Principle Modelling and Testing of an Annular Radial Duct MR Damper

7/27/2019 Principle Modelling and Testing of an Annular Radial Duct MR Damper

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Accepted Manuscript

Title: Principle, Modeling, and Testing of AnAnnular-Radial-Duct Magnetorheological Damper

Author:

Xian-Xu Bai

Dai-Hua Wang Hang Fu

PII: S0924-4247(13)00353-1

DOI: http://dx.doi.org/doi:10.1016/j.sna.2013.07.028

Reference: SNA 8416

To appear in: Sensors and Actuators A

Received date: 25-1-2013

Revised date: 24-7-2013

Accepted date: 25-7-2013

Please cite this article as: X.-X. Bai, D.-H. Wang, H. Fu, Principle, Modeling,

and Testing of An Annular-Radial-Duct Magnetorheological Damper, Sensors and

Actuators: A Physical (2013), http://dx.doi.org/10.1016/j.sna.2013.07.028

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http://dx.doi.org/doi:10.1016/j.sna.2013.07.028http://dx.doi.org/10.1016/j.sna.2013.07.028http://dx.doi.org/10.1016/j.sna.2013.07.028http://dx.doi.org/doi:10.1016/j.sna.2013.07.028


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PRINCIPLE, MODELING, AND TESTING OF AN ANNULAR-

RADIAL-DUCT MAGNETORHEOLOGICAL DAMPER

Xian-Xu Bai1,2,*

, Dai-Hua Wang1,2,

, and Hang Fu1,2

1Key Laboratory of Optoelectronic Technology and Systems of the Ministry of Education of China,

Chongqing University, Chongqing, 400044, Peoples Republic of China2Precision and Intelligence Laboratory, Department of Optoelectronic Engineering, Chongqing

University, Chongqing, 400044, Peoples Republic of China

ABSTRACT

Aiming at improving the efficiency of magnetorhelogical (MR) dampers, the principle of an annular-

radial-duct MR damper (ARDMRD), in which annular-radial ducts in series in MR fluid flow channel are

integrated, is presented and the prototype of the ARDMRD is designed and fabricated. The mathematical

model of the ARDMRD considering the nonlinear flow effect of the MR fluid in the flow channel is

established. The finite element analysis (FEA) is utilized to validate the principle of the ARDMRD and

obtain the magnetic properties of its magnetic circuit. The controllable damping force and equivalent

damping of the ARDMRD are tested on the established experimental setup based on MTS 849 shockabsorber test system and compared with the theoretical results based on the mathematical model and FEA.

The tested controllable damping force of the ARDMRD under excitation velocity of 0.19 m/s is as high as

3149 N and the tested damping force range of the ARDMRD under excitation velocities of 0.025-0.19 m/s

is 140-3149 N. The research results show that the designed magnetic circuit structure of the ARDMRD is

beneficial to improving the efficiency of the MR damper and the established mathematical model of the

ARDMRD can describe and predict its damping force performance accurately.

Keywords: Magnetorheological fluid damper, annular-radial duct, efficiency, magnetic saturation.

I. INTRODUCTION

Magnetorheological (MR) fluids [1-3], as one kind of typical active materials, have attracted considerable

interests recently as it can provide a simple and rapid response interface between electronic control and

mechanical systems. MR dampers, which take the advantages of MR fluids, have excellent performances as

one promising semi-active actuator, including rapid response, controllable damping force, simple structure,

and low power consumption. Even the control systems fail to work, MR dampers can still act as passive

actuators in semi-active control systems based on MR dampers.

Over the past two decades, MR dampers with various magnetic circuit structures have been presented,

studied, and applied in semi-active control systems [4-10]. Carlson and Chrzan [11] presented a MR

damper principle with an annular fluid flow channel in 1994 and developed a commercially available MR

dampers (type: RD-1005-3, LORD Corp.). Later, Carlson and Spencer [10] presented a full-scale MRdamper with the same structure used in civil structures with the maximum controllable damping force of as

high as 20 kN. However, the volume of the MR fluid in one MR damper is over 5 liters. Thence, MR

dampers with bypass valves [12-14] and with bifold valves [15] have been studied. The controllable

damping force of the MR dampers with bypass valves is much larger than that of the traditional ones,

whereas the MR dampers always occupies much larger installation space. As for the MR damper with

