Effect of Magnet Size on Torque Characteristic of ...

Effect of Magnet Size on Torque Characteristic of Three Phase Permanent Magnet Brushless DC Motor M. Norhisam1, A. Nazifah1, I. Aris1 1

Faculty of Engineering, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

H. Wakiwaka2 2

Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano, 380-8553, Japan

Abstract—This paper deals with a design of high torque brushless DC motor (BLDC). This motor is designed in new arrangement of the stator teeth and operated as three phase motor. This motor is developed to produce high torque performance motor that could be used as in-wheel motor for agriculture applications such as tractors. The basic structure and principle of the motor is described briefly. The simulation Finite Element Method (FEM) technique is used in order to analyze the performance of the motor including flux flow path and flux distribution. Various sizes of magnet had been varied for torque and motor efficiency analysis by using simulation and analytical method, respectively. This found that the maximum output torque is achieved when both length and width of magnet is at largest size. The result also signifies that the increment of torque will not determine the increases in the motor efficiency as well. In the end, this paper could be used as a further research for the future. Keywords-high torque; brushless DC motor

I.

M. Nirei3 3

Nagano National College of Technology, 716 Tokuma, Nagano 381-8550, Japan

torque produce by the motor. Finite Element Method (FEM) is used to examine the flux density, the flux path, the flux distribution and the mesh in the BLDC. In order to determine the motor efficiency, the mathematical analysis is presented. II.

BASIC STRUCTURE AND PRINCIPLE

A. Basic Structure The constructional structure of BLDC is shown in Figure 1. The stator comprises eighteen coils and the rotor consists of eighteen permanent magnet poles. The permanent magnets embedded in the rotor are arranged back to back so that the flux flows toward the coil slot in the stator [4]. The coils were winding in each slot of stator in series connection. These coils are grouped according to its phase. Each phase is displaced by 120° electrical degrees to each other.

INTRODUCTION

In recent years, permanent magnet (PM) becoming increasingly competitive in many applications in electrical machines. With advantages such as high efficiency and compact size, PM is used to create the fundamental acting field by replaced the field winding in machines. In permanent magnet brushless DC (BLDC) motor, a strong electromagnetic force exists between the rotor permanent magnets and the stator coils. BLDC has the feature of high-power density, high overload and wide range of weak magnetic, which is much suitable for operation of the vehicle. With such advantages, BLDC has been widely used in electric vehicles. [1]. BLDC operates in bidirectional variable speed operation under full torque mode. Mostly, the existing BLDC available at the market are having coils that are arranged individually over the phases synchronously. Unlike this proposed BLDC, the coils are grouped according to its phase. The performance of high torque BLDC is depending on the permanent magnet properties, and size structure [2]. Thus, to gain the desired torque performance, certain size of magnet, cogging characteristic and other parameters were investigated in this paper. Besides that, the information on the rotor position, pitch arrangement and design on the motor electric magnetic field are essential [3]. This paper studies on the basic constructional features and operating principles of the BLDC. The performance of BLDC including its motor efficiency and cogging characteristic on various sizes of magnet is considered to analyze the maximum

Figure 1. Basic structure of BLDC

In order to arrange the stator teeth for three phase BLDC, the teeth of Phase A is positioned at 0º, the Phase B and Phase C at (1/3)rd and (2/3)rd of the rotor half pitch, σ (20º) respectively. Therefore, the coils are arranged mechanically according to the motor half pitch, σ which are 20° as shown in Figure 1. Each coil phase has to be arranged by (1/3)rd or 6.67° of the motor half pitch. This means that the slot for Phase A coil is situated at the zero half pitch, the coil Phase B is situated

at (1/3)rd of the motor half pitch and coil phase C is situated at (2/3)rd of the motor half pitch. The angle difference between first stator teeth Phase A and last stator teeth Phase C is 2σ/3 which is same as to the first stator teeth Phase C and last stator teeth Phase B. The motor of this type of configuration is displaced by 120° mechanical degrees for each energized phase similar to that of the electrical degree.

