Static and Dynamic Magnetic Pull in Modular Spoke-Type Permanent Magnet Motors

Abstract

This work studied the static magnetic pull of a modular spoke-type permanent magnet motor (MSTPMM) with no rotor eccentricity during the motor’s final assembly process and its dynamic magnetic pull during different motor operating states. A new final assembly scheme was proposed to significantly reduce the static magnetic pull during the final assembly process of the motor. The methods required to reduce the unbalanced radial magnetic pull of the whole stator, which is caused by partial stator module operation, were also studied. Firstly, the structure of the MSTPMM was examined. The static magnetic pull that occurred with the implementation of the two motor final assembly methods was studied in order to prove the effectiveness of reducing the maximum static magnetic pull. Moreover, the maximum magnetic pull during the assembly process was also observed. Then, the dynamic magnetic pull was studied with different motor operating states: no load, on load, and partial stator module operation. To solve the unbalanced radial magnetic pull of the whole stator, which is caused by partial stator module operation, methods of changing the angle between the stator current vector and the q axis (Ψ) or the d axis current (i_d) were also studied.

1. Introduction

The spoke-type permanent magnet motor has been widely studied in home and vehicle appliances because it can concentrate flux and has a high torque density and potential magnet-saving capabilities [1,2,3]. The majority of studies have been mainly focused on the magnet shape [4,5,6,7,8,9,10,11], the analytical model [12,13] and the magnetic barrier, with different shapes and dimensions [14,15,16,17,18,19,20,21], for high-speed spoke-type permanent magnet motors. However, a study on the magnetic pull of modular stators or rotors for modular spoke-type permanent magnet motors has not yet been conducted.

In a modular spoke-type permanent magnet motor (MSTPMM), the modular stator and modular rotor are fixed separately. Therefore, the magnetic pull of the modular stator and rotor in the assembly process, as well as its operating states, need to be analyzed separately. In addition, the magnetic pull that mainly influences the motor’s fixed structure and assembly positioning tooling mechanical strength consists of the following: the radial magnetic pull of one modular rotor core (F_rMR), the tangential magnetic pull of one modular rotor core (F_tMR), the radial magnetic pull of one modular stator core (F_rMS), the tangential magnetic pull of one modular stator core (F_tMS), the magnetic pull of one modular stator core (F_S), and the magnetic pull of the whole stator (F_WS).

This paper proposed two assembly schemes for MSTPMM; found the maximum static magnetic pull during motor final assembly process; and proposed a method to reduce the unbalanced radial magnetic pull of the whole stator, which was caused by part of the stator modules operating. This paper will be organized as follows. First, the structure and parameters of a modular spoke-type permanent magnet motor (MSTPMM) is introduced in the second section. Two motor final assembly methods, which are suited to large-volume permanent magnet motors in order to reduce static magnetic pull, are proposed in Section 3. The static magnetic pulls that occurred following the implementation of the two motor final assembly methods are analyzed. In Section 4, the dynamic magnetic pulls are studied with different motor operating states: no load, on load, and partial stator module operation. Then, in Section 5, to solve the unbalanced radial magnetic pull of the whole stator, which is caused by partial stator module operation, the methods of changing the angle between the stator current vector and the q axis (Ψ) or the d axis current (i_d) are studied.

2. Structure of Non-Magnetic Supports for Spoke-Type Permanent Magnet Motor and Motor Parameters

A diagram of non-magnetic stainless-steel supports for an outer rotor modular spoke-type permanent magnet motor is shown in Figure 1.

The coil layout of one modular stator (10 pole–12 slot) is shown in Figure 2, where the numbers are the stator tooth number, and the letters are the phase of the windings belong. The modular motor parameters are shown in

Table 1. Main parameters of motor.

Parameter	Values and Units
Rated power	160 kW
Rated voltage	1140 V
Rated speed	30 rpm
Rated torque	50,933 N·m
Rated frequency	15 Hz
Stack length (La)	1000 mm
Stator outer diameter (D1)	1149.4 mm
Thickness of stator yoke	40 mm
Air gap (g1)	2.3 mm
Magnet magnetization direction dimension (hm)	10 mm
Magnet width (bm)	40 mm
Thickness of non-magnetic stainless steel (h3)	30 mm
Number of stator slots (z)/rotor pole pairs (p)	72/30
Iron core material	DW470_50
PM material	N42UH
Number of modular stators	6
Number of modular rotors	60

. The stators and rotors are all modular, the number of modular stators is 6, and the number of modular rotors is 60.

