TECHNICAL REPORT

Development of Electromagnetic Field Analysis Technology withHigh Frequency Band
K. INOUE

The electric motor and sensor used in electric power steering require further miniaturization and higher
accuracy, and therefore it is necessary to establish technology that accurately reflects the performance
characteristic of the product in order to satisfy demands. Once this had been achieved, the electromagnetic
phenomenon inside the product was made visible, and electromagnetic field analysis technology was developed
using the Finite Element Method to enable confirmation of the performance characteristic which takes into accountthe influence of the electromagnetic phenomenon. This report introduces verified examples regarding the Variable
Reluctance resolver by using electromagnetic field analysis technology in a high frequency band, while taking into
account the Magnetic Skin Effect, eddy current loss and hysteresis loss.
Key Words: steering system, vr resolver, electromagnetic field analysis, eddy current loss, hysteresis loss,
magnetic skin effect

1. Introduction
The electric power steering (EPS) system, which
provides an assist function using an electric motor,
is expected to evolve into the advanced driving assist
system with the aim of preventing accidents due toincorrect operation or lack of awareness of the driver.
Although the electric and electronic parts to realize
this system are being developed as quickly as possible,
there remain many issues within the system that must
be addressed. One of these issues is the necessity of
optimizing the structure of the VR (Variable Reluctance)
resolver, an angle sensor for the electric motor. Thisrequires determination of the optimal frequency for theVR resolver from the A/D (Analog/Digital conversion)
input cycle of the ECU, after which this frequency isused to maximize the VR resolver output and ensure
detection accuracy. However, it is difficult to estimate
the ratio of effect administered by each parameter
through development based on conventional examinationof an actual machine. Furthermore, as electromagnetic
phenomena inside a product cannot be analyzed, it is alsodifficult to judge whether the parameters are optimal.
As such, after achieving the visualization ofelectromagnetic phenomena inside products andidentifying and examining the mechanisms of these
phenomena, JTEKT has developed electromagnetic field
analysis technology at high frequency bands with the aimof deriving optimal parameters which satisfy the required

performance of the VR resolver. This report introducescase examples of this technology.

2. VR resolver
Figure 1 shows the VR resolver on which this study
has been conducted. The VR resolver has a simple
structure comprised of a rotor core for the rotor, stator
core for the stator, excitation coil for inputting sine wave
signals, and an output coil wound around the stator corefor detecting changes in the magnetic flux which flows
through the stator core.
The turning angle of the VR resolver is detected byrotating the rotor core while sine waves signals flow
through the excitation coil. Rotating the rotor changes theclearance between the stator core and rotor core, whichcauses the magnetic flux flowing within the stator core tochange accordingly. The turning angle of the rotor core isthen calculated from the amount of change in the signalof the output coil which has been affected by the change
in magnetic flux.
Stator core Excitation/output coil [Output (sin) signal][Input (excitation) signal]04590135180225270315360[Output (cos) signal]
0Rotor core

4590135180225270315360

Calculate turning angle

Fig. 1 Variable Reluctance resolver : VR resolver

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−Development of Electromagnetic Field Analysis Technology with High Frequency Band−

3. Electromagnetic field analysis simulation
3. 1 VR resolver model
The VR resolver model is shown in Fig. 2, and thelaminated structure of the VR resolver model in Fig. 3.
The VR resolver model for electromagnetic field analysis
was achieved using the finite element method to create
the shapes of the rotor core, stator core, excitation coiland output coil.
The model shapes of the rotor core and stator core
were created from the values of the VR resolver drawing.
The magnetization characteristic, which demonstrates
the performance of the electromagnetic steel plates used
for the rotor core and stator core, was set as the actual
measurement value on the model in light of the effectof machining and assembly. The electrical conductivity,
which shows the ease of the flow of magnetic flux inside
the plates, was set to the nominal value.
In consideration of the effect of magnetic flux leakage
from the stator core, the model shapes of the excitationcoil and output coil were created using the values of thecross-sectional area of a coil assembled in the slot andfrom the number of turns of each coil. The resistancevalues of each coil on the model were set as the actual
measurement values of an actual VR resolver.
Calculation time was reduced by confining thelaminated structure of the VR resolver model to one halfof its original size due to its symmetry, and by using only
five electromagnetic steel plates for the rotor core andstator core. In addition, the film coating the surface of theplates, which prevents the flow of magnetic flux between
the plates, has been simulated on the model by leaving athin layer of air between each plate.
Stator core

