Qixing GAO, Xiolin WANG,*, Yn ZHANG
aCollege of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
bSchool of Intelligence Science and Control Engineering, Jinling Institute of Technology, Nanjing 211169, China
KEYWORDSFlywheel energy storage;Integrated support system;Multi–physical-field characteristics;Mechanical strength;Rotor dynamics;Ultra-high-speed motor
AbstractIn the aerospace industry, the low-mass ultra-high-speed flywheel system play a critical role.In this paper, a kW-level Ultra-High Speed Permanent Magnet Synchronous Motor(UHSPMSM) as the core component of flywheel system is proposed and analyzed with consideration of multiple physical fields, including electromagnetic characteristics, mechanical strength and rotor dynamics.The integrated support structure is put forward to improve rotation accuracy and operation stability of the UHSPMSM.Further, influence of the integrated support structure on critical speed is explored,and the key parameters such as support position and support stiffness are designed.Moreover,the rotor strength is analyzed by analytical model developed of rotor stress that can deal with multiple boundary types.Material and thickness of the sleeve are optimized,and range of interference value is accurately limited based on four extreme operating conditions.The 3-D Finite Element Model (FEM) is used to validate the strength characteristics and stress distribution of rotor.A 1.5 kW-150000 r/min UHSPMSM with integrated support system is manufactured and tested.The feasibility of UHSPMSM proposed and the accuracy of analysis method are verified through electromagnetic,temperature rise and vibration characteristics test.The machine prototype realizes the load operation at rated speed and the multi-physical-field characteristics achieve the design specification.
At present, the spacecraft storage battery has some shortcomings,such as low energy density,limited service life and unstable working performance1–3.Generally, the energy storage density of chemical battery, superconducting energy storage and supercapacitor can reach 3–15 Wh/kg, 1–10 Wh/kg and 0.2–10 Wh/kg respectively.However, the limit of flywheel energy storage density can reach above 100 Wh/kg4.NASA has developed a flywheel energy storage system for the International Space Station’s propulsion.Energy storage of the system is 2100 Wh at 100% speed5.The design scheme of 100 kWh flywheel for energy storage is proposed in Ref.6.The maximum energy storage is 144 kWh at 9000 r/min, and the energy storage density is 17.4 Wh/kg.A small and efficient flywheel energy storage system for low orbit satellite is introduced in Ref.7.The system mass is 10 kg, the power density is 400 W/kg, and the energy density is 32 Wh/kg when the speed is 60 kr/min.In the aerospace industry, the low-mass ultra-high-speed flywheel system has the advantage of ultrahigh energy storage density, fast charging and discharging speed8.As the core component of flywheel system,UHSPMSM can achieve the functions of energy conversion.However, the development of UHSPMSM faces many challenges9–11, which lays a motivation for this paper.
The research status of ultra-high-speed motor is shown in Fig.1.NASA and the Pennsylvania State University have developed an ultra-high-speed motor with a maximum speed of 300 kr/min and a power of 0.1 kW for the flywheel energy storage system in satellites and the International Space Station12–13.The rotating speed of the spindle motor developed by German Schmoll company is up to 300 kr/min, which can meet the requirements of Printed Circuit Board (PCB) micro hole processing technology in the field of spacecraft equipment or other high-end equipment.The V11 vacuum cleaner developed by Dyson adopts an ultra-high-speed motor system with a maximum speed of 125 kr/min and a power of 525 W,which increases the suction and reduces the weight of whole machine.Further, the research trend of UHSPMSM will mainly focus on two aspects.One is to break the speed limit and develop in the direction of small volume and portability, and at present, the highest-speed motor has a speed of more than 500 kr/min14–15;the other is to develop towards kilowatt-level high power16–17.Scholars from Nagaoka University of Technology have designed a 1.5 kW/150 kr/min motor for automobile supercharger, but only 120 kr/min no-load test and 50 kr/min speed step test are completed18.There are still many challenges in the research of kW-level ultra-high-speed motor,among which the main limiting factors include constraints of multi-physical-field characteristics and the influence of rotation stability.
