Thrust and Thermal Characteristics of Electromagnetic Launcher Based on Permanent

Magnet Linear Synchronous Motors

First A. Baoquan Kou, Second B. Xuzhen Huang, Third C. Hongxing Wu and Fourth D. Liyi Li Dept. of Electrical engineering/Harbin Institute of Technology

Abstract- Compared with steam catapult system, electromagnetic launcher (EML) system is highly integrated, and it has high and well matching performance. It will be widely used aircraft carriers ejection, rocket launchers etc in future. Double-side tabular permanent magnet linear synchronous motor (PMLSM) for electromagnetic launcher can meet the requirements of big thrust and high efficiency etc. It can accelerate the launcher at the expected speed in short time. The thrust characteristic of the launcher is essential to the whole electromagnetic launcher system. Large thrust and small thrust ripple are both expected. This paper studies thrust characteristic of different pole arc coefficients, compares the series and parallel magnetic circuit structures, and analyses the method of staggering a certain distance between poles on both sides. In order to achieve the goal of large thrust, the Launcher is often designed with high current density. As a result, it is of great loss and has quick temperature rise. This paper establishes numerical model of the two-dimensional (2D) primary transient temperature field. The temperature field of the short-term system is analyzed. The calculated and experimental results of the electromagnetic launchers can provide a basis for optimum design.

Keywords-linear motor; EML; thrust force; temperature rise

I. INTRODUCTION High power pulse technology principle is gaining and

storing energy from low power firstly, then changing the high power into high power pulse by pulse generator, and finally transmitting the pulse to load. Double-side tabular PMLSM is integrated with this technology and becomes high power pulsed–PMLSM (PP-PMLSM). The greatest concern of its contemporary application is EML technology, which in the military is mainly used for large load short-range acceleration, such as takeoff of carrier aircraft in the aircraft carrier, ejection of pilotless aircraft and missile/rocket launch. At the same time electromagnetic launcher can make full use of existing civilian technologies, such as energy storage technology, power conditioning technology, control systems and the motor technology. The study and use of these technologies will also develop and promote the application of relevant civilian technology development.

PP-PMLSM for electromagnetic launcher, working in the short-term system, needs large current to produce higher instantaneous thrust. So the thrust characteristics should be improved. Its thrust density should be increased and thrust ripple be reduced. Based on the PP-PMLSM structure and specific work conditions, we study the motor thrust

characteristic on different pole arc coefficients, compare the thrust characteristic with the series and parallel magnetic circuit structures, analyze the method of staggering distance between poles on both sides to improve the force characteristic, and study the primary temperature rise characteristic. Finite element method (FEM) is used to establish primary numerical model of 2D transient temperature field. The law of the temperature field with high thrust is also showed. The simulation analysis, experimental prototype and results provide a basis for PP-PMLSM optimal design.

II. THE OPTIMAL DESIGN OF LINEAR EML Combined with high power pulse technology, the high PP-

PMLSM is used as linear EML. Compared with the DC excitation power system, PP-PMLSM is simplified to reduce cost. In comparison with common linear induction motor, the requirement of air gap is lowered. And the motor can provide high force and high power. Compared with ordinary PMLSM, it can also produce higher instantaneous thrust [1].

The motor used as Electromagnetic catapult should be reliable, safe, and can provide big thrust in short time. These performance indicators raise a certain claims for the optimum design of motor structure. When designing the motor structure and size, improving the thrust characteristic is important. The high current density of windings causes more loss. So the problem of temperature rise and ventilation cooling method must be taken into consideration. And the basic structure of the double-side tabular PMLSM is showed in Fig. 1.

Figure 1. The basic structure of PP-PMLSM

The armature of the PP-PMLSM is dynamic, and stator is bilateral. The size parameters of the model are as follows: 18 poles and 36 slots, length of primary: 360mm, length of secondary: 1065mm, thickness of primary: 65mm, thickness of core laminations: 120mm, polar distance: 60mm, air gap length: 3.5mm. The model of the PP-PMLSM used as electromagnetic

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catapult is showed in Fig. 2. And Fig. 3 is the diagram of flux flow in the coupling part of primary and secondary.