3. Static Magnetic Pull in Different Magnet Assembly Processes

3.1. The Description of the Motor Assembly Scheme

This section proposes two final motor assembly schemes. The final assembly process of Scheme A is shown in Figure 3a and is divided into three steps:

(Step A1) The stator part and rotor part with magnets are independently assembled.

(Step A2) Between the stator and rotor, the magnetic isolated pads are inserted equidistributionally in the circle direction. Then, the stator and rotor are assembled together.

(Step A3) The magnetic isolated pads are removed through assembly holes at the end closure. The hole is shown in Figure 4.

The final assembly process of Scheme B is shown in Figure 3b and is divided into three steps:

(Step B1) The stator part and rotor part with magnets are independently assembled. During the rotor part assembly process, the magnetic bonds assembly process must take place before the magnets are assembled.

(Step B2) Between the stators and rotors, the magnetic isolated pads are inserted equidistributionally in the circle direction. Then, the stator and rotor are assembled together.

(Step B3) The magnetic bonds and magnetic isolated pads are removed through assembly holes at the end closure. The hole is shown in Figure 4.

3.2. The Static Magnetic Pull Description of Motor Assembly Scheme A

N_{rotor_left} is the number of adjacent filled-groove magnets, which are on the left of the analyzed modular rotor core. N_{rotor_right} is the number of adjacent filled-groove magnets, which are on the right of the analyzed modular rotor core. The diagrammatic sketch of N_{rotor_left} and N_{rotor_right} is shown in Figure 5.

The local enlarged rotor schematic of rotor core A is shown in Figure 6, into which magnet grooves 1 and 2 inserted magnets, where the numbers are the magnetic grooves number, the letters are the rotor core letter. The corresponding magnetic flux distribution of Steps A1 and B1 is shown in Figure 7, where, Φ_r, Φ_m, Φ_magA1, and Φ_magA2 are the remanent magnet flux, magnet leakage flux, air-gap flux on the left of core A, and air-gap flux on the right of core A, respectively; Φ_gA11, Φ_gB11, and Φ_gC11 are the core magnetic flux on the bottom of core A, B, and C near the air gap, respectively; and Φ_gA21, Φ_gB21, and Φ_gC21 are the core magnetic flux on top of core A, B, and C near the non-magnetic stainless steel, respectively. Φ_b11 and Φ_b12 are the leakage magnetic flux near the air gap.

The basic formula of electromagnetic suction is shown in expression (1).

$$F=\frac{{\varphi }^2}{2{\mu }_{0}b{L}_{ef}}$$

(1)

where Φ is air-gap flux, μ₀ is the magnetoconductivity of air, b is magnetic field cross section width, and L_ef is the length of stator core.

The tangential magnetic pull of core A (F_tMRA) and the radial magnetic pull of core A (F_rMRA) are shown in expression (2).

$$\{\begin{array}{l}{F}_{tMRA}=\frac{({{\varphi }_{magA1}}^2-{{\varphi }_{magA2}}^2)}{2{\mu }_0{b}_m{L}_{\mathit{ef}}}+\frac{({\varphi }_{b11}{}^2-{\varphi }_{b12}{}^2)}{2{\mu }_0{b}_1{L}_{\mathit{ef}}}\\ F_{rMRA}=\frac{{\varphi }_{gA11}{}^2}{2{\mu }_0{b}_{A1}{L}_{\mathit{ef}}}-\frac{{\varphi }_{gA21}{}^2}{2{\mu }_0{b}_{A2}{L}_{\mathit{ef}}}\end{array}$$

(2)

where b_m is the width of magnet, b₁ is the radial length of the magnetic isolated barrier near the air gap, b_A1 is the bottom arc length of core A near the air gap, and b_A2 is the top arc length of core A near the non-magnetic stainless steel.

