research article effect of temperature and electric field on the...

Hindawi Publishing CorporationAdvances in TribologyVolume 2013 Article ID 526428 10 pageshttpdxdoiorg1011552013526428

Research ArticleEffect of Temperature and Electric Field onthe Damping and Stiffness Characteristics ofER Fluid Short Squeeze Film Dampers

H P Jagadish1 and L Ravikumar2

1 Department of Mechanical Engineering BMS Evening College of Engineering Bangalore 560 019 India2Department of Mechanical Engineering BMS College of Engineering Bangalore 560 019 India

Correspondence should be addressed to H P Jagadish jagadishhawaldaryahoocom

Received 5 June 2013 Accepted 17 September 2013

Academic Editor Marimuthu Uthayakumar

Copyright copy 2013 H P Jagadish and L Ravikumar This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Squeeze film dampers are novel rotor dynamic devices used to alleviate small amplitude large force vibrations and are used inconjunctionwith antifriction bearings in aircraft jet engine bearings to provide external damping as these possess very little inherentdamping Electrorheological (ER) fluids are controllable fluids in which the rheological properties of the fluid particularly viscositycan be controlled in accordancewith the requirements of the rotor dynamic systemby controlling the intensity of the applied electricfield and this property can be utilized in squeeze film dampers to provide variable stiffness and damping at a particular excitationfrequency The paper investigates the effect of temperature and electric field on the apparent viscosity and dynamic (stiffness anddamping characteristics) of ER fluid (suspension of diatomite in transformer oil) using the available literatureThese characteristicsincrease with the field as the viscosity increases with the field However these characteristics decrease with increase in temperatureand shear strain rate as the viscosity of the fluid decreases with temperature and shear strain rate The temperature is an importantparameter as the aircraft jet engine rotors are located in a zone of high temperature gradients and the damper fluid is susceptibleto large variations in temperature

1 Introduction

Theapplication of controllable fluids in engineering is an areawhich began to be explored in the early 1980s and fluids ofinterest in this study are materials that respond to an appliedelectric field with a remarkable change in its rheologicalbehavior The essential characteristic of these controllablefluids is their capability to change from a liquid state into asolid-like gel under the action of an electric fieldThesemate-rials are commonly called electrorheological (ER) fluids andare normally low-viscosity colloidal suspensions When anelectric field is applied the fluid undergoes a seeminglyreversible transition to a solid in milliseconds being able tosupport considerable stress under static load without yieldWillis MWinslow (1949) was the first to discover an ER fluidand introduced the concept of controlling the apparent vis-cosity of an electroviscous fluid by using an electric field

ER fluids usually consist of a base fluid usually some typeof low viscosity insulating liquid mixed with non-conductiveparticles (in the range of 1ndash10120583m diameter) such as corn-starch gypsum and lithium salt

Since its mechanical properties can be easily controlledwithin a wide range by applied voltage (almost from a pureliquid to a solid) the ER fluid could be used as an electricalandmechanical interface in various industrial areas ER fluidscan be utilized in automobile clutch brake and dampingsystems In a vibratory damping system the fluid is to be ofvariable viscosity which is best satisfied by the applicationof smart fluids (ER and MR fluid) The change in the fieldinduced shear stress produces a change in their apparentviscosity and this property is successfully utilized in applica-tions involving valves dampers clutches and adaptive struc-tures but applications in rotor dynamics are far from sat-isfactory and require considerable attention [1ndash3] Limited

2 Advances in Tribology

information is available regarding the stiffness and dampingcharacteristics of ER fluid and their applications in activejournal bearings and squeeze film dampers While generalaspects and applications of MR and ER fluids have been dealtwith to some extent [4 5] sharing their promising character-istics it was only in the last decade that some pieces of liter-ature have appeared on rotor dampers [6 7] Since the avail-able literature regarding the effect of temperature on the stiff-ness and damping characteristics of ER Fluid squeeze filmdampers is very scanty this paper investigates these aspectson a short squeeze film damper using the relation obtainedbetween viscosity and temperature for a particular ER fluidwhich is a suspension of diatomite in transformer oil

