INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2, pp. 175-181
FEBRUARY 2012 / 175
DOI: 10.1007/s12541-012-0022-6
Dynamic Simulation and Experimental Verification of Flux Reversal Linear Synchronous Motor Shi-Uk Chung1,#, Ji-Won Kim1, Byung-Chul Woo1, Do-Kwan Hong1, Ji-Young Lee1 and Dae-Hyun Koo1 1 Electric Motor Research Center, Korea Electrotechnology Research Institute, Changwon, South Korea, 641-120 # Corresponding Author / E-mail:
[email protected], TEL: +82-55-280-1452, FAX: +82-55-280-1490 KEYWORDS: Dynamic simulation, Flux reversal, Linear synchronous motor, Look-up table
This paper presents a dynamic simulation model which fully describes transient and steady-state operation of flux reversal linear synchronous motor (FRLSM). Magnetic field computations by finite element analysis considering inter-phase coupling effect are performed to establish phase decoupled voltage equation for the dynamic simulation. Simulation parameters such as thrust, normal force, flux linkage, and core loss are obtained by magnetic field computation and put into look-up tables. The validity of the model is verified by experiments under various operating conditions. Manuscript received: June 17, 2011 / Accepted: August 31, 2011
1. Introduction For linear motion applications, permanent magnet linear synchronous motors (PMLSMs) have been successfully adopted. However, this solution often results in significant cost increase since a large amount of rare-earth permanent magnet (PM) is laid in stator which spans the entire travel length. PM material cost can be a real challenging issue especially for long-stroke applications. Flux reversal machine (FRM) has been originally suggested to incorporate the advantages of switched-reluctance and PM machines. The conventional FRM consists of a passive rotor and multi-pole PMs of alternating polarity on each stator salient tooth. FRM can exhibit servo quality characteristics when driven by 3phase sinusoidal vector control.1 Most of previous research works related to FRM concentrated mainly on rotary machine except flux reversal linear oscillomachine for short stroke application.2-4 Recent research works on flux reversal linear synchronous motor (FRLSM) showed feasibility for long stroke applications.5 A new magnetic circuit design of FRLSM with auxiliary salient poles has been also suggested to increase thrust density.6 It has been shown that FRLSM with multiple auxiliary salient poles can provide cost effective servo performance.7,8 This paper deals with a dynamic simulation and its experimental verification of FRLSM with multiple auxiliary salient poles since the dynamic simulation model is not analytically defined yet. Therefore, this paper adopts a look-up table based model9 which can fully describe transient and steady-state operation © KSPE and Springer 2012
of the FRLSM. Extensive finite element analysis (FEA) is performed to build look-up tables which consider inter-phase coupling effect under 3phase instantaneous current loading. The look-up tables obtained by the proposed method lead to phase decoupled voltage equations which make simulation model much simpler. All electrical parameters required for the simulation are numerically obtained and some mechanical parameters such as viscous damping and seal friction are experimentally obtained.
2. Analysis FRLSM description Fig. 1(a) illustrates mover and winding arrangement of the analysis FRLSM together with force calculation paths and boundary condition for FEA. Fig. 1(b) illustrates detailed dimensions of the analysis FRLSM. Major specifications are summarized in Table 1. More detailed specification and characteristics of the analysis FRLSM can be found in the previous research.8
3. Dynamic simulation model 3.1 Governing equations and simulation model Fig. 2 schematically illustrates block diagrams of dynamic simulation model. The structure of dynamic simulation model is basically the same as the one presented in previous research9 except
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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
that this paper establishes look-up tables, which leads to phase decoupled voltage equation as shown in Fig. 2(a) since each phase of FRLSM is magnetically coupled. Phase voltage and mechanical equations can be expressed as in (1) and (2).