The magnetic pull is simulated by finite element simulation software (Ansoft Maxwell 16). In order to facilitate the simulation, the following assumptions were made:

(1)

The magnetic pull caused by axial end flux is ignored, and 2D simulation is used.

(2)

The value of magnetic pull shown in the below figures is the maximum magnetic pull among the whole mechanical rotation circle.

(3)

The eccentricities of motor and inconsistencies of permanent magnet performance are not considered.

The simulation tangential magnetic pull of one modular rotor core (F_tMR) and the radial magnetic pull of one modular rotor core (F_rMR) in the process of Scheme A, Step A1 are shown in Figure 8. The magnetic pull of the rotors and stators with different magnetic isolated pad thicknesses in the process of Scheme A, Step A2 are shown in Figure 9. The analyzed modular stator shown in Figure 9b is the one modular stator that had a minimum air-gap distance with the rotor. When the thickness of the magnetic isolated pad is 2.3 mm, then the magnetic pull of the stator and rotor in Step A3 are the same as the magnetic pull of the stator and rotor in Step A2.

Figure 8 and Figure 9 show that in the Scheme A process:

(1)

When the left or right adjacent magnet grooves insert magnets, that is, when (N_{rotor_left}, N_{rotor_right}) = (1, 0) or (0, 1) as in Step A1, the tangential magnetic pull of one modular rotor core (F_tMR) is at the maximum, as shown in Figure 8a.

(2)

The radial magnetic pull of one modular rotor core (F_rMR) is at the maximum when the assembly process is in A2, which is shown in Figure 9a.

(3)

Through increasing the thickness of the magnetic isolated pad, F_rMR, F_WS, and F_MS can be reduced significantly.

3.3. The Static Magnetic Pull Description of Motor Assembly Scheme B

The simulation magnetic pull of one modular rotor in the process of Scheme B, Step B1 is shown in Figure 10. When the radian of the magnetic bond is θ°, the magnetic pull of the whole stator (F_WS) is assumed to be F_WS(θ°), and the magnetic pull of modular stator (F_MS) is assumed to be F_MS(θ°). Then, the reduction percent of the whole stator magnetic pull is assumed to be [F_WS(0°) − F_WS(θ°)]/F_WS(0°); the reduction percent of the modular stator magnetic pull is assumed to be [F_MS(0°) − F_MS(θ°)]/F_MS(0°). The magnetic pull of one modular rotor and stator with different magnetic bond radians and magnetic isolated pad thicknesses during the process of Scheme B, Step B2 are shown in Figure 11, where the analyzed modular stator, shown in Figure 11e,f, has a minimum air-gap distance among all modular stators.

Figure 10 and Figure 11 show that in the Scheme B process:

(1)

When the left or right adjacent filled-groove magnets are (N_{rotor_left}, N_{rotor_right}) = (1, 0), or (0, 1), as in Step B1, then the tangential magnetic pull of one modular rotor core (F_tMR) is at the maximum. This is shown in Figure 10a–c.

(2)

Through increasing the radian of the magnetic bond, the F_rMR, F_WS, and F_MS can be smaller than what is found in Scheme A with the same magnetic isolated pad, especially when the magnetic isolated pad is thin. Figure 11d,e show that the value of F_WS and F_MS with 1.5° radian of magnetic bond can be reduced to 50% value of F_WS and F_MS without magnetic bond.

4. Dynamic Magnetic Pull in Different Operating States

4.1. Full Stator Module Operation

When the d axis current i_d < 0 or i_d > 0, then the stator current can influence the d axis magnetic field of the whole motor, which can then influence the magnetic pull of the rotor. The magnetic pull of the motor and rotor with different loads and Ψ are shown in Figure 12 and Figure 13, respectively. This is where the Ψ is the angle between the stator current vector and the q axis, and i_whole. is the whole stator phase current’s effective value, which is where every stator module’s phase current is i_whole/6.

Figure 12 and Figure 13 show the following:

(1)

Ψ mainly influences the F_rMR, F_WS, F_rMS, and F_MS. The influence degree is directly proportional to the magnitude of the stator current.

(2)

When Ψ is close to −90° and the value of i_whole is at the maximum, then F_rMR, F_MS, and F_rMS can be at the maximum for different load currents and Ψ.

