Comparative Analysis of Aerodynamic Characteristics and Experimental Investigation of a Moving Coil Linear Motor Using Computational Fluid Dynamics.
Zhang, Gong ; Liang, Jimin ; Hou, Zhichen 等
Comparative Analysis of Aerodynamic Characteristics and Experimental Investigation of a Moving Coil Linear Motor Using Computational Fluid Dynamics.
1. Introduction
A linear motor (LM), converting the electromagnetic signals into
the mechanical signals reciprocating linear motion continuously and
proportionally, is looked upon as the most widely employed linear motion
mechanism in various industry driving fields. Normally, LM could be
divided into 2 types based on the moving part [1-2], that is moving iron
LM and moving coil LM. At present, a moving coil linear motor (MCLM) has
been drawing widely attention because of high linearity and small
hysteresis [3-5]. Tanaka, etc. [6-7] pointed out the generated
electromagnetic force is 1.5 times higher than the others with same
size.
Generally, the air damping of the MCLM is usually ignored relative
to electromagnetic force [8-9]. However, the air damping has a close
association with moving speed and the internal shape of the MCLM
[10-11]. Furthermore, along with the raising of the frequency and speed,
the effect of air damping on the kinematics characteristics is
increasingly remarkably. What's more, in most cases the
characteristics are closely related to the properties of the associated
components of the system [12-13]. So it is necessary to study
aerodynamics of the MCLM and take measures to reduce the air damping.
However, as the diversity and complexity of the cavities enclosed by the
MCLM, the normal momentum analysis could no longer be able to evaluate
the air damping in the process of movement accurately and detailed
[14-15]. So the flow fluid simulation method is proposed. In addition,
the analysis of the interior flow fluid is necessary to guide the
optimum design as well.
To address these shortcomings, in this study, an aerodynamics
analysis of an MCLM is conducted using a computational fluid dynamics
(CFD) software Fluent to study the air damping characteristics of the
electromechanical with different thrust coil bobbins (TCBs) and find a
method to reduce.
2. Analytical model
A schematic of an MCLM designed in this study is depicted in Fig.
1, the designed MCLM consists of connector, permanent magnet (PM), coil,
iron core, end shield, thrust coil bobbin (TCB), output shaft, cover,
etc. PMs have been widely used in various applications for many decades
to convert electrical energy into mechanical energy. Several PMs are
fixed on the inner face of the end shield. The iron core is fixed in the
center of the end shield by a screw, and a coil is wrapped on the TCB.
The TCB subassembly connected to both a guide pin and the output shaft
could keep reciprocating linear motion with high frequency in an
airtight cavity enclosed by end shield, cover, PMs, iron core, et al.
A DC voltage signal is applied to the coil through the connector,
so that the output shaft together with the TCB connected to the carrying
currents coil will realize the reciprocating linear motion due to the
effect of the Ampere force of the permanent magnetic field.
To compare the aerodynamic characteristic of the TCB subassembly, a
3D drawing and prototype of three different TCBs with different designs
are compared in Figs. 2 and 3.
Proposal 1: the original design with no hole shown in Fig. 2, a and
Fig. 3, a.
Proposal 2: new TCB with 8 holes of O4mm located the radius of
O20mm on the end face shown in Fig. 2, b and Fig. 3, b.
Proposal 3: new TCB with 8 holes of O4mm located the radius of
O20mm and 15 holes of O3.5mm located the radius of O30mm on the end face
shown in Fig. 2, c and Fig. 3, c.
It is clear that proposal 2 and 3 are the updates of proposal 1
through punching a number of holes on the end face of TCB. It is noted
that the TCB mechanical performance is little affected by the holes
punched on the end face owing to the material of high quality aluminum
alloy ANB79 is used for TCB.
3. Mathematical model
First of all, a qualitative analysis of the effect on the
aerodynamic characteristics of a hole punched on a plate is put forward.
The radial direction of the Navier-Stokes equations in the cylindrical
coordinates of incompressible fluid can be expressed as [16]:
[mathematical expression not reproducible] (1)
When R/h>>1, assuming p=p(r, t), ur=u(r, y, t), due to the
symmetry, Eq. 1 relative to [theta] is ignored and thus the unsteady N-S
equation can be simplified to:
[mathematical expression not reproducible] (2)
Combining with the mass conservation equation, the pressure
distribution on the radial direction can be written as Eq. 3 with the
boundary conditions of u(r, 0, t)=u(r, h, t)=0 and p(R, t) =[p.sub.0]
[17].