V =Ri + j
j
d λ (i, x)
j
, λ = ∑λ ,
j
j
dt
(1)
jk
j , k = PhU . , PhV . , PhW . F = mx + cx + F , x
l
F = µ ( F + mg ) + F l
k
y
r
seal friction
displays non-linear characteristics due to saturation.6,8 Hence, this paper performs extensive magnetic field computations to fully consider inter-phase coupling effect and saturation under instantaneous 3-phase current loading. This paper only takes Ph.U, which consists of U and /U as shown in Fig. 1(a), for example to explain how to establish look-up tables since all other look-up tables can also be obtained in the same manner. For a WYE connected motor, instantaneous 3-phase currents are to flow in such a manner that all 3-phase currents are balanced at any time as shown in Fig. 3. Under such a current
(2)
+F
core loss
where Vj, Rj, ij, λj, Fx, Fy, m, c, x, v Fl, µk, gr, Fseal friction, and Fcore loss denote voltage, resistance, current, flux linkage, thrust, normal force, moving mass, viscous damping coefficient, mover position, velocity, total resistance acting against motor motion, kinetic friction coefficient, gravitational acceleration, linear bearing seal friction, and resistance by core loss, respectively.
Velocity command
v*+ -
U
W
/U
/V
Path2(44mm)
Path3(47mm)
Path4(47mm)
Path5(44mm)
/W
iU* +
PI controller
+
PI controller
-
iW* +
PI controller
-
VU* Voltage iU
Mechanical equation
equation
v
x
1
s
VV* Voltage iV equation
VW* Voltage iW equation
RU +
V U* Look-up table
+
Flux linkage Ph.U
x
Az=0
-
÷
-
Mover 2
V
Fx to current converter
(a) Block diagram of velocity control system
The analysis FRLSM is WYE connected and its magnetic circuit is 3-phase coupled. Moreover, the FRLSM with salient poles τp
Fx*
i V*
3.2 Magnetic Field Computations 3.2.1 Thrust, normal force and flux linkage look-up tables
Mover 1
PI controller
diU dt
iU
1
s
1
∆i
-
Unit
Path1(52mm)
Path6(66mm)
delay
(a) Mover and winding arrangement, force calculation paths and boundary condition
44
v
Flux linkage Ph.U
(b) Block diagram of voltage equation 5 . 9 3
τp 6
y
×
delay
6 1
30
12
1
∆x
Look-up table
Unit
4
+ -
132
6 . 3
Look-up table
Flux linkage Ph.U
iU x
g
iV
x
C1
5 . 5 1
(b) Detailed dimensions
x iW
Fig. 1 Analysis FRLSM Table 1 Specifications of analysis models Item Value 6.0 Pole pitch(τp) PM material Br=1.3T, µr=1.05 Mover/stator core material S23 Mover/stator core stack length 100 Copper wire cross-section 3×1 Number of serial turns/phase(N) 66 Phase resistance 0.14 Rated thrust 600 Rated MMF/Ph. 800 Average airgap length(g) 0.45 Mover assembly weight 17.3
0 2
x iU
Unit mm mm mm Ohm N AT mm kg
x iV x iW x
iU
Look-up table
Look-up table
Fx Ph.U
Look-up table
Fx Ph.V
Core Loss
v +
+
Fx
+
+
+
-
-
1
v
ms+c
Seal friction Look-up table
Fx Ph.W
Look-up table
Fy Ph.U
Look-up table
+
Fy Ph.V
+
Look-up table
+
Fy
+ +
µk
mgr
Fy Ph.W
(c) Block diagram of mechanical equation Fig. 2 Block diagram of dynamic simulation model of FRLSM (* denotes command value)
INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
loading condition, thrust and normal force by each phase can be obtained by Maxwell stress method along the paths illustrated in Fig. 1(a). Thrust and normal force by Ph.U can be obtained along the paths 1 and 4 which cover U and /U as shown in Fig. 4(a) and (b), respectively. Flux linkage of Ph.U can be also obtained from the corresponding windings as shown in Fig. 4(c). Fig. 4 shows the look-up tables of Ph.U obtained by the proposed method.
