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 DOI: 10.1177/1045389X13489361

2013 24: 2036 originally published online 8 May 2013Journal of Intelligent Material Systems and StructuresN Hoang, N Zhang, W H Li and H Du

reduction of a powertrain test rigDevelopment of a torsional dynamic absorber using a magnetorheological elastomer for vibration

  

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Original Article

Journal of Intelligent Material Systemsand Structures24(16) 2036–2044� The Author(s) 2013Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/1045389X13489361jim.sagepub.com

Development of a torsional dynamicabsorber using a magnetorheologicalelastomer for vibration reduction of apowertrain test rig

N Hoang1,2, N Zhang1, W H Li3 and H Du4

AbstractThis article presents the development of a torsional adaptive tunable vibration absorber using a magnetorheological elas-tomer for vibration reduction of a powertrain test rig. The magnetorheological elastomer used to develop the adaptivetunable vibration absorber consists of silicone polymer, silicone oil and magnetic particles with the weight percentages of60%, 20% and 20%, respectively. Experimental testing is conducted to obtain the magnetorheological elastomer’s proper-ties, such as Young’s modulus and the damping ratio, and effective formulas are derived to facilitate the design of theadaptive tunable vibration absorber. With the derived formulas, a magnetorheological elastomer–based adaptive tunablevibration absorber is designed and manufactured, and experimental testing is also conducted to validate the design. Theresults of experiments show that the magnetorheological elastomer–based adaptive tunable vibration absorber can workin a frequency range from 10.75 to 16.5 Hz (53% relative change). Both the designed and experimental results of theadaptive tunable vibration absorber’s frequencies are in good agreement. A powertrain model is used to validate themagnetorheological elastomer–based adaptive tunable vibration absorber’s effectiveness, and the numerical simulationsshow that the powertrain frequencies are shifted away from the resonant frequency; thus, the powertrain’s steady-statevibration can be significantly reduced. This magnetorheological elastomer–based adaptive tunable vibration absorber willbe a promising new device for vibration reduction of vehicle powertrains.

KeywordsAdaptive tunable dynamic absorber, vibration reduction, powertrain vibration, magnetorheological elastomer

Introduction

A magnetorheological elastomer (MRE) is a smartmaterial whose mechanical properties can be magneti-cally controlled. As such, it is potentially a suitablematerial for developing structures of varying stiffness(Carlson and Jolly, 2000; Kallio, 2005).

One of the most popular applications of MRE mate-rial is that this material is used as an adaptive elementfor developing adaptive tuned vibration absorbers(ATVAs). Because of the increase in elastic modulusunder the application of an external magnetic field,MRE-based ATVAs can work in a wide frequencyrange instead of a specific frequency or narrow band-width, as a traditional vibration absorber does. Forinstance, Ginder et al. (2001) used a MRE as a variable-spring-rate element to develop an ATVA, which wasthen experimentally investigated. The experimentalresults show that the frequency range of the ATVA isfrom 500 to 610 Hz under a magnetic field of 0.56 T.

Deng et al. (2006) developed an MRE-based ATVA forvibration reduction of a beam with two supported ends.The authors reported that this ATVA works effectivelyin a frequency range from 55 to 81.25 Hz (relative fre-quency change 49%) in a magnetic field produced byan electromagnetic coil with a direct current (DC)

1School of Electrical, Mechanical and Mechatronics Systems, Faculty of

Engineering, University of Technology, Sydney, Sydney, NSW, Australia2Mechatronics Department, Institute of Mechanics, Vietnam Academy of

Science and Technology, Hanoi, Vietnam3School of Mechanical, Materials & Mechatronic Engineering, University

of Wollongong, Wollongong, NSW, Australia4School of Electrical, Computer and Telecommunications Engineering,

University of Wollongong, Wollongong, NSW, Australia

Corresponding author:

N Hoang, School of Electrical, Mechanical and Mechatronics Systems,

Faculty of Engineering, University of Technology, Sydney, PO Box 123,

Broadway, Sydney, NSW 2007, Australia.

