Numerical Calculation for Asynchronous Magnetic Coupling

Kaikai Zhou

, Peng Wang

, Zhi Yuan

and Yanjun Ge

College of Mechanical Engineering, Dalian Jiaotong University, Huanghe Street, Shahekou Distict, China

Keywords: Asynchronous magnetic coupling, Mechanical properties, Magnetic field analysis, Vector magnetic

potential

Abstract: The available magnetic circuit algorithm is difficult to calculate exactly the electromagnetic torque of the

asynchronous magnetic coupling (AMC). The present study establishes the gap flux density theory model

by the use of vector magnetic potential method and the two-dimensional field boundary condition, and then

analyzes the variation law of induction current among the cage bars along with the spatial phase and electric

angle. The Lorenz force is integrated around the circumferential direction, and then the electromagnetic

torque model was established according to the current superposition principle. The obtained theoretical gap

flux density, cage bars induced current and torque were analyzed comparatively with the finite element

method. The revolving speed curve, torque curve and current curve of AMC under rated condition were

obtained by the method of finite element dynamic analysis, and then the electromagnetic torque

characteristic curve was draw to reveal its dynamic operation law. At last, the correctness of the mechanical

characteristics of AMC was verified by experimental results.

1 INTRODUCTION

In recent years, adjustable-speed magnetic couplings

have been very successfully introduced to provide a

high-efficiency alternative means of control by

matching the motor output speed and torque to the

requirements of the load[1, 2]. Compared with the

ordinary couplings, magnetic coupling has the

advantages of non-contact power transmission, no

friction, stable transmission, low working condition,

low maintenance cost, etc. Compared with variable-

frequency drives (VFD)[3], magnetic coupling do

not generated electronic harmonics which will cause

system problems and may overheat motor windings.

The squirrel cage rotor has been tested for a long

time, and the theory is relatively mature. Therefore,

the use of standard squirrel cage rotor design

magnetic coupling has the advantages of low design

cost, easy to manufacture, and can be applied to the

field of electromagnetic braking, and has attracted

widespread attention of scholars. The Flux Drive

company in the United States has commercial

production of speed adjustable squirrel cage rotor

couplings, but its cage rotor needs to be redesigned

and has a longer design cycle, and there is no

literature to report its mechanical properties[4]. To

solve this problem, an asynchronous magnetic

coupling based on an existing squirrel cage rotor is

proposed[5,6].

The mechanical analysis of magnetic drive

mainly includes analytic method[7,8] and finite

element method[9,10]. In this paper, the two

methods are combined to do the following research

work: the gap flux density theory model is

established by the use of vector magnetic potential

method, and then the variation law of induction

current among the cage bars along with the spatial

phase and electric angle are analyzed. The torque is

analyzed by Faraday law of electromagnetic

induction. The obtained theoretical gap flux density,

cage bars induced current and torque are analyzed

comparatively with the finite element method.

2 STRUCTURE OF AMC

The asynchronous magnetic coupling is mainly

composed of the outer rotor, the squirrel cage rotor

and the air gap. The structure of the asynchronous

magnetic coupling is shown in Fig.1.

1. Permanent magnet 2. Cage bar 3. Yoke 4. Fill block（

Non-magnetic material） 5. Air gap 6. Cage rotor

Figure 1: The structure of the asynchronous magnetic

coupling.

3 TORQUE CALCULATION

The air gap magnetic field plays a decisive role in

the torque transmission of the asynchronous

magnetic coupling. Paper [1] has calculated the

radial component B

and the tangential component

of the air gap magnetic field by using the vector

magnetic potential method. The formula is as

follows:

()

111

,cos()

np np

rnn

B r np A r B r np

θθ

∞

−−−

∑

(1)

()

111

,sin

np np

B r np A r B r np

θθ

∞

−−−

=− −

∑

(2)

Where p is the pole-pairs of permanent magnet, r

is the air gap radius, A

and B

are constants for

calculation, the formula is as follows:

()()

()

22 11

2332

1122

3223

2222

1223

2222

231 2

np np np np

np np

np np np np

RRRR

npRRRR

RRRR

RR np

RRRR

−− −−

−

−−−−

−−

−−−−

⎡⎤

+−

⎢⎥

+− −

⎣⎦

⎡⎤

−+

⎡⎤

⎢⎥

−

⎣⎦

⎢⎥

+− +

⎣⎦

(3)

()()

()

22 11

2332

112 2

3223

2222

1223

2222

231 2

np np np np

np np

np np np np

RRRR

npR R R R

RRRR

RR np

RRRR

−− −−

−−−−

−−

−−−−

⎡⎤

+−

⎢⎥

+− −

⎣⎦

⎡⎤

−+

⎡⎤

⎢⎥

−

⎣⎦

⎢⎥

+− +

⎣⎦

(4)

Where

is the vacuum permeability, and the M

is the coefficients of the Fourier series expansions

(n=1, 2...), R

is the outer diameter of the squirrel

cage rotor, R

is the inner diameter of the permanent

magnet, and R

is the outer diameter of the

permanent magnet.