Kilowatt-level UHSPMSM usually needs to pass through the first-order critical speed.How to smoothly pass through the critical speed and keep the critical speed away from the rated speed has become a key focus.In Ref.19, the length of shaft is adjusted so that the rated speed of test platform with two coaxial motors is between the second and third bending modes.In Ref.20, the rotor model is discretized for rotor dynamics analysis and bearing parameter verification.The research results provide a basis for rotor structure design and support system optimization of 200 kW/60 kr/min motor.In Ref.21, the rotor dynamics of turbomolecular pump assembly supported by magnetic bearing is analyzed by transfer matrix method, and the relationship among rigid mode,bending mode and support stiffness in the established dynamic model of magnetic bearing is obtained.In Ref.22, an air bearing is selected for the 20 kW/50 kr/min motor,and the critical speed and model of the motor under different support stiffness are calculated,so as to provide the design basis for rotor structure.It can be seen that the dynamic modeling of specific bearing support system is an important part of modal analysis for UHSPMSM.At present, the symmetrical distribution of two bearings on both sides of the rotor is usually used in the traditional support structure,in order to play the role of stable support.However, with the development of ultra-high-speed micro motor, the advantages of single end bearing are gradually developed, and the dynamic analysis of that has become a research focus.
In order to achieve higher speed and more power,the rotor volume and loss density of motor must be allowed to increase,which poses a severe challenge to rotor mechanical strength.In Ref.23, the influence of speed and rotor radius on equivalent stress is studied through the established analytical model of rotor strength.The optimum interference fit meeting the mechanical stress requirements of high-speed motor is obtained.In Ref.24,taking the 400 kr/min three-stage rotor structure as the model, the effects of four sleeve materials and two PM materials on the rotor mechanical stress of UHSPMSM are studied.In Ref.25, by considering the nonisothermal distribution of rotor temperature, the 3D temperature stress coupling analysis is carried out to obtain the optimal sleeve thickness.In Ref.26, with consideration of the strength and electromagnetic limit, the optimal dimensions of rotors with three sleeves are obtained.In Ref.27, aimed at the influence of uneven heat distribution,a reasonable mechanical design scheme is put forward.The material properties of kWlevel UHSPMSM need to be used to the limit, so an accurate rotor stress model is an important prerequisite.Moreover,reasonable choice of interference fit considering machining accuracy and the verification of stress characteristics under multiple extreme operating conditions are the key to ensure the safety of rotor strength.
Fig.1 Research status of ultra-high-speed motor.
This paper focuses on the multi-physical-field characteristics modeling and structural design of 1.5 kW/150 kr/min UHSPMSM with integrated support system.Rotor part of the motor adopts a three-layer surface mounted structure,and shaft of the rotor is equipped with a new type of integrated support system, so as to realize the advantages of high assembly accuracy and good rotation characteristics.Further, influence of the integrated support system on the critical speed of rotor is explored.With the consideration of load, natural frequency of the bending mode is simulated, and the key parameters such as support position and support stiffness are optimized.Moreover, the rotor strength is analyzed by the established analytical model of rotor stress that can deal with multiple boundary types.Material and thickness of the sleeve are optimized, and range of interference value is accurately limited based on four extreme operating conditions.A modified rotor mechanical structure is established, and its stress characteristics are verified by 3D accurate FEM.Various evaluations including electromagnetic,temperature rise and vibration tests have been completed to verify the characteristics of the proposed motor.The prototype realizes the maximum speed of 200 kr/min under no-load and the rated speed of 150 kr/min under load.It has great significance for kW-level UHSPMSM design and accuracy enhancement of multiphysical-field characteristics analysis.
The main contributions of this paper are presented as follows:
(1) A new type of integrated support structure is proposed for UHSPMSM,which solves the problems of low rotation accuracy and poor operation stability.Based on the support structure, the rotor dynamics are analyzed and key parameters such as support position and support stiffness are designed to ensure that the motor can pass the critical speed and operate stably at ultra-high speed.
(2) An analytical model of rotor strength suitable for various boundary types of UHSPMSM is established to realize the optimization of sleeve material, sleeve thickness and precise limit of interference fit.
(3) The machined 1.5 kW/150 kr/min UHSPMSM runs stably and has good characteristics in the loading experiment, whose achievement is rarely presented in the existing literature.