2 The Herschel-Bulkley Model

The one-dimensional Herschel-Bulkley model is used tomodel the shear thinning of ER fluid in the post-yield regionThe constitutive equation for this model [9] is

120574 = 0 120591 le 120591yd (1a)

120591 = 120591yd sgn ( 120574) + 119870 120574 120591 ge 120591yd (1b)

where 120591 is the shear stress 120574 is the shear strain rate and 120591ydis the dynamic yield stress 119870 and 119899

1are two parameters that

describe themagnitude and slope of the curveThe parameter119870 is sometimes referred to as the ldquoconsistency indexrdquo Theexponent 119899

1is dimensionless and is called the ldquobehavior

indexrdquo Both 119870 and 1198991depend on material properties and

working conditions such as friction and temperatureFor steady shear flow (|120591| gt 120591yd) assume that 120574 gt 0 (1b)

can be written as

120591 = (120591yd + 119870 1205741198991minus1) 120574 (2)

The apparent viscosity thus is

120578app = 119870 1205741198991minus1 (3)

For shear thinning of ER suspensions with 0 lt 1198991lt 1 the

apparent viscosity decreases with the increment of shear rateThe temperature affects both the values 119870 and 119899

1and is res-

ponsible for the variation in the apparent viscosity of the ERfluid

3 Temperature Effect on Viscosity of ER Fluid

Changes in the temperature of ER fluid due to working con-ditions like friction or electrical power dissipation mayinfluence its performance in ER devicesThe temperature de-creases the viscosity of the ER fluid and consequently affectsboth the static and dynamic characteristics of the squeeze filmdamperThe viscosity-temperature relation of the ER Fluid ata particular electric field intensity can be modeled by theexponential decay type Reynolds equation or the Arrheniusequation outlined as (4) and (5) respectively as

120578app (119879) = 1205780exp (minus119861119879) (4)

where 119879 is the temperature and 1205780and 119861 are coefficientsThis

is an empirical model that usually works for a limited rangeof temperatures

120578app (119879) = 1205780exp ( 119864

119877119879) (5)

where 119864 is the activation energy and 119877 is the universal gasconstant A first-order fluid is another name for a power lawfluid with exponential dependence of viscosity on tempera-ture

This can be also be presented as

120578app (119879) = 1205780exp(119861

119879) (6)

where 119861 = 119864119877

4 Stiffness and Damping Characteristics ofSqueeze Film Dampers with Orbital Motion

These squeeze film dampers (Figure 2) find application in theair craft engine rotors and are usually mounted on rolling ele-ment bearings with little or no inherent damping to fight theunbalance response especially at critical speeds and to elim-inate rotor dynamic instabilities The coordinates of the orbitare presented as [10]

119911 = 119890 cos120596119905

119910 = 119890 sin120596119905

119903 = 119890

119903 = 119881119903= 0

119881119905= 119890120596

(7)

Ignoring the stiffness terms the radial and tangential forcesacting on the system are

119865119903= 119862119903119903119881119903+ 119862119903119905119881119905= 119862119903119905120596119890

119865119905= 119862119905119903119881119903+ 119862119905119905119881119905= 119862119905119905120596119890

(8)

The direct damping coefficient is

119862119905119905=

119865119905

120596119890 (9)

and the cross-coupled damping coefficient is

119862119903119905=

119865119903

120596119890 (10)

The radial component of the force 119865119903is considered as a stiff-

ness force defined as the direct stiffness coefficient given by

119870119903119903=119865119903

119890= 119862119903119905120596 (11)

The squeeze film velocity is

120597ℎ

120597119905= 119890120596 sin 120579 (12)

Advances in Tribology 3

e

C

C998400120596

y

h120588

z 120579

Figure 1 Squeeze film dampers with orbital motion

The Reynolds equation for the present case with zero spinvelocity for the short bearing case reduces to

1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app sin 120579 (13)

The governing Reynolds equation for the short bearing casewith zero spin velocity is

1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app119890120596 sin 120579 (14)

