In this paper, influence of vibration on cogging torque and Radial Magnetic Force(RMF) imbalance was investigated in the IPM type BLDC motor. Design of cogging torque reduction and the RMF equilibrium was proceed applied to Design of Experiment(DOE). Vibration test results, the RMF imbalance was confirmed that a significant impact of vibration.
1. Introduction
Interior Permanent Magnet Synchronous Motor(IPMSM) has permanent magnets embedded in the robust rotor core. So a reluctance torque is generated by the difference in daxis, qaxis inductance, and the torque of IPMSM is greater than Surface Permanent Magnet Synchronous Motor (SPMSM). But local flux saturation is generated due to inserting permanent magnet into the rotor and the large magnetic flux density at small effective airgap makes a loud noise and the vibration occurs when the motor is operating
[1

3]
. Vibration causes of the motor are cogging torque and RMF imbalance action on the motor stator or rotor.
Especially, the resonance was produced in case of the frequency of torque in the same band with the natural frequency. The resonance degraded the performance of motor and adversely affected other systems
[4

6]
.
In this paper, the cogging torque and RMF were the causes of electromagnetic vibration. So, the notch was installed for the reduction of cogging torque. Meanwhile, the RMF equilibrium model was designed by changing radius of rotor and installed notch in order to reduce vibration caused by RMF imbalance. Permanent magnets were arranged by dividing in order to compensate for decrease of the magnetic flux density according to air gap increment with variation of rotor radius.
The RMF imbalance could have a larger impact on vibration during BLDC driving mode IPM motor than cogging torque. So, the equilibrium of RMF is an efficient method of vibration reduction better than reduction of cogging torque.
2. Optimal Design to Model
 2.1 Design models and specifications
The specifications of basic model are shown in
Table 1
. The basic model core shapes are shown in
Fig. 1
.
The specification of basic model
The specification of basic model
The shape of basic model
 2.2 Design of notch
The position and width of a notch, which can offset the cogging torque can be calculated with the energy distribution of the airgap using a Fourier series
[7
,
8]
. The position function of notch derives formula from assuming infinite energy of slot. So the energy distribution of actual notch was varied. Consequently, the notch size was chosen using (Design of Experiments)DOE and (Finite Element Method)FEM.
Fig. 2 (a)
shows the shape of the rotor core installed notch and the diameter A of the design variables was selected rotor shape when the cogging torque is minimum.
Fig. 2 (b)
shows the cogging torque variation conditions according to the change of notch width.
The cogging torque according to the rotor notch width
 2.3 Shape optimization
The unbalanced RMF refers to a vibration source that the axis ratio of RMF is closing to zero. The RMF axis ratio is the ratio of the major and minor axis. The more the RMF axial ratio is closer to 1, the more the RMF is balanced.
Fig. 3
shows the rotor parameters for the design of equilibrated RMF. The design of RMF equilibrium was performed at the rotor of minimized cogging torque model. The design was proceed by DOE. At this time, the design parameters are
α
,
β
and
L
.
α
is the angle of beginning to decrease the radius of the rotor from the daxis,
β
is slope of the permanent magnet. And
L
is the reduced length of the rotor diameter. The more
α
was larger, the more RMF was equilibrated. Especially, 0.878 of RMF axial ratio, it was achieved to 2.51 times RMF equilibrium from
α
= 30°,
L
=0.4(mm) compared to basic model.
The Parameters for the design of RMF equilibrium
As a result of equilibrium RMF design, RMF equilibrium became maximum from
β
= 10°. In this case, 0.888 of the axial ratio compared to the basic model was achieved to 2.54 times equilibrium. The RMF changes according to the design parameters shown in
Table 2
and
3
.
The RMF axial ratio according toαandL
The RMF axial ratio according to α and L
The RMF axial ratio according toβ
The RMF axial ratio according to β
Fig. 4
shows the cogging torque measurement equipment. It was used by Protec corp, PT1940.
Cogging torque tester
The cogging torque experimental values of each model were compared to calculation values in
Fig. 5
.
The cogging torque
The cogging torque of minimized cogging torque model compared with the cogging torque of basic model was reduced by 62%, the cogging torque of RMF equilibrium model compared with the cogging torque of basic model was increased by 77%. The experimental values measured 21 (mN·m) largely than calculation values. This is thought to be caused by the friction according to bearings etc.