Figure 2. Model of the linear electromagnetic catapults

Figure 3. Diagram of flux flow in the coupling part of primary and

secondary

A. Thrust Characteristic of Different pole Arc Coefficients The pole arc coefficient of linear motor is defined as the

ratio of magnet width to polar distance. It has great impact on the air gap magnetic field and thrust [2]. Now by choosing a group of the pole arc coefficients from 0.4 to 1, the thrust characteristics are calculated and analyzed correspondingly. Fig. 4 and Fig. 5 are average thrust and thrust ripple curves with pole arc coefficients variables.

Figure 4. Average thrust variable as different pole arc coefficients

Figure 5. Thrust ripple variables as different pole arc coefficient

It can be seen that, when the coefficient is small, as it increases, the average thrust increases linearly，but when the coefficient is up to a certain value and increases continually, the thrust becomes saturated and maintains at a constant. The thrust ripple curve is like wave changes. The trough points are at point 0.55, 0.75 and 0.9. When the pole arc coefficient is 0.75, the ripple is the minimum. Therefore if the pole arc coefficient is too small, the launcher thrust is also too small, but it results in the wasting of materials when the coefficient is too big.

B. Series and Paraller Magnetic Circuit Structures PMLSM with double-side tabular structure generates

normal force in both two sides. The force can offset and the impact of single-side magnetic force can be eliminated. The magnetic poles structures on different sides can be classified as series (N face to N) and parallel (N face to N) magnetic circuit. By analysis and comparison, it can be concluded that the series structure can generate bigger average thrust and smaller thrust ripple than the parallel one. So the prototype is made in the form of series structure. Fig. 6 shows the thrust characteristic of motor with series and parallel structures.

Figure 6. Thrust characteristic on series and parallel magnetic circuit structures

C. The Method of Staggering a Certain Distance Between Poles on Both Sides Staggering the poles at both sides a certain distance can not

only reduces the cogging force and thrust ripple to a certain extent, but also reduces the average thrust and generates big normal force. Range the stagger distance from 2mm to 10mm, and the corresponding thrust calculation results are showed in Fig. 7 and Fig. 8. It can be seen that, with the increase of stagger distance, the thrust decreases, the rate of its decline increases, and the thrust ripple becomes smaller and smaller.

Figure 7. The average thrust curve as the stagging distance variable

Figure 8. Thrust ripple rate curve as the staggering distance variable

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III. EML TRANSIEBNT TEMPERATURE FIELD As analysis above, it can be seen that when linear catapult

works in the short-term system, it requires large current density to generate big thrust. But the large current density will lead to much loss and high temperature rise [3]. So the study of temperature field is one of the key issues.

A. Heat Conduction Eequation of 2D transient temperature field and Equivalent Variation In 2D Descartes coordinate system, the basic equation of

transient heat conduction can be expressed as: 2 2

'2 2( )T T Tc

t x yρ λ ρ∂ ∂ ∂= + +

∂ ∂ ∂ (1)

Where c is the specific heat capacity, ρ is the density,λ is the thermal conductivity, 'ρ is the density of heat.

The differential equation boundary conditions of heat conduction are given.

The first boundary condition:

01

TTL

= (2)

Where 1L expresses the boundary of solution region, 0T is the temperature value that given after steady heat process.

The second boundary condition:

λ−=

∂∂ 0

2

qnT

L

(3)

Where 0q is the heat flux of the given edge ( 2L ), which is a constant in the steady heat conduction process and a function of time in non-static process.

The third boundary condition:

3

( )fL

T T Tn

λ α∂− = −∂

(4)

Where α and fT can be constant or function of time and position.

Composition of the above formulas expresses the boundary value problem of 2D temperature field:

1 0

23 x y 0

S : T

S : ( n n ) q (T T ) 0

TT Tx y

λ α

= ∂ ∂ + + + − = ∂ ∂

(5)

Where 0T is the known temperature distribution on the

boundary, q is the heat transferred on the boundary caused by thermal conduction,α is the surface heat coefficient, Xn is the cosine of the angle that from the boundary’s normal direction to x shaft. yn is the cosine of the angle that from the boundary’s normal direction to y shaft.