The short bearing approximation is applicable in cases inwhich the end seals are absent For the short bearing approx-imation the journal axis remains parallel to the bearing underthe steady state operating condition In such a case thechange in pressure in the circumferential direction is negli-gible in relation to the pressure change in axial directionTheReynolds equation modifies to

ℎ3 1198892119901

1198891199092= 12120578app119890120596 sin 120579 (15)

The pressure distribution in the film is obtained by integra-tion as

119901 =6120578app120596

ℎ3

119889ℎ

119889120579

1199092

2+

119860

ℎ3119909 + 119861 (16)

The constants in the above equation are evaluated from theboundary conditions

119901 = 0 at 119909 = plusmn119871

2 (17)

where the coordinate system of Figure 1 is reckoned midwayalong the length 119871 of the bearing (perpendicular to the planeof the paper) The two constants are evaluated to give thepressure 119901 as

119901 =3120578app120596

ℎ3

119889ℎ

119889120579(1199092minus1198712

4) (18)

Using the film thickness Equation and ignoring the pressuredistribution in the diverging wedge that is using the halfSommerfeld condition one gets

119901120579minus 119901119900

=6120578app120596119899 (119871

24minus 119909

2)

1198882[

sin 120579(1 + 119899 cos 120579)3

] for 0 le 120579 le 120587

(19a)

p120579minus po = 0 for 120587 lt 120579 lt 2120587

(19b)

Considering the equilibrium of the journal the load capacitycan be obtained from the integration of the following equa-tions

2int

120587

0

int

1198712

0

prcos 120579119889119909 119889120579 = minus119882 cos120572

2 int

120587

0

int

1198712

0

prsin 120579119889119909 119889120579 = minus119882 sin120572

(20)

where

119882 sin120572 =120587120578app120596119863119899119871

3

81198882(1 minus 1198992)32

119882 cos120572 =120578app120596119863119899

21198713

21198882(1 minus 1198992)2

(21)

The load capacity119882 is

119882 =120578app120596119903119899119871

3

21198882(1 minus 1198992)2radic161198992 + 1205872 (1 minus 1198992) (22)

The radial and the tangential force generated in the damperare components of the load capacity and are defined as

119865119903= 119882 cos120572 =

120578app12059611986311989921198713

1198882(1 minus 1198992)2

119865119905= 119882 sin120572 =

120587120578app1205961198631198991198713

41198882(1 minus 1198992)32

(23)

The direct stiffness direct damping and cross-coupleddamping coefficients are respectively

119870ds =120578app120596119863119899119871

3

1198883(1 minus 1198992)2 (24)

119862ds =120587120578app119863119871

3

41198883(1 minus 1198992)32

(25)

119862119903119905119904

=120578app119863119899119871

3

1198883(1 minus 1198992)2 (26)


Table 1 Damper specifications

Description ParametersClearance 119888 mm 01 02Length 119871 mm 30 40Diameter 119863 mm 100 100119871119863 ratio 03 04Excitation frequency 120596 radsec 100 100Eccentricity ratio 119899 01 01

Table 2 (a) Values of the consistency index119870 [8] (b) Values of theexponent 119899

1[8]

(a)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 0045 0038 0028 00126119864 = 25 kVmm 891 557 246 04

(b)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 086 0861 0873 0957119864 = 25 kVmm 0057 0129 0256 0551

Table 3 Constants 1205780and 119861

Governingequation

119864 = 0 kVmm 119864 = 25 kVmm120574 (sminus1)

2 4 2 4Reynoldsequation

1205780

005322 004383 12899 3489871119861 001324 000839 00512 0018498

Arrheniusequation

1205780

002405 002650 05983 115023119861 105892 670760 40944 1479864

5 Methodology Proposed

The effect of electric field intensity and temperature onthe theoretical squeeze film dynamic (damping and stiff-ness) characteristics can be obtained using the viscosity-temperature relations [8] using the damper specifications andrelevant ER fluid data outlined in Tables 1 2(a) and 2(b)respectively

