Temperature Rise and Thermal Deformation of Magnetic Pole of MLDSB under Multiple Physical Field Coupling

: The thermal deformation of magnetic poles caused by the heat loss of the coils of Magnetic Liquid Double Suspension Bearing (MLDSB) can reduced the gap between magnetic poles and magnetic sleeve, and the probability and degree of impact-rub can be increased in the working process of MLDSB. And the coatings of magnetic poles and magnetic sleeve can be worn overly, and the operation stability and service life of MLDSB will be reduced severely. The thermal deformation of magnetic poles can be affected by the material property of magnetic pole, the electric current of the coils, and the cooling effect of the lubricants and so on, so it belongs to the multiple 1 physical field coupling. Therefore, the flow-solid-thermal coupled mathematics model of MLDSB is established and solved with ANSYS in this paper, and the distribution law of flow field of the magnetic pole is explored. The transfer path and distribution principles of heat loss are revealed and the distribution law of temperature rise and thermal deformation of magnetic pole in different operating conditions are explored. The results indicate that the temperature rise and thermal deformation of the stator is symmetrically distributed in the center, it gradually increase from the outside to the center, and the thermal deformation near the corner of magnetic pole is largest. The most heat loss can be taken away by the lubricants under the condition of heat balance. The thermal deformation of magnetic pole can increase linearly as the current gradually increase, and the stress is concentrated in the threaded hole and magnetic pole. The thermal deformation decreases linearly as the inlet pressure of the lubricants gradually increase. The PIV results of flow trace are basically consistent with the simulation results. The research in this paper can provide the theoretical reference for the structural design and the optimization of MLDSB.


Introduction
The hydrostatic bearing is introduced into the magnetic suspension to form Magnetic Liquid Double Suspension Bearing (MLDSB). MLDSB is mainly supported by electromagnetic suspension and assisted by hydrostatic supporting, and then its bearing capacity and stiffness can be greatly improved. It's suitable for the occasions of medium speed, heavy load [1][2] .
MLDSB is composed of bracket, motor, coupling, multi-diameter shaft, journal bearing unit, axial bearing unit, journal loading motor, axial loading motor and so on as Fig.1. can form between two adjacent magnetic poles and the rotor, and then electromagnetic suspension force will produce. There is inlet hole in the magnetic pole, and the end face of magnetic pole is the hydrostatic bearing face.
The hydraulic resistance can form when the lubricant flows through the gap between magnetic sleeve and magnetic pole, and then the hydrostatic force will produce in the end face of magnetic pole [3][4] . Professor HU [5] researched experimentally the temperature field and the distribution law of radial magnetic suspension bearing.
Professor WANG [6] calculated the heat loss of heavy load magnetic bearing in the energized state with Maxwell and then studied the temperature field distribution of the magnetic bearing by using Workbench software.
Professor YANG [7]  Professor ZHANG [8] analyzed the temperature field of solid thrust electromagnetic bearing by using the software Maxwell 2D in order to keep the heat balance of the bearing system, reduce the eddy current loss, improve the temperature rise characteristics and the service life.
Professor XIE [9] designed the homopolar and heteropolar radial magnetic suspension bearings with the same performance parameters which was applied to the magnetic suspension bearing-rotor test system, and analyzed the effect on the support loss under different structures and current control models.
Professor LIU [10] analyzed the magnetic field of the rotor of magnetic bearing with yoshimoto's radial magnetic suspension bearing model under the assumption of the linear magnetic permeability. Then the eddy-current loss of the rotor was estimated under the constant angular velocity harmonic magneto motive force, and the curve of the eddy-current loss change with rotational speed and the conductivity of rotor material are obtained.
Professor YANG [11] summarized the calculation methods of copper loss, iron loss and wind loss of active magnetic bearing at high speed, and gave the applicable range of the corresponding models.