U
V
/U
W
/V
Ph.U
Ph.V
i
Ph.W
0.5i
2τp
/W
0.5i
2τp
2τp
Fig. 3 Phase winding connection and instantaneous current loading condition for look-up tables of Ph.U
n
2
0AT
0 -200
0
2
2
1.5
-1600AT
] T [
-2800AT
B ,
4
(3)
Bx By
y
10
12
3000 2500
2800AT
2000
1600AT
1500
800AT
1000 y
0AT
DFT B
-800AT
Core Loss Coefficients
kh
] x T [ x 1f 2f 3f 4f 5f 6f B ] y [Ty 1f 2f 3f 4f 5f 6f B
-1600AT
1f Flux density[T]
Discrete Fourier Transform
-2800AT
4f
s o l e r o C
Time[sec]
Displacement [mm] (a) Thrust
8f
W [ s
x
8
Core Loss Curves
] g k /
B
6
}
2
Finite Element Analysis
-800AT
-400
2
π σd ρ 6.0
kc ≈
800AT
200
-600
F Ph.U[N]
∞
i =1 k =1
1600AT
400
F Ph.U[N]
Core loss, which is dependent upon motor speed and applied current, is one of the resistances acting against motor motion and it is also considered in the dynamic simulation model as shown in Fig. 2(c). The core loss can be calculated by (3) under 3-phase sinusoidal currents input at steady-state.10 For the core loss computation, from the fundamental to the 10th harmonic components are considered. In the simulation, the core loss is considered as a resistance defined as the loss divided by the motor speed. Fig. 5 schematically illustrates core loss computation procedure by FEA. Bx and By, which are x, y components of flux density, can be obtained in every iron core element. Their pulsating components can be extracted by discrete Fourier transform. To obtain core loss coefficients of S23 with respect to frequency and induction, core loss test on specimen is needed. Some of representative test results are shown in Fig. 6 and the corresponding core loss coefficients are summarized in Table 2. Fig. 7 shows the core loss look-up table with respect motor speed and MMF.
2800AT
600
-800
3.2.2 Core loss look-up table
Pc = ∑∑ { kh Bk kf + kc ( Bk ⋅ kf ) + ke ( Bk ⋅ kf )
800
x
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: Hysteresis Loss Coeff.
kc
DFT B
: Eddy Current Loss Coeff.
ke
Frequency[Hz]
: Excess Loss Coeff.
500 0
0
2
4
6
8
10
0.05
2800AT 1600AT 800AT 0AT
0.00
-800AT
-0.05
-1600AT
0.15 0.10
-0.10
100 80
-2800AT
-0.15 -0.20
Fig. 5 Core loss computation procedure
Core loss[W/kg]
Flux linkage Ph.U[Wb]
0.20
0
2
4
6
8
Displacement [mm] (c) Flux linkage
Fig. 4 Look-up tables of Ph.U
Core Loss Computation
12
Displacement [mm] (b) Normal force
10
12
60 400Hz
40
200Hz 150Hz
20 0 0.0
300Hz
100Hz 50Hz
0.3
0.6
0.9
Induction[T] Fig. 6 S23 core loss test results
1.2
1.5
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250
1600AT 1400AT 1200AT 1000AT 800AT 600AT 400AT 200AT
200
Core loss[W]
INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
150 100 50 0 0.0
0.6
1.2
1.8
2.4
Speed[m/s]
Fig. 7 Look-up table core loss Table 2 Representative core loss coefficients kc Frequency[Hz] kh 50 0.0474107 0.0001561 100 0.0534347 0.0001561 150 0.0570867 0.0001561 200 0.0550111 0.0001561 300 0.0562819 0.0001561 400 0.0491140 0.0001561
ke 0.0009857 0.0011520 0.0013014 0.0012832 0.0015013 0.0014965
(σ[S/m] = 2941176.5, d[mm] = 0.5, ρ(kg/m3) = 7750) 620
F [N]
600 Avg. 596.3N
580
800AT/Ph.
Avg. 596.2N
x 320
400AT/Ph.
Avg. 316.9N
300
Symbol : By direct FEA Line : By look-up table method
Avg. 315.2N 280
0
2
where Pc, kh, kc, ke, k, f, n, ρ, σ, and d denote total core loss, hysteresis loss coefficient, eddy current loss coefficient, excess loss coefficient, harmonic order, frequency, number of finite elements, density, conductivity and thickness, respectively. Fig. 8 compares computation results obtained by direct FEA and the look-up tables under 3-phase sinusoidal currents input at steady-state. It can be stated that the proposed look-up tables are numerically valid since the values obtained by the two different methods agree quite well with each other with negligible numerical errors. Efficiency and power factor of the analysis FRLSM at several different operating conditions are show in Fig. 9(a) and (b), respectively. The efficiency and the power factor shown in Fig. 9 are computed by the dynamic simulation model at constant speed region. In the computation, all mechanical losses are not considered since those mechanical losses depend heavily on mechanical components. Therefore, copper and core losses are considered to characterize the analysis FRLSM. It can be stated that the FRLSM shows quite a good efficiency characteristics especially lower thrust region. This is quite significant especially long stroke applications since, in constant speed region, the linear motor needs only to overcome friction resistance, which is typically much lower than the rated thrust. However, the analysis FRLSM suffers poor power factor like all other similar machines11-14 and requires a comparatively high capacity drive system.