[mathematical expression not reproducible] (3)
[mathematical expression not reproducible] (4)
Where: h and h are the velocity and acceleration of the plate which
is moving towards the lower boundary.
Focus on the mathematical model 1 with only one side closed
(depicted in Fig. 4). Integrating Eq. (3) on the area s, the air damping
of the plate [F.sub.s] can be expressed as.
With regard to mathematical model 2 with all four sides closed
(depicted in Fig. 5), similarly, the air damping of the plate [F.sub.c]
can be written as [18-19].
[mathematical expression not reproducible] (5)
Where: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE] H and H are the
velocity and acceleration of the plate which is moving towards the upper
boundary.
It is evident from Eq. (5), the air damping is related to not only
geometry dimensions of R, h, H, L, R1 but also movement parameters of h,
h, H,H and so on.
Then when it comes to mathematical model 3 with all four sides
closed and a hole in the middle of plate (depicted in Fig. 6), it can be
predicted that while the plate is moving downwards, the air will be
squeezed out through the hole and the gap between the plate and the end
shield. Thus a section where the velocity is zero is provided. Using
relation [r.sub.m]=(R+[r.sub.0])/2, the distribution of pressure can be
expressed as:
[mathematical expression not reproducible] (6)
The air damping of the plate in model three [F.sub.0] can be
achieved by Eq. 6 over integral on the area s.
[mathematical expression not reproducible] (7)
where: [mathematical expression not reproducible]
Comparing Eq. (5) and Eq. (7), it is evident that FO is smaller
than FC. This implies that the air damping of the plate is decreased
after holes are punched. In order to evaluate the air damping
characteristics intuitively and conduct the simulation below, choosing
R=20 mm; R1=22 mm; L=10 mm; h=2-0.5sin(4000xt) mm;
H=2+0.5sin(4000xt) mm. Fig.6 reveals the air damping diagram of
model 1, model 2 and different model 3. The r0/R is 0.1, 0.25, 0.5 for
model three (a), model three (b), models three (c) respectively. As
evident in Fig. 7, the air damping is smaller while [r.sub.0]/R is
increasing.
Though the theoretical analysis above via the MATLAB (MathWorks,
Inc.) could reflect the change regulation of the pressure and air
damping, it can be just used for the simple models and do some
qualitative analysis. As for complex model, the finite element method
needs to be used. Thus using CFD software Fluent 14.0 (ANSYS, Inc. USA)
for aerodynamics analysis of an MCLM is necessary. In simulation
process, the mass conservation equation, the Reynolds equation and the
k-e turbulent control equation is used [20].
When the TCB subassembly is moving, the calculation domain is
always changing as well. Thus the dynamic meshes technique is required,
and unstructured tetrahedral meshes are put in use, which can renew more
easily than hexahedral mesh [21]. Fig. 8 presents meshes of the air
cavity corresponding to TCB of proposal 1.
Adopting the methods of spring and remeshing to renew the meshes,
and setting the outline of the TCB sub-assembly to rigid wall and the
outer boundary of the air cavity to wall, the movement form of the TCB
subassembly is defined by User Defined Function (UDF).
4. Results and discussion
The TCB subassembly would be set to move periodically from -0.5 mm
to +0.5 mm according to the sinusoid, the velocity magnitude is 1 m/s, 2
m/s and 3 m/s respectively, and starts from the middle position. Fig. 9
illustrates the air damping curves of three different proposals at
different speed, Fig. 8 is substantial accordant with Fig. 6 as evident.
However, there are still some differences between them, as follows.
1. In initial phase, there is a huge deviation. This is mostly
because at the beginning of iterating, the calculation in the set time
doesn't converge. But over time, along with stability of the flow
field, the calculation becomes to converge, which ensures the accuracy
of the subsequent data.
2. The curve fluctuates at the peak of the air damping. The reason
is that the position of TCB subassembly at this time is at the maximum
displacement, and unit of h and H is just millimeter. As can be seen in
Eq. 5 and Eq. 7, a small change in the displacement will result in a big
impact on the air damping.
