Load Carrying Capacity Enhancing Design and Lubrication Investigation of the Magnetic-Water Double Suspension Elastic Support Thrust Bearing

: Aiming at the problem that the traditional water-lubricated bearing cannot carry the heavy load and adapt to the constantly changing operating conditions for the high-power Rim Driven Thruster (RDT), the principle structure of the Magnetic Water-double-suspension Elastic-support Thrust Bearing (MWETB) is designed and the optimal structure parameters of the bearing are selected using simulation. To demonstrate the reliability of the MWETB under the RDTs’ actual working conditions, performance tests, which include the magnetic ﬂux density, magnetic force, and lubrication performance, are carried out. The simulation and experimental results indicate that the optimal offset ratios are in two intervals, and the magnetic alignment and sheath materials have a great effect on the load reduction. The load-carrying force has obvious zoning characteristics with the change in bearing clearance. Besides, compared with the water-lubricated thrust bearings, the MWETB has advantages in terms of minimum ﬁlm thickness and friction coefﬁcient.


Introduction
To adapt to the global trend of energy-saving, green, and comfortable technology, the non-transmitted conversion of electrical to mechanical energy using means of direct electric drive is an important development direction for energy and power equipment [1].A kind of highly integrated direct drive equipment called Rim-driven thruster (RDT) has been developed in the marine field, which integrates a permanent magnet motor, propellers, and several bearings [2][3][4].Compared with traditional mechanical propulsion, the RDT has significant advantages in terms of high power density, high system efficiency, low vibration and noise, and small cabin space occupation [5,6].
Some small RDT prototypes choose rolling bearings to support the propeller thrust.Hiseh et al. [7] manufactured a 0.5 kW RDT with rolling ball bearings embedded in the duct.However, the actual rotational speed at rated voltage was only 83.3% of the designed speed due to the bearing friction.Richardson et al. [8] conducted a 5 kW RDT prototype.The test showed that the measured friction power consumption was 1.5 kW, and the rolling bearing tends to wear easily in a sediment environment.Therefore, water-lubricated sliding bearings may be the appropriate choice for RDTs.The power of large ships' RDTs is much greater than 1 MW; research shows that the water-lubricated thrust bearing (WTB) is one of the bottlenecks of RDTs' power breaking to the MW level [9].The WTBs of RDTs operate at heavy loads and low viscosity [10], which often leads to lubrication failure and abnormal wear of water-lubricated bearings [11][12][13][14].Besides, in order to adapt to the change in ship speed, the RDTs' rotational speed changes frequently, the traditional fixed-pad WTB cannot continue to work at the optimal design point, and the bearing performance deteriorates sharply when the slope or step of the pad are worn out [15].The unsteady force and impact generated by the motor and propeller near the bearings will also cause abnormal friction, vibration, and noise [16].In this case, it is of significance to conduct research on innovative schemes and mechanisms of low-speed and heavy-load WTBs to promote the development of high-power RDTs.
The sandwich structure [17,18], which is jointly carried by the liquid film force and magnetic force, provides an idea for the design of the RDT bearing.Bekinal et al. [19] installed a permanent magnetic bearing between two radial foil bearings to improve highspeed stability.However, the separated magnetic-fluid combination scheme is complex and requires a large installation space.Samanta et al. [20] embedded permanent magnetic blocks in an aluminum bearing ring to form a magnetic-liquid double suspension radial bearing.Test results showed that this solution can improve load-carrying capacity and stability.Zhao et al. [21] innovatively integrated electromagnetic and hydrostatic suspension in one bearing to improve the stability of the shaft system.Xu et al. [22,23] put forward an idea of combining superconducting magnetic force with liquid film force by using the natural low-temperature environment of rocket engine turbine pumps and designed schemes for combining superconducting magnetic force with hydrodynamic force and hydrostatic force, respectively.These studies have confirmed the feasibility of magneticliquid double suspension.However, simple unidirectional magnetization schemes result in a small magnetic force, which can still not meet the requirements of a high-power RDT's large load-carrying capacity.
In summary, the bearing schemes reported at present mainly focus on low-power RDTs.This paper intends to propose a magnetic water double suspension elastic-supported thrust Bearing (MWETB), which utilizes the water film and permanent magnetic force to improve the bearing capacity.Simulation and optimal parameter selection of the MWETB are confronted with difficulties: in order to share the load, the magnetic force needs to be excavated as much as possible, and the magnetic and fluid fields must be coordinated.Thus, separate simulations are carried out according to the characteristics of MWETB.

The Structural Characteristics of the MWETB 2.1. The Geometry of the MWETB
The geometry of the MWETB is shown in Figure 1.The bearing consists of thrust pads and a thrust collar in which several arranged fan-shaped magnets are embedded.The working layers of the pads and collar are made of polymer and metallic materials, respectively.Friction occurs on those two surfaces to achieve hydrodynamic lubrication.The pads connect the rubber cushion to the support ring by means of dowels.Through which the pads could tilt in radial and circumferential directions under the dynamic pressure.

The Alignment of Magnets
Magnets are filled in the sheaths of the thrust collar and pads, whose combination scheme has a great influence on magnetic shedding [15].As shown in Figure 2a, each pad is composed of six fan-shaped magnets.As for the thrust collar, three magnets are com-

The Alignment of Magnets
Magnets are filled in the sheaths of the thrust collar and pads, whose combination scheme has a great influence on magnetic shedding [15].As shown in Figure 2a, each pad is composed of six fan-shaped magnets.As for the thrust collar, three magnets are combined into one group, and thirty groups are arranged along the circumference.Among them, m t and m p are the thicknesses of the magnetics in the thrust collar and pad, respectively.r ti and r pi are the inner radii of the magnets in the thrust collar and pad, respectively.The red arrow indicates the direction of the magnetic induction line inside the magnet, from the S pole to the N pole.