4.2. Partial Stator Module Operation

The maximum magnetic pull of the modular rotor (F_tMR, F_rMR) and the modular stator’s magnetic pull (F_tMS, F_rMS) were not influenced by the number of stator modules operating. Therefore, this section only shows the magnetic pull of the whole stator (F_WS), which is influenced by the number of operating stator modules (shown in Figure 14). Here, i_m is the operating stator module phase current and the operating stator module that is adjacent to it.

Figure 14 shows the following:

(1)

With the same number of adjacent stator modules operating, when Ψ is close to 90° and the value of i_m is at the maximum, then the magnetic pull of the whole stator (F_WS) can be at the maximum;

(2)

With the same current and Ψ, and when half of the stator is operating (i.e., the number of adjacent modular stators is three), then the magnetic pull of the stator (F_WS) can be at the maximum.

5. A Method for Reducing the Unbalanced Magnetic Pull of the Whole Stator

Section 4.2 shows that Ψ or i_d can significantly influence the magnetic pull of the stator (F_WS and F_rMS) with the same stator current. Based on this conclusion, the way to reduce the unbalanced magnetic pull of the whole stator (F_WS) is proposed by a change in Ψ or when the proportion of i_d is in line with the stator current.

5.1. One Operating Modular Stator

The modular stators are numbered from 1 to 6 (shown in Figure 15). Additionally, the corresponding current expressions are shown in (3), where k = 1, 2, 3, 4, 5, 6 represents the stator number; i_d(k) is the d axis current of the stator module k; i_q(k) is the q axis current of the stator module k; i_A(k), i_B(k), and i_C(k) are the three phases of the current of stator module k; and θ is the angle between the d axis of the rotor and the winding axis of A phase (electrical degree).

$$\left[\begin{array}{l}{i}_{d(\mathrm{k})}\\ i_{q(\mathrm{k})}\end{array}\right]=\sqrt{\frac{2}{3}}\left[\begin{array}{l}\cos \theta \begin{array}{c}\end{array}\cos (\theta -\frac{2\mathsf{\pi }}{3})\begin{array}{c}\end{array}\cos (\theta +\frac{2\mathsf{\pi }}{3})\\ -\sin \theta \begin{array}{c}\end{array}-\sin (\theta -\frac{2\mathsf{\pi }}{3})\begin{array}{c}\end{array}-\sin (\theta +\frac{2\mathsf{\pi }}{3})\end{array}\right]\left[\begin{array}{l}{i}_{A(k)}\\ i_{B(k)}\\ i_{C(k)}\end{array}\right]$$

(3)

The radial magnetic pull of the whole stator (F_rWS), the load torque (T), the stator copper loss with a single modular stator operating (ρ_cu), and stator iron loss (ρ_fe) are shown in Figure 16 and Figure 17.

In addition, the expression of magnetic pull (F), load torque (T_em), and copper loss (ρ_cu) are shown in (4)–(6), where f is frequency, K_dp is winding coefficient, N is the number of series winding turns per phase, K_Φ is the waveform coefficient of air-gap magnetic flux, E₀ is the no-load phase back electromotive force, X_ad is the d axis armature reaction reactance, X_aq is the q axis armature reaction reactance, p is the number of pole pairs, ψ_f is the magnetic flux linkage of the rotor, L_d is the d axis inductance, L_q the q axis inductance, m is the number of phase, and R₁ is the phase resistance.

$$F=\frac{1}{2{\mu }_{0}b{L}_{ef}}\frac{{(E_0-I_d{X}_{ad})}^2+{(I_q{X}_{\mathrm{aq}})}^2}{{\left(4.44f{K}_{dp}N{K}_{\varphi }\right)}^2}$$

(4)

$$T=p\left[{\psi }_f{i}_q+(L_d-L_q)i_d{i}_q\right]$$

(5)

$${\rho }_{\mathit{cu}}=m(i_q^2+i_d^2)R_1$$

(6)

Figure 16 and Figure 17 and expressions (4)–(6) show the following:

(1)

The magnetic pull is a function associated to i_d², i_d, i_q², and i_q, and with the same (i_d² + i_q²) and i_q, the absolute value of F_rWS with i_d < 0 is higher than the absolute value of F_rWS with i_d > 0;

(2)

The load torque is a function associated to i_q and i_di_q, and with same i_q, the maximum torque is in the area of i_d < 0;

(3)

The stator copper loss is a function associated to (i_d² + i_q²);

(4)

The stator iron loss is mildly influenced by the current with the same i.