Email: Nga.Hoang@uts.edu.au

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current of 1.5 A. Albanese and Cunefare (2003) pre-sented a state-switched absorber (SSA) using a MREmaterial and found that with iron particles 35% by vol-ume, the MRE material has the largest magnetorheolo-gical effect and the natural frequency of the SSA can betuned from 45 to 183 Hz (360% increase in frequencyshift). In addition, Lerner and Cunefare (2008) testedthe SSA operating in different working modes ofMREs. These authors reported that the increase in thefrequency range of the SSA is 183%, 473% and 510%for shear, longitudinal and squeeze modes, respectively.

Even though a great number of MRE-based ATVAshave been studied, their use has only been applied tosingle-degree-of-freedom (SDOF) systems. The applica-tion of ATVAs for multi-degrees-of-freedom (MDOF)systems is an area that has not been fully addressed sofar. In addition, no ATVA using MREs has beenapplied to torsional vibration reduction of mechanicalsystems, which constitute a major proportion of engi-neering vibration problems, of which, vehicle power-trains are a typical example.

The powertrain is a crucial subsystem of vehiclesand is also a source of vibration (Couderc et al., 1998;Crowther, 2004; Zhang et al., 2003). Because of thewide range of operating frequencies of the powertrain,the likelihood of the engine working speed being in theresonance area is very high. Moreover, the resonancecan be unavoidable when the engine speed passesthrough one or more powertrain frequencies, for exam-ple, when the engine accelerates from idle to top work-ing speeds. Consequently, powertrains may experiencea high level of vibration if the acceleration time is notrapid enough, and this vibration reduces the comfortperformance of vehicle (Hoang et al., 2009, 2011).Clearly, this vibration needs to be minimized.

Hoang et al. (2009) proposed a concept design of aMRE-based ATVA for steady-state vibration controlof powertrains. The authors reported that by using asoft MRE developed by Abramchuk et al. (2006), theATVA can work in a frequency from 7 to 70 Hz. In thisstudy, the influence of the ATVA parameters and itslocation in the powertrain system was also examined.Although the soft MRE shows a significant increase inshear modulus, the damping of this MRE was notreported, and the damping model of another MREreported by Zhou (2003) was used instead. As a result,the damping model may not accurately represent thedamping properties of the soft MRE.

Hoang et al. (2011) used a new MRE reported byChertovich et al. (2010) to develop a MRE-basedATVA for transient vibration control of a powertrain,in which the new MRE has significant increase in shearmodulus and low damping. With the new MRE, theATVA can work in a frequency between 10 and 55 Hz;thus, the ATVA can be tuned to deal with the reso-nance occurring in a powertrain transient state withexcitation frequency of 20–40 Hz. Although the

capacity of the MRE-based ATVA was numericallyvalidated, two shortcomings are apparent. First, it isdifficult and impractical to supply DC to the magneticcircuit, which includes three electromagnetic coils and amild steel core, when the circuit rotates with the power-train shaft. Second, with the rotating magnetic circuit,the inertia of the MRE-based ATVA will be high;worse, the three electromagnetic coils and mild steelcore may generate the imbalanced forces on the power-train system. As a result, the powertrain may experi-ence a higher level of vibration.

This study presents the development of a torsionalATVA using a MRE for vibration control of power-train systems in which a torsional MRE-based ATVAis experimentally validated. The first section is theintroduction. The second section presents a MRE andexperimental testing for determining its properties forthe design of the ATVA. The third section proposes thedesign of a MRE-based ATVA and conducts an experi-ment to validate the ATVA design. Numerical simula-tions are conducted to validate the ATVA’seffectiveness for vibration control of a powertrain in asteady state in section ‘Numerical simulations’, and thelast section presents the conclusion of this work.

A MRE and its characteristics

MRE preparation and experimental set-up

The MRE consists of a rubbery silicone polymermatrix; silicone oil, which serves as a plasticizer; andmagnetic particles having weight fractions of 60%,20% and 20%, respectively. The size of the magneticparticles is 6–7 mm. To enhance the MR effect, themixed material was placed in a magnetic field before itwas cut into rectangular prism samples 16 mm 3 16mm 3 45 mm for testing. This MRE material was fab-ricated at the University of Wollongong, Australia.The test was conducted at the Dynamic and SolidMechanics Laboratory, University of Technology,Sydney (UTS). The experimental set-up for measuringMRE Young’s modulus is shown in Figure 1.