In order to meet the requirements of multi-field characteristics of UHSPMSM, the coupling relationship among the basic structure, design parameters and multi-physical-field characteristics of the motor is summarized.The comprehensive design process of UHSPMSM is shown in Fig.2.According to the design indexes, the motor structure (Section 2) and its FEM model are designed to evaluate electromagnetism (Section 2), rotor dynamics (Section 3), mechanical strength (Section 4), support stability (Section 5) and other characteristics of the UHSPMSM.When any characteristic index does not meet the requirements, motor structural, interference parameters, cooling mode, loss suppression strategy, and detailed dimension can be adjusted and optimized.Through multiple iterations of optimization design, the characteristics of multiple physical fields and output index can meet the system requirements, and then the design process is completed.
2.1.A new type of integrated support structure
The traditional supporting structure contains two bearings,which are symmetrically installed on both sides of the rotor.And the support system including bearings, rotating shaft,end cover and shell is composed of multiple nested components, which results in the poor rotation accuracy at ultrahigh speed.Thus the poor support stability seriously limits the development of ultra-high-speed motor.
The rotation accuracy of support system is the key to ensure the stable operation of UHSPMSM,which leads to a new type of integrated support structure being build as shown in Fig.3.The support part is on one side of the PM rotor to form a cantilever support structure.An outer raceway is set on the support shaft, and the bearing outer ring and ball are tightly installed with the shaft, which results in the ellipsis of the traditional bearing inner ring.In addition, the bearing outer ring is connected to the motor shell.
The outer ring of bearing is installed together with shell to avoid the problems of poor assembly accuracy and scattered expansion stress caused by multiple nesting of the end cover,bearing and shell, which greatly reduces the vibration and improves the rotation accuracy.Then, the bearing outer ring is in direct contact with shell, and the contact area is large,which greatly improves heat dissipation performance and improves the motor durability.Moreover, the outer raceway is set on shaft, which saves traditional bearing inner ring,reduces the overall size of UHSPMSM, and expands application range of the equipment.Table 1 shows the comparison between the proposed integrated support system and the traditional support system.
2.2.Surface mounted rotor structure with alloy sleeve
The rotor is a three-layer annular structure.The innermost layer is a solid rotating shaft and the shaft is bonded with the 2-pole hollow PM.The outermost layer of rotor is the alloy sleeve, which is installed with the PM by interference fit, so as to provide preload for the PM material.
Compared with the three-stage rotor structure10, the stress characteristics of surface mounted rotor structure are reduced,but a more compact structure and better stability can be achieved.Compared with carbon fiber sleeve, the yield strength of alloy sleeve decreases, but its thermal conductivity is much higher than that of carbon fiber,which is conducive to the balanced temperature distribution between PM and sleeve.Meanwhile, the kW-level UHSPMSM puts forward more strict requirements for the mechanical characteristics of rotor.The higher assembly accuracy can be achieved between the alloy sleeve and the PM, so as to increase the utilization rate of allowable stress of rotor material.To sum up, the surface mounted rotor structure with alloy sleeve is adopted,as shown in Fig.4 and d is outer diameter of the sleeve.
Fig.2 Flowchart of design for UHSPMSM.
Fig.3 Structure of the proposed UHSPMSM with integrated support system.
2.3.Stator structure with toroidal windings
A virtual slot is set on the outside of a 6-slot stator, and the coil is circularly wound on inner and outer sides of the stator,so that the full-pitch windings is realized and the power density is improved.The material of stator silicon steel sheet is supercore 10JNEX900 with low loss coefficient, and the loss coefficient is shown in Table 2.The Kh, Kcand Keare respectively hysteresis loss coefficient, eddy current loss coefficient and additional loss coefficient.The Litz-wire with the specification of 100 × 0.1 mm is selected as the windings material, so as to reduce the high-frequency eddy current copper loss.The structure of motor stator is shown in Fig.5.
Table 1 Comparison of different support systems.
Fig.4 Surface mounted rotor structure with alloy sleeve.
2.4.Electromagnetic characteristic check
The parameters of the proposed motor are shown in Table 3,and its basic electromagnetic characteristics are presented in Fig.6.The weight of UHSPMSM used for aviation flywheel systems is 0.75 kg, the rated power is 1.5 kW, and the rated speed is 150 kr/min.Power density of the PM motor can reach 2 kW/kg, which means that a very high power density drive system has been realized.The flywheel made of high-strength carbon fiber is used, and the flywheel energy storage density can reach 41 Wh/kg at 100% speed.The variation curve of radial air gap magnetic density Brwith position and time is shown in Fig.6(a).It can be seen that the maximum magnetic density at the air gap is B = 1.3 T.The maximum magneticdensity of stator core is 1.5 T, which appears in stator yoke,as shown in Fig.6(b).When the motor operates at rated speed of 150 kr/min,the electromagnetic torque is 106 mN∙m and the amplitude of back Electromotive Force (EMF) is 102 V.The electromagnetic FEM results show that the electromagnetic power is 1.6 kW, which meets the electromagnetic design requirements.