3. The upper and lower peak value is different. Definitely, the
left and right air cavity of the TCB subassembly is asymmetric.
Fig. 10 details the air damping peaks of three different proposals
under different magnitudes of speed. It is evident from the Figure that
the air damping of the TCB subassembly increases along with the speed.
When the velocity is 3m/s, 2m/s and 1m/s, the peaks of the air damping
are 20.3N, 9.01N and 2.32N respectively, which means the air damping is
nearly proportional to the square of the speed. What's more, when
it comes to the velocity magnitude of 3m/s, the air damping peaks of
three different proposals are 20.3N, 7.24N and 0.58N respectively.
Compared with proposal 1, the air damping of proposal 2 and proposal 3
is decreased by 64.3% and 97.1% respectively. As seen from the figure
that punching on end face of TCB improves obviously aerodynamics.
For a better understanding of simulation results, a detailed
analysis of the flow field is required. Because the beginning of flow
filed is unstable, so four positions started from the 1/4 phase are
chosen. When the movement time is 0.5T, the TCB subassembly is moving
toward the left and provided with a maximum velocity. Pressure contour
diagrams and velocity vector diagrams of three different proposals at
the time of 0.5T with the speed of 3m/s are shown in Fig. 11 and Fig. 12
respectively.
As seen in Fig. 11, the pressure difference between left and right
cavity in proposal 2 and 3 are greatly reduced compared with proposal 1.
Especially in proposal 3, the left and right cavity's pressure is
almost equal, so the air damping is smaller. As detailed in Fig. 12, as
for proposal 1, the air flow rate in the narrow channel between TCB
subassembly and end shield is very high. There is eddy current at the
import and export of the flow channels. However, with regard to proposal
three, not only the fluid velocity but also the eddy current region and
intension are definitely reduced.
Fig. 13 lists the pressure and velocity of three different
proposals, the maximum pressure of proposal 1 is
3908.5Pa, while proposal 3 is only 202.5Pa, which reduces by 94.9%.
In addition, the maximum velocity is reduced from 47.4m/s to 14.9m/s by
68.6%.
As for the narrow up-channel AB and down-channel CD of three
proposals exhibited in Fig. 11, their pressure curves are illustrated in
Fig. 14 and Fig. 15. It can be seen from the figure that two channels of
proposal 1 are provided with a higher pressure and pressure gradient.
This is because the channel is narrow so that eddy current occurs at the
import and export, the pressure curve experiences a larger change at
point B nearby. As regards proposal three, the pressure is obviously
reduced and is not high at point C while low at point D any more, the
pressure gradient is reversed, high pressure areas appear near the tail
of the cavity where contributes little to the air damping.
Combined with the streamline diagrams depicted in Fig.16, air
flowing from right cavity to left cavity needs to pass the long narrow
channel and can't arrive at the left cavity timely, then results in
air blo[ck.sub.in]g phenomenon. While in proposal three, almost all of
the air flowing from right to left cavity gets across the punched holes.
As a result, the air flow stress in the narrow channel is relieved and
air damping is decrease as well.
Using software MATLAB 9.1 (MathWorks, Inc. USA) for control
analysis, curves of step response and frequency response of three
different proposals are compared in Fig. 17 and Fig. 18, respectively.
Dynamic performance characteristics of three different proposals are
listed in Table 1. As evident in figure and table, the dynamic
performance index of proposal 3 is better than proposal 1 and proposal
2, the response time and frequency of the proposal 3 arrives at 2.3ms,
386Hz/-3dB, 440Hz/-90o, respectively. Simulation results show that the
dynamic performance of proposal 3 is improved after punching a number of
holes on the end face of the TCB.
5. Experimental procedures
Experimental analyses had been carried out at a designed MCLM with
proposal 3 under actual testing conditions. A digital controller
collects the desired position signal and position feedback signal
generated by the position sensor on the output shaft. After comparison
and compilation, the controller provides a drive current to different
coils via a connector, so that the designed MCLM can keep the
reciprocating linear motion.