The MRE sample was placed in the middle of twopermanent cylindrical magnets (D-D50H12.5-N45-disc50 mm diameter 3 12.5 mm high). The fixture is a steelframe support, which is used to locate the handle. Thefixture ensures that the distance between the two mag-nets can be adjusted easily by turning the handle.Consequently, the magnetic field applied to the MREsample can be varied. The MRE magnetic flux densityis measured by BELL 610 Gauss-meter. The force Fand the length change of the MR specimen are pro-vided by Device Instron. The MRE Young’s modulusis measured by using the following equation

E =s

e=

F=A0

Dl=l0=

Fl0

A0Dlð1Þ

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where E is the Young’s modulus, F is the applied force,A0 is the original cross-sectional area through whichthe force is applied, Dl is the length change of the MRspecimen, and l0 is the original length of the MREspecimen.

To measure the MRE damping ratio, a weight isattached to the MRE specimen. By measuring thevibration attenuation of the weight, the damping ratiocan be calculated as

§=dffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

(2p)2 + d2

q ð2Þ

The logarithmic decrement d = ln(x1/x2), in whichx1 and x2 are vibration amplitudes measured from onecycle for the vibration of the weight. In other words, bymeasuring the free vibration of the weight, vibrationamplitudes x1 and x2 can be determined; the dampingratio is then calculated by equation (2).

Experimental results and the proposed model

Young’s modulus and the damping ratio of the MREare measured using the experimental set-up as pre-sented in section ‘MRE preparation and experimentalset-up’. To facilitate the ATVA design, models for bothYoung’s modulus and damping ratio are derived. Theprocedure for proposing these models is similar to thoseintroduced by Hoang et al. (2011).

Young’s modulus of the MRE is approximated bythe following equation

E =E(B)=

E0 B<B0

E0 +(Emax � E0)B2

B2S

(3� 2 BBS) 0\B\BS

Emax B � BS

8<:

ð3Þ

Here, B0 = 0.05 T is the value of magnetic field den-sity, from which the MRE material is initially effected,BS = 0.225 T is the saturated point, E0 = 114.2 kPaand Emax = 270.9 kPa.

The experimental data and the proposed model ofMRE Young’s modulus are shown in Figure 2.

Also, the damping ratio is proposed as equation (4)

§=0:126+ 4:9794B2 � 33:1958B3 0<B\BC

0:1412+0:0256B� 0:1281B2 BC<B<Bmax

�

ð4Þ

with BC = 0.1 T, Bmax = 0.35 T, and the proposeddamping ratio and experimental data are shown inFigure 3.

It can be seen that the experimental data and theproposed models in Figures 2 and 3 are in good agree-ment. These models will be used to design the MRE-based ATVA in the following section.

A proposed design of MRE-based ATVAand experimental validation

In this section, an MRE-based ATVA is designed for apowertrain test rig at the UTS. For more details of theUTS powertrain test rig, see Crowther (2004). In thisapplication, the MRE-based ATVA will be mountedon the propeller shaft of the test rig; the shaft has a dia-meter of 86 mm.

Figure 1. Experimental set-up for measuring Young’s modulus.MRE: magnetorheological elastomer.

Figure 2. Proposed model of Young’s modulus andexperimental data.

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Proposed design of MRE-based ATVA

The proposed ATVA design is shown in Figure 4, andthe cross section of the ATVA is shown in Figure 5.

In Figure 4, the rotating part, which is the main partof ATVA, consists of an outer ring, inner ring and eightMRE specimens located in the gap between the rings,and two mild steel overlap sheets, which are used todirect the magnetic flux to the MRE specimens. TheMRE specimens act as springs to ensure that the rotat-ing part is a torsional SDOF system, and it is locatedon the powertrain propeller shaft. The ATVA is fixedon the frame support, and this support is used to locatethe ATVA to the powertrain test bed.

It is noted that the eight MRE specimens operate aseight translational springs in tangent direction. Thesespecimens create elastic forces between the outer andinner rings. The magnetic flux path and equivalentmagnetic circuit of the ATVA are shown in Figure 6(a)and (b), respectively. In this design, to enhance the fluxfrom the magnetic coil to the MRE specimens rather

than the brass outer ring, two mild steel overlap sheetsare bolted to both sides of the outer ring as shown inFigure 6(a).