If the rotation speed of motor is close to the critical speed,there will be violent vibration and even serious bending deformation.For rigid rotors, rated speed N is limited below the first critical speed Nc1, i.e.N<0.7 × Nc1.For flexible rotors,the rated speed N is limited between two critical speeds, i.e.1.4Nck< N < 0.7Nc(k+1).Therefore, in order to avoid resonance, it is necessary to accurately predict the critical speed of rotor system and ensure that the critical speed is within a reasonable range.
3.1.Support position
Table 2 Loss coefficient for 10JNEX-900.
Fig.5 Stator structure with toroidal windings.
The distance between bearing and PM is h,as shown in Fig.7.The influence of integrated bearing position h on the critical speed of no-load rotor is analyzed in Fig.8.If there is no bearing support constraint, the first-order critical speed of rotor is 540.12 kr/min.After the rotor is constrained by bearing support, the critical speed of rotor decreases.It is found that the critical speed of rotor decreases with the increase of h.When h changes in the range of 4–6 mm,the first-order critical speed of rotor is in the range of 90.004–105.19 kr/min,which satisfies the condition of 1.4Nc1< N.
3.2.Support stiffness
In the approximate calculation of critical speed, the support will be assumed to be absolutely rigid.However, in fact, support components in the system are all elastomers,their stiffness cannot be identified as infinity, and the critical speed of rotor will be affected by support stiffness.As shown in Fig.9,if the bearing stiffness is in the range of 1 × 106–5 × 107N/m, the first-order critical speed of no-load rotor changes significantly with bearing stiffness.If the bearing stiffness is greater than 5×107N/m,the first-order critical speed of rotor changes very slowly and tends to be constant.It can be seen that if the bearing stiffness is less than 5 × 107N/m, the first-order critical speed of rotor satisfies the condition of 1.4Nc1 Fig.6 Electromagnetic characteristics under rated operating conditions. Fig.7 Schematic diagram of bearing support position. Fig.8 The first critical speed varies with h. Fig.9 Critical speed of no-load rotor varies with support stiffness. In the FEM,the bearing support is replaced by spring,and the stiffness value is 1 × 107N/m.With consideration of the gyro effect, the simulation results of no-load rotor are shown in Fig.10.The natural frequency of the first-order bending mode of rotor is 1668.7 Hz, and its corresponding critical speed is 100.122 kr/min.The natural frequency of the second-order bending mode is 10860 Hz,and its corresponding critical speed is 651.600 kr/min.It can be seen that the design results meet the requirement of 1.4Nck< N < 0.7Nc(k+1). To sum up, for the integrated support structure,the modal analysis will be more complex after the load is installed on the rotor.If the bearing support is elastic support, there will be a certain degree of interaction between the components on both sides of bearing.The degree of influence is related to the structure and material of the rotor, the stiffness and support position of the bearing.During the design of rotor, the above influence factors need be adjusted reasonably to ensure that the rotation frequency of rotor is far away from the natural frequency of its bending mode. To solve the internal force per unit area(i.e.stress),the boundary conditions of each component need to be obtained as the basis of deriving the stress expression.In multi-layer rotor structure,the expression of plane stress is suitable for any single rotor component,so obtaining the boundary conditions of each component has become the key to solve the stress analytical expressions. In this paper,an analytical model of rotor stress suitable for multiple boundary types is established,which can deal with the boundary conditions of any multi-layer rotor component in consideration of the interference fit and temperature variation.The schematic diagram of rotor stress analysis is shown in Fig.12.The rotor components are composed of N-layer annular components or solid cylindrical components.The order of each layer of rotor is defined by serial number k,and the value of k increases from inside to outside.Meanwhile the positive direction definition of radial displacement of rotor components s and the definition of interference value δ are given in the schematic diagram. Fig.10 Bending mode of no-load motor. Fig.11 Bending mode of load motor. Fig.12 Schematic diagram of rotor stress analysis suitable for multiple boundary types. In order to realize the analytical calculation of rotor strength, the boundary conditions need to be specified as follows: (1) According to whether the inner diameter of the first layer (k = 1) part is 0 mm, the displacement constraint relationship of the