3. Analysis of RMF
As shown in
Fig. 6
, for electromagnetic machines, the causes of noise can come from several factors: an electromagnetic factor, a mechanical factor, and an aerodynamic factor.
Origins of noise and vibration and transfer process
Fig. 7
shows the effects of the RMF on the airgap unbalance due to mechanical factors of various kinds. The RMF was generated by a combination of electromagnetic and mechanical phenomena
[9]
.
RMF by unbalance of airgap
 3.1 Analysis of natural frequency
Mode represents unique dynamic aspects, when stator was vibrated by RMF with any frequency, the behavior of the stator appears through unique mode aspects in frequency band of RMF
[10]
.
The natural frequency of stator takes a dominant role in vibration and resonance, Modal analysis was performed. Material of the stator is silicon steel(S2350PN800), and mass density is 7850(Kg/m³). Poisson ratio is 0.24 and Young’s modulus is 200(Gpa).
Fig. 8
shows the modal analysis results. It is mode shape about natural frequency of the stator and each natural frequency which shows frequency of each modes of analytical model.
Fig. 8 (a)
and
(b)
in each 2402(Hz) and 4293(Hz) is elliptical workout mode. Compared to other frequency modes it is main mode that generate large vibration and noise, therefore it should be avoided resonance in elliptical workout mode such as
(a)
and
(b)
.
Mode shape about natural frequency
 3.2 Calculation of RMF
Natural frequency analysis did not consider effect of rotor. So it is hard to compare to vibration effect according to rotor shape change. Therefore, in order to analyze basic model and improved model vibration caused by changing in airgap magnetic flux were compared with aspect and distribution of RMF.
Electromagnetic vibration source was caused by mechanical factors and electromagnetic phenomena of mutual organic relationship. If frequency of electromagnetic RMF is similar area to natural frequency of motor structure, it causes resonance. Wear of parts and motor driving performance debase, influence other system.
The source of electromagnetic vibration and noise is generated by radial force density of stator’s surface from airgap magnetic field. The radial force density can be calculated by Maxwell’s stress tensor method as (1)
[11]
.
Here,
F_{rad}
is the radial component of force density,
B_{r}
and
B_{θ}
are radial and tangential components of the airgap flux density,
μ
_{0}
is permeability of free space,
θ_{s}
is the angular position and
t
is the time.
Fig. 9
is result that compare distribution pattern of RMF. The more RMF pattern was similar to the circle, the more was balanced. Compared to the basic model, minimized cogging torque model was increased in size of minor axis and major axis. RMF equilibrium model was shown result that decrease of minor axis and increase of major axis. Calculating proportion of minor axis and major axis, minimized torque model was balanced more than basic model that proportion of axis is 0.43 from 0.35. Proportion of axis of RMF equilibrium model is 0.888, more than basic model was 2.5 times balanced.
RMF distribution
Fig. 10 (a)
is harmonic analysis of cogging torque and
(b)
is result of harmonic analysis in natural vibration frequency band of RMF. Result of harmonic analysis of cogging torque, amplitude is small on elliptical motion mode in 2402(Hz) and 4293(Hz). Therefore it is considered that vibration according to cogging torque is not big. But harmonic component of RMF was overlapped in unique vibration mode 1 and 2. Accordingly, it is considered that according to RMF occurred big vibration.
Harmonic analysis of natural frequency band
4. Vibration Test
Fig. 11
shows vibration test equipments. The acceleration sensor was used by the PV97C model. A signal analyzer was used for SA01A4 model. Vibration signal was amplified to use UV06A amplifier. Vibration signals of shock by electromagnetic absorbing force were measured in the direction of radiation.
Experimental equipment and acceleration sensor
Fig. 12 (a)
shows the vibration test results of the basic model and the minimized cogging torque model.
(b)
shows the vibration test results of the basic model and the RMF equilibrium model. And
(c)
shows the vibration test results of the minimized cogging torque model and the RMF equilibrium model.
Vibration test result
As results, it can be seen that the size of the vibration of the minimized cogging torque model was increased than the basic model, the size of the vibration of the RMF equilibrium model was greatly reduced than the basic model.
