J Electr Eng Technol Vol. 9, No. ?: 742-?, 2014 http://dx.doi.org/10.5370/JEET.2014.9.?.742

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A Stress Analysis Method for the Rotor Design of an IPMSM Considering Radial Force

Won-Ho Kim†

Abstract – In the design of the rotor of an interior permanent magnet synchronous motor (IPMSM), the bridge between the permanent magnets helps prevent the scattering of permanent magnets and pole pieces during high-speed operation. In the design of a motor, if the bridge is too thick, its performance will be largely degraded because of flux leakage. Additionally, if the bridge is too thin, its mechanical safety cannot be guaranteed. Thus, an accurate analysis method is required to determine the thickness of the bridge. Conventional stress analysis methods determine the thickness of the bridge by only considering the centrifugal force of the rotors. In this study, however, a method that additionally considers the radial force generated by the air-gap flux density based on the conventional methods is proposed and reflected in the design of a traction motor for electric vehicles. Finally, the validity of this study is verified through a reliability test related to high-speed operation.

Keywords: IPMSM, Radial force, Stress analysis

1. Introduction Recently, the interior permanent magnet synchronous

motors (IPMSMs) have been frequently used in traction motors for vehicles, and their driving scope has also been extended to high-speed operation at more than 10,000 rpm in order to increase power densities [1-2]. For such high-speed motor operation, the accurate stress analysis of rotors is an important factor in the reliability of motors. If the safety factor is not properly calculated because of an inexact stress analysis, it will cause a serious problem in the reliability test at high-speed operation owing to mechanical interference between the rotor and the stator, as presented in Fig. 1.

In this study, a method that considers the additional radial force caused by an electromagnetic phenomenon in addition to the conventional stress analysis method, which

usually considers the centrifugal force of the rotors [3], is proposed for calculating the safety factors more exactly. The motor used in this study is in the 120-kW class used for traction applied to military trucks, and its performance specifications, dimensions, and material information are presented in Table. 1. Additionally, Fig. 2 shows the shape of this motor.

2. Calculation of the Radial Force The radial force is not a type of actual force (tangential

force) but rather affects the vibration or acoustic performance [4-6]. Furthermore, the direction of this force coincides with the scattering direction of the rotors, which is caused by the centrifugal force of the rotors, and is used to produce a more exact result when it is accounted for in the calculation of stresses.

For the calculation of the radial force, the worst

† Corresponding Author: Material & Device Research Center, Samsung Advanced Institute of Technology, Samsung Electronics Co., Korea. (wonho79@nate.com)

Received: September 29, 2013; Accepted: : November 28, 2013

ISSN(Print) 1975-0102ISSN(Online) 2093-7423

Fig. 1. Mechanical interference between the rotor and the

stator

Fig. 2. Model of a 120-kW motor

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condition is a point at which the motor is operated at the maximum speed (10,000rpm) while applying current (with a phase current of 500Apeak and a current phase angle of 76.8°) or the coasting speed (12,000rpm) without applying a current at a downward slope.

The radial force can be calculated using Eq. (1), in which the radial flux density in the air gap can be obtained using FEA [7].

( ) ( )2

02gr

r

Bf

θθ

μ= (1)

where Bgr is the radial flux density at the air gap, θ is the rotor position, and μ0 is the permeability of free space.

Figs. 3 and Fig. 4 show the radial flux density and flux density distribution plots at two driving points. The flux density distribution at the maximum speed shows a wide magnetic saturation area. However, the condition at the coasting speed exhibits a radial flux density approximately 24% higher than the condition at the maximum speed

according to the comparison of the integration values of Bgr

2, which are proportional to radial force. It is expected that the flux weakening current is generated along the direction of decreasing air-gap flux. Based on this fact, it is revealed that the worst condition of the calculated stress is the coasting speed region that exhibits a large radial force and centrifugal force.

Fig. 5 shows the spatial distribution of the radial force per unit area at the coasting speed. When comparing this result with the shape of the rotor in Fig. 2, it is verified that the radial force is symmetrically distributed, and most of the force is focused on the pole piece, which is the front side of the permanent magnet.