inner surface of the first layer part is distinguished.If the innermost part is a solid rotor, the innermost boundary displacement is 0 mm.If the innermost part is a hollow rotor,the radial stress at the innermost boundary is 0 MPa. (2) For the mating boundaries of adjacent components, the radial stress at the adjacent interfaces is equal.In addition,if the two parts are not separated,the deformation vector difference between adjacent interfaces is always equal to the initial amount of interference. (3) For the outer boundary of the outermost part (k = N),since there is no displacement constraint, the radial stress is 0 MPa. According to the different structural types of the first layer components of the rotor,the boundary conditions of the rotor plane stress model are summarized as follows: As a matter of fact, the kingdom had never known such commercial success. Nothing was left of anything resembling a sword or building material, or a wagon13 to hold it, or an animal to pull it, and there was not a drop of liquid left in all the kingdom but ordinary water. If the first floor component is the hollow structure, i.e.R1i≠0, the boundary condition is where k=1,2,∙∙∙N-1;r is the rotor radius;subscripts i and o represent the inner surface and outer surface of the part respectively; the subscript λ indicates that the direction is radial;σλk=Rkorepresents the radial stress on the outer surface of the kth layer component; Pkis the compressive radial stress on the outer surface of kth layer or the inner surface of(k + 1)th layer. Then,the expression of rotor stress in plane stress model is deduced.In the analysis,it is assumed that the rotor material is isotropic and linear, and the generalized Hooke’s law in polar coordinates is where ε,q,α,ν,E,ω are the strain,material density,coefficient of thermal expansion, Poisson’s ratio, elastic modulus and angular velocity of rotor components respectively; subscripts λ and θ represent radial and tangential directions respectively;T0and Tmare initial temperature and the temperature during rotor operation respectively, and ΔTm=Tm-T0is the temperature difference. By substituting geometric equations ελk=dsk/dr and εθk=sk/r into Eq.(3), the functional equation of stress and displacement can be obtained: where σλk, σθk,σmiseskrepresent the radial stress, tangential stress and equivalent stress of the k-th layer rotor respectively.Combined with boundary conditions (1) & (2), radial displacement Eq.(6) and radial stress expression Eq.(7), the boundary displacement of each component expressed by Pkcan be obtained.Then, the radial displacement and stress results of all parts can be obtained by the boundary radial displacement. In the above analysis process, the corresponding relationship among the structure,size,material,interference fit,speed,temperature and rotor stress of high-speed rotor is presented,which lays a theoretical foundation for further rotor strength analysis and structural optimization. Inconel 718 and titanium alloy are the two most common highstrength non-magnetic alloy materials as sleeve of high-speed motors.The material parameters are shown in Table 4.In the simulation of rotor strength, the surface mounted rotor structure mentioned in Fig.4 is adopted.Meanwhile, the amount of interference between sleeve and PM remains constant,and the variation curve of rotor stress with sleeve thickness and sleeve materials is shown in Fig.13.Firstly,under the condition of the same sleeve thickness, the maximum equivalent stress of Inconel 718 is greater than that of titanium alloy.However,the yield strength of Inconel 718 is 1100 MPa,which is greater than that of titanium alloy.It can be seen that equivalent stress of the two materials is less than 80% of the yield strength of their respective materials, which provides safety margin to a certain extent.Secondly,the tangential stress curve of PM changes obviously with the sleeve material and thickness.If the design is unreasonable, the tangential stress of PM will be close to the tensile strength of material.It can be seen from the figure that the maximum tangential stress of PM with Inconel 718 is less than that with titanium alloy,and with the increase of sleeve thickness, the stress difference between them will be greater.Meanwhile, considering that the thermal expansion coefficient of Inconel 718 is greater than that of titanium alloy, which will greatly reduce the assembly difficulty between sleeve and PM,Inconel 718 is a better choice as the rotor sleeve material in this paper.Thirdly, the increase of sleeve thickness will reduce the stress of PM and sleeve.However, it also brings some problems, such as the increase of rotor eddy current loss and rotor wind friction loss, the decrease of air gap magnetic density, and so on.Therefore,considering the factors of