* E-mail: [email protected] (Xian-Xu Bai) Author to whom any correspondence should be addressed. E-mail: [email protected] (Dai-Hua Wang); Tel: +86 23 6511 2105; Fax: +86 23 6511 2105;URL: http://www.pilab.coe.cqu.edu.cn/


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bifold valves, two identical MR valves are set at the two ends of the cylinder of the MR damper, which

makes the structure of the MR damper complex. How to improve the controllable damping force and the

efficiency simultaneously and guarantee the installation space of MR dampers is a challenge which should

be confronted and solved when designing MR dampers. Besides, in order to control the MR dampers based

semi-active systems efficiently, the mathematical models of the MR dampers, i.e., the damping force

performance, should be described and predicted efficiently by the established models. For the MR dampers

that are applied in low-speed environments, the quasi-steady models [16,17] are adequate to describe the

damping force of the MR dampers. While for the high-speed applications, the nonlinear flow effect of the

MR fluid [14,18,19] or the effect of MR fluid-walls of the MR dampers [20-23] are of significance and not

negligible.

Ai and Wang [24,25] presented an MR valve with both annular and radial fluid flow resistance gaps and

the efficiency of the MR valve was improved apparently. Nguyen et al [26,27] further simulated and

optimized the structure of the MR valve based on the principle for optimizing MR valves and MR dampers

with constrained volume presented by Rosenfeld and Wereley [28], and obtained the same results with

those by Ai and Wang [24,25].

Based on the structural principle of the MR valve presented by Ai and Wang [24,25], this paper presents

an annular-radial-duct MR damper (ARDMRD) with integrated annular-radial ducts in series in the MR

fluid flow channel. The prototype of the ARDMRD is designed, fabricated, and mathematically modelled.The principle and performances of the ARDMRD are theoretically and experimentally validated. In

addition, the performances of the developed ARDMRD are compared with a commercially available MR

damper (type: RD-1005-3, LORD Corp.).

II. PRINCIPLE AND PROTOTYPE

Figures 1(a) and 1(b) show the structural principle and three-dimensional (3D) drawing of the

ARDMRD, respectively, and figure 1(c) shows the photograph of the exploded components of the

ARDMRD fabricated with the structural dimensions and materials properties as listed in table 1.

Observing figure 1, the ARDMRD comprises the piston unit, piston rod, and damper cylinder. The piston

unit consists of a magnetic core with a through-hole in center, two magnetic circular disks, an exciting coilwound on the nonmagnetic bobbin, a magnetic core cylinder, nonmagnetic washers, and nonmagnetic

positioning pins. Two identical circular disks are connected to the two ends of the magnetic core by pins

and the radial ducts are formed. The washers that are coaxially installed with the corresponding pins

guarantee the thickness of the radial ducts. The core that is housed in the bobbin and connected with two

circular disks is coaxially positioned in the core cylinder. Then the annular ducts are formed between the

inner circumference of the core cylinder and the outer circumferences of the circular disks, as shown in

figures 1(a) and 1(b). As it can be seen in figures 1(a) and 1(b), as the piston compresses (rebounds)

relative to the damper cylinder, the MR fluid flows from the lower (upper) annular duct into lower (upper)

radial duct. Then the MR fluid flows into the upper (lower) radial duct through the central hole of the core.

At last, the MR fluid flows out of the piston through the upper (lower) annular duct. The MR fluid is filled

in to flow in the channels by a pressure drop, which is controlled by the magnetic field.The magnetic field generated by the exciting coil with current starts from the core, goes though the radial

duct, circular disk, annular duct, along the core cylinder, through the annular duct, circular disk, and radial

duct to complete a closed magnetic circuit. When applying a magnetic field, the MR fluid flowing through

the annular-radial duct will give rise to pressure drop at the two ends of the duct because of the yield stress

of the MR fluid. The yield stress continuously increases with increasing the current applied to the exciting

coil before the magnetic field strength for the MR fluid/ARDMRD structure is saturated. In this way, the

damping force generated by the ARDMRD can be controlled continually by tuning the current applied to

the exciting coil.


