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Study of the response time of MR dampers

Xinchun Guan*aPengfei Guo

aJinping Ou

a,b

aSchool of Civil Engineering, Harbin Institute of Technology, Harbin, China, 150090;bSchool of Civil and Hydraulic Engineering, Dalian University of Technology, Dalian, 116024,

China

ABSTRACT

Response time is an important parameter which determines the applied fields and practical vibration reduction effects of

magnetorheological (MR) dampers. However, up to now, only a few papers discuss the test and analysis of response

times. In this paper, the response time of a large-scale MR damper at different velocities and currents was firstly tested.Then, the transient magnetic field excited by the time-variant excitation current was simulated by finite element method

(FEM). Based on the variation of the shear yield stress of magnetorheological fluids in the gap between the cylinder and

the piston, the response time of the MR damper was investigated. Influences of eddy current and excitation current

response time on the dampers response were also explored. Results show that by utilizing finite elements method, thecalculated average effective shear yield strength can be used to predict the response time of a MR damper.

Electromagnetic response is the predominant factor influencing the response time of a MR damper, and reducing eddycurrents is the key to accelerate the response of a MR damper. Moreover, influence of eddy currents is much largerunder stepping down excitation currents than stepping up currents, and with a same magnitude of step, no matter when

the current increases or decreases, the smaller the initial current, the greater the eddy current affects a dampers response

and the longer the response time of damping force is. A fast response excitation current may induce large eddy currents

which reduce the response of the damper instead.

Keywords: magnetorheological damper, eddy current, response time, finite element analysis, magnetic field

1. INTRODUCTIONWith the ability that quickly responds an external magnetic field with a dramatic change in rheological behavior,magnetorheological fluids (MRF) have received a lot attention over the past several decades. A variety of MRF based

devices are developed, among which MR dampers have been widely used in vibration controls of civil engineering

structures, automobile suspension systems, etc [1,2]. Unfortunately, response of force output of a MR damper is far moreslowly than MRF itself and response time of a damper is a key parameter that determines its applied fields and practical

damping effects. However, presently most studies mainly focus on analysis of static magnetic field, modeling ofdamping force in control strategy, and investigation of controlling effects, etc. Few papers discuss the response time of

MR dampers and published results are also different because of different testing methods and structural parameters of

MR dampers. For example, the response time of a MR damper made by Lord Company is between 7.5 ms and 85mstested by Koo [3], and that of a valve MR damper tested by Milecki is between 30 and 180ms [4], and that of a MR

damper fabricated and tested by Soda is about 300 to 400ms [5]. Besides, variation of magnetic field in the damper

which directly determines the changing of the damping force is not discussed in these studies.

In this paper, the response time of a large scale MR damper whose maximum damping force is about 270kN will be

tested. By utilizing the finite element software ANSYS, magnetic field in the gap between cylinder and piston will becalculated. Then based on the calculated shear stress of MRF in the gap, response time of the MR damper will be

analyzed theoretically. Finally, possible influencing factors of the response time of MR dampers such as eddy currents

and response of excitation current will be explored.

2. EXPERIMENTAL STUDY2.1 Experimental instruments

[email protected]; phone 86 451 8628-2367; fax 86 451 8628-2367; Harbin Institute of Technology

Second International Conference on Smart Materials and Nanotechnology in Engineering,edited by Jinsong Leng, Anand K. Asundi, Wolfgang Ecke, Proc. of SPIE Vol. 7493,

74930U 2009 SPIE CCC code: 0277-786X/09/$18 doi: 10.1117/12.840217

Proc. of SPIE Vol. 7493 74930U-1

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The damper was tested with a servo-hydraulic test facility (MTS) whose maximum driving force is about 2500kN.

Main parameters of the MR damper are listed in Table 1. Experimental results show that its maximum damping force atvelocity of 40 mm/s is about 270kN.