multiple physical fields, the sleeve with thickness of 0.8 mm is selected.That can not only improve the efficiency and power density of the motor, but also ensure the strength demand of the rotor. Table 4 Material parameters. Fig.13 Variation curves of rotor stress with sleeve thickness. Due to the machining tolerance, the interference fit should be limited to an accurate range rather than a specific value.In this paper, the influence of initial interference fit on rotor stress is analyzed under four working conditions: 0 r/min-22 °C, 100 kr/min-30 °C, 150 kr/min-40 °C and 150 kr/min-80 °C.80%of the material tensile limit is selected as the limit boundary of stress.When the rotor stress is less than the limit boundary,the rotor is in the safe range.As shown in Fig.14(a),under the condition of 150 kr/min-80 °C, the tensile stress of PM is the largest, and it decreases with the increase of interference fit.The limit boundary of Nd14Fe2B is 64 MPa.Therefore, when the interference fit is greater than 0.015 mm, the stress of PM can be guaranteed to be in the safe range under multiple operating conditions.As shown in Fig.14(b), the equivalent stress of sleeve increases inversely with interference fit.Under the four operating conditions, the equivalent stress of sleeve is close.The limit boundary of Inconel 718 is 880 MPa, so in order to ensure that the sleeve is in a safe range, the interference fit needs to be less than 0.03 mm.Considering the stress of PM and sleeve under extreme working conditions,the interference fit needs to be limited to 0.015–0.03 mm. The 3D FEM and the stress distribution of rotor with an interference fit of 0.025 mm are shown in Fig.15 and Fig.16 respectively.It can be seen that the analytical calculation is in good agreement with the 3D FEM.Under rated working conditions of 150 kr/min-80 °C, the maximum equivalent stress of the sleeve is 680.2 MPa, and the maximum tensile stress of the PM is 53.5 MPa,both of which are within the allowable stress of the material. Fig.14 Variation curves of rotor stress with interference fit. Fig.15 Rotor stress at 150 kr/min-80 °C. Fig.16 Rotor stress distribution at 150 kr/min-80°C. Fig.17 Variation trend of rotor stress with speed and temperature. In order to verify the feasibility of the motor designed and analysis method, a 1.5 kW-150 kr/min UHSPMSM with integrated support system is manufactured.Driver of the motor is mainly composed of power conversion module, digital controller module and sampling module.The power converter adopts the LMG3411 module of TI company as the threephase full bridge Voltage Source Inverter (VSI); the digital controller adopts TMSF28337D of TI company.The prototype and test platform are shown in Fig.18. In the control strategy, the double closed-loop control of current and speed is adopted, and the command voltage uα;uβoutput by the current loop is converted into duty cycle by SVPWM algorithm and acts on the inverter to realize voltage output.The control frequency is 80 kHz and the control diagram of the proposed UHSPMSM is shown in Fig.19. The prototype was dragged to 150 kr/min,and the three-phase back EMF measured is shown in Fig.20(a).It can be calculated that the root mean square of back EMF at 150 kr/min is about 69 V.When the machine operates as an electric motor,the current waveform at rated speed is shown in Fig.20(b).Due to no-load operation, the current harmonic is large.Meanwhile, the maximum speed of 200 kr/min has been achieved by the proposed UHSPMSM, and the current waveform is shown in Fig.20(c).The experiment proves the reliability of rotor structure designed. Fig.18 Prototype of UHSPMSM with integrated support system and test platform. Fig.19 Control diagram of proposed UHSPMSM. Fig.20 No-load electrical characteristics. Fig.21 No-load temperature variation under different heat dissipation conditions. Temperature variation under different heat dissipation conditions is shown in Fig.21.It can be seen that if natural cooling is adopted,the motor temperature rises quickly.When the motor runs for 20 min, the temperature of bearing outer ring and winding are 58.9°C and 54.6°C respectively.At this time,in order to protect the motor,the test was stopped.However,if forced air cooling is adopted, fast air flow significantly improves heat dissipation.Under this cooling mode, the bearing outer ring temperature is stable at 39.9 °C after 38 min of operation and the winding temperature is stable at 33.3 °C after 29 min of operation. The dynamic characteristic test results of the loading UHSPMSM are as follows.As can be seen from Fig.22,when the motor is suddenly loaded at time t1, the torque current iqincreases instantaneously and remains constant at about 8 A until time t2.Since the control strategy of id= 0 A and equal amplitude Park transformation are