2011 International Conference on Electronic & Mechanical Engineering and Information Technology

Calculation of Eddy Current Loss and Thermal Analysis for Adjustable Permanent

Magnetic Coupler

Xu Wang Dazhi Wang

School of Information Science & Engineering School of Information Science & Engineering

Northeastern University Northeastern University

Shenyang, Liaoning,China Shenyang, Liaoning,China

e-mail: wxl908@126.com e-mail: wxl908@126.com

Abstract—Adjustable permanent magnetic coupler adopts a new type of magnetic circuit coupling principle, generates inductive magnetic field in copper collar surface by cutting magnetic induction lines, transmits torque by coupled action between inductive magnetic field and permanent magnetic field. Hence, it necessarily causes eddy current loss and heating problem. The paper builds the mathematical model of 3D sporting eddy current field according to the relevant theory of electromagnetism, employs the 3D finite element method to calculate eddy current field in copper collar region, then determines eddy current and eddy current loss in copper collar surface, finally, studies the influence of related design parameters on heat.

Key words: Adjustable permanent magnetic coupler; Eddy current loss; Sporting eddy current field; Finite element method

I. INTRODUCTION

Adjustable permanent magnetic coupler is a new type of energy saving equipment, is installed between motor and load, changes speed and torque by adjusting air gap according to different needs of the load. When the environmental temperature is increased to a certain extent, permanent magnetic characteristics will be degraded because the performance of permanent magnet is greatly influenced by temperature rise. Hence, the calculation of eddy current loss has become an important part of adjustable permanent magnetic coupler design.

In recent years, foreign scholars have employed different methods to study adjustable permanent magnetic coupler, and have achieved certain results. Documents [1-3] have given the analytical model and studied the influence of related structural parameters on mechanical characteristic. Documents [4-6] mainly analyze permanent magnetic eddy current coupler which has the same transmission principle with adjustable permanent magnetic coupler. Documents [7-9] introduce the processing methods of eddy current for disc permanent magnetic motor because the structure of two devices has similarities. At present, the domestic scholars' research about adjustable permanent magnetic coupler is very limited, mainly concentrates the radial magnetic coupler. The above analysis shows that domestic and foreign

research work is not sufficient about adjustable permanent magnetic coupler. Especially the research that eddy current loss generates heat is not deep enough. The paper first designs the low power adjustable permanent magnetic coupler and introduces its mechanism and working principle, second builds the finite element model of 3D sporting eddy current field and calculates eddy current and eddy current loss of adjustable permanent magnetic coupler, last studies the influence of structural parameters on heat.

II. MECHANICAL DESIGN AND WORKING PRINCIPLE

C. Mechanical design The schematic of Fig. 1 shows the basic configuration of

adjustable permanent magnetic coupler. Active rotor is a composite disc, includes steel disc and copper collar, rotates with the input shaft. Driven rotor is also a composite disc, includes aluminum disc> steel disc and permanent magnet. The axially moveable aluminum disc supports arrays of axially polarized NdFeB permanent magnets and rotates with the output shaft. When the air gap between the permanent magnet and the copper collar is small, relative angular speed (slip) is minimized by the strong coupling. The slip increases as the air gap increases, thus enabling a form of speed control of the load. Air gap adjusting device is usually installed in the output shaft, includes manual control and signal control, may choose the common screw adjusting device.

978-l-61284-088-8/ll/$26.00 ©2011 IEEE 4405 12-14 August, 2011

Steel disc

Copper collar

Permanent magnet

Aluminum disc

Figure 1. Mechanical schematic of adjustable permanent magnetic coupler

C. Working principle The active and driven rotors of adjustable permanent

magnetic coupler may free independently rotate. When motor drives active rotor rotation, active rotor generates eddy current and inductive magnetic field in copper collar surface by cutting magnetic induction lines of permanent magnet. Inductive magnetic field generates suction and repulsion for the adjacent permanent magnets, these two forces are known as coupling force. Suction and repulsion superimpose in the rotational direction, thus drive driven rotor and output shaft consistent rotation with active rotor, Air gap adjusting device may be manual and electrical control, can achieve closed-loop automatic control when it is connected with the stepper motor. The system drives hand wheel adjusting the air gap by controlling speed and direction of stepper motor, achieves the control of output speed.