4
6
8
10
12
Displacement [mm] (a) Thrust
4. Experimental verification 4.1 Experimental identification of damping coefficient Servo drive XENUS XSL-230-40 (Copley Controls) and motion controller UMAC Turbo (DeltaTau) were used to operate
2900 2800
95
400AT/Ph.
Avg. 2628.6N 2500
Avg. 2622.1N
0
2
4
Symbol : By direct FEA Line : By look-up table method 6
8
10
12
Efficiency[%]
F [N]
Avg. 2783.4N
y 2600
2400
100
800AT/Ph.
Avg. 2791.5N 2700
Displacement [mm] (b) Normal force
85 80 75 200
At 3.0m/s At 2.0m/s At 1.0m/s 400
600
800
600
800
Thrust[N]
800AT/Ph.
0.08
(a)
1.2
0.04 1.0
400AT/Ph.
0.00
Power factor
Flux linkage Ph.U[Wb]
0.12
90
-0.04 -0.08 Symbol : By direct FEA Line : By look-up table method -0.12 0 2 4 6
8
10
0.8 0.6
12
Displacement [mm] (c) Flux linkage
Fig. 8 Comparison between direct FEA and look-up table simulation at steady-state
0.4 200
At 3.0m/s At 2.0m/s At 1.0m/s 400
Thrust[N]
(b) Fig. 9 Efficiency and power factor obtained by simulation
INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
2
2
1
_
No load
1
(v + v ) 2 2
(4)
1
where Fl_No load is total resistance at no load state.
Velocity[m/s]
Motion controller DeltaTau UMAC Turbo
Command and measured velocity/acceleration are compared in Fig. 12(a), (b), 13(a), and (b), which reveal that the motor well follows motion command from the motion controller. Simulated and measured current Ph.U are compared in Fig. 12(c), (d), 13(c), and (d), which display that the simulation model well describes transient and steady-state operations. The measured acceleration in Fig. 13(b) displays overshoots (in dotted circles) and the measured current shown in Fig. 13(d) also displays overshoots (in dotted boxes). However, there is no overshoot (in dotted boxes) in simulated current shown in Fig. 13(c). This discrepancy seems to be inevitable because the simulation model is based on an ideal one dimensional rigid body motion which assumes motion in moving direction only without any external disturbance. And the whole FRLSM structure is assumed as rigid body. Therefore, the simulation model can describe dynamics as long as the motion satisfies those assumptions. When the measured velocity profile is used in the simulation, simulated current becomes more similar to the measured current as shown in Fig. 13(e). This implies the simulation model physically well simulates motor dynamics. Fig. 13(f) shows thrust component decomposition by the simulation
20
1.0
10
0.5
5
0.0
0
-1.0 -1.5
-5
Vel. Acc. 0
-10
100
200
300
400
2
-15 500
Time[msec] (a) Free-run starts at 2.0m/s 2.5
25
Velocity[m/s]
P2(t2,v2)
20
1.5
15
1.0
10
0.5
5
0.0
0
-0.5 -1.5
-5
Vel. Acc.