Using Ohm’s law for the magnetic circuit, the mag-netomotive force NI can be designed. Here fS , fB andfMRE are magnetic flux through steel, brass and MRE,respectively; RAir, RBrass and RMRE are magnetic reluc-tance of air, brass andMRE, respectively; N is the num-ber of turns of the coil and I is the DC input currentsupplied to the electric coil. In this design, N = 1000,and input current varies from 0 to 5.75 A. Main para-meters of the ATVA are shown in Table 1.

Because the inner ring is fixed in the propeller shaftof powertrain, the inertia of ATVA can be calculatedby

JA = JOuter ring + 2JOverlap sheet ð5Þ

Here, the outer ring and each of the overlap sheetsare treated approximately as a hollow cylinder asshown in Figures 7 and 8.

By using the mass element of a cylinderdm= rdV = rLrdrdu, as shown in Figure 8, the inertiaof the holed cylinder can be calculated

JO =

ðr2dm= rL

ð2p

0

ðRo

Ri

r3drdu= rL

ð2p

0

du

ðRo

Ri

r3dr

= 2prL

ðRo

Ri

r3dr=prL

2(R4

o � R4i )

It is noted that m=prL(R2o � R2

i ) is the mass of thecylinder, thus, the moment of inertia

JO =1

2m(R2

o +R2i ) ð6Þ

Figure 3. Damping ratio proposed model and experimentaldata.

Figure 4. ATVA exploded view.ATVA: adaptive tuned vibration absorber.

Figure 5. Cross section of ATVA design.ATVA: adaptive tuned vibration absorber; MR: magnetorheological.

Hoang et al. 2039

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With the parameters of the outer ring and overlapsheet as shown in Table 1, the inertia moment of theinner ring and each overlap sheet is calculated by equa-tion (6), then, the inertia moment of ATVA JA = 0.021kg m2 is calculated by equation (5).

It is assumed that each MRE specimen works as atranslational spring, and the stiffness of a specimen canbe calculated as follows (Lerner and Cunefare, 2008)

k =EA

Lð7Þ

Because there are eight MRE specimens, the tor-sional stiffness of the MRE-based ATVA can beexpressed by

kA = 8EA

Ld ð8Þ

Figure 6. (a) Magnetic flux path, 1: coil, 2: outer ring, 3: mild steel overlap sheet, 4: inner ring, 5: MRE specimen, and 6: mild steelcore and (b) ATVA magnetic circuit.ATVA: adaptive tuned vibration absorber; MR: magnetorheological elastomer.

Table 1. ATVA’s mechanical parameters.

Items Material Mass estimation Dimensions (mm)

Outer ring Brass 1.6 kg Ri = 70, Ro = 90, L = 18Inner ring Brass 0.8 kg Ri = 48, Ro = 57, L = 16Overlap sheet Mild steel 0.8 kg Ri = 58, Ro = 90, L = 7Mild steel core Mild steel 7 kg Ri = 74, Ro = 139, L = 7Electric coil Copper 5.3 kg Ri = 92, Ro = 132, L = 34

ATVA: adaptive tuned vibration absorber; Ro: outer radius, Ri: inner radius, L: length.

Figure 7. Cylinder model to calculate inertia moment.Figure 8. Mass element of cylinder.

2040 Journal of Intelligent Material Systems and Structures 24(16)

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Here d is the distance from the centre of a MRE speci-men to the centre of the propeller shaft. In this design,d = 65 mm, and L = 35 mm and A = 7 mm 3 8 mmare the length and the cross section, respectively, of aMRE specimen, and E is the MRE Young’s modulus,which was shown in Figure 2. The ATVA’s natural anddamped frequencies can be calculated by equations (9)and (10)

fn =1

2p

ffiffiffiffikA

JA

qð9Þ

fd = fn

ffiffiffiffiffiffiffiffiffiffiffiffiffi1� §2

A

qð10Þ

and the damping coefficient can be calculated

cA = 2vnJA§A = 4pfnJA§A ð11Þ

With JA = 0.021 kg m2, the stiffness kA calculated inequation (8) and the damping ratio §A as shown inequation (4), and the frequency of the designed ATVAcan be calculated by equation (10).

Experimental validation

The experimental set-up for measuring the ATVA fre-quency is shown in Figure 9.