Considering the association shown in expressions (4)–(6), the fitted expression of the unbalanced radial magnetic pull of the whole stator (F_rWS), the average load torque, and the copper loss are shown in (7)–(9); Figure 18, Figure 19 and Figure 20 show that the simulation value and fitted value are matched.

$$F_{rWS\left(k\right)}=\{\begin{array}{l}\left(\begin{array}{l}-0.02633i_{d(k)}^2+2.474i_{d(k)}\\ -0.003863i_{q(k)}^2+0.08312i_{q(k)}-2.534\end{array}\right), i_{d(k)}<0\\ 0.006319i_{q(k)}^2-0.4675i_{q(k)}+0.731,i_{d(k)}=0\\ \left(\begin{array}{l}-0.03545i_{d(k)}^2+2.025i_{d(k)}\\ -0.007533i_{q(k)}^2-0.2287i_{q(k)}+0.1279\end{array}\right),i_{d(k)}>0\end{array}$$

(7)

$$T=\{\begin{array}{l}0.5306i_{q(k)}-0.005427i_{d(k)}{i}_{q(k)}+0.1765, i_{d(k)}<0\\ 0.4963i_{q(k)}+0.434,i_{d(k)}=0\\ \left[0.4981i_{q(k)}-0.008608i_{d(k)}{i}_{q(k)}+0.3892\right],i_{d(k)}>0\end{array}$$

(8)

$${\rho }_{\mathit{cu}(k)}=0.003148(i_{q(k)}^2+i_{d(k)}^2)$$

(9)

5.2. Several Modular Stators Operating

The combined modular stator operating scheme is classified by the number of modular stators operating. The illustration of the schemes is as follows:

1: a single modular stator operating (for an example, see Figure 21);

2A: a two-space symmetrical modular stator operating (for an example, see Figure 22a);

2B: a two-space adjacent modular stator operating (for an example, see Figure 22b);

2C: two modular stators with no adjacent symmetrical spaces and no symmetrical spaces operating (for an example, see Figure 22c);

3A: a three-space symmetrical modular stator operating (for an example, see Figure 23a);

3B: a three-space adjacent modular stator operating (for an example, see Figure 23b);

3C: three modular stators with no adjacent symmetrical spaces and no symmetrical spaces operating (for an example, see Figure 23c);

4A: a four-space symmetrical modular stator operating (for an example, see Figure 24a);

4B: a four-space adjacent modular stator operating (for an example, see Figure 24b);

4C: four modular stators with no adjacent symmetrical spaces and no symmetrical space operating (for an example, see Figure 24c);

5: five modular stators operating (for an example, see Figure 25a);

6: six modular stators operating (for an example, see Figure 25b).

The magnetic pull and current expression for reducing the unbalanced radial magnetic pull of the whole stator (F_rWS) with different combined stator schemes are shown in

Table 2. The magnetic pull and current expression for reducing the unbalanced magnetic pull of the whole stator with different combined stator schemes.