In order to calculate the motor efficiency of BLDC based on the FEM simulation result, its produced torque is calculated separately by using

The rotor and stator are made from magnetic material such as laminated iron. However the shaft is made from non ferromagnetic material. The Neodymium-iron-boron (NdFeB) permanent magnets are magnetized in width direction as shown in Figure 2. The magnets are placed between wedges of magnetic material of the pole pieces in the rotor. The basic flux path of the BLDC is also shown in Figure 2. As can be seen, the N pole PM flux flows through the small air gap into the stator yoke teeth. The flux then travels along the stator yoke and also along the stator core. Subsequently, the flux will return across the air gap and then enter the rotor core through the S pole PM.

where τ is the produced torque in [Nm], Kτ is torque constant in [Nm/A], KE is the back emf constant in [V/rads-1], and ω is the rotational speed in [rads-1].

௄ഓ (௏೅ ି௄ಶ .ఠ)

߬=

(2)

ଶ.ோ೎

The input power, Pin which as known as electrical power of the motor in [W] is determined using

ܲ௜௡ = ‫ܧ‬௔ . ‫ ܫ‬+ ‫ ܫ‬ଶ . ܴ௖

(3)

While the mechanical power of the motor as output power, Pout in [W] is calculated as

ܲ௢௨௧ = ߬. ߱

(4)

Finally, the resultant efficiency of BLDC is calculated using

ߟ= III.

Figure 2. Basic flux path of BLDC

B. Principle of Calculation Figure 3 shows the basic per phase electrical equivalent circuit of the brushless motor. This circuit is used as a reference in order to determine the performance of the BLDC.

௉೚ೠ೟

SIMULATION ANALYSIS

Table I shows the fixed dimension and parameter of BLDC. For clearer view, the dimension is illustrated in Figure 4. Then, the models are imported to the FEM software and the material properties are assigned. TABLE I. Part Stator

DIMENSION AND PARAMETER OF BLDC Element

Value

Unit

Outer radius, Ros

100

mm

Inner radius, Ris

40.5

mm

90

mm

Teeth radius, Rt

42.5

mm

Slot inner opening, Sio

10/16

deg

Slot outer opening, Soo

6

deg

Outer radius, Ror

40

mm

Inner radius, Rir

16

mm

Mechanical Air Gap, g

0.5

mm

0.0008

mm

120/170/220

turns

Wire Diameter

0.8

mm2

Current

3.9

A

Phase Resistance

4.7

Ω

Power

225

W

Inner of outer radius, Rios

Rotor

Figure 3. Basic electrical equivalent circuit

Here, VT is the DC voltage supply in [V], I is the current flow through the circuit in [A], RC is the internal resistance of the coil winding in [Ω], LC is the self inductance of the motor both in [H] and Ea is the Back Electromotive Force (back emf) in [V]. The basic equivalent circuit equation can be written as ்ܸ = ‫ܧ‬௔ + ‫ܫ‬. ܴ௖

(1)

Where LC is neglected as only will be considered if in steadystate condition.

(5)

௉೔೙

Air Gap

Mesh Air Gap Sizing Coil

Winding

the BLDC is rotates for 40º as one pitch to generate a complete sinusoidal waveform. From the simulation results, the creation of mesh for the BLDC model as shown in Figure 5(a) is done since the FEM is just a static simulation data only. The magnetic analysis is flux flow path as in Figure 5(b), and flux distribution as shown in Figure 5(c). To find the average value of the flux per pole in the air gap between stator and the rotor, a probe method need to be performed so that the location of the desired air gap flux density can be pointed easily. The flux per pole is calculated by multiply the value of flux density with the cross section area of the stator teeth Figure 4. Basic dimension of BLDC

The analysis of BLDC starts by simulating the best value of design parameter. At the early analysis, the calculation of output torque based on simulation that carried out is done when

Figure 5(c) shows the flux distribution in BLDC is high at the body of rotor because the flux is concentrated at the restrict area between the two PM and then deflect to the others part. From the overall simulation result in Figure 5, it can be observed that the flux leakage between PM and stator teeth is reduced. This means that all the generated flux is not wasted 1.8 T 1.6 T 1.1 T 0.8 T 0.0 T

(a) Mesh

(b) Flux flow path

(c) Flux distribution

Figure 5. Mesh, flux flow, and flux distribution in BLDC

IV.