The induction electromotive force in each cage

bar of the squirrel cage rotor is proportional to the

magnetic field density, and the current direction can

be determined by the right-hand rule.

According to Faraday's electromagnetic

induction theorem, the maximum induction potential

induced by cutting magnetic induction lines in each

cage is as follows:

maxsr

EBLv= (5)

Where v is the relative rotation speed of internal

and external rotor, and

() ()

60 2 60

zl zl

Dn n pn n

−−

==⋅=

(6)

Because the squirrel cage rotor winding is self-

closing and the loop is formed, the terminal voltage

is in short-circuit state, and its terminal voltage is

zero. Each loop is routed by two cage bars, so that

the total potential in the circuit E

=2E

. According

to Kirchhoff's second law, the voltage balance

equation in the rotor winding is as follows:

EIZ

••

−= (7)

RjsX

σσ

•

(8)

The effective value of the rated current is as

following:

()

RsX

(9)

The expression for the electromagnetic torque

can be expressed as follows:

()

15 ( )

fwk

TTsZBL

pR sX

nwk

sZ B L

RsX

∑

(10)

4 FINITE ELEMENT ANALYSIS

The model parameters are shown in Table 1.

2-Dimension model is established according to

Tab.1 model parameters. Defining material attribute:

the materials of air gap, outer rotor, inner rotor and

permanent magnets should be defined when

analyzing the asynchronous magnetic coupling. The

model is divided into meshes, the result is shown in

Fig.2.

Table 1: Model parameters of SCRMC.

Figure 2: Radial air gap flux density diagram.

The remanence of the permanent magnet

material is 1.18T. In Fig.1, the average value of the

air gap magnetic density is about 1.1T, and the air

gap magnetic density distribution fluctuates slightly.

The minimum value is 0.9T, and the maximum

value is 1.18T, which indicates that there is leakage.

Figure 3: Speed diagram for AMC.

Using the dynamic analysis model, adding

motion conditions of outer rotor and an inner rotor,

and the setting conditions are as follows: outer rotor

speed is set to 1000 rpm, the initial rotational speed

of the inner rotor is set to 0 rpm, the moment of

inertia is 0.094 kgm2, the output power is 30 kW,

the solution time is 0.3 s, the step is set to 0.0004 s.

After the solution and the post-processing, the

results are obtained respectively, as shown in Fig.3

and Fig.4.

Figure 4: Torque diagram for AMC.

In order to further study the mechanical

characteristics of AMC, external rotor speed is fixed

as 1000 rpm and only the squirrel cage rotor speed is

changed, the cage rotor inertia, damping and other

mechanical properties are not considered. The final

mechanical characteristics of AMC are shown in

Fig.5.

Name

numerical

value

Pole pair of permanent magnet 7

The outer diameter of the yoke

/mm

120

The outer diameter of the

ermanent ma

net /mm

100

The inner diameter of the

ermanent ma

net /mm

The outer diameter of squirrel-cage

roto

89.35

The inner diameter of squirrel-cage

roto

Air gap /mm 0.65

Axial length /mm 85

Figure5: Mechanical characteristic diagram.

As shown in Figure 5: the mechanical properties

of AMC and three-phase asynchronous motor are

similar, slip ratio and torque are on a linear

relationship above the maximum torque, and on a

nonlinear relationship between the maximum torque

and maximum starting torque; the maximum torque0

Tm is 502.9 Nm, the corresponding slip is 0.18. The

maximum torque is greater than the rated torque,

which means that the AMC has overload ability. The

maximum starting torque is 306.8 Nm, and the load

torque from the start to the steady-state is less than

the corresponding torque from the motor mechanical

characteristic curve, which in accordance with the

design requirements of the working conditions.

5 CONCLUSIONS

In this paper, the static air gap magnetic field is

analyzed by ANSYS software, in good agreement

with the analytical method. The mechanical

performance of the squirrel cage rotor magnetic

coupling is analyzed from the start to the steady state

when the actual load is simulated by dynamic

analysis. When running stably, the output torque is

923.5 rpm and the output torque is 385.3 Nm; its

mechanical characteristic curve is also given.

ACKNOWLEDGEMENTS

This work is supported by Project of National

Natural Science Foundation of China (No.

51285092), all support is gratefully acknowledged.

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