The Alignment of Magnets
Magnets are filled in the sheaths of the thrust collar and pads, whose combination scheme has a great influence on magnetic shedding [15].As shown in Figure 2a, each pad is composed of six fan-shaped magnets.As for the thrust collar, three magnets are combined into one group, and thirty groups are arranged along the circumference.Among them, mt and mp are the thicknesses of the magnetics in the thrust collar and pad, respectively.rti and rpi are the inner radii of the magnets in the thrust collar and pad, respectively.The red arrow indicates the direction of the magnetic induction line inside the magnet, from the S pole to the N pole.

Load Carrying Capacity Enhancing Design
In order to meet the high power requirement of RDTs, it is of great significance to design the optimal structure for load reduction.The MWETB can be regarded as a combination of magnetic and elastic-support bearings, which means it can be separated in the optimization of the structure.In this case, the load-carrying force of the bearing is the sum of the magnetic and water film forces.By applying the magnetic force as well as the film force into the control equation [24,25], the load-carrying capacity of the bearing can be obtained.

Load Carrying Capacity Enhancing Design
In order to meet the high power requirement of RDTs, it is of great significance to design the optimal structure for load reduction.The MWETB can be regarded as a combination of magnetic and elastic-support bearings, which means it can be separated in the optimization of the structure.In this case, the load-carrying force of the bearing is the sum of the magnetic and water film forces.By applying the magnetic force as well as the film force into the control equation [24,25], the load-carrying capacity of the bearing can be obtained.

Numerical Simulation Model
Under the action of non-uniform pressure, the pad moves in three degrees of freedom: axial movement, radial, and circumferential tilts around the virtual pivot, which leads to uneven deformation of the rubber cushion [26,27], as shown in Figure 3.The film thickness h z of the virtual pivot can be seen as the distance between the two planes.Suppose the intersection lines of the reference and pad planes are x-axis and y-axis, respectively.The circumferential and radial tilt angles around the virtual pivot are β p and γ p ; θ e is the pad angle.
It is assumed that a slight tilt angle has no effect on the distribution of the magnetic force; the effect of the magnetic moment M m is not considered.The conditions required for the pad to reach an equilibrium state are as follows: where M wx and M wy are the tilting moments of the pad along the x-axis and y-axis produced using water film pressure, respectively; M rx and M ry are the restoring moments of the rubber along the x-axis and y-axis produced using the distributed rubber cushion stress, respectively.

Numerical Simulation Model
Under the action of non-uniform pressure, the pad moves in three degrees of freedom: axial movement, radial, and circumferential tilts around the virtual pivot, which leads to uneven deformation of the rubber cushion [26,27], as shown in Figure 3.The film thickness hz of the virtual pivot can be seen as the distance between the two planes.Suppose the intersection lines of the reference and pad planes are x-axis and y-axis, respectively.The circumferential and radial tilt angles around the virtual pivot are βp and γp; θe is the pad angle.It is assumed that a slight tilt angle has no effect on the distribution of the magnetic force; the effect of the magnetic moment Mm is not considered.The conditions required for the pad to reach an equilibrium state are as follows: where Mwx and Mwy are the tilting moments of the pad along the x-axis and y-axis produced using water film pressure, respectively; Mrx and Mry are the restoring moments of the rubber along the x-axis and y-axis produced using the distributed rubber cushion stress, respectively.

Fluid field model
The Reynolds equation, Energy equation, and the viscosity-temperature equation of water film are as Equations ( 2)- (5), respectively [25]:  (3) where the position of h z is (r e , θ e ); r and θ are the coordinate values in the circumferential and radial directions, respectively; δ (r, θ) is the deformation of the pad's working layer, which can be obtained using the Finite Element Method (FEM); p is water pressure.h is water film thickness.ω is the angular velocity of the thrust collar.T is the water temperature.ρ is water density.C p is the specific heat of water.µ 0 is the water viscosity at inlet temperature t 0 .β is the temperature coefficient.Boundary conditions: where Γ is the boundary of the pad; Γ 1 is the rupture boundary of the water film.

Magnetic field model
The classical description of a magnetic field is Maxwell's equation system, which is represented using a potential function.The homogeneous wave equation satisfied using the solution of the static magnetic field and eddy current field is as follows: where H is the magnetic field strength; ε is the dielectric constant of the medium; µ is the permeability of the medium; σ is the conductivity of the medium; j is the magnetic standard position.
The step-by-step iterative technique employed for numerical simulation is illustrated in Figure 4.The static parameters of the rubber cushion and magnetic field and the deformation of the pad's working layer are solved using the Finite Element Method (FEM) [28][29][30][31].By applying the magnetic force as well as the rubber elastic force and moment into the fluid governing equation, the static parameters of the fluid field are solved using the Finite Difference Method (FDM) [32][33][34].When the convergence condition is reached, the model is solved to obtain the load-carrying characteristics of the MWETB.According to Ref. [11], the optimal rubber offset ratios of bearings are independent of rotational speed and specific pressure.Taking the rotational speed of 1000 r/min and specific pressure of 0.1 MPa as an example, simulations on the minimum film thickness of