Fig. 19 reveals an image of the prototype of the designed MCLM. A
signal generator provides ten groups sinusoidal AC voltage with
amplitude of 5 V and frequency from 1 Hz to 320 Hz to the coils of TCB,
respectively. Both the input signals provided by the signal generator,
and the feedback signal generated by the displacement sensor on the
output shaft are collected to an oscilloscope, as detailed in Fig. 20.
As we can see from figure, when the input signal frequency is 1Hz,
the output voltage amplitude would be 1.26V. In this case, there is a
good linear relationship between input and output, and the phase
difference between them is close to 0 (Fig. 20, a). While the input
signal frequency is 150Hz, the output voltage amplitude would be 1.08V.
Likewise, there is also a good linear relationship between input and
output, and the phase difference between them is small as well (Fig. 20,
b).
While the input signal frequency is 260 Hz, the output voltage
amplitude would be 0.938 V. There is a good linear relationship between
input and output similarly. However, the phase difference between them
is larger than before (Fig. 20, c). While the input signal frequency is
320 Hz, at this point, phase difference between input and output is over
90 degrees. However, they still keep a good linear relationship (Fig.
20, d).
Table 2 exhibits the output voltage amplitude provided by the
displacement sensor on the output shaft with different input signal
frequency provided by the signal generator.
According to the tra[ck.sub.in]g characteristics of sinusoidal
signal based on the output shaft of the designed MCLM, a curve of the
experimental magnitude-frequency characteristics of the designed MCLM is
presented Fig. 21. As evident in figure, the experimental frequency of
the designed MCLM arrives at 300Hz at 3dB.
In addition, after a square wave signal with amplitude of 5V and
frequency of 25Hz provided by the signal generator is loaded into the
coils of bobbins, the feedback signal generated by the displacement
sensor on the output shaft are collected to an oscilloscope, as detailed
in Fig. 22.
As evident in figure, the experimental response time of the
designed MCLM is close to 4ms.
Furthermore, after a triangle wave signal with amplitude of 2.5 V
and frequency of 12.5 Hz provided by the signal generator is loaded into
the coils of bobbins, the feedback signal generated by the displacement
sensor on the output shaft are collected to an oscilloscope, as detailed
in Fig. 23. As detailed in figure, under this situation, there is a good
linear relationship between input and output, and the phase difference
between them is close to 80ms.
Experimental procedures show promising results that the designed
MCLM displays high frequency and rapid response, and the designed
control technology can realize high performance.
6. Conclusions
A three-dimension aerodynamics analysis and experimental
investigation of the designed MCLM provided with different TCBs based on
dynamic meshes technique using CFD software are proposed in this study.
Conclusions are as follows:
The air damping loaded to moving TCB subas-sembly is nearly
proportional to the square of the speed, which is provided with a
significant influence on the kinematics characteristics of the MCLM
working at conditions of high-frequency and high-speed.
Punching a number of holes on the end face of the TCB could greatly
enhance the air flow capacity and improve the distribution of pressure
and velocity of the flow field around. Compared with proposal 1, the air
damping of proposal 2 and proposal 3 is decreased by 64.3% and 97.1%,
respectively. Results show the effectiveness of the proposed
optimization of the TCB is verified.
The simulation response time and frequency of the designed MCLM
with proposal 3 arrives at 2.3ms,
386 Hz/-3 dB, 440 Hz/-90o, respectively. Simulation results show
that the dynamic performance index of the designed MCLM with proposal 3
is better than those with proposal 1 and proposal 2. In addition, the
experimental frequency and response time of the designed MCLM with
proposal 3 are 300 Hz at 3 dB and 4ms, respectively.
As evident in this study, analysis and experimental results show
that the air damping can be decreased by the structural optimization of
the MCLM at the high speed working conditions, and the designed MCLM
with proposal 3 can realize good performance of high frequency and rapid
response.
7. Acknowledgments
This research is supported by the National Natural Science
Foundation of China (Grant No. 51307170), the Guangzhou Scientific
Planning Programs of China (Grant No. 201607010041), and the Shenzhen
Basic Research Projects of China (Grant No. JCYJ20160531184135405). The
authors gratefully acknowledge the help of Guangzhou Institute of
Advanced Technology, Chinese Academy of Sciences and Shenzhen Institute
of Advanced Technology.