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MRF

2rd

ta2rp tc

trha

h

tr

ha

2rc

x(t)

Piston rod

Damper cylinder

Circular disk

Core

Core cylinder

Magnetic flux

Exciting coil

Bobbin

Radial duct

2rpr

2ro

Annularduct

(a)

Piston rod

Diversion hole

Annular duct

Radial ductWasher

Magnetic flux

Exciting coil

Central hole of coreCore

Core cylinder

Positioning disk

MR fluidFloating piston

Accumulator

Circular diskCircular disk

Positioning pin

(b)

(c)

Figure 1. Developed ARDMRD: (a) the structural principle, (b) the 3D drawing, and (c) the photograph of

the exploded components.


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Table 1. Structural dimensions and materials properties of the developed ARDMRD.

Parameter Symbol Value

Damper length lD 185 [mm]

Damper radius rD 24 [mm]

Radius of piston rod rpr 5 [mm]

Piston radius rp 20 [mm]

Radius of circular disk rd

12.84 [mm]

Radius of core rc 10.54 [mm]

Radius of central hole of core ro 3.5 [mm]

Height of annular duct ha 8.6 [mm]

Thickness of radial duct tr 1.0 [mm]

Thickness of annular duct ta 1.0 [mm]

Thickness of core cylinder tc 6.36 [mm]

Core height h 30 [mm]

Piston maximum displacement s 50 [mm]

Exciting coil turns N 280 [Turns]

Magnetic steel material 20#

steel

Nonmagnetic steel material 304#

steelDensity of MR fluid 3.0810

3[kg/m

3]

III. THEORETICAL MODELING

As it can be seen from figure 1, the operation mode of the MR fluid in the ARDMRD is the valve mode

[2]. The damping force of the ARDMRD can be expressed as

apmlra

fAPPPF (1)

where aP and rP are the pressure drops through the annular ducts and the radial ducts, respectively;

ml

P is the minor loss pressure drop due to the elbows, such as sudden expansions and contractions alongthe MR fluid flow channels; fa is the force generated by the accumulator; Ap is the effective area of the

piston and can be written as

2pr2

d

2

ad

2

pp rrtrrA (2)

where pr , dr , and prr are the radii of the piston, circular disk, and piston rod, respectively; at is the

thickness of the annular duct.

The pressure drop through the annual ducts can be expressed as

aaa2 PPP (3)

wherea

P and aP are the viscous component and field-dependent induced yield stress component,

respectively, and can be expressed as

ad

3

a

aaa

2

1

6

trt

hQP

(4)

a

ayaa

at

hcP

(5)

where is the viscosity of the MR fluid without magnetic field; aQ is the volume flow rate of the MR

fluid through the annular duct and dpa VAQ if dV is the piston velocity; ah is the height of the annular


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duct;ya

is the yield stress of the MR fluid in the annular duct; ac is a correction factor dependent on the

volume flow rate and yield stress of the MR fluid through the annular ducts or the pressure drop through

the annular ducts and can be given by [27]

ya

2

aada

aa

2

18.012

1207.2

ttrQ

Qc

(6)

The pressure drop through the radial ducts of the piston can be expressed as

rrHrCr2 PPPP (7)

whererCP and rHP are the pressure drops due to the MR fluid when flowing into and out from the

central hole of the core, respectively; rP is the pressure drop due to the yield stress of the MR fluid

through the radial ducts.rCP , rHP , and rP can be respectively expressed as

o

c

3

r

rC

3

r

rCrC ln

6d

6c

o r

r

t

Qr

rt

QP

r

r

(8)

c

o

3

r

rH

3

r

rHrH ln

6d

6o

c

r

r

t

Qr

rt

QP

r

r

(9)

ocr

yrr

r

yrr

r dc

o

rrt

cr

t

cP

r

r

(10)

where rCQ and rHQ are the volume flow rates of the MR fluid when flowing out from and into the central

hole of the core, respectively, and arHrC QQQ ; rt is the thickness of the radial duct; rc = ac [17]; yr is

the yield stress of the MR fluid in the radial ducts.