3. Stress Analysis Method Considering the Radial Force

In general, the stress analysis considers only the centrifugal

Table 1. Specifications of the 120-kW motor

Item VALUE Instantaneous Power (1 min.) 120kW

Torque @ Rated Speed 403Nm @ 2,843rpm Instantaneous Torque @ Maximum Speed 115Nm @ 10,000rpm

Continuous Power (60 min.) 65kW Torque @ Rated Speed 218Nm @ 2,843rpm

Instantaneous Torque @ Maximum Speed 62Nm @ 10,000rpm Maximum Coasting Speed (1 min.) 12,000rpm

Stator Dia. / Rotor Dia. 300mm / 148mm Stack Length (Stator / Rotor) 210mm / 232mm

Magnet Thickness 10mm Rib Thickness 1mm

Air-gap Thickness 1.2mm Phase Voltage Limit 346Vpeak Phase Current Limit 550Apeak

No-load EMF Limit (@ Coasting Speed) 164Vpeak Young’s Modules (Core / Magnet) 162.4MPa / 140MPa Poisson’s Ratio (Core / Magnet) 0.33 / 0.24 Tensile Strength (Core / Magnet) 550MPa / 120MPa Yield Strength (Core / Magnet) 440MPa / 80MPa

Fig. 3. Radial flux density at two driving points

Fig. 4. Flux density distribution plot at two driving points

Fig. 5. Spatial distribution of the radial force at 12,000rpm

A Stress Analysis Method for the Rotor Design of an IPMSM Considering Radial Force

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force:

2mvF

r= (2)

where F is the centrifugal force, m is the mass, v is the rotational velocity, and r is the radius of the mass.

The stress analysis shows differences in the results according to the boundary conditions. In this paper, there are no friction conditions on the contact face between the magnet and the pole piece, and a bonding friction condition is only applied to the backside of the magnet. In addition, the calculated radial force is mapped to the thick area on the pole piece in Fig. 6. The final equivalent stress is calculated using FEA after applying all these conditions at 12,000 rpm.

The safety factor can be calculated as:

( ) ( ) ( )( )

2 2 2

2 2 26

2

Yieldsafe

E

x y y z z x

xy yz zxE

kσσ

σ σ σ σ σ σ

σ σ σσ

=

+ +

+ + +=

(2)

where σYield is the yield strength, σE is the equivalent stress, and σx, σy, σz, σxy, σyz, and σzx are the direct stress components.

Table 2 shows the equivalent stress, safety factor, torque, and efficiency for various bridge thicknesses by using FEA simulation. In the analysis of the results, the safety factor and torque represent a tradeoff relation and do not affect the efficiency significantly. The motor used in this study is a military type, and its safety factor is conservatively limited by more than 2.4. The bridge thickness of 1mm that satisfies the target safety factor and torque (more than 403Nm) simultaneously is selected for the final model.

To determine the effect of the radial force, the final

model is analyzed using the conventional and proposed methods. The results of this comparison are presented in Figs. 7 and Table 3. Fig. 7 is intended to more reliably confirm that the result was 170 times larger than the actual deformation. It is verified that the stress is usually distributed in the rib and bridge of the rotor in these two cases. However, there is a difference in its equivalent stress of approximately 9MPa when considering the radial force.

(a) Conventional method

(b) Proposed method

Fig. 7. Results of equivalent stress distribution plot

Table 2. Results for various bridge thicknesses

Bridge Thickness 0 mm 0.5 mm 0.75 mm 1 MM Equivalent stress [MPa] 647.06 283.87 188.84 181.57

Safety factor 0.68 1.55 2.33 2.42 Torque [Nm] 431 422 418 415

Efficiency [%] 97.8 97.5 97.4 97.4

Table 3. Comparison with the conventional and proposed methods

Condition Conventional method (Centrifugal force)

PROPOSED METHOD (CENTRIFUGAL FORCE +

RADIAL FORCE) Equivalent stress 172.53MPa 181.57MPa

Safety factor 2.55 2.42

Fig. 6. Boundary conditions and the radial force mappingarea

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The difference is equivalent to the safety factor of 0.13 and cannot be neglected in the precise design of the bridge.

