Stator Core Shape Design for Low Core Loss and High Power Density of a Small Surface-Mounted Permanent Motor

In this paper, a stator core shape design of a small SPM motor for low core loss, high power density, and keeping a winding region constant is proposed. For the confirmation of low core loss on the stator core shape design, the analysis technique, which can obtain the detailed core loss distribution of a stator core, is required. Although there have been investigations into the calculation of the core loss of a motor, those techniques can obtain total core loss but cannot obtain core loss distributions [ 14 18 ]. Furthermore, although core loss distribution is obtained in [ 19 ], it is not taking into consideration the rolling direction of the steel sheet. Since the rolling direction of the steel sheet affects the magnetic flux density distribution of a motor, the rolling direction cannot be ignored in the analysis of a small motor [ 20 ]. However, we can evaluate the core loss of a motor by changing the shape of a stator core because we have the analysis technique using a detailed magnetic property called the vector magnetic property [ 21 ]. The accuracy of our analysis technique has been previously reported [ 22 ]. The analysis technique is described in the next section.

On the other hand, it is difficult to dissipate the heat of a small motor used for a space probe because it is used in a vacuum. It is necessary to suppress the generation of the heat in a motor as much as possible. In this paper, the core loss of a small SPM motor increases in order to achieve the high power of a motor by high-frequency excitation. Therefore, we have to decrease the core loss of a motor. Although there have been investigations into the reduction of core loss of a motor, they have carried out the core loss reduction of a stator core by replacing a general steel sheet with nonconventional magnetic materials with low core loss [ 7 10 ]. However, the nonconventional magnetic materials are unsuitable for the stator core of a small motor of less than 30 mm from the viewpoints of difficulty of process. Therefore, the stator core of our small motor is made of a steel sheet. Furthermore, although there have been investigations into the reduction of harmonic core loss, those techniques are not effective as the core loss reduction of our small motor because our motor is driven by a three-phase sinusoidal wave voltage but not pulse width modulation (PWM) [ 11 12 ]. Therefore, a stator core shape in a small SPM motor was investigated for core loss reduction [ 13 ]. Core loss is reduced by attaching the corner radius Rto the tooth root of the previous stator core shape shown with the broken line, as shown in Figure 1 . The core loss reduction effect is large when the corner radius Ris large. However, a winding region decreases because a stator core region increases when the corner radius Rincreases, as shown in Figure 1 . Consequently, when a sufficient winding region is not securable, it is necessary to make the winding fill factor increase in order to obtain the same value as the back electromotive force (EMF) of a motor with a previously stator core shape. Generally, it is difficult to manufacture a small motor with a high winding fill factor. Additionally, as shown in Figure 1 , the area of the stator core increases by attaching the corner radius Rto the tooth root, so that the motor weight also increases. Unless the torque of the motor is increased, the power density of the motor decreases. Therefore, it is necessary to establish a stator core design method that keeps a winding region constant when improving the power density of a small motor.

Although there have been investigations into the development of the high power density of a motor, they are not investigations about a small motor of less than 30 mm [ 1 5 ]. Moreover, it is difficult to miniaturize those high power density motors because those motors have a complex structure. As for a small motor, the structure becomes simple. A surface-mounted permanent magnet (SPM) motor that is used generally for a space probe was selected as a small motor for the development of a high power density motor. A stator core shape in a small SPM motor was investigated for improving power density [ 6 ]. When the tooth length is shortened, the power density increases, because the torque increases and the weight of the motor decreases. Moreover, core loss decreases because the weight of the stator core decreases. However, it is necessary to make the winding fill factor increase because the winding region decreases in this case.

Recently, the development of an unmanned space probe has become very important for space exploration. However, the cost for launch becomes large in proportion to the weight of a space probe. To launch a space probe into space by a rocket, the space probe must be as light weight as possible. Since many kinds of small motors are used for a space probe, it is necessary to realize the light weight and small size of a motor without decreasing the torque of a motor. Furthermore, a motor used for a space probe must be efficient in order to utilize a limited energy in space effectively.

2. Analysis Condition and Analysis Technique

We previously investigated the characteristics of a motor with the same shape as the base of an analysis model [ 6 20 ]. We use again the same motor shape as a base model in this paper. Figure 2 shows the base model in our stator core shape design. In our stator shape design method, only a stator shape is changed without changing a rotor shape. Both the lamination thickness of the stator and the rotor are constant at 12.5 mm. In this paper, we analyze the motor by using the database of vector magnetic properties of the non-oriented steel sheet in which accuracy is already verified. The arrows in the stator core show the rolling direction of the steel sheet. The stator winding method is a concentrated winding. Coil U*, V*, and W* respectively mean the coil of an opposite winding direction to the coil U, V, and W. The magnets used for an SPM rotor are magnetized in parallel with the direction of arrows, and the remanent magnetization of the magnets is constant at 0.4 T.