The minor loss pressure drop mlP in Equation (1) can be given by [14,18,19]

ml2o2r2aml 222

KVVVP

(11)

where is the mass density of the MR fluid; Va, Vr, and Vo are the average flow rates of the MR fluid in

the annular duct, radial duct, and central hole of the core, respectively; Kml is the overall minor loss

coefficient [14,18,19].

Combining Equations (1)-(3), (7), and (11), the damping force of the ARDMRD can be rewritten as

aml2o2r2a

r

ocyrr

a

ayaa

o

c

3

r

a

ad

3

a

aap 22

2

22ln

12

2

1

12fKVVV

t

rrc

t

hc

r

r

t

Q

trt

hQAF

(12)

The equivalent damping [29], which is defined by the ratio of the energy dissipated over a closed circle in

a sinusoidal displacement excitation system to the properties of the excitation conditions, can be expressedas

2eq X

EC

(13)

where and X are the frequency and amplitude of the sinusoidal displacement excitation to the

ARDMRD, respectively; E is the energy dissipated in one cycle, i.e., the area enclosed by the force-

displacement diagram, and can be written as


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cycle

2

0dd

txFxFE (14)

where x is the velocity of the piston of the ARDMRD under the sinusoidal displacement excitation.

IV. FINITE ELEMENT ANALYSIS

FEA on the ARDMRD is conducted based on the software package Maxwell 2D. Considering that theARDMRD is an axis-symmetric structure, as shown in figure 1, a model of the magnetic circuit of the

ARDMRD is utilized to conduct the FEA. Figure 2 shows the axisymmetric entity model of the piston of

the ARDMRD with the structural dimensions and materials properties as listed in table 1 for FEA using

Maxwell 2D. Figures 3(a) and 3(b) show the corresponding contours of the magnetic flux density and the

magnetic flux of the ARDMRD applied with a 2.00 A current, respectively. Figure 4 shows the magnetic

flux densities along the annular and radial ducts of the ARDMRD applied with a 2.00 A current.

Observing figure 3(a), when the exciting coil is applied with a current of 2.00 A, the magnetic flux

densities in the areas of the annular ducts and radial ducts are nearly 0.5 and 1.0 Tesla, respectively.

Observing figure 3(b), the contours of the magnetic flux of the ARDMRD show the closed magnetic circuit,

which validates the principle presented in section II.

Circular disk #1

MRfluid

Core

Excitingcoil

Radial duct #1

Annularduct#1

Radial duct #2 Annularduct#2

Corecylinder

Bobbin

Circular disk #2

Figure 2. Axisymmetric entity model of the ARDMRD.


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(a)

Detectingline #1

Detectingline #2

Detectingline #3

Detectingline #4

(b)

Figure 3. Contours of the magnetic circuit of the ARDMRD applied with a 2.00 A current: (a) the magnetic

flux density contours and (b) the magnetic flux contours.


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Figure 4. Magnetic flux densities along the MR fluid flow ducts when the ARDMRD applied with a 2.00 A

current.

Observing figure 4, at the field-on state, i.e., the maximum current case, the magnetic flux densities along

the radial and annular ducts are obtained by using four detecting lines (#1-#4) in the radial and annular

ducts as shown in figure 3(b). The magnetic flux densities of the radial ducts along the detecting lines #2

and #3 are larger than those of the annular ducts along the detecting lines #1 and #4, and the magnetic flux

densities of the radial ducts and annular ducts are 1.0 and 0.43 Tesla, respectively, as also shown in figure

3(a). In addition, according to the FEA results given above and literatures [26,27], the magnetic properties

of the ARDMRD can be further optimized by considering the thickness of the annular and radial ducts.

As given by Equations (1)-(12), the damping force of the ARDMRD is determined by the geometries of

the ARDMRD, the yield stress of the MR fluid in the MR fluid flow ducts, and the excitation velocity. In

other words, if the magnetic flux density along the MR fluid flow ducts, which determines the yield stressof the MR fluid, can be obtained, the damping force of the prototype of the ARDMRD could be calculated

using the theoretical model (Equations (1)-(12)). Similar with the field-on state shown in figure 4, by using

FEA, the magnetic properties of the magnetic circuit of the ARDMRD when applied with 0.5 A, 1.0 A, and

1.5 A currents can also be obtained. The magnetic flux density along the annular and radial ducts of the

ARDMRD applied with 0.5 A, 1.0 A, and 1.5 A, are 0.13 Tesla and 0.25 Tesla, 0.23 Tesla and 0.51 Tesla,

and 0.34 Tesla and 0.75 Tesla, respectively.