adopted, the amplitude of phase current iais also about 8 A under loading. Fig.22 Variable load test. Fig.23 Acceleration test. Fig.24 Vibration test in different speed ranges. The acceleration test is shown in Fig.23.In the initial state,the UHSPMSM rotates at 100 kr/min and the rotation cycle is 600 μs.At time t3, the machine accelerates suddenly.Within 1.7 s,the UHSPMSM is stable at 150 kr/min and the rotation cycle is 400 μs at this time. Vibration test in different speed ranges is shown in Fig.24.The amplitudes of vibration acceleration corresponding to 50 kr/min, 83 kr/min and 150 kr/min are 2 g, 8 g and 4 g respectively.It can be seen that the vibration acceleration at 83 kr/min is the largest,because the speed is in the first critical speed range.During the test,when the rotating speed passes through the range of 70–93 kr/min,obvious vibration and noise can be felt by the human body.Therefore,the resonance region needs to be passed quickly.Based on the experimental results, it can be concluded that the proposed rotor dynamics design is reasonable and feasible.The rotor design meets the requirements of 1.4Nc1< N < 0.7Nc2, and the rotor developed can pass through the first critical speed smoothly. Fig.25 Variation curves of vibration and temperature rise characteristics with speed. The motor system characteristics with the integrated support structure at different speeds are tested as shown in Fig.25.The vibration acceleration does not change linearly with the speed,as shown by the red curve.In the critical speed range of 70–90 kr/min,the amplitude of vibration acceleration is the largest,about 4g.At rated speed,the motor operates stably, and the amplitude of vibration acceleration is about 2g.Further, when forced air cooling is adopted, the temperature rise of bearing outer ring increases with the speed, as shown by the blue curve.Temperature rise test is not carried out in the critical speed range and the temperature rise of the bearing is stable at 13 K when the motor is running at 150kr/min. In this paper,a kW-level UHSPMSM with integrated support system as the core component of flywheel battery is proposed.The ultra-high speed and high power performance can help the flywheel to realize high capacity storage and sufficient charging and discharging time.The multi-physical-field characteristics modeling, characteristic analysis and structural optimization of the machine are carried out. (1) For ultra-high-speed micro motor,an integrated support structure is proposed, which solves the problems of low rotation accuracy and poor operation stability caused by multiple nesting of end cover, bearing and shell. (2) The influence of the integrated support structure on the critical speed of the rotor is explored.According to the load setting and speed target, the support position is designed as h = 4 mm and the support stiffness needs to be designed in the range of 1 × 106–5 × 107N/m.The loading test results show that the first-order critical speed belongs to the range of 70000–90000 r/min which ensures that the motor can not only smoothly pass the first-order critical speed, but also operate stably at the rated speed. (3) The rotor strength characteristics are analyzed on the basis of the established rotor stress analytical model with multiple boundary conditions satisfied.The sleeve material and sleeve thickness are optimized, and the interference fit is accurately limited.Under rated working conditions, the maximum equivalent stress of the sleeve is 680.2 MPa, the maximum tensile stress of the PM is 53.5 MPa, and the rotor stress has more than 20%safety margin from the allowable stress of material. The 1.5 kW-150 kr/min machine prototype is manufactured and tested.The prototype achieves the maximum speed of 200 kr/min under no-load and the rated speed of 150 kr/min under load.The experimental results and explanations verify the advantages of the proposed UHSPMSM and the accuracy of analysis method.The UHSPMSM with integrated support system with high power density can guarantee operation stability.Thus this design strategy can be used as one of the future options for ultra-high-speed machine in aerospace industrial applications. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (No.52177048), the Natural Science Foundation of Jiangsu Province, China (No.BK20201297), the University Science Research Project of Jiangsu Province,China(No.21KJB120003),and the Industry University Research Cooperation Project of Jiangsu Province,China (No.BY2021358).
3.3.Load model evaluation
4.1.An analytical model of rotor stress suitable for multiple boundary types
4.2.Sleeve material selection and thickness optimization
4.3.Interference fit limit
4.4.Evaluation of rotor stress characteristics
5.1.Test platform and control strategy
5.2.No-load test
5.3.Load test