In the process of adjusting speed, motor speed is unchanged. The input torque and output torque of adjustable permanent magnetic coupler are always equal. This equipment changes speed by adjusting air gap according to the different needs of the load, achieves the purpose of energy saving.

III. MATHEMATICAL MODEL OF THREE-DIMENSIONAL SPORTING EDDY CURRENT FIELD

Because the 3D sporting eddy current field belongs time-varying field, therefore there is no static charge in adjustable permanent magnetic coupler, displacement current density may be neglected. Maxwell's equations are simplified as:

fV x H = J

dt (D V B 0

current density, ^is conductivity; E is electric field intensity; B=juH is magnetic flux density, ju is magnetic permeability.

Magnetic flux density B can be expressed by magnetic vector potential A The expression is

B = V xA (2 ) Because there is no source current input in adjustable

permanent magnetic coupler, therefore solution area does not exist source current density and exist only eddy current density. Current density's expression is

[j = Jm +J=JP

[je = a [-V0 + V x (V x A)] (3)

Where F i s the relative speed of conductor. This paper adopts the method of A,0-A to establish

mathematical model for three-dimensional sporting eddy current field[10]. The solution area is divided in to eddy current area VI, permanent magnet area V2, air area V3. Equation of each region is

" cN(j) - a[v x ( V x i 4 ) ] = 0 (4 ) VI: V x ■VxA

V2:

V3:

V x - (V x A

V x - (V x A)

* , ) = »

0

(5)

(6 )

Where Br is residual magnetic flux density. Flux parallel boundary condition is applied on the outer

boundary of solution region. The paper calculates the magnetic flux density B, current density / within field by magnetic vector potential A and scalar electric potential 0. When the relative velocity is constant, eddy current density of each unit changes over time, but the total eddy current loss of copper collar is equal at all times, therefore the instantaneous current density / can be directly used to calculate eddy current loss. Eddy current loss of copper collar is

Ploss = I2* = \pJ2dV ( 7 ) V

Where p is resistivity of copper collar.

IV. ANALYSIS OF EXAMPLE

C. Modeling Table 1 Simulation parameter list to adjustable permanent magnetic coupler

Parameters Parameter values Parameters Parameter values

magnetic pole number 18

air's relative permeability 1

copper collar outer radius 140mm

copper collar axial length 10mm

copper collar inner radius 90mm

resistivity of copper 7.1E-08Q-m

air gap width 3 mm

coercive force 875000A/m

steel plate outer radius 140mm

steel plate axial length 10mm

steel plate inner radius 90mm

motor speed 1455r/min

permanent magnet's 1.05 permanent magnet size 30><30x20(mm)

relative permeability (length,width, height)

Where H is magnetic field intensity; / = oE is conduction

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Figure 2. Simulation model of adjustable permanent magnetic coupler

For more closer to the actual situation of equipment running, permanent magnetic materials select NdFeB, copper materials choose brass of H62 specification, steel materials choose 45 steel. Simulation parameters of adjustable permanent magnetic coupler are shown in Table 1, simulation model is shown in Fig. 2.

C. Eddy current analysis Eddy current of copper collar surface is shown in Fig 3.

The figure shows, distribution of eddy current is not uniform, mainly exists a thin layer of copper collar surface, particularly concentrates in the edge of both inner diameter and outer diameter for copper collar. Skin effect is significant. The eddy current has formed 18 loops in the copper collar surface, loop number corresponds to the number of permanent magnet, current direction of adjacent loops is at opposite poles. Hence, the inductive magnetic field which eddy current generates is equivalent to 18 magnetic poles, and N> S poles are arranged alternately in copper collar.

adopt air or water cooling way to cool. The influence of copper collar thickness on heat is

shown in Fig. 5. The figure shows, as copper collar thickness increases, eddy current will increase, eddy current loss also increases. When copper collar thickness increases to a certain extent, eddy current tends to be saturated. If thickness continues to increase, eddy current loss continues to increase, eddy current which generates inductive magnetic field will reduce.