Optimal Offset Rations and Pad Angles
According to Ref. [11], the optimal rubber offset ratios of bearings are independent of rotational speed and specific pressure.Taking the rotational speed of 1000 r/min and specific pressure of 0.1 MPa as an example, simulations on the minimum film thickness of different offset ratios and pad angles are carried out.The results for the optimal offset ratios of the rubber cushion are shown in Figure 5a, where E c and E r are the offset ratios in the circumferential and radial directions of the rubber relating to the pad, respectively.Taking the offset rations with larger film thickness as the optimal offset ratios, which are in two intervals: E r = 0.475~0.48,E c = 0.595~0.60 and E r = 0.48~0.495,E c = 0.605~0.62.The deformation of the pad's working layer considered in the simulation results in different optimal offset ratios with Ref. [11].The area of interval 2 is larger than that of interval 1, which indicates that the error tolerance rate of the offset ratios in interval 2 is higher in the actual manufacturing process.
Figure 5b presents the minimum and virtual pivot film thickness diagram of the bearing at different pad angles with E r = 0.485, E c = 0.615.There is a peak of minimum film thickness at the pad angles of 25 • , 26 • , and 27 • , and the values are almost the same, which is consistent with the tendency of the virtual pivot film thickness, and the working conditions are the same.Therefore, those pad angles should be taken into account during the design process.
Lubricants 2023, 11, x FOR PEER REVIEW 7 conditions are the same.Therefore, those pad angles should be taken into account d the design process.

Optimal Magnetic Alignment
To determine the optimal magnetic alignment of the MWETB, the simulation o magnetic force of three different arrays is carried out.The main structural paramet the bearing are listed in Table 1.The gaps between the magnets are equal to the su the bearing clearance and the thickness of the working layers.Ignoring the effect of s material, the variation of magnetic force with the bearing clearance is shown in Figu When the clearance is less than 5 mm, the magnetic force generated using the Ha array is the largest, and the Linear array is the smallest.With the clearance increasin magnetic force tends to be similar.Interestingly, the change rates of the magnetic generated using the Halbach and Simple array are much larger than those of the L array.It is indicated that the convergence effect of these two arrays on the magnetic is limited to the bearing clearance.As shown in Figure 6b, when the WTB works in no operating conditions (the bearing clearance is 0~100 µm), the change rate of magnetic generated using the Halbach array is only 1.48%.Therefore, the Halbach array is th timal magnetic alignment for the MWETB.

Optimal Magnetic Alignment
To determine the optimal magnetic alignment of the MWETB, the simulation of the magnetic force of three different arrays is carried out.The main structural parameters of the bearing are listed in Table 1.The gaps between the magnets are equal to the sum of the bearing clearance and the thickness of the working layers.Ignoring the effect of sheath material, the variation of magnetic force with the bearing clearance is shown in Figure 6a.When the clearance is less than 5 mm, the magnetic force generated using the Halbach array is the largest, and the Linear array is the smallest.With the clearance increasing, the magnetic force tends to be similar.Interestingly, the change rates of the magnetic force generated using the Halbach and Simple array are much larger than those of the Linear array.It is indicated that the convergence effect of these two arrays on the magnetic field is limited to the bearing clearance.As shown in Figure 6b, when the WTB works in normal operating conditions (the bearing clearance is 0~100 µm), the change rate of magnetic force generated using the Halbach array is only 1.48%.Therefore, the Halbach array is the optimal magnetic alignment for the MWETB.

Optimal Sheath Material
The selecting principles of the sheath materials can be summarized as (1) low magnetic resistance, which does not affect the magnetic force generated using the magnets; (2) small deformation, which provides enough strength to protect the magnetics in the sheath.After a comparative analysis of stainless steel, aluminum alloy, and pure metal materials, it is found that stainless steel meets the requirements of the selection principles above.The properties of different stainless steels are listed in Table 2. To determine the optimal sheath material of the MWETB, a simulation of the magnetic force of different stainless steels is carried out.The variation of magnetic force with different sheath materials is shown in Figure 7a.When the values of relative permeabilities are close, the sheath materials have basically the same effect on the magnetic force.However, when the values of relative permeability are much greater than 1, the sheath materials cause the magnetic force of the bearing to be in the opposite direction, which is due to the magnetization of the sheath materials by the magnets.It is indicated that the relative permeability of the sheath materials is the most important factor affecting the magnetic force, and the optimal sheath material is 0Cr17Ni12Mo2.Figure 7b presents the compression simulation result of the pad sheath when the specific pressure is 0.5 MPa.The maximum deformation occurs at the edge of the pad on the water inlet side, which is 3.6 × 10 −4 mm.The deformation is much smaller than the thickness of the working layer (1 mm),

Optimal Sheath Material
The selecting principles of the sheath materials can be summarized as (1) low magnetic resistance, which does not affect the magnetic force generated using the magnets; (2) small deformation, which provides enough strength to protect the magnetics in the sheath.After a comparative analysis of stainless steel, aluminum alloy, and pure metal materials, it is found that stainless steel meets the requirements of the selection principles above.The properties of different stainless steels are listed in Table 2. To determine the optimal sheath material of the MWETB, a simulation of the magnetic force of different stainless steels is carried out.The variation of magnetic force with different sheath materials is shown in Figure 7a.When the values of relative permeabilities are close, the sheath materials have basically the same effect on the magnetic force.However, when the values of relative permeability are much greater than 1, the sheath materials cause the magnetic force of the bearing to be in the opposite direction, which is due to the magnetization of the sheath materials by the magnets.It is indicated that the relative permeability of the sheath materials is the most important factor affecting the magnetic force, and the optimal sheath material is 0Cr17Ni12Mo2.Figure 7b presents the compression simulation result of the pad sheath when the specific pressure is 0.5 MPa.The maximum deformation occurs at the edge of the pad on the water inlet side, which is 3.6 × 10 −4 mm.The deformation is much smaller than the thickness of the working layer (1 mm), and the sheath material meets the strength requirements of the bearing.Under the large specific pressure, the magnets inside the sheath can be effectively protected.