6 Results and Discussions

The theoretical results are discussed under two headings

(a) effect of temperature on the viscosity and dynamiccharacteristics (stiffness and damping characteris-tics)

(b) effect of electric field intensity and shear strain rateon the viscosity and dynamic characteristics (stiffnessand damping characteristics)

0

0005

001

0015

002

0025

003

0035

004

0045

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)

Temperature T (∘C)

(a) = 2 sminus1 E = 0kVmm(b) = 4 sminus1 E = 0kVmm

Figure 2 Viscosity (Pas) versus temperature (∘C) for (a) = 2 sminus1119864 = 0 kVmm and (b) = 4 sminus1 119864 = 0 kVmm

0

05

1

15

2

25

3

35

4

45

5

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)


(a) = 2 sminus1 E = 25 kVmm(b) = 4 sminus1 E = 25 kVmm


61 Effect of Temperature on the Viscosity Stiffness andDamp-ing Characteristics This section presents the effect of tem-perature on the viscosity and dynamic characteristics of thesqueeze filmdamper for the specifications presented in Tables1 2(a) and 2(b)

The effect of temperature on the viscosity for differentstrain rates without the electric field is presented in Figure 2The viscosity decreases with the temperature owing to loos-ening of the fibrillar structures with temperature

Figure 3 indicates the variation of viscosity with tempera-ture with the applied electric field at 25 kVmmThe viscosityis also found to decrease with the strain rate as indicated byFigures 2 and 3 since the ER Fluid is a shear thinning fluid


0

05

1

15

2

25

3

0 20 40 60 80 100

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

E = 0kVmm 120574 = 2 sminus1

c = 01 mm LD = 03 n = 005c = 01 mm LD = 04 n = 005c = 02 mm LD = 03 n = 005c = 02 mm LD = 04 n = 005c = 01 mm LD = 03 n = 010c = 01 mm LD = 04 n = 010c = 02 mm LD = 03 n = 010c = 02 mm LD = 04 n = 010


(a)


0

50

100

150

200

250

300

350

0 20 40 60 80

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

) E = 25 kVmm 120574 = 2 sminus1


(b)

Figure 4 Direct stiffness coefficient 119870ds (MNm) versus temperature (∘C) for (a) 119864 = 0 kVmm and (b) 119864 = 25 kVmm under a constantstrain rate 120574 = 2 sminus1

0

005

01

015

02

025

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(a)

0

5

10

15

20

25

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(b)

Figure 5 Direct damping coefficient 119862ds (MNsm) versus temperature (∘C) for (a) 119864 = 0 kVmm and (b) 119864 = 25 kVmm under a constantstrain rate 120574 = 2 sminus1


0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)c = 01 mm LD = 03 n = 005c = 01 mm LD = 04 n = 005c = 02 mm LD = 03 n = 005c = 02 mm LD = 04 n = 005c = 01 mm LD = 03 n = 010c = 01 mm LD = 04 n = 010c = 02 mm LD = 03 n = 010c = 02 mm LD = 04 n = 010


(b)

Figure 6 Cross-coupled damping coefficient 119862119903119905119904 MNsm versus temperature (∘C) for (a) 119864 = 0 kVmm and (b) 119864 = 25 kVmm under a

constant strain rate 120574 = 2 sminus1

0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)

Shear strain rate (sminus1)

T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)

Figure 7 Apparent viscosity 120578app Pas versus shear strain rate for (a) 119864 = 0 kVmm and (b) 119864 = 25 kVmm for different temperatures


0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

Shear strain rate 120574 (sminus1)

E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)

Figure 8 Direct stiffness coefficient MNm versus shear strain rate sminus1 for (a) 119864 = 0 kVmm 119879 = 20∘C (b) 119864 = 25 kVmm 119879 = 20∘C (c)119864 = 0 kVmm 119879 = 60∘C and (d) 119864 = 25 kVmm 119879 = 60∘C

However it should be noticed that the viscosity increases bymany orders under the action of the field

The constants 1205780and 119861 of the temperature- viscosity

model of the ER fluid (using either the Reynolds equation orthe Arrhenius equation as outlined in (4) and (5) resp) arepresented in Table 3