It can be seen that the RMF imbalance has a significant impact on the vibration than the cogging torque.
5. Conclusion
In this paper, the influence of the RMF imbalance and cogging torque on the vibration were compared and analyzed in IPM type BLDC motor.
The minimized cogging torque model and the RMF equilibrium model were designed by using the FEM and DOE. The cogging torque of the minimized cogging torque model was 62% reduction compared to the basic model. But RMF corresponding to the 1st mode of vibration was increased 1.1 times compared to the basic model. Rather, the vibration was increased.
Meanwhile, the cogging torque of the RMF equilibrium model was increased 1.77 times compared to the basic model. But RMF was 70 % reduction compared to the basic model. So, the vibration was reduced.
In other words, it was confirmed that RMF imbalance is affecting significantly the vibration than cogging torque in IPM type BLDC drive motor.
Acknowledgements
This work was supported by the Human Resource Training Program for Regional Innovation and Creativity through the Ministry of Education and National Research Foundation of Korea (2015H1C1A1035824)
BIO
GyeongDeuk Lee He received B.S degree in electrical engineering from Changwon National university. His research interests are electrical machine and FEM analysis.
GyuTak Kim He received B.S, M.S and Ph.D degree in electrical engineering from Hanyang University, Korea. He is presently a Professor of Changwon National University. His research interests are electrical machine and FEM analysis.
Kang GyuHong
,
Song YoungDae
,
Kim GyuTak
,
Hur Jin
2009
“A Novel Cogging Torque Reduction Method for Interior Type Permanent Magnet Motor”
IEEE Transaction on. Industry Applications
45
(1)
161 
167
DOI : 10.1109/TIA.2008.2009662
Hong J. P.
1997
“Analysis of radial force as a source of vibration in an induction motor with skewed slots,”
IEEE Transaction on. Magnetics
33
(2)
1650 
1653
DOI : 10.1109/20.582587
Hur Jin
,
Kim ByeongWoo
2010
“Rotor Shape Design of an Interior PM Type BLDC Motor for Improving Mechanical Vibration and EMI Characteristics”
Journal of Electrical Engineering & Technology
5
(4)
592 
596
DOI : 10.5370/JEET.2010.5.4.592
Colby R. S.
,
Mottier F. M.
,
Miller T. J. E.
1996
“Vibration modes and acoustic noise in a fourphase switched reluctance motor,”
IEEE Transaction on. Industry Applications
32
(6)
1357 
1363
DOI : 10.1109/28.556639
Hur Jin
,
Reu JinWook
,
Kim Byeongwoo
,
Kang GyuHong
2011
“Vibration Reduction of IPMType BLDC Motor Using Negative Third Harmonic Elimination Method of AirGap Flux Density,”
IEEE Transactions on. Industry Applications
47
(3)
1300 
1309
DOI : 10.1109/TIA.2011.2128850
Kim WonHo
2014
“A Stress Analysis Method for the Rotor Design of an IPMSM Considering Radial Force”
Journal of Electrical Engineering & Technology
9
(3)
882 
887
DOI : 10.5370/JEET.2014.9.3.882
Hsieh M.F.
,
Dorrell D. G.
,
Yeh Y.H.
,
Ekram S.
2009
“Cogging torque reduction in axial flux machines for small wind turbines,”
Proc. 35th IEEE Annu. Conf. Ind. Elect. (IECON)
4435 
4439
Wang Xiuhe
,
Yang Yubo
,
Fu Dajin
2003
“Study of cogging torque in surface mounted permanent magnet motors with energy method,”
Journal of Magnetism and Magnetic Materials
267
(1)
80 
85
DOI : 10.1016/S03048853(03)00324X
Dorrell D. G.
,
Thomson W. T.
,
Roach Steven
1997
“Analysis of air gap flux, current, and vibration signals as a function of the combination of static and dynamic airgap eccentricity in 3phase induction motor”
IEEE Transaction on. Industry Applications
33
(1)
24 
34
DOI : 10.1109/28.567073
Logan Daryl L.
2007
“A First Course in the Finite Element Method”
Thomson Learning
Gieras Jacek F.
,
Wang Chong
,
Lai Joseph Cho
2006
“Noise of Poly phase Electrical Motors”
Taylor & Francis Group