In this experiment, the device BELL 610 Gauss-meter is used to measure the magnetic field on the sur-face of each MRE sample. Two accelerometersCrossbow CXL01LF1 are also used to measure the freevibration of the ATVA. These sensors are connected tothe Dynamic Signal Analyser 35665A (HewlettPackard), which has two channels, numbered 1 and 2,to connect to the accelerometers.

It can be seen in Figure 9 that the accelerometers areused to pick up the signal of acceleration in tangentdirections, and the signals are transferred to the chan-nels of the analyser. The data from channels 1 and 2are averaged in time domain, and fast Fourier transfor-mation (FFT) is used to obtain the frequency domainof the free vibration of the ATVA. As a result, the freevibration of the MRE-based ATVA can be measured,and its natural frequency can be obtained.

Experimental results

By varying the input current from 0–5.75 A, the depen-dence between the measured magnetic flux density andthe input current is shown in Figure 10.

Clearly, the magnetic flux density B of the magneticcircuit is proportional to the input current I. A compar-ison of the ATVA designed frequency, which is calcu-lated by equation (10), and the experimental results areillustrated in Figure 11.

It is obvious that the ATVA frequencies for bothexperimental data and the design are in good agree-ment. The ATVA frequency range is from 10.75 to 16.5Hz (the relative change in the frequency is 53%). It isnoted that the maximum frequency of 16.5 Hz is mea-sured at magnetic flux density B = 0.21 T (at maxi-mum input current I = 5.75 A).

Numerical simulations

The MRE-based ATVA can work effectively in a tun-able frequency range from 10.75 to 16.5 Hz. To showthe capacity of the MRE-based ATVA for vibrationcontrol of powertrains, a simplified powertrain modelconsisting of inertias, stiffness and damping is shown inFigure 12.

Figure 9. Experimental set-up for measuring the ATVAfrequency – 1: analyser, 2: DC power supply, 3: Gauss-meter, 4:powertrain shaft, 5: accelerometer, and 6: ATVA.ATVA: adaptive tuned vibration absorber; DC: direct current.

Figure 10. Dependence between magnetic flux density B andinput current I.

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The powertrain is modelled as a 4-degree-of-freedomsystem in which the engine is modelled by the first iner-tia. The second and third inertias represent the clutchor the torque converter (TC) and the transmission gearbox, respectively. The drive line components of thepowertrain are modelled by the fourth inertia.

The powertrain has a number of gear ratios, whichare used to set the optimal engine speed according tothe vehicle speed. These gears are characterized by vary-ing the stiffness k2. In this study, it is assumed that onlythe first transmission gear is used. When the powertrainis in a resonant range, the ATVA is considered to workeffectively if the powertrain’s natural frequencies can beshifted away from the resonance; hence, powertrain’ssteady-state response is reduced significantly.

By using Lagrange’s equation, the equation ofmotion of the system before adding the ATVA can beexpressed as the equation as below

J€u+C _u+Ku=T ð12Þ

where u= u1 u2 u3 u4½ �T and T= T (t) 0 0 0½ �T are vectorsof generalized coordinates and external torque.

The inertial matrix J and the stiffness and dampingmatrices, K and C, have the following forms

J=

J1 0 0 0

0 J2 0 0

0 0 J3 0

0 0 0 J4

2664

3775 ð13Þ

K=

k1 �k1 0 0

�k1 k1 + k2 �k2 0

0 �k2 k2 + k3 �k3

0 0 �k3 k3

26664

37775;

C=

c1 �c1 0 0

�c1 c1 + c2 �c2 0

0 �c2 c2 + c3 �c3

0 0 �c3 c3

26664

37775

ð14Þ

By solving equation (12), both free and forced vibra-tions of powertrain can be obtained. As a result,powertrain’s vibration characteristics such as naturalfrequencies and frequency response can be obtained.

To investigate the effectiveness of the ATVA,the powertrain vibration parameters are set asJ1 = 0.4 kg m2, J2 = 0.05 kg m2, J3 = 0.1 kg m2, andJ4 = 8 kg m2; c1 = 6 N m s/rad, c2 = 4 N m s/rad andc3 = 4 N m s/rad and k1 = 20,000 N m/rad, k2 =18,000 N m/rad and k3 = 5350 N m/rad.

With these parameters, the powertrain has three nat-ural frequencies f1 = 13.8891 Hz, f2 = 62.0286 Hz andf3 =148.4882 Hz.