The effect of temperature on the direct stiffness directdamping and cross-coupled damping coefficients are pre-sented through Figures 4(a) 4(b) 5(a) 5(b) 6(a) and 6(b)

for electric field intensities of 0 kVmm and 25 kVmm Thedynamic coefficients decrease with temperature in accor-dance with (4) and (5) respectively

62 Effect of Electric Field Intensity and Shear Strain Rateon the Viscosity Stiffness and Damping Characteristics of ERSqueeze Film Dampers The apparent viscosity of the ERfluid is depicted in Figures 7(a) and 7(b) as a function ofthe shear strain rate for different electric field intensities


0

005

01

015

02

025

0 2 4 6 8 10Shear strain rate 120574 (sminus1)

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)

Figure 9 Direct damping coefficient MNsm versus shear strain rate sminus1 for (a) 119864 = 0 kVmm 119879 = 20∘C (b) 119864 = 25 kVmm 119879 = 20∘C (c)119864 = 0 kVmm 119879 = 60∘C and (d) 119864 = 25 kVmm 119879 = 60∘C

119864 = 0 kVmm and 25 kVmm respectively The viscosity in-creases by many orders on the application of the field anddecreases with increase in the shear strain rate as envisagedin these diagrams

The effect of electric field on the dynamic characteristicsof the ER damper are presented for temperatures 20∘C and60∘C with and without the electric field through

Figures 8 9 and 10 as a function of the shear strain rate Allthe dynamic characteristics show identical behavior and in-crease with the electric field through Figures 8 9 and 10respectively as is apparent from these plots However thesecharacteristics decrease with temperature as can be seenthrough Figures 8 9 and 10 respectively for 20∘C and 60∘Ctemperatures However the dynamic characteristics decrease


0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)

Figure 10 Cross-coupled damping coefficient MNsm versus shear strain rate sminus1 for (a) 119864 = 0 kVmm 119879 = 20∘C (b) 119864 = 25 kVmm 119879 =20∘C (c) 119864 = 0 kVmm 119879 = 60∘C and (d) 119864 = 25 kVmm 119879 = 60∘C

with increase in the strain rate in accordance with the viscos-ity behavior (shear thinning fluid)

7 Conclusions

The effect of temperature on the dynamic (stiffness anddamping) characteristics of an ER Fluid short squeeze film

damper is presented in this paper The dynamic coefficientsincreasewith the electric field due to increase in viscositywiththe electric field since it produces fibrillar chains or layerswhich retard the flow of the fluid and consequently increasesthe viscosity However the opposite effect happens at hightemperatures and the fibrillar structures are broken at thistemperature resulting in decreased viscosity These coeffi-cients thus decrease with increase in temperature of the ER


fluid They also decrease with the shear strain rate as theviscosity decreases with shear strain rate For a particulardamper configuration these coefficients increase with de-crease in clearance increase in 119871119863 ratio and eccentricityratio

Nomenclature

120591 Total shear stress Nm2 (Pa)120591yd Dynamic yield stress Nm2 (Pa)120578 Field independent plastic viscosity Nsm2120596 Excitation frequency rads120588 Density kgm3120572 Attitude angle degree120579 Angular coordinate of the damper degree120574 Shear strain rate sminus1

120578app Apparent viscosity due to the field Pas119888 Clearance in the damper m119862119903119903119904 Short bearing radial damping coefficient

MNsm119862119903119905119904 Short bearing cross-coupled damping

coefficient MNsm119862tts = 119862ds Short bearing tangential or direct damping

coefficient MNsm119863 Damper diameter m119890 Eccentricity or whirl radius m119864 Electric field intensity kVmm119865119903 Radial force in the damper N

119865119905 Tangential force N

119870 Consistency index and119870 gt 0

119870ds = 119870119903119903119904 Short bearing direct stiffness coefficientGNm

119871 Length of the damper m119898 Fluid parameters and119898 gt 0

119899 Eccentricity ratio = 119890119888

1198991 Viscosity exponent or behavior index

119903 Damper radius msgn( 120574) Signum function119905 Time s119880 Surface velocity ms119881119903 Radial whirl velocity ms