Load-Carrying Capacity of the MWETB
Based on the optimal structure, a case study of load-carrying capacity for the MWETB is carried out.The simulation parameters are set as follows: The number of pads is 4, the inlet water temperature is 25 °C, the offset ratio is Er = 0.485, Ec = 0.615, the pad angle is 27°, and the rotational speed is 600 r/min.
The relationship between the three forces and micron-level bearing clearance is shown in Figure 8a.It can be seen that as the bearing clearance increases, the water film force decreases rapidly.When the bearing clearance is greater than 18.51 µm, the film force changes slowly and gradually tends to remain unchanged.However, when the bearing clearance changes at the micron level, the magnetic force is almost constant.Since the magnetic force Fm is not sensitive to the clearance, the trend of bearing load-carrying force Fc with the clearance is similar to that of the water film force Fw.When the bearing clearance is greater than 12.85 µm, the magnetic force dominates the load-carrying force.When the bearing clearance is about 12.85 µm, the water film force is equal to the magnetic force.With the clearance further reduced, the water film force tends to be dominant in the loadcarrying force.The relationship between the three forces and the millimeter-level bearing clearance is shown in Figure 8b.It can be seen that the load-carrying force has obvious zoning char-

Load-Carrying Capacity of the MWETB
Based on the optimal structure, a case study of load-carrying capacity for the MWETB is carried out.The simulation parameters are set as follows: The number of pads is 4, the inlet water temperature is 25 • C, the offset ratio is E r = 0.485, E c = 0.615, the pad angle is 27 • , and the rotational speed is 600 r/min.
The relationship between the three forces and micron-level bearing clearance is shown in Figure 8a.It can be seen that as the bearing clearance increases, the water film force decreases rapidly.When the bearing clearance is greater than 18.51 µm, the film force changes slowly and gradually tends to remain unchanged.However, when the bearing clearance changes at the micron level, the magnetic force is almost constant.Since the magnetic force F m is not sensitive to the clearance, the trend of bearing load-carrying force F c with the clearance is similar to that of the water film force F w .When the bearing clearance is greater than 12.85 µm, the magnetic force dominates the load-carrying force.When the bearing clearance is about 12.85 µm, the water film force is equal to the magnetic force.With the clearance further reduced, the water film force tends to be dominant in the load-carrying force.

Load-Carrying Capacity of the MWETB
Based on the optimal structure, a case study of load-carrying capacity for the MWETB is carried out.The simulation parameters are set as follows: The number of pads is 4, the inlet water temperature is 25 °C, the offset ratio is Er = 0.485, Ec = 0.615, the pad angle is 27°, and the rotational speed is 600 r/min.
The relationship between the three forces and micron-level bearing clearance is shown in Figure 8a.It can be seen that as the bearing clearance increases, the water film force decreases rapidly.When the bearing clearance is greater than 18.51 µm, the film force changes slowly and gradually tends to remain unchanged.However, when the bearing clearance changes at the micron level, the magnetic force is almost constant.Since the magnetic force Fm is not sensitive to the clearance, the trend of bearing load-carrying force Fc with the clearance is similar to that of the water film force Fw.When the bearing clearance is greater than 12.85 µm, the magnetic force dominates the load-carrying force.When the bearing clearance is about 12.85 µm, the water film force is equal to the magnetic force.With the clearance further reduced, the water film force tends to be dominant in the loadcarrying force.The relationship between the three forces and the millimeter-level bearing clearance is shown in Figure 8b.It can be seen that the load-carrying force has obvious zoning characteristics with the change in bearing clearance.When the bearing clearance is greater than 0.2 mm, the load-carrying force changes slowly, and the magnetic force is the mainstay in this stage.When the bearing clearance is less than 0.2 mm, the load-carrying force increases sharply as the bearing clearance decreases, and the effect of the water film force gradually increases.From this changing pattern, the magnetic force plays the role of load reduction, especially to prevent direct contact at the bearing interface and reduce wear when hydrodynamic lubrication has not been generated.Therefore, the magnetic force not only improves the load-carrying capacity at high speed but also avoids bearing wear at low speed.

Test Rigs and Signal Acquisition 4.1. Test Rigs
In order to investigate the load-carrying performance of the MWETB under actual working conditions, the bearing is manufactured.As shown in Figure 9, the magnets are installed in the sheath by the water-proof glue.The special magnetic-steel adhesive is used to fix the magnets, preventing them from popping out of the sheath.The dimensions and material properties of the MWETB are listed in Table 3.
Lubricants 2023, 11, x FOR PEER REVIEW 10 of 18 than 0.2 mm, the load-carrying force changes slowly, and the magnetic force is the mainstay in this stage.When the bearing clearance is less than 0.2 mm, the load-carrying force increases sharply as the bearing clearance decreases, and the effect of the water film force gradually increases.From this changing pattern, the magnetic force plays the role of load reduction, especially to prevent direct contact at the bearing interface and reduce wear when hydrodynamic lubrication has not been generated.Therefore, the magnetic force not only improves the load-carrying capacity at high speed but also avoids bearing wear at low speed.