Known as the variation principle, the condition variation problem of (1) and (5) can be expressed as:

02 3

22

2

S

1 0

T crF (T)= + d2 x 2

qT+ min 2

S :

T

T TT pTy t

T T T dS

T T

λ

α α

Ω

∂ ∂ ∂ + − Ω ∂ ∂ ∂ + − =

=

∫∫

∫、

(6)

Where Ω expresses the solved region, S is the boundary which is composed of

1S and2S ,

3S

By discretizing the variation problem given above, the finite element equation of 2D temperature field can be expressed as.

K T F⋅ = (7) Where T is the unknown temperature column vector of the node, the coefficient matrix K is the overall temperature stiffness matrix. By using the method TLDL to solve the above equation, every node temperature within the solved region can be derived.

B. Transient Temperature Field and Thermal Parameters Because the region between primary and secondary is open

and the major source of heat is copper loss on the primary, we only analyze the temperature field of the primary. The calculation model of 2D temperature field is based on the following simplified assumptions [4]:

• The thermal conductivity of copper is large, so the temperature gradient along the direction of copper wire is small. Temperature is equivalent everywhere along the copper wire.

• The vertical thermal conductivity of silicon steel is far greater than that of the horizontal thermal conductivity, so heat can be considered to transmit primarily along the vertical orientation, and then conduct into air.

• The change of surrounding temperature results from the fever of linear motor is ignored and the room temperature remains constant.

• The structure of double-side tabular PMLSM is symmetry. The horizontal centre section of primary is the solving field. Because the primary is symmetry in axial direction, we calculate half of the primary in axial direction to save calculation time.

The assumptions above are reasonable. So model of linear motor temperature field simplified from 3D to 2D is also reasonable. It reduces the computational time greatly. Fig. 9 is the calculation model of primary.

The distribution and arrangement of wire are disordered and the situation of impregnating varnish is good and well distributed. The insulation paint of wire is also distributed uniformly. The slot insulation and core are close. The thermal properties of the various insulating materials in the slot are the same. We can see the copper (not including the paint film) can be equivalently considered as a thermal conductor, and the copper paint film, impregnating varnish and slot insulation as

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another thermal conductivity body. Fig. 10 shows the calculation model of slot. The equivalent thermal conductivity can be computed by:

∑

∑

=

== n

1i i

i

n

1ii

eq

K

Kδ

δ (8)

Where eqK is the equivalent heat conductivity,

iδ ( 1,2,3,..,i n= ) is the thickness of different heat conductor,

iK is the average heat conductivity.

The equivalent specific heat capacity can be computed by:

1

n

i i ii

c vc

v

ρ

ρ==∑

(9)

Where ic is the specific heat capacity of component unit. ρi is

the density of component unit, iv is the volumes of component units.

Figure 9. Model of primary

Figure 10. Model of slot domain

In addition, the method of ventilation and cooling is non-forced. When primary moves, the convection occurs on the surface of primary. The Reynolds number on the primary surface can be expressed as:

euxRv

= (10)

Where eR is the gas Reynolds number, u is the flow velocity

of air, χ is the distance from the point to the forefront of primary, v is the kinematic viscosity of air.

The heat convection coefficient of air can be expressed as:

1 / 2 1/ 30.332 e rh R Pxλ= (11)

Where h is the convection coefficient. rP is Pulangte

coefficient, λ is the thermal conductivity coefficient of air.

C. The Calculation of Loss and Temperature According to the winding current and flux density

waveform of air gap, the copper loss and iron loss can be calculated. Because the flux distribution is different in yoke and tooth as showed in Fig. 3, and the craftwork is also different, the core in yoke and tooth are calculated respectively.

When the virtual value of unilateral phase current is 310A, the loss can be derived [5]. The results are showed in Table I.

TABLE I. LOSS OF MOTOR (UNIT: W)

Loss Copper Loss Tooth Iron Loss Yoke Iron Loss Value 35750 130 113

Based on the actual fever circumstance, it can be assumed that the distribution of loss in each part is uniform. The loss is the heat source of temperature field. As a result, the simulation and computation model of 2D transient temperature can be established.

Fig. 11 shows the temperature variation of the hottest node of core, Fig. 12 is the temperature curve of the hottest part of winding.

Figure 11. Temperature changes of core

Figure 12. Temperature changes of the winding

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Fig. 13 is the primary temperature distribution when motor continuously works for 10 seconds under short-term work system.