-1.0 0
100
-10 200
300
400
Time[msec] (b) Free-run starts at 2.5m/s Fig. 11 Free run test results
-0.4
-10
Velocity Acceleration
-0.8 -1.2
0
40
-20 -30
80
120
160
200
240
280
320
2
-40 360
1.6
40
1.2
30
0.8
20
0.4
10
0.0
0
-0.4
-10
Velocity Acceleration
-0.8 -1.2
0
40
-20 -30
80
120
160
200
240
280
320
-40 360
320
360
2
Time[msec]
(b) Measured velocity and acceleration 16 12 8 4 0 -4 -8
-15 500
-16 -40
0
40
80
120
160
200
240
280
Time[msec]
(c) Simulated current of Ph.U
Acceleration[m/s ]
30
P1(t1,v1)
0
-12
3.0 2.0
10
0.0
-1.6 -40
Current[A]
Velocity[m/s]
15
Velocity[m/s]
2.0
Acceleration[m/s ]
25
-0.5
20
0.4
Time[msec]
2.5
P2(t2,v2)
30
0.8
(a) Motion command
Fig. 10 Prototype FRLSM, servo drive and motion controller
P1(t1,v1)
40
1.2
-1.6 -40
Servo drive Copley Controls XENUS XSL-230-40
1.5
1.6
Acceleration[m/s ]
m (v − v ) + Fl c = − (t − t )
4.2 Comparison between simulation and experiment
Acceleration[m/s ]
the motor and Fig. 10 shows an experimental setup to evaluate motor dynamics. To complete the dynamic simulation model, mechanical parameters such as c, µk, and Fseal friction have to be defined in the mechanical equation. In this paper, 0.002 was used for µk, which is provided from the manufacturer. Fseal friction was measured with respect to position at no load state. The average measured value was 35N while the maximum value provided by the manufacturer is 42N. It seems that the measured seal friction value falls within a reasonable range compared to the maximum possible value. c can be determined by motor free run test and its result is shown in Fig. 11. Region from P1 to P2 is a constant deceleration zone. The value can be experimentally estimated by (4) and the estimated value was 44.6N⋅s/m on average.
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2
4A/div
(d) Measured current of Ph.U Fig. 12 Simulation and measurement comparison at 1.2m/s and 20m/s2
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]s / m [y itc ol e V
INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
3.2
40
2.4
30
1.6
20
0.8
10
0.0
0 -10
-0.8
Velocity Acceleration
-1.6 -2.4 -3.2 -30
0
30
-20 -30
60
90
120
150
180
210
240
2 ] s/ [m no tia re le cc A
-40 270
Time[msec]
5. Conclusion
(a) Motion command s]/ [m yti co le V
3.2
40
2.4
30
1.6
20
0.8
10
0.0
0
2
-10
-0.8
Velocity Acceleration
-1.6 -2.4 -3.2 -30
0
30
-20 -30
60
90
120
150
180
210
240
] s/ m [n iot ar el ec c A
-40 270
Time[msec]
(b) Measured velocity and acceleration 24 18
] A t[n err uC
12 6 0 -6 -12 -18 -24 -30
0
30
60
90
120
Time[msec]
150
model. Moving the mover of 17.3kg at 2.4m/s and 30m/s2 needs inertial thrust of 517N. However, the estimated resultant thrust is about 711N when all the resistances from the different losses are added.
180
210
240
270
This paper has proposed a look-up table based dynamic simulation model for FRLSM which simulates both transient and steady-state operations since it considers inter-phase coupling effect, saturation, core loss, and mechanical losses. The validity of the model was confirmed by experiments. The simulation model is especially useful when a linear motor test equipment is built for performance evaluation. Because the mechanical parameters can remain almost same for the test equipment regardless of linear motor and all electromagnetic parameters can be analytically estimated. Therefore, it can be stated that, with given information on mechanical parameters, dynamics of a linear motor can be virtually investigated even before prototyping.
(c) Simulated current of Ph.U
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6A/div (d) Measured current of Ph.U 24
2. Boldea, I., Wang, C., Yang, B. and Nasar, S. A., “Analysis and design of flux-reversal linear permanent magnet oscillating machine,” 33rd IAS Annual Meeting, Vol. 1, pp. 136-143, 1998.
18
]A t[n err uC
12 6 0 -6
-12 -18 -24 -30
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60
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120
150
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Tim e[m sec]
(e) Simulated current of Ph.U (measured velocity profile is used) 900
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600 ] N 300 [ t s u r 0 h t l a -3 0 0 i t r e n -6 0 0 I
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-9 0 0 300
Resultant resistance By viscous friction By core loss By seal friction By Coulomb friction
240 ] N 180 [ e c n 120 a t s i 60 e R
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0 900 600 ] N [ t 300 s u r h 0 t t n a -3 0 0 t l u s -6 0 0 e R -9 0 0
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0
30
60
90
120
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270
Tim e[m sec]
(f) Thrust component decomposition Fig. 13 Simulation and measurement comparison at 2.4m/s and 30m/s2
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INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 13, No. 2
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