Test Rigs
In order to investigate the load-carrying performance of the MWETB under actual working conditions, the bearing is manufactured.As shown in Figure 9, the magnets are installed in the sheath by the water-proof glue.The special magnetic-steel adhesive is used to fix the magnets, preventing them from popping out of the sheath.The dimensions and material properties of the MWETB are listed in Table 3.The test of the MWETB is conducted on a horizontal WTB test rig, and the key aspects of the test rig are presented in Figure 10.The thrust shaft is driven using a variable frequency motor, and it is connected to the torque meter through the coupling.The torque meter outputs the friction torque of the whole test rig in real time.The thrust pads are installed in the test cabin, and the thrust collar is fixed on the thrust shaft using the flange.During the test, the test bearing is cooled and lubricated using the recycling water.The force sensor is installed between the shaft and the load spring, which indicates the resultant force of the thrust collar acting on the pad surface.By adjusting the bolt on the load spring, different loads can be applied to the bearing.The test of the MWETB is conducted on a horizontal WTB test rig, and the key aspects of the test rig are presented in Figure 10.The thrust shaft is driven using a variable frequency motor, and it is connected to the torque meter through the coupling.The torque meter outputs the friction torque of the whole test rig in real time.The thrust pads are installed in the test cabin, and the thrust collar is fixed on the thrust shaft using the flange.During the test, the test bearing is cooled and lubricated using the recycling water.The force sensor is installed between the shaft and the load spring, which indicates the resultant force of the thrust collar acting on the pad surface.By adjusting the bolt on the load spring, different loads can be applied to the bearing.

Signal Acquisition (1) Force signal acquisition
The force signal is measured using the force sensor, which indicates the resultant force of the thrust collar acting on the pad surface.The spring loading device in the test cabin is shown in Figure 11a.By adjusting the bolt on the load spring, the cylinder liner moves axially.The axial loading force is transmitted to the thrust collar fixed on the thrust shaft through the rolling bearing.According to force equilibrium, the loading force is equal to the load-carrying capacity of the bearing at a certain bearing clearance.(

2) Displacement signal acquisition
The displacement signal is measured using the high-precision eddy current sensor in the test, which indicates the change in bearing clearance between the thrust collar and pads when the rotational speed and load change.Figure 11b depicts a measurement schematic diagram for the bearing clearance.It is considered that the magnetic force is maximum when the force varies with the change rate of the clearance.At this point, the position of the thrust collar is noted as the initial position (ht is equal to 0), and the indication of the eddy current sensor is recorded as b.When the rotational speed or load changes, the axial displacement of the thrust collar occurs.At this time, the indication of the eddy current sensor is recorded as a.Based on the classical principle of geometry, the bearing clearance h can be calculated as follows:

Signal Acquisition
(1) Force signal acquisition The force signal is measured using the force sensor, which indicates the resultant force of the thrust collar acting on the pad surface.The spring loading device in the test cabin is shown in Figure 11a.By adjusting the bolt on the load spring, the cylinder liner moves axially.The axial loading force is transmitted to the thrust collar fixed on the thrust shaft through the rolling bearing.According to force equilibrium, the loading force is equal to the load-carrying capacity of the bearing at a certain bearing clearance.

Signal Acquisition
(1) Force signal acquisition The force signal is measured using the force sensor, which indicates the resultant force of the thrust collar acting on the pad surface.The spring loading device in the test cabin is shown in Figure 11a.By adjusting the bolt on the load spring, the cylinder liner moves axially.The axial loading force is transmitted to the thrust collar fixed on the thrust shaft through the rolling bearing.According to force equilibrium, the loading force is equal to the load-carrying capacity of the bearing at a certain bearing clearance.(

2) Displacement signal acquisition
The displacement signal is measured using the high-precision eddy current sensor in the test, which indicates the change in bearing clearance between the thrust collar and pads when the rotational speed and load change.Figure 11b depicts a measurement schematic diagram for the bearing clearance.It is considered that the magnetic force is maximum when the force varies with the change rate of the clearance.At this point, the position of the thrust collar is noted as the initial position (ht is equal to 0), and the indication of the eddy current sensor is recorded as b.When the rotational speed or load changes, the axial displacement of the thrust collar occurs.At this time, the indication of the eddy current sensor is recorded as a.Based on the classical principle of geometry, the bearing clearance h can be calculated as follows: (

2) Displacement signal acquisition
The displacement signal is measured using the high-precision eddy current sensor in the test, which indicates the change in bearing clearance between the thrust collar and pads when the rotational speed and load change.Figure 11b depicts a measurement schematic diagram for the bearing clearance.It is considered that the magnetic force is maximum when the force varies with the change rate of the clearance.At this point, the position of the thrust collar is noted as the initial position (h t is equal to 0), and the indication of the eddy current sensor is recorded as b.When the rotational speed or load changes, the axial displacement of the thrust collar occurs.At this time, the indication of the eddy current sensor is recorded as a.Based on the classical principle of geometry, the bearing clearance h can be calculated as follows:

Experimental Results of MWETB with Non-Lubrication
The load-carrying capacity results of the MWETB under non-lubrication conditions can be regarded as those of the magnetic bearing.To reduce the contingency of the test and improve the credibility of the data, acceleration and deceleration tests of the rotational speed are conducted in the experiment.During the non-lubrication test, the bearing load is set to be no more than 800 N to avoid pad wear.During the lubrication test, the bearing load is set to be more than 800 N to ensure that the bearing works in hydrodynamic lubrication.