Table 1. Main parameters of the MR damper

Maximum Stroke

(mm)Numberof coils

Turns ofeach coil

Gap

(mm)

Diameter of cylinder

(mm)

Effective length of piston

(mm)

50 4 900 1.5 200 120

2.2 Testing methodThe testing method and experimental set up are shown in Fig.1. Driven by MTS, the piston of the MR damper is pulled

out and back at a constant velocity. Two voltage signals are sent out at the same time by an industry computer. One was

sent to the current driver which then supplies direct currents to coils of the damper. Meanwhile the other voltage wassent to the MTS system to record times of current changes. Consequently, four signals operation time of MTS, time of

current driver, displacement and damping force of the MR damper were stored in MTS.

Fig.1 Experiment set up for testing of response time of the MR damper

As shown in Fig.2, when damping force gradually changes from one stable state Fi to another, Ff, response time is

defined as the time span from the end time of Fi to the time instant that damping force reaches F i+0.632 (Ff-Fi). A high

frequency sampling was adopted to ensure that the whole changing process of the damping force accompanied with

varying currents could be captured.

(a) Damping force under stepping up current (b) Damping force under stepping down current

Fig.2 Definition of the response time


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2.3 Experimental resultsThe response time of the damper is tested with piston at velocities of 1cm/s, 2cm/s and 4cm/s and step currents 0.0A-0.8A-0.0A, 0.4A-1.2A-0.4A, 0.0A-0.4A-0.0A, 0.4-0.8A-0.4A are applied for each velocity case. Time history cure of

damping force under 4 cm/s piston velocity and 0.4A-1.2A-0.4A step current is shown in Fig.3 and results under all

other conditions have similar characters.

(a) Stepping up current 0.4A-1.2A (b) Stepping down current 1.2A-0.4A

Fig.3 Typical experimental curves

(a) Stepping up current (b) Stepping down current

Fig. 4 Statistical results of the tested response time of the MR damper

In each operation condition, the response time is tested 3 times and average value is obtained, as plotted in Fig.4. It can

be observed that:

(1) Although with a same stepping magnitude, 0.4A, response time under the step current 0A-0.8A is much longer thanthat of 0.4A-1.2A, no matter whether the current is stepping up or down. This indicates that with a same stepping

magnitude, a larger initial current leads to a shorter response time.

(2) With a same stepping magnitude, response time under the stepping down current is longer than under the stepping up

current, especially for the current decreasing to zero.

(3) It still takes as long as 160ms-240ms for the MR damper to response under stepping up currents.

(4) A fast piston velocity results in a fast response.


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3. THEORETICAL INVESTIGATION BASED ON MAGNETIC FINITE ELEMENTANALYSIS

The adjustable damping force induced by modifying excitation current in a MR damper mainly comes from the changingof shear yield strength of MRF. In addition, given that the damping force is mainly predicted based on quasi-static model

[6, 7] at present, in this paper, the response time of the MR damper was investigated by observing the variation of the

shear yield strength of MRF, instead of damping force directly.3.1 Magnetic finite element model of the MR damperA 2D axial symmetric finite element model of the MR damper is constructed in ANSYS, as shown in Fig.5. Elementstypes used for the piston, rod, cylinder, MRF and air are PLANE53, and the whole model is enclosed by a layer of

INFIN110 elements. CIRCU124 elements are used for the independent current source (ICS) and four parallel connected

coils.

A small element size applied for the gap, piston, and cylinder which together constitute the magnetic circuit of the MRdamper. It should be noted that in ANSYS an arbitrary transient excitation can be implemented by modifying REAL

CONSTANT within load steps.

Fig.5 Finite element model of the MR damper

3.2 Average effective shear strength of MRFSince the adjustable damping force of a MR damper results from the changing of shear yield strength of parts of MRF inthe gap which is named effective MRF (shown in Fig.6) hereafter for convenience, transient damping force should be

predictable by calculating time-variant shear yield strength of the effective MRF.