References
1. Takezawa, M.; Kikuchi, H.; Suezawa, K. et al. 1998. High
frequency carrier type bridge-connected magnetic field sensor, IEEE
Transactions on Magnetics 34(4): 1321-1323. https://doi.org/ 10.1109 /
INTMAG.1998.742576.
2. Goll, D.; Kronmuller, H. 2000. High-performance permanent
magnets, Naturwissenschaften 87(10): 423-438.
https://doi.org/10.1007/s001140050755.
3. Zhao, S.; Tan, K. K. 2005. Adaptive feedforward compensation of
force ripples in linear motors, Control Engineering Practice 13:
1081-1092. https://doi.org /10.1016/j.conengprac.2004.11.004.
4. George, A.; William, T. 2000. Performance evaluation of a
permanent magnet brushless DC linear drive for high speed machining
using finite element analysis, Finite Elements in Analysis and Design
35: 169-188. https://doi.org/10.1016/S0168-874X(99)00064-5.
5. Ruan, X. F. 2013. Simulation model and experimental verification
of electro-hydraulic servo valve, Applied Mechanics and Materials 328:
473-479. https://doi.org/10.4028/www.scientific.net/AMM.328.473.
6. Zhang G.; Yu, L Y.; Ke, J. 2007. High frequency moving coil
electromechanical converter, Electric Machines and Control 11(3):
298-302. https://doi.org/10.1002/jrs.1570.
7. Sadre, M. 1997. Electromechanical converters associated to wind
turbines and their control, Solar Energy 6(2): 119-125.
https://doi.org/10.1016/S0038-092X(97)00034-0.
8. Amirante, R.; Catalano, L A.; Tamburrano, Paolo. 2014. The
importance of a full 3D fluid dynamic analysis to evaluate the flow
forces in a hydraulic directional proportional valve, Engineering
Computations 31(5): 898-922. https://doi.org/10.1108/EC-09-2012-0221.
9. Sorli, M.; Figliolini, G.; Pastorelli, S. 2004. Dynamic model
and experimental investigation of a pneumatic proportional pressure
valve, Mechatronics,
IEEE/ASME Transactions on 9(1): 78-86.
https://doi.org/10.1109/TMECH.2004.823880.
10. Amirante, R.; Moscatelli, P G.; Catalano, L A. 2007. Evaluation
of the flow forces on a direct (single stage) proportional valve by
means of a computational fluid dynamic analysis, Energy Conversion &
Management 48: 942- 953. https://doi.org/10.1016/j.enconman.2006.08.024.
11. John, A. Fundamentals of aerodynamics, McGraw Hill Higher
Education, New York, 2010.
https://doi.org/10.1001/jama.1943.02840050078041.
12. Ryashentsev, N. P.; Kovalev, Y. Z.; Fedorov, V. K. et al. 1978.
A mathematical model of an electromechanical converter, Mechanization
and Automation in Mining, (4): 47-55.
https://doi.org/10.1007/BF02499577.
13. Ismagilov, F. R.; Khairullin, I. H.; Riyanov, L N. et al. 2013.
A mathematical model of a three-axis electromechanical converter of
oscillatory energy. Russian Electrical Engineering 84(9): 528-532.
https://doi.org/10.3103/S106837121309006X.
14. Huang, L. H.; Xu, Y. L.; Liao, H. L. 2014. Nonlinear
aerodynamic forces on thin flat plate: Numerical study, Journal of
Fluids and Structures 44: 182-194.
https://doi.org/10.1016/j.jfluidstructs.2013.10.009.
15. Miguel, M. P.; Gonzalo, L. P.; Jimenez, L. et al. 2013. CFD
model of air movement in ventilated fa-cade: comparison between natural
and forced air flow, International Journal of Energy & Environment
4(3): 357-368. http://www.ijee.ieefoundation.org/vol4/issue3/IJEE_01
_v4n3.pdf.
16. John, A. Fundamentals of aerodynamics. McGraw Hill Higher
Education, New York, 2010.
https://doi.org/10.1001/jama.1943.02840050078041.
17. Kuzma, D. C. 1967. Fluid intertia effects in squeeze films,
Appl. Sci. Res 18: 16-20. https://doi.org/10.1007/bf00382330.