ANALYSIS ON VARIOUS SIZES OF MAGNET

The performance of high torque BLDC is depending on the permanent magnet properties, and its size. Therefore, to achieve the desired torque performance, analysis on various sizes of magnet needs to be done. The design of BLDC is fixed with diameter and thickness of 200 mm and 30 mm respectively. Since the torque characteristic of the 40 mm rotor radius BLDC is investigated with the fixed 30 mm length of the magnet, Lm, the height and width of magnet was varied from 8 mm to 14 mm and 1 mm to 7 mm respectively due to their limited space available in the rotor slot. For more clear view, the dimension of the magnet structure and its position in the rotor is shown in Figure 6. Table II shows the overall dimension for the various sizes of the magnet which used in the investigation of the torque behavior according to the modification of the magnet structure.

TABLE II. Model Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Model 11 Model 12 Model 13 Model 14 Model 15 Model 16

DIMENSION FOR VARIOUS SIZES OF PM Dimension Height, Hm

Width, Wm

Length, Lm

8 8 8 8 10 10 10 10 12 12 12 12 14 14 14 14

1 3 5 7 1 3 5 7 1 3 5 7 1 3 5 7

30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 a. All unit in mm

Rotor Lm

PM

Hm Wm Figure 6. Dimension of permanent magnet

A. Cogging Torque Characteristic Figure 7 shows the cogging torque of BLDC for difference sizes of magnet. The minimum and maximum cogging torque is 0.00496 Nm and 0.79353 Nm. For instances, the output cogging torque of BLDC is increases due to expansion on both parameter for height of the magnet, Hm and width of the magnet, Wm.

gn

7

Cogging Torque TC [Nm]

Ma

M 14 ag ne 2 th1 eig 10 ht Hm

] et h mm [ 3 m e ig 1 ht th W d Hm i tw [m gne m] a M 5

8 [m m

]

70 60 50 40 30 20 10 0 7 m] [m 5 m 3 W 1 dt h i tw ne g a M

Figure 7. Maximum cogging torque for various sizes of magnet Figure 9. Motor efficiency for various sizes of magnet

B. Torque Characteristic Figure 8 shows the peak torque that achieved on same injected current, 3.9 A The minimum and maximum values of peak torque are 0.60232 Nm and 6.4887 Nm. It can be seen that, the value of output torque is raise gradually as the both Hm and Wm are increased. The average incremental ratio of the torque to Wm is 17.86 % greater than Hm.

Figure 10. Ratio of maximum cogging over maximum torque on various sizes of magnet

V.

CONCLUSION

In this paper, the development of a three phase brushless DC motor (BLDC) was discussed. The performance of the motor as well as the effect of magnet sizing has been studied by using FEM. Based on the result, it shows that the modification of the magnet influences the output torque of the motor. It is observed from the result that the maximum output torque is achieved when both length and width of magnet is largest. The result also signifies that the increment of torque will not determine the increases in the motor efficiency as well. REFERENCES

Figure 8. Maximum torque for various sizes of magnet

C. Efficiency Analysis Figure 9 shows that the motor efficiency is slightly increases when the sizes of magnet are decreased. The maximum efficiency is about 60% at smallest size of magnet. This indicates that when the torque is high, it will not define that the efficiency is also high. D. Ratio of Cogging and Torque Analysis Figure 10 shows the percentage of maximum cogging over torque, Tc/T on various sizes of magnet with fixed length of magnet, Lm. At the first glance, the ratio is increase due to both expansion However, percentage of Wm(1 mm) is higher than Wm(3 mm) when Hm is 12 mm and 14 mm. In theoretically, the produced torque is better when the percentage is higher.

[1]

[2]

[3]

[4]

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