Figure 13. Temperature distribution of primary in the 10th second

Evidently, winding temperature increases linearly with time approximately. At the 10th second, the highest temperature reaches 133. The core temperature rises slowly at the initial stage, and rises more and more quickly later, which is due to low iron loss and high copper loss. The heat mainly concentrates on the windings, and the thermal conductivity coefficient of slot insulation material is smaller than that of copper. So in the initial phase copper loss in windings can not yet reached to the core. But with the growth of time, copper loss conducts to core and core temperature rises more quickly. For such high power density of PMLSM, if copper loss is too much, the motor can not work for long time.

IV. PROTOTYPE EXPERIMENTS The prototype motor has been developed. Fig. 14 is the

picture of the prototype motor.

Figure 14. Prototype of the EM

By measuring winding resistance, the winding temperature can be gained. When the unilateral current is 310amp, the winding phase resistance is measured by LCR apparatus, and the temperature can be calculated basing on the follow formula.

( )[1 ]a a aR R α θ θ= + − (12)

Where aθ is the environmental temperature at the beginning of test. aR is winding resistance and aα is the temperature coefficient when temperature is aθ , R is the winding resistance when temperature is θ .

We can get the corresponding temperature values. The winding resistance and average temperature value in the experimental process can be known in Table II.

TABLE II. Winding resistance and the relevant temperature values

Time (s) 0 0.3 0.8

Resistance (ohm) 0.149 0.155 0.164

Temperature () 25 35.60 51.50

Time (s) 2.5 5 8

Resistance (ohm) 0.178 0.187 0.2

Temperature () 76.23 92.12 115.08

According to the variation of resistance, we calculate the average temperature value of windings. Fig. 15 shows the average temperature variation of windings during the experimental process. From the figure, it can conclude that the experimental results match with the simulation results. The electromagnetic catapult with high current density and high thrust works in the short-term system. When it works, the heat comes from copper loss primarily. In the initial period, winding temperature rises very quickly, but core temperature does not. Then as time grows, copper loss goes through insulating layer, arrives at core, so core temperature rises faster and faster

Figure 15. Average temperature of winding

V. SUMMARY Electromagnetic launchers technology for improving the

performance of weapons and equipment is of great significance, and the system will also promote the development and applications of related civilian technologies (such as storage technology, electrical technology, electronics technology etc). In this paper, the design of the thrust launcher is optimized. The law of the thrust as pole arc coefficient variable, the comparison results of series and parallel magnetic circuit structures, and the analysis of staggering relative poles in improving force characteristic provide the guidance to design EML with the greater thrust and less materials. The 2D numerical model of transient temperature field and the law of temperature rise are the basis of choosing cooling method. By testing the prototype, it can be seen that the experimental results are consistent with the theoretical analysis results. In short, in the design of the EML process, one should take full account of the great thrust and small thrust ripple demands, etc. And the indicator of big thrust requires larger current, so loss is high, winding and core temperature rise fast. Choosing the reasonable ventilation and cooling method is necessary if the EML works for long time.

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ACKNOWLEDGMENT The work described in this paper has been supported by

Doctoral Foundation of P. R. China (No. 20050213036). Its powerful supports are gratefully

REFERENCES [1] J. Xia, “Research on ending-effects thrust ripples of high precision

permanent magnet linear motor and compensation approach,” Dissertation for the Master Degree in Shenyang University of Technology. China, pp. 8-11, 2006.

[2] J. Cui, “Study on thrust force of permanent magnet linear synchronous motor and its direct thrust force control system,” Dissertation for the Master Degree in Shenyang University of Technology, China, pp. 14-21, 2006.

[3] Y. Guo, J. Zhu, W. Wu. “Thermal analysis of soft magnetic composite motors using a hybrid model with distributed heat sources,” IEEE Transactions on Magnetic. vol. 41, pp. 2124-2128, 2005.

[4] Y. Wei, “Thermal exchange in motors,” Beijing: Machinery Industry Publishing House, China, pp. 30-40, 1998.

[5] Chunting Mi, Gordon R.Slemon, Richard Bonert, “Modeling of iron losses of permanent magnet synchronous Motors,” IEEE Transactions on Industry Applications, pp. 734-741, 2003.

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