119881119905 Tangential whirl velocity ms

119909 119910 and 119911 Coordinate axes

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] O Bonneau and J Frene ldquoNon-linear behaviour of a flexibleshaft partly supported by a squeeze filmdamperrdquoWear vol 206no 1-2 pp 244ndash250 2007

[2] S Morishita and T Ura ldquoER fluid applications to vibration con-trol devices and an adaptive neural-net controllerrdquo Journal ofIntelligentMaterial Systems and Structures vol 4 no 3 pp 366ndash372 1993

[3] K D Weiss T G Duclos J D Carlson M J Chrzan and A JMargida ldquoHigh Strength Magneto- and Electro-rheologicalFluidsrdquo SAE Technical Paper 932451 1993

[4] W Kordonsky ldquoElements and devices based on magnetorheo-logical effectrdquo Journal of Intelligent Material Systems and Struc-tures vol 4 no 1 pp 65ndash69 1993

[5] K DWeiss and J D Carlson ldquoA growing attraction tomagneticfluidsrdquoMachine Design vol 66 no 15 pp 61ndash64 1994

[6] C Carmignani and P Forte ldquoActive squeeze film dampersin rotor dynamics AIMETArdquo International Journal of AppliedMechanics and Engineering vol 6 no 4 pp 1ndash8 2001

[7] P Forte M Paterno and E A Rustishi ldquoMagneto Rheologicalfluid damper for Rotor applicationsrdquo International Journal ofRotating Machinery vol 10 no 3 pp 175ndash182 2004

[8] B Mohammad Ayani and L Hosseini ldquoThe Effect of Temper-ature and Electric Field on the Behavior of ElectrorheologicalFluidsrdquo in Proceedings of the 14th Annual International Mechan-ical Engineering Conference 2006

[9] C Guang and Y Song Huat ldquoResearch on MR fluidsrdquo AppliedResearch Project Report RG6396 School of Mechanical andProduction Engineering Nanyang Technological UniversitySingapore 1996

[10] J S Rao Rotordynamics New Age International New DelhiIndia 3rd edition 2006

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SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



information is available regarding the stiffness and dampingcharacteristics of ER fluid and their applications in activejournal bearings and squeeze film dampers While generalaspects and applications of MR and ER fluids have been dealtwith to some extent [4 5] sharing their promising character-istics it was only in the last decade that some pieces of liter-ature have appeared on rotor dampers [6 7] Since the avail-able literature regarding the effect of temperature on the stiff-ness and damping characteristics of ER Fluid squeeze filmdampers is very scanty this paper investigates these aspectson a short squeeze film damper using the relation obtainedbetween viscosity and temperature for a particular ER fluidwhich is a suspension of diatomite in transformer oil

2 The Herschel-Bulkley Model

The one-dimensional Herschel-Bulkley model is used tomodel the shear thinning of ER fluid in the post-yield regionThe constitutive equation for this model [9] is

120574 = 0 120591 le 120591yd (1a)

120591 = 120591yd sgn ( 120574) + 119870 120574 120591 ge 120591yd (1b)

where 120591 is the shear stress 120574 is the shear strain rate and 120591ydis the dynamic yield stress 119870 and 119899

1are two parameters that

describe themagnitude and slope of the curveThe parameter119870 is sometimes referred to as the ldquoconsistency indexrdquo Theexponent 119899

1is dimensionless and is called the ldquobehavior

indexrdquo Both 119870 and 1198991depend on material properties and

working conditions such as friction and temperatureFor steady shear flow (|120591| gt 120591yd) assume that 120574 gt 0 (1b)

can be written as

120591 = (120591yd + 119870 1205741198991minus1) 120574 (2)

The apparent viscosity thus is

120578app = 119870 1205741198991minus1 (3)

For shear thinning of ER suspensions with 0 lt 1198991lt 1 the

apparent viscosity decreases with the increment of shear rateThe temperature affects both the values 119870 and 119899