3. 2 Eddy current loss and hysteresis loss
The VR resolver uses a high frequency range over
1 kHz. It is generally known that the effects of eddy
current loss and hysteresis loss must be considered when
conducting electromagnetic field analysis on productsof high frequency. Consequently, we have developed
a VR resolver model which takes into account theeffects of eddy current loss and hysteresis loss during
electromagnetic field analysis of the VR resolver.
Figure 4 shows the theoretical formula of the VR resolver
model. The first term represents VR resolver output,
the second term represents eddy current loss, and thethird term represents hysteresis loss. Eddy current loss
and hysteresis loss increase with higher frequencies,
while output decreases.
Actual measurements of these values have been taken
in order to confirm the degree of effect eddy current lossand hysteresis loss have on the VR resolver. Figure 5
shows the VR resolver used for the measurements ofeddy current loss and hysteresis loss, and Fig. 6 indicatesthe results of these measurements. Loss in total output
is approximately 20% when the excitation frequency
is around 12.5 kHz, and approximately 60% around 20
kHz. This demonstrates the necessity of considering eddy
current loss and hysteresis loss during electromagnetic
field analysis of the VR resolver.

Wout = VI cosh − [ K e ƒ 2 B 2 + K h ƒ B 2 ]OutputEddy current loss Hysteresis loss

Wout: Electrical energy, V: Excitation voltage, I: Excitation current,
h: Phase difference of excitation voltage and excitation current,
Ke: Eddy current coefficient, Kh: Hysteresis coefficient, f: frequency,
B: magnetic flux density

Fig. 4 Theoretical formula of VR resolver model

Excitation coil
Output coil

Stator core

Rotor core

Rotor coreFig. 2 VR resolver modelFig. 5 VR resolver used for real machine examination
Eddy current loss

Hysteresis loss

1≪Model side view≫
Excitation coil, output coil Electromagnetic steel plate
Loss ratio

0.8
0.6
0.4
0.2

Fig. 3 Laminated structure of VR resolver model

0212.520Frequency, kHzFig. 6 Result of a measurement of eddy current loss andhysteresis loss

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−Development of Electromagnetic Field Analysis Technology with High Frequency Band−Figure 7 shows an image of magnetic flux flowing
inside the electromagnetic steel plates. When thefrequency is low, the magnetic flux inside a plate flows
uniformly. However, higher frequencies increase theeffect of eddy currents, which cause the magnetic flux toconcentrate on the surface of the plate and stop flowing
at its center. This electromagnetic phenomenon is known
as the skin effect of magnetic flux. As previously stated,
the VR resolver is of high frequency, and thus it canbe assumed that the skin effect is visible in the resultsof its electromagnetic field analysis. Therefore, it wasnecessary to create a model of the laminated structure on
which the skin effect can be simulated. From this model,
we calculated the depth of penetration of the magnetic
flux on the VR resolver using a formula shown in Fig. 7
for calculating the depth to which magnetic flux has
penetrated (depth of penetration of magnetic flux) inside
the plates. From this value, were able to integrate into
electromagnetic field analysis a method of calculating theoptimum number of low-thickness divisions into which
the plates could be divided in the layering direction.
≪Skin effect: Phenomenon in which magnetic flux concentrates
on the surface of a conductor≫≪Frequency: 50 Hz≫ ≪Frequency: 1 kHz≫ ≪Frequency: 100 kHz≫Single steelplate(0.5 mm)

Magnetic flux
is flowing(Red)

Magnetic flux
is not flowing(Blue)

Magnetic flux
is not flowing(Blue)

Penetration thickness ofmagnetic flux: d
Penetration thickness of =magnetic flux dqp ƒ µq : Electrical resistivityµ : Magnetic permeability
f : Frequency

same peak as the frequency characteristic of the actualmachine, confirming that the model is valid. Furthermore,
the results of the comparison of both simulations
clearly demonstrate that effects of eddy current loss andhysteresis loss are factors in the decrease of the output
signal at higher frequencies.
Output signal/excitation signal
Large

3. 3 Skin effect of magnetic flux

Simulation(Loss not considered)
Simulation(Loss considered)

Actual machine
Large
Frequency

Fig. 8 Frequency characteristic of VR resolver

Furthermore, as shown in Fig. 9, we created a coloredcontour to visualize the size of magnetic flux density
flowing inside the electromagnetic steel plates, in order
to confirm the effect of the skin effect on the VR resolver.
Areas with high magnetic flux density are red, and thosewith low magnetic flux density are blue. These results
enabled the visualization of the range inside the plates inwhich magnetic flux does not flow, and confirmed thatthe size of this range is dependent on the frequency.
≪Top view≫≪Side view≫
Electromagnetic steel plate