Magnetic Flux Density
As shown in Figure 12, the magnetic flux density simulation of the magnets in the thrust collar and pads is carried out.The values of magnetic flux density on the surface of the thrust pad and thrust collar are mainly concentrated in the range of 400~500 mT.In order to verify whether the magnetic flux density of the magnets in the MWETB is consistent with the simulation, the magnetic flux densities of each ring in the thrust collar and pads are tested sequentially.The test is applied with a Gaussian TD8620 M-sensor.During the test, the probe is close to the S and N poles of the magnets, and the test result is shown in Figure 13.The magnetic flux density of the magnets is distributed uniformly.The fluctuation of the magnetic flux density of the magnets in the same ring is less than 5%, and the values are equivalent to those of the simulation.

Experimental Results of MWETB with Non-Lubrication
The load-carrying capacity results of the MWETB under non-lubrication conditions can be regarded as those of the magnetic bearing.To reduce the contingency of the test and improve the credibility of the data, acceleration and deceleration tests of the rotational speed are conducted in the experiment.During the non-lubrication test, the bearing load is set to be no more than 800 N to avoid pad wear.During the lubrication test, the bearing load is set to be more than 800 N to ensure that the bearing works in hydrodynamic lubrication.

Magnetic Flux Density
As shown in Figure 12, the magnetic flux density simulation of the magnets in the thrust collar and pads is carried out.The values of magnetic flux density on the surface of the thrust pad and thrust collar are mainly concentrated in the range of 400~500 mT.In order to verify whether the magnetic flux density of the magnets in the MWETB is consistent with the simulation, the magnetic flux densities of each ring in the thrust collar and pads are tested sequentially.The test is applied with a Gaussian TD8620 M-sensor.During the test, the probe is close to the S and N poles of the magnets, and the test result is shown in Figure 13.The magnetic flux density of the magnets is distributed uniformly.The fluctuation of the magnetic flux density of the magnets in the same ring is less than 5%, and the values are equivalent to those of the simulation.The load-carrying capacity of the MWETB without lubrication (magnetic bearing) in a non-rotation condition is shown in Figure 14.The test value of bearing magnetic force is

Load-Carrying Capacity of MWETB without Lubrication (1) Non-rotating condition
The load-carrying capacity of the MWETB without lubrication (magnetic bearing) in a non-rotation condition is shown in Figure 14.The test value of bearing magnetic force is smaller than that of the simulation at the same bearing clearance, which is related to the friction caused by the seal ring and journal bearing in the test cabin.When the bearing clearances are in the ranges of 1.3~1.6 mm, 3.5~3.8mm, and 4.5~5.0mm, the magnetic force fluctuates significantly, which shows that as the bearing clearance increases, the magnetic force first increases and then decreases sharply.It is caused by the change in magnetic force not being sufficient to overcome the static friction between the seal ring and the thrust collar sheath.The friction is static during the phase of increasing magnetic force and dynamic during the phase of sharply decreasing magnetic force.
However, at the same bearing clearance, the average percentage difference between the simulated and tested magnetic forces is 16.8%.When the clearance is less than 0.1 mm (MWETB stable operating condition), the average difference in magnetic force is only 16.7 N, which indicates that the magnet structure meets the designed requirement.(2) Rotating condition Figure 15 shows the variation of bearing clearance and magnetic force with different loads and rotational speeds.When the loads are less than 550 N, there is almost no change in bearing clearance or magnetic force with the change in rotational speeds.When the load is 550 N, the bearing clearance and magnetic forces start to change at the rotational speed of 400 r/min, which is related to the eddy currents on the sheath surface.The change in rotational speeds changes the eddy current magnetic field, which affects the strength of the magnetic flux density of the magnets in the bearing.During the acceleration process, the magnetic force increases with the increase in rotational speed, and the bearing clearance decreases with the increase in the rotational speed.However, during the deceleration process, the magnetic force and bearing clearance accomplish the opposite.Although the eddy currents have a certain effect on the magnetic force, it is seen that the effect on the magnetic force is less than 5%.The results of the analysis are consistent with those of Figure 9b, which indicates that the current effect can be ignored in the actual operation.(2) Rotating condition Figure 15 shows the variation of bearing clearance and magnetic force with different loads and rotational speeds.When the loads are less than 550 N, there is almost no change in bearing clearance or magnetic force with the change in rotational speeds.When the load is 550 N, the bearing clearance and magnetic forces start to change at the rotational speed of 400 r/min, which is related to the eddy currents on the sheath surface.The change in rotational speeds changes the eddy current magnetic field, which affects the strength of the magnetic flux density of the magnets in the bearing.During the acceleration process, the magnetic force increases with the increase in rotational speed, and the bearing clearance decreases with the increase in the rotational speed.However, during the deceleration process, the magnetic force and bearing clearance accomplish the opposite.Although the eddy currents have a certain effect on the magnetic force, it is seen that the effect on the magnetic force is less than 5%.The results of the analysis are consistent with those of Figure 9b, which indicates that the current effect can be ignored in the actual operation.
the magnetic flux density of the magnets in the bearing.During the acceleration process, the magnetic force increases with the increase in rotational speed, and the bearing clearance decreases with the increase in the rotational speed.However, during the deceleration process, the magnetic force and bearing clearance accomplish the opposite.Although the eddy currents have a certain effect on the magnetic force, it is seen that the effect on the magnetic force is less than 5%.The results of the analysis are consistent with those of Figure 9b, which indicates that the current effect can be ignored in the actual operation.