Fig. 6 Effective parts of magnetorheological fluid

However, magnetic fields in elements of effective MRF differ from each other, the concept of the average effective shear

strength *(t) is put forward and given by


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* 2

3 4 5

( ) 3632 + 206593.4

178444.2 + 5023.3 + 23023.4

t B B

B B B

=

(1)

Here, relationship between magnetic flux density and shear yield strength of MRF is fitted from the experimental data

(see Fig.7);B,the average effective magnetic flux density, is time dependent and given by.

1

1

( )

( )

n

i i

i

n

i

i

B t V

B t

V

=

=

=

(2)

Here, Vi andBi(t) are volume and radial magnetic flux density of effective MRF element i at time instant trespectively.

Fig.7 Magnetic flux density vs. shear yield strength of MRF Fig.8 Testing method of excitation currents

The calculating procedure for* at time t, *(t), is as follows. Firstly, implement time history curve of the excitationcurrent in the finite element model in section 3.1. When the solution is done,Bi (t)and Vi (t) are retrieved by using APDL

language of ANSYS. Then they are substituted into equation (2) to get the average effective magnetic flux density B(t).

At last, substitutingB(t) into equation (1) will obtain *(t).

In the above procedure, the time history curve of the electric current is experimental data and measured by placing the

damper on the ground. As shown in Fig.8, the entire electric circuit in this test is composed of four parallel-connected

coils of the damper, one standard resistance and one current power supply. The voltage signal sent out by the industrialcomputer is proportionally changed by current driver into a current signal which is then used as the dampers excitation

current. Time-variant current in the circuit is obtained by dividing the voltage drop on the stand resister by its resistance

and this current can be used to check that whether the current is loaded as expected.

3.3 Results and discussionTested damping force (4cm/s) and calculated shear yield strength are shown in Fig.9. Same time scale and range are usedfor these two time-history curve to make them comparable. Due to the influences of system stiff of the whole experimentset up, tested response time of a MR damper is greatly depend on the dampers velocity. The larger the velocity, the

smaller the influence is [1]. It can be observed from statistical results in Fig.4 that 4cm/s is large enough to ignore such

influence, thus the corresponding test data are used in Fig.9.

Time history curve of damping force is in well agreement with that of average effective shear yield strength, as shown in

Fig.9. This indicates that the calculating method for response time of MR dampers in this paper is correct, i.e. transient

damping fore can be predicted by average effective shear yield strength.


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In fact, response of excitation current and magnetic field are both taken into account in the above calculation in which

the former is considered by using test data and the latter by transient magnetic finite element method. Agreement in Fig.9indicates that the response time of a MR damper is mainly composed of the response of excitation current and that of

magnetic field.

4. INFLUENCES OF EDDY CURRENT AND EXCITING CURRENTS4.1 Influence of eddy currentBy comparing tested history-curves of currents and damping forces as shown in Fig10, it can be found that response of

magnetic field lags far behind its exciting current. Given the fact that MRF response to an applied magnetic field within

several milliseconds, the lag of damping force can be considered as the lag of magnetic field which is caused by eddycurrents according to the Faraday electromagnetic induction law.

In condition that electric currents step up or down from 0A to 0.8A, the response time of a magnetic field for the former

is about 300ms and 520ms for the latter. The response time of the magnetic field for the current stepping from 0.4A to

1.2A is about 20ms, 150ms conversely. This means that, with a same stepping magnitude, eddy currents have larger

effects on the magnetic field for stepping up excitation currents than stepping down. Furthermore, the lower the initialexcitation current, the larger the effects are.

(a) Current steps up from 0.0A to 0.8A (b) Current steps down from 0.8A to 0.0A

(c) Current steps up from 0.4A to 1.2A (d) Current steps down from 1.2A to 0.4A

Fig. 9 Tested damping force and calculated shear yield strength


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Fig. 10 Experimental time-history curves of current and damping force

4.2 Influence of exciting currentsResults in section 3.3 have shown that the response time of damping force mainly depends on the electromagnetic

response of the damper and the lag of magnetic field is also studied in section 4.1. This section will continue to explore

the influence of response time excitation currents on that of damping force, i.e. whether a fast changing current will leadto a fast response damper.

