant axial magnetic bearing be repeatedly magnetized in the rotation process, resulting in a obvious increase in the overall temperature with the increase of the revolving speed. This structure in the design to the six ring redundant axial magnetic bearing stator should be optimized by the removal of the wall. The simulation result of the redundant axial magnetic bearing without wall shows that the overall temperature in the process of the rotor’s rotation will not change, and is lower than the temperature in six redundant ring axial magnetic bearing with wall structure.

5. Conclusions

Bearing capacity of AMB-MRC is nearly equal to bearing capacity of AMB-MRR with 2 rings but the redundancy of the former structure is better than that of the latter structure when their volume and magnetic flux density are the same, AMB-MRC can improve the reliability of the system.

The distribution of magnetic field is more uniform and the magnetic flux density value B is smaller when the sequence of magnetic poles is N-S-S-N for both of the two kinds of structures. Therefore, bearing capacity of the magnetic bearing is the better.

Through the analysis of the temperature field, it is known that the average temperature of AMB-MRC with wall structure is higher than the average temperature of AMB-MRR with two rings.

Although bearing capacity of magnetic bearing without wall structure has a small degree of decline, magnetic saturation phenomenon is not easy to occur. The bearing capacity of magnetic bearing can be increased by increasing the current through coils, probably down about 5%. The eddy current loss and temperature rise effect in AMB-MRC without walls decrease because of having no repeated magnetization.

Footnotes

Acknowledgments

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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Structural design and performance analysis of a new type of axial magnetic bearings with multi-ring redundant structure in circular direction

Abstract

Keywords

1. Introduction

2. Performance of circular multi ring redundant axial magnetic bearings

2.1 Structural design

Table 1 Initial conditions for the design of AMB-MRC

2.2.1 Bearing capacity analysis of AMB-MRC

Table 3 Bearing capacity of AMB-MRR

Table 5 Comparison of bearing capacity of AMB-MRC before and after failure

3.1 Heat generating rate of axial magnetic bearing

Table 8 The results of temperature field analysis of AMB-MRR with 2 rings and AMB-MRC with 6 rings

Table 9 Temperature field analysis results of AMB-MRC with 6 rings without walls and AMB-MRC with 6 rings with walls

4.1 Experimental measurement of the temperature field of rotor under remagnetization

Table 11 Maximum temperature of stator and coils when magnetized after the removal of influence of wind speed

5. Conclusions

Footnotes

Acknowledgments

References

Table 1
Initial conditions for the design of AMB-MRC

Table 3
Bearing capacity of AMB-MRR

Table 5
Comparison of bearing capacity of AMB-MRC before and after failure

Table 8
The results of temperature field analysis of AMB-MRR with 2 rings and AMB-MRC with 6 rings

Table 9
Temperature field analysis results of AMB-MRC with 6 rings without walls and AMB-MRC with 6 rings with walls

Table 11
Maximum temperature of stator and coils when magnetized after the removal of influence of wind speed