Fig. 7 Flow of magnetic flux inside electromagnetic steel

4. Model verification
To verify the validity of the model, the stator core of
the VR resolver was affixed using a fixture, and the rotor
was rotated while sine waves signals flowed through theexcitation coil. A comparison (transformation ratio) of theoutput signal and excitation signal was measured for eachwave when the amplitude of the output signal was at its
maximum, and these measurements were compared withthe results of the simulation.
Figure 8 shows the frequency characteristic, with theexcitation frequency on the x-axis and transformation
ratio on the y-axis. The black line indicates actualmachine data, the red line indicates simulation data whichtakes into account eddy current loss and hysteresis loss,
and the blue line indicates simulation data which does
not consider eddy current loss and hysteresis loss. The
frequency characteristic of the simulation taking intoaccount eddy current loss and hysteresis loss has theJTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

Magnetic flux density: High Magnetic flux density: LowFig. 9 Contour chart of magnetic induction in VR resolver

5. Design study on robustness
5. 1 Effect of rotor eccentricity
The rotor core and stator core are separated inside
the structure of the VR resolver, which may cause therotation centers of both to deviate (rotor eccentricity) due
to incorrect assembly. This causes variation in the output
signal, which leads to errors in the detection of the turningangle. Figure 10 shows the results of the measurement ofthe detection error margin of the turning angle caused byrotor eccentricity.

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Large−Development of Electromagnetic Field Analysis Technology with High Frequency Band−

Angle error

6. Conclusion

Large
Amount of eccentricity

Fig. 10 Measurement result of detection error margin ofturning angle by rotor eccentric

5. 2 VR resolver design with high robustness
The effect of rotor eccentricity was confirmed bysimulation during the study of robustness when rotor
eccentricity exists. These results are shown in Fig. 11. As
visible in the results, rotor eccentricity causes variation in
the amplitude of the output signal.
Rotor eccentricity present

Rotor eccentricity absent

Output signal

Amplitudevaries

Turning angle

Fig. 11 Signal pulse type of output coil by rotor eccentric

Angle error

Large

Using the analysis technology developed at JTEKT,
we have created prototype countermeasure parts byderiving design parameters for a VR resolver which
incorporates measures to suppress amplitude variation of
the VR resolver output signal due to rotor eccentricity,without reducing the amplitude of the output signal. The
actual measured results using the countermeasure parts
are shown in Fig. 12. With the countermeasure parts, themargin of error in turning angle detection due to rotor
eccentricity is small, which confirms that the JTEKT
analysis technology is useful in robustness design.

The development of electromagnetic field analysis
technology for high frequency band has accomplished thefollowing results.
• Established a method for electromagnetic field analysis
at high frequency bands using a model which takes
into account eddy current loss and hysteresis loss fromhigh frequencies, and by setting the optimal number ofdivisions in the layering direction in consideration to
the skin effect of magnetic flux.
• Clearly demonstrated that at high frequency bands, theoutput signal of the VR resolver is reduced by eddy
current loss, hysteresis loss, and the skin effect, all ofwhich are due to frequency.
• The newly developed analysis technology can be usedsufficiently in robustness design.
Although this report covers electromagnetic field
analysis technology at high frequency bands, it is also
necessary to conduct electromagnetic field analysis withconsideration to the effects of temperature fluctuation andstress strain on the electromagnetic steel plates as well.
Moreover, in order to be able to utilize this technology
in the development of advanced driving assist systems, itis necessary to develop analysis technology that enables
design study of not only the individual components,
but the entire system, including peripheral devices andcontrols, as well.

Acknowledgements
Special thanks to Professor Yoshihiro Kawase andAdjunct Professor Tadashi Yamaguchi of Gifu University
for their collaboration and guidance, and to everyone atthe research laboratory.

Currentparts

Countermeasure
parts
Large
Amount of eccentricity

Fig. 12 Measurement result of measures goods

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References
1)

2)

3)

4)

Y. kawase, S. Ito,: ”New Practical Analysis of Electricaland Electronic Apparatus using 3-D Finite Element
Method”, Morikita Publishing Co. (1997) 199.
S. Ito, Y. kawase,: ”Computer Aided Engineering ofElectric and Electronic Apparatus Using Finite Element
Method”, Morikita Publishing Co. (2000) 162.
K. Nakata, S. Ito, Y. kawase,: ” Design and application ofAC-DC Electromagnet Using Finite Element Method”,
Morikita Publishing Co. (2000) 170.
Y. kawase, T. Yamaguchi, K. Tanaka, S, Ota,: ”3-D Eddy
Current Analysis in Electrical Steel sheet of IPM Motor
Driven by Voltage Source Inverter”, IEE Japan, 21-22(2012) 2.

K. INOUE**JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

System Development Dept., Steering Systems OperationsHeadquarters

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