Experimental Results of MWETB with Lubrication
The analysis of the test with the non-rotational condition above shows that there is friction between the seal rings and the sheath of the thrust collar.In the lubrication performance test of the MWETB, friction is a source of interference torque and must be eliminated.Therefore, the interference torque test is carried out by applying no axial loads to the trust collar.
The variation of interference torque with rotational speed is shown in Figure 16a.When the rotational speed is lower than 300 r/min, a hydrodynamic water film is formed

Experimental Results of MWETB with Lubrication
The analysis of the test with the non-rotational condition above shows that there is friction between the seal rings and the sheath of the thrust collar.In the lubrication performance test of the MWETB, friction is a source of interference torque and must be eliminated.Therefore, the interference torque test is carried out by applying no axial loads to the trust collar.
The variation of interference torque with rotational speed is shown in Figure 16a.When the rotational speed is lower than 300 r/min, a hydrodynamic water film is formed between the seal ring and the sheath as the rotational speed increases.The thicker the water film there is the smaller the friction torque, which results in a decrease in the interference torque with increasing rotational speed.When the rotational speed is higher than 300 r/min, the heat generated by friction causes the expansion of the seal ring, which increases the preload force.It results in an increase in interference torque with increasing rotational speed.
Figure 16b shows the friction coefficient of the MWETB versus rotational speed at different loads after eliminating the interference torque.It can be seen that when the rotational speed is 100 r/min, there is a larger difference in the friction coefficient under different loads, which is caused by the difference in force proportion in the load-carrying force.The greater the proportion of magnetic force in the load-carrying force, the smaller the contact friction and friction coefficient.When the rotational speeds are 200~600 r/min, the friction coefficient is relatively stable.Within this range, the friction coefficient gradually decreases with an increase in rotational speed.The result above is consistent with that in Ref. [11].However, under the same operating conditions, the friction coefficient of the MWETB is obviously smaller than that of the elastic-supported water-lubricated thrust bearing, and its lubricating performance is better.between the seal ring and the sheath as the rotational speed increases.The thicker the water film there is the smaller the friction torque, which results in a decrease in the interference torque with increasing rotational speed.When the rotational speed is higher than 300 r/min, the heat generated by friction causes the expansion of the seal ring, which increases the preload force.It results in an increase in interference torque with increasing rotational speed.
Figure 16b shows the friction coefficient of the MWETB versus rotational speed at different loads after eliminating the interference torque.It can be seen that when the rotational speed is 100 r/min, there is a larger difference in the friction coefficient under different loads, which is caused by the difference in force proportion in the load-carrying force.The greater the proportion of magnetic force in the load-carrying force, the smaller the contact friction and friction coefficient.When the rotational speeds are 200~600 r/min, the friction coefficient is relatively stable.Within this range, the friction coefficient gradually decreases with an increase in rotational speed.The result above is consistent with that in Ref. [11].However, under the same operating conditions, the friction coefficient of the MWETB is obviously smaller than that of the elastic-supported water-lubricated thrust bearing, and its lubricating performance is better.Taking the load of 0.3 and 0.4 MPa as an example, Figure 17 presents the variation of the simulated and tested film thickness with rotational speed.At the load of 0.3 MPa, the test film thickness of the bearing fluctuates with the increase in rotational speed.Under this load, the load-carrying capacity of the bearing is jointly borne by the magnetic and Taking the load of 0.3 and 0.4 MPa as an example, Figure 17 presents the variation of the simulated and tested film thickness with rotational speed.At the load of 0.3 MPa, the test film thickness of the bearing fluctuates with the increase in rotational speed.Under this load, the load-carrying capacity of the bearing is jointly borne by the magnetic and water film forces, and the values of those are almost equal.It leads to a weak relative equilibrium relationship between the magnetic and water film forces.When the rotation speed is lower than 200 r/min, the load reduction effect of the magnetic force is more obvious, and the film thickness increases with the increase in rotation speed.As the rotational speeds increase, the hydrodynamic water film gradually thickens, and the water film force dominates the load-carrying force.When the sum of the water film and the magnetic forces is greater than the load, the film thickness decreases to correct the water film force, which results in a decrease in film thickness with increasing rotational speed.However, at the same rotational speed, there is a gap between the test and simulation film thickness values, which occurs at the rotational speed of 400 r/min, and the value is 67.9%.It is related to the transient relationship that is not considered in the simulation.
With a load of 0.4 MPa, the water film force dominates the bearing capacity.Under this load, the test film thickness increases with the increase in rotational speed, which is consistent with the results obtained from the simulation.The results of the test and simulation film thickness values are close.The largest difference occurs at the rotational speed of 100 r/min, and the value is 33.7%.The smallest difference occurs at the rotational speed of 500 r/min, and the value is 5.2%.