It is noted that a commercial available MR fluid (MRF-132DG) [30] from LORD Corporation is used for

FEA, numerical simulation, and experimental testing in this study. The magnetic properties of the MR fluid

was curve fitted using least-squares method and given in literature [19].

V. EXPERIMENTAL TESTING AND CHARACTERIZATION

The ARDMRD, as well as a commercially available MR damper (type: RD-1005-3, LORD Corp.) with

an annular fluid flow channel [11], are tested on the established experimental setup based on the MTS 849

shock absorber test system and auxiliary devices, as shown in figure 5. Figure 6 shows the measured

damping force-displacement-frequency of the developed ARDMRD under 1 Hz and 3 Hz sinusoidal

displacement excitations with amplitude of 10 mm for nine current levels, 0 A, 0.25 A, 0.50 A, 0.75 A,

1.00 A, 1.25 A, 1.50 A, 1.75 A, and 2.00 A. Figure 7 shows the tested and theoretically predicted damping

forces generated by the ARDMRD under 1 Hz sinusoidal displacement excitation with amplitude of 10 mm


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Figure 6. Measured damping forces of the developed ARDMRD.

Figure 7. Measured and predicted damping forces of the developed ARDMRD under 1 Hz sinusoidal

displacement excitation with amplitude of 10 mm.

As it can be seen from figure 7, the established mathmatical model using the magnetic properties of the

MR fluid flow ducts of the ARDMRD presented in FEA section could describe and predict the damping

force performance of the ARDMRD accurately. For the field-off state, i.e., no current case, the viscousdamping force of the ARDMRD is difficult to model due to its complex structure and MR fluid flow

channel. However, as presented in figure 7, the calculated damping force tracks very well the tested

damping force, which shows the effectiveness of the established model. As the current increases, the tested

and predicted damping forces increase and the damping force calculated by the model could still track the

tested damping force well. It should be noted that both the deformations on the top left corner and lower

right corner, as shown in figures 6 and 7, result from the insufficient pressure of the exterior accumulator

[32].


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Observing figure 8(a), the experimental and theoretical results are nearly the same for the field-off state,

as also shown in figure 7. For the field-on state, the difference between the experimental and theoretical

results increases with increasing the excitation velocity, which might attribute to the deformation of the

measured force-displacement curves for higher velocities due to the insufficient pressure of the accumulator,

as shown in figures 6 and 7. According to above analysis, the mathematical model of the ARDMRD

considering the nonlinear flow effect of the MR fluid can predict the damping force performance of the

ARDMRD effectively.

(a)

(b)

Figure 8. Damping force ranges of: (a) the ARDMRD and (b) the commercially available MR damper

(type: RD-1005-3, LORD Corp.).


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(a)

(b)

Figure 9. Equivalent damping of the developed ARDMRD and the commercially available MR damper

(type: RD-1005-3, LORD Corp.) under the sinusoidal displacement excitations with frequency of: (a) 1 Hz

and (b) 3 Hz.

As seen from figures 8(a) and 8(b), the damping force range of the ARDMRD is much larger than that of

the RD-1005-3 when the same electric power and excitation velocity applied to the ARDMRD and the RD-

1005-3. It is worth noting that the diameter (40 mm) of the piston of the ARDMRD is close to that (38 mm)

of the RD-1005-3. With identical electric powers, as the states of the MR dampers switches from the field-

off to the field-on, the damping force of the ARDMRD increases as much as around twice as the RD-

1005-3 does. This means that the ARDMRD structure could use the electric power more efficiently.