The time-history curve of the average effective shear stress of MRF are computed as the time for excitation currentstepping from one level to another is shorten to 50ms., i.e. in 50ms, electric current complete the process of jumping

from 0.0A (0.4A) to 0.8A (1.2A). The calculated average effective shear stress of MRF and the tested damping force in

section 2 are plotted together in Fig.11.

Fig.11 shows that after excitation current shortened to 50ms, the response time of the damping force is shortened only a

little, except for the current stepping from 0A to 1.2A. The reason for this perhaps is larger eddy currents that caused byfaster variations of excitation currents.

Excitation currents response time has bilateral effects on the damping force. A fast electric current change, on one hand,

will directly shorten the response time of the damping force; on the other hand, it will induce a larger eddy current which

slows the response of the damping force. Consequently, a fast excitation current response doesnt necessarily means a

fast response of the damping force and the fastest response should be reached at the balance point of bilateral effects.

As discussed in sections 4.1 and 4.2, reducing the eddy current is the key to accelerate the response of a MR damper.


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Fig. 11 Time-history curves of calculated shear strength and experimental damping force

5. CONCLUSIONSIn this paper, experimental study and finite element method based theoretical analysis of response time of a MR damper

are conducted and the following conclusions are achieved.

(1) By utilizing finite elements method, the calculated average effective shear yield strength can be used to predictresponse time of a MR damper.

(2) The response time of a MR damper mainly depends on its electromagnetic response, and reducing the eddy current is

the key to develop a fast response MR damper.

(3) With a same stepping magnitude, eddy currents have larger effects on the magnetic field for stepping up excitation

currents than stepping down currents and response of damping force is longer in the former condition. Furthermore, the

lower the initial excitation current, the larger the effects are.

(4) Due to the bilateral influences of excitation current, a fast current change may not result in a fast response of the

damping force.


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6. ACKNOWLEDGEMENTSThis research is financially supported by the National Natural Science Foundation of China under grant number

90815027High-Tech Research and Development of China under grant number 2006AA03Z103 and National Basic

Research Program of China under grant number 2007CB714204, Commonweal Vocation Scientific Research Program of

China under the grant number 2008419073, National Science and Technology Support Plan under number

2006BAJ03B06.

REFERENCES

1. J. D. Carlson, D. M. Catanizarite, K. A. Clair, "Commercial magneto-rheological fluid device," Proc. 5th Int. Conf.ER Fluids, MR Suspensions and Associated Technology, Singapore, 2857-2865(1996).

2. Wojciech Szelag, "Finite element analysis of the magnetorheological fluid brake transients," The InternationalJournal for Computation and Mathematics in Electrical and Electronic Engineering, 23(3), 758-766(2004).3. J. H. Koo, F. D. Goncalves, Mehdi Ahmadian. "Investigation of the response time of magnetorheological fluiddampers,"Proc. SPIE 5386, 63-71(2004).

4. Andrzej Milecki. "Investigation of Dynamic Properties and Control Method Influences on MR Fluid DampersPerformance,"Journal of Intelligent Material Systems and Structures, 13, 453-458(2002).

5. Satsua Soda, Haruhide Kusumoto, et al., "Semi-active seismic response control of base-isolated building with MRdamper,"Proc. SPIE 5052, 460-467(2003).

6. Young Tai Choi, Norman M. Wereley. "Assessment of time response characteristics of electrorheological andmagnetorheological dampers," Proc. SPIE 4331, 92-102(2001).

7. Yang G. "Large-scale magnetorheological fluid damper for vibration mitigation: modeling, testing and control,"Notre Dame, Indiana. Ph.D. Dissertation University of Notre Dame, 2001.


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