Meshing and boundary condition
The design parameters and material properties of MLDSB are shown in Tab [12] .
(1) Screw threads on inlet and outlet are ignored.
(3) Shaft shoulder on the rotor is ignored.
(4) End cover is ignored, and the contact face between lubricant and air is adiabatic surface. is automatically solved in FLUENT [13,14] . The heat transfer surface of MLDSB is shown as Fig.6. The heating loss of the coil is calculated as Eq.1 [15] . The heating power of single coil is 1.47 W when the current is 1.7 A, and then heat generation rate is 824 KW/m 3 .
(2) Heat transfer between rotor and air When the rotor rotates, the convective heat transfer coefficient between the rotor end and air can be calculated as follows [16] : Where h1--Heat transfer coefficient between rotor and air, W/(m 2 ·℃); u--Linear velocity of rotation axis, m/s; r--Rotation radius, m; n--Rotation speed of rotor, r/min; The heat transfer coefficient between the rotor and air is h1= 22.66 W/(m 2 ·℃) when the rotation speed is n=1000 r/min.

(3) Heat transfer between stator, lubricant and air
The heat transfer between stator and air is the combined form of natural convection and radiation heat transfer. According to Reference [17], the heat transfer coefficient between rotor and air is h2=9.7 W/(m 2 ·℃).

Temperature rise and thermal deformation of MLDSB
According to the parameters in Tab.1 and Tab.2, the heat loss of the coils in Eq.2 is taken as the heat source of MLDSB in order to simulate the fluid-solid heat coupling of bearing system with ANSYS software. The boundary conditions can be shown as follows: Current is 1.7 A, pressure is 1.0 MPa, environment and lubricant temperature is 25℃.

Analysis of bearing temperature field
The temperature of MLDSB is distributed symmetrically in the center. The largest temperature rise occurs near the coil and magnetic pole, and it decreases to the environmental temperature along the radius direction as Fig.7. As the heat transfer of the outlet, forced fluid convection is better than natural convection, so the temperature of the outlet is slightly lower than the other parts.

Heat distribution law of coil
The heat transfer rates of fluid-solid surface and solid-solid surface are extracted and the distribution rule of coil heat loss is presented as Fig.12. Therefore, as the maximum heat dissipation path, the lubricant can absorb 11.51 W heat loss (97.9%) of the coil while the others are absorbed by air.

Thermal deformation analysis of stator
The thermal deformation of the stator can be presented as Fig.13.

Thermal stress analysis of stator
The thermal stress of the stator is presented as Fig.15.

Effect of operation parameter on thermal deformation of magnetic pole 4.1 Effect of current on temperature
The temperature of each part of MLDSB is presented as the current increases gradually as Fig.16.

Effect of current on heat distribution of coil
The heat transfer rates between coil/lubricant and

Effect of pressure on temperature of magnetic pole
As the input pressure increases successively, temperature of MLDSB can be shown as Fig.18.

Effect of pressure on heat distribution of coil
As the inlet pressure increases successively, the ratio of heat transfer rate between coil/lubricant and coil/stator can be shown as Fig.19.

PIV measure system
PIV measure system is composed of pulse transmitter, light arm, CCD camera, synchronizer, frame receiver, tracer particle system, frame trap, simulation software and so on [18] , and its principle and connected relation are respectively shown as Fig.21 and Fig.22.

Lubricant Supply System of MLDSB
For the sake of observing the position of the tracing particles [19][20] , the water is taken as the lubricant of PIV measure system. The lubricant supply system is composed of pump, flow gauge, throttle valve, pressure gauge, water tank and so on as Fig.23. (3) Pressure gauge, range: 0.02~0.6 MPa.

Model of journal bearing unit
Model of journal bearing unit is composed of stator (organic glass), skeleton seal, rotor (organic glass), end cap (organic glass), magnetic sleeve (organic glass), cover (organic glass) and so on as Fig.24.

Conclusion
(1) The temperature rise and thermal deformation of the stator is symmetrically distributed in the center and gradually increase from the outside to the center, and then the thermal deformation near the corner of magnetic pole is largest. (2) The most heat loss can be taken away by the lubricants under the condition of heat balance. (3) As the current increases, the temperature of coils increase, the cooling efficiency decreases, and the thermal deformation of magnetic pole increases linearly, and the stress is concentrated in the threaded hole and the middle of the magnetic pole. (4) As the inlet pressure increases, the cooling efficiency increases and the temperature rise and thermal deformation of magnetic pole can be decreases.

Availability of data and materials
The datasets supporting the conclusions of this article are included within the article.