Combined Operating Stator Scheme Number	Expression
1	FrWS1 = 0; id1 < 0
2A	FrWS1 = FrWS4 < 0; id1 = id4 < 0; iq1 = iq4
2B	FrWS1 = FrWS2 = 0; id1 = id2 < 0; iq1 = iq2
2C	FrWS1 = FrWS3 = 0; id1 = id3 < 0; iq1 = iq3
3A	FrWS1 = FrWS3 = FrWS5 < 0; id1 = id3 = id5 < 0; iq1 = iq3 = iq5
3B	FrWS1 = FrWS3 = −0.5FrWS2 ≤ 0; FrWS2 ≧ 0; id1 = id3 ≤ 0; id2 ≧ 0; iq1 = iq3
3C	FrWS1 = FrWS4 < 0; FrWS2 = 0; id1 = id4 < 0; id5 > 0; iq1 = iq4
4A	FrWS1 = FrWS2 = FrWS4 = FrWS5 < 0; id1 = id2 = id4 = id5 < 0; iq1 = iq2 = iq4 = iq5
4B	FrWS1= FrWS4 < 0; id1 = id4 < 0; iq1 = iq4; FrWS2 = FrWS3 = 0; id2 = id3 > 0; iq2 = iq3
4C	FrWS1 + FrWS2 = FrWS5 < 0; FrWS1 = FrWS3 ≤ 0; id1 = id3 ≤ 0; id2 ≤0; id5 < 0; iq1 = iq3
5	FrWS1 = FrWS2 = FrWS4 = FrWS5< 0; FrWS3 = 0; id1 = id2 = id4 = id5 ≤ 0; id3 > 0; iq1 = iq2 = iq4 = iq5
6	FrWS1 = FrWS2 = FrWS3 = FrWS4 = FrWS5 = FrWS6 = 0; id1 = id2 = id3 = id4 = id5 = id6 < 0; iq1 = iq2 = iq3 = iq4 = iq5 = iq6

.

When the stator combined number is N, the load torque is assumed to be T(N), and the stator copper loss and iron loss are assumed to be ρ_cu(N) and ρ_fe(N). Then, the reduction percent of torque is assumed to be [T(6) − T(N)]/T(6), the rising percent of stator copper loss is assumed to be [ρ_cu(N) − ρ_cu(6)]/ρ_cu(6), and the rising percent of stator copper loss+ iron loss is assumed to be [ρ_cu(N) + ρ_fe(N) − ρ_cu(6) − ρ_fe(6)]/[ρ_cu(6) + ρ_fe(6)]. Under the premise of F_rWS = 0, the optimized maximum load torque and loss with different combined operating stator schemes and different phase currents are shown in Figure 26, Figure 27, Figure 28 and Figure 29. Under the premise of F_rWS = 0, Figure 26, Figure 27, Figure 28 and Figure 29 show the following:

(1)

With the same whole current (i_whole) and the same number operating modular stator, sorted by the value of the load torque, the stator combined scheme number is: 2A > 2C > 2B, 3A > 3C > 3B, 4A > 4B > 4C; sorted by the value of core loss, the stator combined scheme number is: 2A < 2C < 2B, 3A < 3C < 3B, 4A < 4B < 4C;

(2)

With same whole current (i_whole), the value of loss is inversely proportional to the number of operating stator modules, especially with respect to copper loss.

6. Discussion

This study mainly focused on examining the maximum static of the magnetic pull during the final assembly process of a motor and the dynamic magnetic pull during different motor operating states. New final assembly schemes designed to significantly reduce the static magnetic pull during the motor’s final assembly process were proposed, and a method to reduce the unbalanced radial magnetic pull of the whole stator, which is caused by partial stator module operation, was studied.

When the out diameter of the bearings is smaller than the out diameter of the air gap, Scheme A can be used; when the motor is a spoke-type permanent magnet motor and the out diameter of the bearings is smaller than the out diameter of the air gap and rotor, Scheme B can be used. In Scheme B, the value of F_WS and F_MS with 1.5° radian of magnetic bond can be reduced to 50% value of F_WS and F_MS with Scheme A; the method to reduce the unbalanced radial magnetic pull of the whole stator, which is caused by part of the stator modules operating, can be used for all modular stator motors with all speeds.

The rotor eccentricity and motor assembly tolerance can also cause an unbalanced magnetic pull. The proposed method to reduce the unbalanced radial magnetic pull of the whole stator can also be influenced by rotor eccentricity and motor assembly tolerance. Therefore, further studies will focus on reducing the unbalanced radial magnetic pull considering rotor eccentricity and motor assembly tolerance.

7. Conclusions

The novelty of the paper is:

(1)

proposing two assembly scheme for motors, in which the out diameter of bearings is smaller than the out diameter of the air gap, especially in Scheme B for a spoke-type permanent magnet motor.

(2)

finding out the maximum static magnetic pull during the motor final assembly process.

(3)

a method to reduce the unbalanced radial magnetic pull of the whole stator, which is caused by part of the stator modules operating.