It is assumed that excitation frequency O is equal tothe frequency of the engine speed. If the engine speed is825 r/min, it gives O= 2p3 13.75 rad/s. Clearly, aresonance occurs in powertrain because f1 = 13.8891Hz is close to the excitation frequency. To deal with theresonance, the MRE-based ATVA is added to thepowertrain as in Figure 13. Here, the input currentI = 4 A is tuned, at which magnetic flux density =0.14 T, as shown in Figure 10; thus, the ATVA’s fre-quency f = 13.75 Hz, as shown in Figure 11.

With the ATVA, the system has 5 degrees of free-dom, and the equation of motion has the same form asequation (12) with u= u1 u2 u3 u4 uA½ �T , and the inertiamatrix is expressed in the following form

Figure 11. ATVA experimented and designed frequencies.ATVA: adaptive tuned vibration absorber.

Figure 12. A powertrain model.

Figure 13. A powertrain model with an ATVA.ATVA: adaptive tuned vibration absorber.

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J=

J1 0 0 0 0

0 J2 0 0 0

0 0 J3 0 0

0 0 0 J4 0

0 0 0 0 JA

266664

377775 ð15Þ

the stiffness and damping matrix have forms of

K=

k1 �k1 0 0 0

�k1 k1 + k2 �k2 0 0

0 �k2 k2 + k3 + kA �k3 �kA

0 0 �k3 k3 0

0 0 �kA 0 kA

266664

377775

ð16Þ

C=

c1 �c1 0 0 0

�c1 c1 + c2 �c2 0 0

0 �c2 c2 + c3 + cA �c3 �cA

0 0 �c3 c3 0

0 0 �cA 0 cA

266664

377775

ð17Þ

With the inertial matrix J and stiffness and dampingmatrices K and C, as shown in equation (15), (16) and(17), the vibration characteristics of the powertrainafter adding the ATVA can be solved. For example, letT0 = 3 N m, the powertrain’s steady responses for thefundamental frequency of powertrain f1 = 13.5 Hzbefore and after adding the ATVA are shown inFigure 14.

It can be seen in Figure 14 that the powertrain’svibration frequency response is reduced significantlyafter adding the ATVA. To be specific, the resonance

f = 13.75 Hz was shifted away from the excitation fre-quency, and two new frequencies of 13 and 14.6 Hz areintroduced. It confirms that the ATVA workseffectively.

Conclusion

This work has presented a MRE-based ATVA forvibration control of powertrains. A MRE material wasfabricated, and the MRE properties were measured.An ATVA was subsequently designed for the power-train test rig in UTS and was experimentally investi-gated. The experimental results show that the ATVAcan work in a frequency range from 10.75 to 16.5 Hz(53% relative change). Both the designed and experi-mental results of ATVA’s frequency are in good agree-ment. This MRE-based ATVA can be applicable notonly to the UTS powertrain test rig but also to someother vehicle powertrains. However, a potential draw-back is that with the number of wire turns N = 1000,the magnetic flux density B of 0.21 T at current of 5.75A is small. In other words, the magnetic circuit of theATVA should be optimized. This limitation will beimproved in future work.

To show the capacity of the ATVA’s effectivenessfor vibration control of powertrain systems, a power-train fitted with the ATVA was numerically investi-gated. It was found that by adding the MRE-basedATVA, the powertrain frequencies could be shiftedaway from the resonant frequency. As a result, theforced vibration of the powertrain was reduced signifi-cantly. This finding confirms that the ATVA works

Figure 14. Powertrain vibration response.ATVA: adaptive tuned vibration absorber.

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effectively in a tunable range of frequency. Althoughthe frequency of the ATVA was measured, the vibra-tion reduction of the powertrain was not conducted inreal time. This is also a shortcoming of this study. Theexperimental validation of real time control of theATVA for the UTS powertrain test rig will beaddressed in our future studies.

Acknowledgement

The support from Professor Peter Watterson, Mr ChristopherChapman, Mr Michael Tran and Mr Lifu Wang, from theUniversity of Technology, Sydney, and Mr Tongfei Tian,from University of Wollongong for experimental testing isacknowledged.

Funding

This study was financially supported by the AustralianResearch Council (ARC DP1096847) and the University ofWollongong URC Small Grant.

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