18. Huang, S. J.; Andra, D.; Tasciuc, B. et al. 2011. A simple
expression for fluid inertia force acting on micro-plates undergoing
squeeze film damping, Proceedings: Mathematical, Physical and
Engineering Sciences 467(2126) : 522-536.
https://doi.org/10.1098/rspa.2010.0216.
19. Joseph, Y. J. 1998. Squeeze-film damping for MEMS structures,
Massachusetts Institute of Technology.
20. Lomax, H.; Pulliam, T. H.; David, W. Z. 2001. Fundamentals of
computational fluid dynamics. Springer Verlag,
https://doi.org/10.1007/978-3-662-04654-8. 21. Smolarkiewicz, P. K.;
Szmelter, J.; Wyszogrodzki, A. A. 2013. An unstructured-mesh atmospheric
model for nonhydrostatic dynamics, Journal of Computational Physics 254:
184-199. https://doi.org/10.1016/j.jcp.2013.07.027.
G. Zhang, J. Liang, Zh. Hou, Q. Lin, Zh. Xu, J. Wang, S. Liang, W.
Wang
COMPARATIVE ANALYSIS OF AERODYNAMIC CHARACTERISTICS AND
EXPERIMENTAL INVESTIGATION OF A MOVING COIL LINEAR MOTOR USING
COMPUTATIONAL FLUID DYNAMICS
Summary
This study tries to observe the aerodynamics of a moving coil
linear motor (MCLM) under the conditions of high frequency and high
speed, a three-dimension aerodynamics analysis and experimental
investigation of the designed MCLM provided with different thrust coil
bobbins (TCBs) based on dynamic meshes technique using computational
fluid dynamics (CFD) are proposed. Results show that with the increase
of moving frequency and speed, the air damping of TCB subassembly is
nearly proportional to the square of the speed. Punching a number of
holes on the end face of the TCB could greatly improve the air flow
capacity and enhance the distribution of pressure and velocity of the
flow field around. Compared with proposal 1, the air damping of proposal
2 and proposal 3 is decreased by 64.3% and 97.1%, respectively.
Simulation results show that the response time and frequency of the
designed MCLM with proposal 3 is better than those with proposal 1 and
proposal 2. In addition, the experimental frequency and response time of
the designed MCLM with proposal 3 are 300Hz at 3dB and 4ms,
respectively. As evident in this study, analysis and experimental
results show that the air damping can be decreased by the structural
optimization of the MCLM, and the designed MCLM with proposal 3 can
realize good performance of high frequency and rapid response.
Keywords: moving coil linear motor; thrust coil bobbin;
aerodynamics; dynamic mesh; experimental investigation.
Received May 07, 2018
Accepted December 12, 2018
Gong ZHANG (*), Jimin LIANG (*,**), Zhichen HOU (*), Qunxu LIN
(***), Zheng XU (*), Jian WANG (*), Xiangyu BAO (*), Weijun WANG (*)
(*) Guangzhou Institute of Advanced Technology, Chinese Academy of
Science, Guangzhou, 511458 Guangdong, China, E-mail:
gong.zhang@giat.ac.cn
(**) Shenzhen Institute of Advanced Technology, Shenzhen, 518055
Guangdong, China, E-mail: jm.liang@giat.ac.cn
(***) Wuyi University, Jiangmen, 529020 Guangdong, China, E-mail:
qx.lin@giat.ac.cn crossref http://dx.doi.org/10.5755/j01.mech.24.6.22463
Table 1
Dynamic performance characteristics of three different proposals
Category Proposal Proposal Proposal
1 2 3
Step Adjusting 3.2 2.7 2.3
response time(ms)
Overshoot 8.7% 7.3% 4.1%
Gain(Hz/- 362 375 386
Frequency 3dB)
response Phase(Hz/- 408 427 440
90[degrees])
Table 2
The output voltage amplitude with different input signal frequency
Input signal 1 7 20 30 100
frequency (Hz)
Output voltage 1.26 1.24 1.24 1.21 1.17
amplitude (V)
Input signal 150 200 260 300 320
frequency (Hz)
Output voltage 1.08 1.03 0.938 0.919 1.01
amplitude (V)
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