Conclusions
To improve the reliability of MWETB in high-power RDTs, performance enhancement design and bearing load shedding performance tests are carried out.By comparing the simulation and experimental results of magnetic flux density, magnetic force, and lubrication performance, the following conclusions are obtained: (1) The structure of the MWETB has a great influence on bearing performance.The optimal offset ratios of the rubber cushion are Er = 0.475~0.48,Ec = 0.595~0.60 and Er = 0.48~0.495,Ec = 0.605~0.62,and the optimal pad angle of the pads is 27°.The optimal magnet layout and sheath material are the Halbach array and 0Cr17Ni12Mo2, respectively.Besides, the eddy current generated by the changing speed can be ignored in actual operation.
(2) The load-carrying force has obvious zoning characteristics with the change in bearing clearance.Under different bearing clearances, the magnetic and water film forces dominate the load-carrying capacity of the MWETB, respectively.The magnetic force not only improves the load-carrying capacity at high speed but also avoids bearing wear at low speed.
(3) The tested magnetic flux density and magnetic force are similar to the simulation results.Besides, the variation of the friction coefficient with rotation is consistent with that of the elastic-supported water-lubricated thrust bearing.Under the same operating conditions, the friction coefficient of the MWETB is smaller, and its lubricating performance is better.

Conclusions
To improve the reliability of MWETB in high-power RDTs, performance enhancement design and bearing load shedding performance tests are carried out.By comparing the simulation and experimental results of magnetic flux density, magnetic force, and lubrication performance, the following conclusions are obtained: (1) The structure of the MWETB has a great influence on bearing performance.The optimal offset ratios of the rubber cushion are E r = 0.475~0.48,E c = 0.595~0.60 and E r = 0.48~0.495,E c = 0.605~0.62,and the optimal pad angle of the pads is 27 • .The optimal magnet layout and sheath material are the Halbach array and 0Cr17Ni12Mo2, respectively.Besides, the eddy current generated by the changing speed can be ignored in actual operation.
(2) The load-carrying force has obvious zoning characteristics with the change in bearing clearance.Under different bearing clearances, the magnetic and water film forces dominate the load-carrying capacity of the MWETB, respectively.The magnetic force not only improves the load-carrying capacity at high speed but also avoids bearing wear at low speed.
(3) The tested magnetic flux density and magnetic force are similar to the simulation results.Besides, the variation of the friction coefficient with rotation is consistent with that of the elastic-supported water-lubricated thrust bearing.Under the same operating conditions, the friction coefficient of the MWETB is smaller, and its lubricating performance is better.
(4) When the load is small, there is a weak relative equilibrium relationship between the magnetic and water film forces, which leads to a film thickness fluctuation with the increase in rotational speed.When the load is large, the variation in film thickness is consistent with the results obtained from the simulation.Besides, the results of the test and simulation film thickness values are closer.It indicates the feasibility of applying magnetic load shedding to higher-power RDTs.

Figure 6 .
Figure 6.The magnetic force of different arrays: (a) Force variation of three arrays; (b) Force of the Halbach array.

Figure 6 .
Figure 6.The magnetic force of different arrays: (a) Force variation of three arrays; (b) Force of the Halbach array.

Figure 7 .
Figure 7. Magnetic force and deformation: (a) Magnetic force with different materials; (b) Deformation of 0Cr17Ni12Mo2.

Figure 8 .
Figure 8. Three forces versus bearing clearance: (a) Micron level bearing clearance; (b) Millimeter bearing clearance.The relationship between the three forces and the millimeter-level bearing clearance is shown in Figure 8b.It can be seen that the load-carrying force has obvious zoning characteristics with the change in bearing clearance.When the bearing clearance is greater

Figure 10 .
Figure 10.The diagram of the test bench.

Figure 10 .
Figure 10.The diagram of the test bench.

Figure 12 .
Figure 12.Simulation of magnetic flux density of the magnets.

Figure 12 . 18 Figure 13 .
Figure 12.Simulation of magnetic flux density of the magnets.Lubricants 2023, 11, x FOR PEER REVIEW 13 of 18

Figure 13 .
Figure 13.The magnetic flux density of the magnets in the MWETB: (a) Thrust pads; (b) Outer ring of the thrust collar; (c) Middle ring of the thrust collar; (d) Inner ring of the thrust collar.

Figure 14 .
Figure 14.Load-carrying capacity of the magnetic bearing with non-rotation.

Figure 15 .
Figure 15.The variation of bearing clearance and capacity during the test: (a) Bearing clearance; (b) Load-carrying capacity.

Figure 15 .
Figure 15.The variation of bearing clearance and capacity during the test: (a) Bearing clearance; (b) Load-carrying capacity.

Figure 16 .
Figure 16.The variation of torque and friction coefficient during the test: (a) Interference torque; (b) Friction coefficient of the bearing.

Figure 16 .
Figure 16.The variation of torque and friction coefficient during the test: (a) Interference torque; (b) Friction coefficient of the bearing.
Lubricants 2023, 11, x FOR PEER REVIEW 16 of 18 of 100 r/min, and the value is 33.7%.The smallest difference occurs at the rotational speed of 500 r/min, and the value is 5.2%.

Figure 17 .
Figure 17.The variation of film thickness: (a) Comparison results at a load of 0.3 MPa; (b) Comparison results at a load of 0.4 MPa.

Figure 17 .
Figure 17.The variation of film thickness: (a) Comparison results at a load of 0.3 MPa; (b) Comparison results at a load of 0.4 MPa.

Table 1 .
Main structural parameters of the magnetics.

Table 1 .
Main structural parameters of the magnetics.

Table 2 .
Properties of different stainless steel.

Table 2 .
Properties of different stainless steel.

Table 3 .
The geometric parameters of the MWETB.

Table 3 .
The geometric parameters of the MWETB.