Observing figure 9, under the identical excitations of the electric power and sinusoidal displacement, the

equivalent damping of the ARDMRD is much larger than that of the RD-1005-3. In addition, the equivalent

damping of the ARDMRD saturates significantly when the current reaches over 1.50 A, while the

equivalent damping of the RD-1005-3 saturates when the current reaches over 1.00 A. That is, the magnetic


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circuit of the ARDMRD is better than that of the RD-1005-3. We can draw a similar conclusion indicated

by figure 8 that the magnetic circuit structure of the ARDMRD with the annular-radial duct structure could

use the magnetic field generated by the exciting coil more efficiently. That is to say, the electric power can

be utilized more efficiently and the efficiency of the MR damper is improved by using better structures.

However, as it can be seen from figures 8(a) and 8(b), as the excitation velocity increases from 0.025 m/s

to 0.19 m/s, the maximum controllable damping force of the ARDMRD increases from 2327 N to 3149 N,

while that of the RD-1005-3 increases from 1217 N to 1638 N. This increased damping force is totally

generated by the viscous pressure drop. Similarly, as shown in figures 9(a) and 9(b), as the displacement

excitation frequency increases, the equivalent damping for the non-zero current cases decreases while the

equivalent damping for the no current case increases, which means that the controllable damping ratio of

the ARDMRD decreases dramatically as the excitation velocity increases. According to the definition of the

controllable damping ratio [31], Equation (12) indicates that the controllable damping ratio of the

ARDMRD would be influenced by the excitation velocity and could be enlarged by optimizing the

thickness of the annular ducts and radial ducts and the length of the central hole of the core.

VI. CONCLUSION

In this paper, the principle of the ARDMRD, in which annular-radial ducts in series in MR fluid flowchannel were integrated, was presented to improve the efficiency of MR dampers. Based on the ARDMRD

principle, the ARDMRD prototype was designed and fabricated. Considering the nonlinear flow effect of

the MR fluid in the flow channel, the theoretical model of the ARDMRD was derived to demonstrate its

damping force performance. The principle of the ARDMRD was validated by FEA and the magnetic

properties of the magnetic circuit of the ARDMRD was obtained by FEA. Under the same excitations of

electric power and sinusoidal displacement, the experimentally tested characteristics of the ARDMRD were

compared with those of the RD-1005-3 from LORD Corp., including the controllable damping force and

equivalent damping. According to the experimental results, the ARDMRD could provide a large

controllable damping force as high as 3149 N under excitation velocity of 0.19 m/s and a large damping

force range from 140 N to 3149 N under excitation velocities from 0.025 m/s to 0.19 m/s. The magnetic

circuit of the ARDMRD is superior to the RD-1005-3 and the ARDMRD could use the electric power more

efficiently than the RD-1005-3. In addition, thanks to considering the nonlinear flow effect, the derived

mathematical model of the ARDMRD could describe and predict the damping force performance of the

ARDMRD accurately.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the financial support of the National Natural Science Foundation of

China (Grant No. 60774042), the Fundamental Research Funds for the Central Universities (project No.

CDJXS11122217), the Program for New Century Excellent Talents in University (grant No. NCET-05-0765), and the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (grant

No. 200132).

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BIOGRAPHIES

Xian-Xu Bai is a Ph.D. student in Department of Optoelectronic Engineering at Chongqing University,Chongqing, China. His current research interests focus on the magnetorheological damper/energy absorber

for vibration and shock mitigation and energy harvesting based on smart materials and structures. He is

now a student member of ASME and SPIE.

Dai-Hua Wang received the Doctor of Engineering degree in instrument science and technology from

Chongqing University, Chongqing, China, in 1999. Now he is a professor with Chongqing University andthe founding director of the Precision and Intelligence Laboratory (http://www.pilab.coe.cqu.edu.cn/) there.

Currently, he serves on the Editorial Board of the IOP Journal of Smart Materials and Structures. His

current research interests include fiber optic sensor technology, opto-mechatronic technology &equipments, micro-/nano-manipulation technology and systems, smart structures and systems, and super-

precision measurement technology.

Hang Fu received his BEng. and MEng. degrees in instrument science and technology from ChongqingUniversity, Chongqing, China, in 2009 and 2012, respectively. He is currently an employee of Zoomlion

Heavy Industry Science & Technology Development Corp., Ltd., Changsha, China.

Documents

Principle Modelling and Testing of an Annular Radial Duct MR Damper