4. Experiment To verify the validity in the design of the bridge, the

final model was fabricated, and tests were performed. Figs. 8 and Fig. 9 represent the fabricated cores, motor, and dynamometer.

In order to verify the validity of the radial force simulation, the no-load EMF at 3,000 rpm is compared with experimental data and FEA. The results are shown in Fig. 10 and Table 4, and it was verified that the radial force simulation is valid.

The profile of the high-speed cycle durability test is presented in Fig. 11, where the test had duration of 36,000 cycles for 500 hours. The coasting speed test rotated the fabricated motor compulsorily by operating the test dynamometer at 12,000 rpm for 5 min. Based on the results

of these two tests, there were no mechanical problems and no changes in motor performance. Additionally, it was verified that the stress analysis method and bridge design proposed in this study are reasonable.

5. Conclusion In this study, a stress analysis method considering the

radial force was proposed and applied to the design of a 120-kW IPMSM. Additionally, the validity of this method was verified by fabrication of a model and testing.

The results of this study show that the proposed method

Fig. 8. Fabricated stator and rotor core

Fig. 9. 120-kW IPMSM and test dynamometer

Table 4. Comparison with the experiment and FEA

Item RMS 1st 5th/1st 7th/1st THD Experiment 63.88V 87.76V 2.36% 0.95% 2.87% Simulation 64.51V 91.25V 2.50% 0.83% 2.82%

Error 0.98% 3.82% 0.14%p 0.12%p 0.05%p

Fig. 10. No-load EMF at 3000rpm

Fig. 11. Profile of the high-speed cycle durability test

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is effective for a switched reluctance motor (SRM) with a very large radial force and small air gap [8-9].

References

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[2] Zhang Lei, Wen Xuhui, Zhang Jian, Wang Youlong, “Research of high power-density permanent magnet synchronous motor and driving system,” Electric Information and Control Engineering (ICEICE), pp. 6052-6055, 2011.

[3] Jae-Woo Jung, Byeong-Hwa Lee, Do-Jin Kim, Jung-Pyo Hong, Jae-Young Kim, Seong-Min Jeon, Do-Hoon Song, “Mechanical Stress Reduction of Rotor Core of Interior Permanent Magnet Synchronous Motor,” Magnetics, IEEE Transactions on., Vol. 48, pp. 911-914, 2012.

[4] Cameron, D.E., Lang, J.H., Umans, S.D., “The origin and reduction of acoustic noise in doubly salient variable-reluctance motors,” Industry Applications, IEEE Transactions on., Vol. 28, pp. 1250-1255, 1992.

[5] Guandong Jiao, Rahn, C.D., “Field weakening for radial force reduction in brushless permanent-magnet DC motors,” Magnetics, IEEE Transactions on., Vol. 40, pp. 3286-3292, 2004.

[6] Krotsch, J., Ley, T., Piepenbreier, B., “Reduction of torque and radial force fluctuation in permanent magnet synchronous motors by means of multiobjective optimization,” Electric Drives Production Conference (EDPC), pp. 40-48, 2011.

[7] Zhu, Z.Q., Xia, Z.P., Wu, L.J., Jewell, G.W., “Analytical Modeling and Finite-Element Computation of Radial Vibration Force in Fractional-Slot Permanent-Magnet Brushless Machines,” Industry Applications, IEEE Transactions on., Vol. 46, pp. 1908-1918, 2010.

[8] Anwar, M.N., Husain, O., “Radial force calculation and acoustic noise prediction in switched reluctance machines,” Industry Applications, IEEE Transactions on., Vol. 36, pp. 1589-1597, 2000.

[9] Feng-Chieh Lin, Sheng-Ming Yang, “Modeling and Control of Radial Force in Switched Reluctance Motor,” Power Electronics Specialists Conference (PESC), pp. 1-7, 2006.

Won-Ho Kim He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 2005, 2007 and 2011 respectively. He is now working in Samsung Advanced Institute Of Tech-nology. His research interests include motor design, analysis of motor /

generator; and applications of motor drive, such as electric vehicles, home appliances