Design of disk type PM synchronous generator based on halbach

This paper expounds the application merits of disk type PM synchronous generator in small-scale wind power generation .The characteristics of the disk type PM synchronous generator were analyzed and 8P, 200W disk type generator with 90 degree Halbach magnet structure was designed. Simulation and calculation are carried out by using finite element method. By comparing the 90 degree Halbach magnet structure and the traditional magnet structure of the disk type generator, the results shows that the 90 degree Halbach magnet structure can improve the air gap magnetic density, reduce the leakage of main magnetic circuit and the loss.


Introduction
Disc type permanent magnet synchronous motor with axial flux characteristics plays an irreplaceable role in many fields.Various studies have been made about the axial permanent magnet motor in the application of high speed motor and generator [1][2][3][4] , also it has a wide application in electric vehicle [5][6] , flywheel energy storage [7] , driven ship elevator [8] , and ship drive [9] .A coreless axial-flux machine with Halbach structure in direct-drive wind power generation field has the following advantages: (1) small axial size, high power density, simple structure; (2) coreless structure has no cogging effect which can effectively reduce the motor vibration and noise caused by the cogging; (3) the magnetic pole has a special Halbach structure which hold better sine degree of air gap magnetic density, meanwhile, avoiding the additional loss caused by harmonic.Thus, the study on the coreless disc generator with Halbach structure in the direct drive wind power generation field has important practical significance.
The main contributions of this paper can be summarized as follows.Regarding to the Halbach array structure of coreless double disc rotor permanent magnet generator, the structure and corresponding design features were analyzed.And, the three dimensional electromagnetic finite element calculation of the designed 8P and 200W disk motor is carried out The characteristics of magnetic field distribution of motors are studied through the analysis of the finite element field plots results and numerical results; The influence of different Halbach magnetic pole structure and magnetic pole thickness on the air magnetic flux and peak value is studied as well.

Structure of magnetic circuit Based on Halbach
Coreless double exterior rotor disc type generator is composed of the pole, the back iron , armature windings, bearings and other structures.Magnet is made of special structural configuration of Halbach array and it is attached to the back of a certain thickness of ductile iron that has a strong magnetic permeability.Armature winding consists of multi-strand wire wrapped package in accordance with a certain pitch.The structure of disc type generator with Halbach array shown in figure 1.As shown in figure.1 a , each magnetic pole is composed of axial magnetization pole a and auxiliary magnetic pole b which is perpendicular to a. Every four different polarization direction of the magnetic poles formed a set of loop.The material of back iron is made of nodular cast iron which can ensure the strength of the rotor as well as lower the cost of machine.Windings were wrapped by using a tool specially designed for this machine.After the windings were made we encapsulated the windings into epoxy resin which can leave out the iron core and solve the problem of cogging torque when the speed of wind power generate is low.As shown in figure 1(b),the path of main magnetic flux are marked with dotted lines.In figure 1 (b), there are a pair of upper and lower rotor NS poles respectively.It is shown in the figure that the main magnetic circuit starts from the N pole on the right side of the rotor to the S pole in lower rotor through the winding, and then gets to the N pole on the left side of the rotor.Then it gets through the wingding again into the S pole in upper rotor, and finally returns to the N pole on the right rotor to complete a closed magnetic circuit.

Determination of inner and outer diameter of double external rotor disc type generator
The direction of magnetic field line through stator winding is axial direction and the conductor which parallel to the pole is the effective part.The position of a single conductor in the plane is represented by r andT as shown in figure 2.

Figure 2. electromagnetic calculation diagram
Air gap magnetic density at the mean radius of generator is represented by B δ (θ).The mechanical angle is represented by Ω .The average electromotive force of each conductor can be expressed by [4]   ) ) (2) The electrical load av A at mean radius of the generator can be expressed by [4] : Set D o , A av and B δ as constant and γ as the variable.Taking the derivative of the last formula, it can be seen that the output is maximized when the Ratio of inner and outer radius is set toγ= D o / D i= 3 [10]   Also the motor inertia, the magnetic flux leakage factor, efficiency and other factors should be considered synthetically.Generally speaking, the ratio of inner and outer diameter of the axial flux disc type permanent magnet generator is between 1.5-2.2 [11].
3 Magnetic field simulation

Basic parameters of generator
The rated speed of the disc type generator is 500 rpm, and alternating current with 50Hz is desired when the speed is between 350 rpm and 500 rpm.According to formula 60 f p n , the values of p range from 6 to 8, and it set to 8 in this article.The basic parameters of double exterior rotor disc type generator is shown as Table 1.

Simulation and analysis of magnetic field of disk type generator
The 3-D model of disc type generator can be build based on the parameters given in Table 1 and   The section of the center line in Figure 3 is the position of the magnetic field analysis.After the calculation, the scalar diagram corresponding to the section in figure 3 is shown in figure 4. The air gap magnetic density of the 90 degree Halbach magnet structure and the traditional magnet structure all have the characteristics of uniform distribution.In the case of the Halbach magnet structure, the maximum magnetic density of the back iron is about 1.8T.In the case of the traditional magnet structure, the maximum magnetic density of the back iron is about 2.2T which presents the saturation phenomenon.Because of the magnetic flux is shared by the he Halbach magnetic pole structure, the magnetic density in the back iron part is small in the case of Halbach magnet structure.
The section of the center line in Figure 3 is the position of the magnetic field analysis.After the calculation, the scalar diagram corresponding to the section in figure 3 is shown in figure 4. The air gap magnetic density of the 90 degree Halbach magnet structure and the traditional magnet structure all have the characteristics of uniform distribution.In the case of the Halbach magnet structure, the maximum magnetic density of the back iron is about 1.8T.In the case of the traditional magnet structure, the maximum magnetic density of the back iron is about 2.2T which presents the saturation phenomenon.Because of the magnetic flux is shared by the he Halbach magnetic pole structure, the magnetic density in the back iron part is small in the case of Halbach magnet structure.

Disk type generator air gap magnetic density of Halbach magnet structure
For easy quantitative analyzing the air gap magnetic density, it draw a center line of the air gap that direction is perpendicular to the axial in the middle of the air gap as shown in figure 3. The pole-arc coefficient of the magnet is 30°/45°.In other words the axial magnetization magnetic pole angle is 30 degrees.Axial magnetic density of the air gap on the center line of the curve is shown in figure 5 (a)schematic diagram of magnet with Halbach array (b) a pair of magnetic pole expansion Figure 1.the expand structure of disc type generator with 90 Halbach array :

I
is the effective value of phase current and ) E is effective value of phase voltage.Phase number is represented by m .Air gap flux density is represented by G B .Average air gap magnetic density in each pole distance is Put formula (3) into formula (2) : the simulative calculation for electromagnetic field can be made.The finite element model of generator is shown in figure3.Halbach magnet structure is shown in figure3 (a) and traditional pole structure is shown in figure3 (b).In order to observe the air gap flux density only the lower Halbach pole group and back iron are left in figure3.

Figure 3 .
Figure 3. finite element model of disk type generator (a) the magnetic flux density corresponding to the section in figure3(a) (b) the magnetic flux density corresponding to the section in figure3(b)

Figure 4 .
Figure 4. magnetic density distribution map of the disk type generator with Halbach magnet structure or traditional magnet structure

Table 1 .
The basic parameters of double exterior rotor disc type generator.
computed by the magnetic