1and is res-

ponsible for the variation in the apparent viscosity of the ERfluid

3 Temperature Effect on Viscosity of ER Fluid

Changes in the temperature of ER fluid due to working con-ditions like friction or electrical power dissipation mayinfluence its performance in ER devicesThe temperature de-creases the viscosity of the ER fluid and consequently affectsboth the static and dynamic characteristics of the squeeze filmdamperThe viscosity-temperature relation of the ER Fluid ata particular electric field intensity can be modeled by theexponential decay type Reynolds equation or the Arrheniusequation outlined as (4) and (5) respectively as

120578app (119879) = 1205780exp (minus119861119879) (4)

where 119879 is the temperature and 1205780and 119861 are coefficientsThis

is an empirical model that usually works for a limited rangeof temperatures

120578app (119879) = 1205780exp ( 119864

119877119879) (5)

where 119864 is the activation energy and 119877 is the universal gasconstant A first-order fluid is another name for a power lawfluid with exponential dependence of viscosity on tempera-ture

This can be also be presented as

120578app (119879) = 1205780exp(119861

119879) (6)

where 119861 = 119864119877

4 Stiffness and Damping Characteristics ofSqueeze Film Dampers with Orbital Motion

These squeeze film dampers (Figure 2) find application in theair craft engine rotors and are usually mounted on rolling ele-ment bearings with little or no inherent damping to fight theunbalance response especially at critical speeds and to elim-inate rotor dynamic instabilities The coordinates of the orbitare presented as [10]

119911 = 119890 cos120596119905

119910 = 119890 sin120596119905

119903 = 119890

119903 = 119881119903= 0

119881119905= 119890120596

(7)

Ignoring the stiffness terms the radial and tangential forcesacting on the system are

119865119903= 119862119903119903119881119903+ 119862119903119905119881119905= 119862119903119905120596119890

119865119905= 119862119905119903119881119903+ 119862119905119905119881119905= 119862119905119905120596119890

(8)

The direct damping coefficient is

119862119905119905=

119865119905

120596119890 (9)

and the cross-coupled damping coefficient is

119862119903119905=

119865119903

120596119890 (10)

The radial component of the force 119865119903is considered as a stiff-

ness force defined as the direct stiffness coefficient given by

119870119903119903=119865119903

119890= 119862119903119905120596 (11)

The squeeze film velocity is

120597ℎ

120597119905= 119890120596 sin 120579 (12)


e

C

C998400120596

y

h120588

z 120579



1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app sin 120579 (13)


1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app119890120596 sin 120579 (14)


ℎ3 1198892119901

1198891199092= 12120578app119890120596 sin 120579 (15)


119901 =6120578app120596

ℎ3

119889ℎ

119889120579

1199092

2+

119860

ℎ3119909 + 119861 (16)


119901 = 0 at 119909 = plusmn119871

2 (17)


119901 =3120578app120596

ℎ3

119889ℎ

119889120579(1199092minus1198712

4) (18)


119901120579minus 119901119900

=6120578app120596119899 (119871

24minus 119909

2)

1198882[

sin 120579(1 + 119899 cos 120579)3

] for 0 le 120579 le 120587

(19a)


(19b)


2int

120587

0

int

1198712

0

prcos 120579119889119909 119889120579 = minus119882 cos120572

2 int

120587

0

int

1198712

0

prsin 120579119889119909 119889120579 = minus119882 sin120572

(20)

where

119882 sin120572 =120587120578app120596119863119899119871

3

81198882(1 minus 1198992)32

119882 cos120572 =120578app120596119863119899

21198713

21198882(1 minus 1198992)2

(21)


119882 =120578app120596119903119899119871

3



119865119903= 119882 cos120572 =

120578app12059611986311989921198713

1198882(1 minus 1198992)2

119865119905= 119882 sin120572 =

120587120578app1205961198631198991198713

41198882(1 minus 1198992)32

(23)


119870ds =120578app120596119863119899119871

3

1198883(1 minus 1198992)2 (24)

119862ds =120587120578app119863119871

3

41198883(1 minus 1198992)32

(25)