The influence of air gap on heat is shown in Fig 6. The figure shows, as air gap width increases gradually, magnetic-flux density of copper collar area reduces gradually, eddy current also reduces gradually, therefore eddy current loss reduces along with it.

Figure 4. Thermal distribution map of copper collar surface

Figure 5. Relational curve of both copper collar thickness and heat

Figure 3. Eddy current vector distribution map of copper collar surface

C. Thermal analysis Eddy current in copper collar surface mainly has two

aspect purposes, a part of eddy current generates inductive magnetic field, another part of eddy current loses as heat. The specific situation of thermal distribution is shown in Fig 4.The figure shows, heat distribution in copper collar surface is not uniform, mainly concentrates in the radial junction of adjacent eddy current loops. Therefore this device can use fin to cool according to the related theory of heat transfer, and fin is installed in steel disc behind copper collar. High-power adjustable permanent magnetic coupler can

Figure 6. Relational curve of both air gap and heat

V. CONCLUSIONS

1) Through numerical calculation of eddy current field for adjustable permanent magnetic coupler can be seen that

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the distribution of both eddy current and eddy current losses are not uniform. Eddy current mainly concentrates in the edge of both inner diameter and outer diameter for copper collar.

2) Eddy current is lose by thermal form, mainly concentrates in the radial junction of adjacent eddy current loops. Therefore this device installs fin in steel plate behind copper collar, uses thermal transfer for cooling.

3) Heat and copper collar thickness are concerned. As copper collar thickness increases, eddy current will increase, eddy current loss also increases.

4) Heat and air width are concerned. As air gap width increases gradually, eddy current also reduces gradually, therefore eddy current loss reduces along with it.

VI. REFERENCES

[1] A .Wallace, A .Von Jouanne, R. Jeffreys, Comparison testing of an adjustable-speed permanent - magnet eddy-current coupling [EB/OL]. [2011-2-2 8]. http://www.engineeringvillage.com.

[2] A. Wallace, A. Von Jouanne, A. Ramme, A. Smith, A permanent-magnet coupling with rapid disconnect capability [EB/OL]. [2011-2-28]. http://www.engineeringvillage.com

[3] M. H. Nagrial, Finite element analysis and design of variable reluctance (VR) torque coupler [EB/OL]. [2010-11-11]. http://www. engineeringvillage.com.

[4] W.Nehl Thomas, Lequesne Bruno, Gangla Vineeta, Nonlinear two-dimensional finite element modeling of permanent magnet eddy current couplings and brakes [EB/OL]. [2011-2-28]. http:// www. engineeringvillage. com

[5] Lequesne Bruno, Liu Buyun, W.Nehl Thomas, Eddy-current machines with permanent magnets and solid rotors [EB/OL]. [2011-2-28]. http://www.engineeringvillage.com

[6] Canova Aldo,Vusini Bruno, Design ofaxial eddy-current couplers [EB/OL]. [2011-2-28]. http://www.engineeringvillage.com

[7] R.Rabinovici, Eddy current losses of permanent magnet motors [EB/OL]. [2011-2-28]. http://www.engineeringvillage.com

[8] M.Vasiliu,Eddy current core losses of permanent magnet motors [EB/OL]. [2011-2-28]. http://www. engineeringvillage. com

[9] A.Boglietti, M. Chiampi, D.Chiarabaglio, Finite element analysis of permanent magnet motors [EB/OL]. [2011-2-28].http ://www. engineeringvillage. com

[10] Dexin Xie, Baodong Bai, Jinbiao Li, Finite element analysis of three-dimensionaleddy current field [M].Bejing: Machinery Industry Press, 2001:6-25.

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