Generally, the current flowing through a coil is determined by the applied voltage, coil resistance, and coil inductance in a motor. Consequently, the characteristics of a motor, such as the core loss and torque, should be compared under the same applied voltage condition. However, if the stator core shape is changed, it is expected that the value of the back EMF will change because the slot shape is also changed. Therefore, in order to compare and investigate the various motors whose stator core shape is different, analysis conditions of the motors are made consistent according to the following procedure.

• Change the number of winding turns to keep the effective value of the back EMF constant whether the stator shape is changed.

• Calculate the coil resistance using the turn’s number ratio because the diameter of the winding wire is constant.

• Analyze various motors with different stator core shapes by inputting the same three-phase sinusoidal wave voltage.

It is possible to compare and investigate motors of different structures. In this paper, the voltage effective value of a three-phase sine wave is 6 V and the frequency

f

is 667 Hz (i.e., 10,005 rpm).

B

max is the maximum flux density. The inclination angle

θB

is defined as the angle between the rolling direction and the direction of the maximum flux density vector. The axis ratio

α

is the ratio of the minimum flux density

B

min to the maximum flux density

B

max. These three parameters define the flux density condition on the vector magnetic property. Therefore, the E&S model is expressed as a function of these parameters.

In order to evaluate the core loss and torque of the motor designed by our method, the motor is analyzed using the Finite Element Method (FEM) program, which we created by MATLAB. The Enokizono & Soda (E&S) model is introduced in FEM because the E&S model can express in detail a vector magnetic property of an electromagnetic steel sheet used as a stator core [ 21 ]. We previously reported the accuracy of our FEM program into which the E&S model was introduced [ 22 ]. The vector magnetic properties have the alternating magnetic flux condition and the rotating magnetic flux condition. Figure 3 a,b show the alternating magnetic flux condition and the rotating magnetic flux condition, respectively.is the maximum flux density. The inclination angleis defined as the angle between the rolling direction and the direction of the maximum flux density vector. The axis ratiois the ratio of the minimum flux densityto the maximum flux density. These three parameters define the flux density condition on the vector magnetic property. Therefore, the E&S model is expressed as a function of these parameters.

H k ( τ ) = ν k r ( B max , θ B , α , τ ) B k ( τ ) + ν k i ( B max , θ B , α , τ ) ∫ B k ( τ ) d τ ,

(1)

k

=

x

or

y

,

νkr

is the magnetic reluctivity coefficient, and

νki

is the magnetic hysteresis coefficient [

∂ ∂ x ( ν y r ∂ A ∂ x ) + ∂ ∂ y ( ν x r ∂ A ∂ y ) + ∂ ∂ x ( ν y i ∫ ∂ A ∂ x d τ ) + ∂ ∂ y ( ν x i ∫ ∂ A ∂ y d τ ) = − J 0 − ν 0 ( ∂ M y ∂ x − ∂ M x ∂ y ) ,

(2)

A

,

J

0,

ν

0,

Mx

, and

My

respectively are the magnetic vector potential, exciting current density, magnetic reluctivity in vacuum, and x and y-components of magnet magnetization. Additionally, the circuit equation is written as

V 0 n = ∂ ∂ t ∫ c A d s + R m n I m n ,

(3)

V

0

n

(

n

= 1–3),

Rmn

, and

Imn

respectively are the terminal voltage, resistance of an exciting coil, and exciting current. In our analysis, the core loss in each finite element,

Pi

is calculated directly from analysis results by the following equation:

P i = 1 ρ T ∫ 0 T ( H x d B x d t + H y d B y d t ) d t ,

(4)

ρ

is the material density and

T

is the period of the exciting waveform. This analysis technique is able to calculate the core loss distribution in a motor core directly from magnetic flux density vector

B

and magnetic field intensity vector

H

by using Equation (4). Additionally, the total core loss can be calculated as the sum of core loss

Pi

[

The E&S model introduced into FEM is as follows:where subscriptoris the magnetic reluctivity coefficient, andis the magnetic hysteresis coefficient [ 21 ]. The 2D governing equation in this analysis is as follows:where, andrespectively are the magnetic vector potential, exciting current density, magnetic reluctivity in vacuum, and x and y-components of magnet magnetization. Additionally, the circuit equation is written aswhere= 1–3),, andrespectively are the terminal voltage, resistance of an exciting coil, and exciting current. In our analysis, the core loss in each finite element,is calculated directly from analysis results by the following equation:whereis the material density andis the period of the exciting waveform. This analysis technique is able to calculate the core loss distribution in a motor core directly from magnetic flux density vectorand magnetic field intensity vectorby using Equation (4). Additionally, the total core loss can be calculated as the sum of core loss 22 ].

Power density is calculated from the torque and weight of the motor. Torque is calculated from the analyzed result by using Maxwell’s stress tensor method. The weight of the motor is calculated as the sum of the weight of the stator core, coils, and rotor. Since the diameter of the winding wire is constant at 0.38 mm, the weight of the coils is calculated from the number of winding turns. The weight of the rotor is constant at 11 g. The stator core weight is calculated based on the shape of the stator core.