119862119903119905119904

=120578app119863119899119871

3

1198883(1 minus 1198992)2 (26)





1[8]

(a)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 0045 0038 0028 00126119864 = 25 kVmm 891 557 246 04

(b)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 086 0861 0873 0957119864 = 25 kVmm 0057 0129 0256 0551


Governingequation

119864 = 0 kVmm 119864 = 25 kVmm120574 (sminus1)


1205780

005322 004383 12899 3489871119861 001324 000839 00512 0018498

Arrheniusequation

1205780

002405 002650 05983 115023119861 105892 670760 40944 1479864







0

0005

001

0015

002

0025

003

0035

004

0045

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)




0

05

1

15

2

25

3

35

4

45

5

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)








0

05

1

15

2

25

3

0 20 40 60 80 100

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

E = 0kVmm 120574 = 2 sminus1



(a)


0

50

100

150

200

250

300

350

0 20 40 60 80

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

) E = 25 kVmm 120574 = 2 sminus1


(b)


0

005

01

015

02

025

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(a)

0

5

10

15

20

25

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(b)



0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm



(b)



0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)



0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










e

C

C998400120596

y

h120588

z 120579



1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app sin 120579 (13)


1

1199032

120597

120597120579[ℎ3 120597119901

120597120579] + ℎ3 1205972119901

1205971199092= 12120578app119890120596 sin 120579 (14)


ℎ3 1198892119901

1198891199092= 12120578app119890120596 sin 120579 (15)


119901 =6120578app120596

ℎ3

119889ℎ

119889120579

1199092

2+

119860

ℎ3119909 + 119861 (16)


119901 = 0 at 119909 = plusmn119871

2 (17)


119901 =3120578app120596

ℎ3

119889ℎ

119889120579(1199092minus1198712

4) (18)


119901120579minus 119901119900

=6120578app120596119899 (119871

24minus 119909

2)

1198882[

sin 120579(1 + 119899 cos 120579)3

] for 0 le 120579 le 120587

(19a)


(19b)


2int

120587

0

int

1198712

0

prcos 120579119889119909 119889120579 = minus119882 cos120572

2 int

120587

0

int

1198712

0

prsin 120579119889119909 119889120579 = minus119882 sin120572

(20)

where

119882 sin120572 =120587120578app120596119863119899119871

3

81198882(1 minus 1198992)32

119882 cos120572 =120578app120596119863119899

21198713

21198882(1 minus 1198992)2

(21)


119882 =120578app120596119903119899119871

3



119865119903= 119882 cos120572 =

120578app12059611986311989921198713

1198882(1 minus 1198992)2

119865119905= 119882 sin120572 =

120587120578app1205961198631198991198713

41198882(1 minus 1198992)32

(23)


119870ds =120578app120596119863119899119871

3

1198883(1 minus 1198992)2 (24)

119862ds =120587120578app119863119871

3

41198883(1 minus 1198992)32

(25)

119862119903119905119904

=120578app119863119899119871

3

1198883(1 minus 1198992)2 (26)





1[8]

(a)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 0045 0038 0028 00126119864 = 25 kVmm 891 557 246 04

(b)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 086 0861 0873 0957119864 = 25 kVmm 0057 0129 0256 0551


Governingequation

119864 = 0 kVmm 119864 = 25 kVmm120574 (sminus1)


1205780

005322 004383 12899 3489871119861 001324 000839 00512 0018498

Arrheniusequation

1205780

002405 002650 05983 115023119861 105892 670760 40944 1479864







0

0005

001

0015

002

0025

003

0035

004

0045

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)




0

05

1

15

2

25

3

35

4

45

5

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)








0

05

1

15

2

25

3

0 20 40 60 80 100

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

E = 0kVmm 120574 = 2 sminus1



(a)


0

50

100

150

200

250

300

350

0 20 40 60 80

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

) E = 25 kVmm 120574 = 2 sminus1


(b)


0

005

01

015

02

025

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(a)

0

5

10

15

20

25

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(b)



0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm



(b)



0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)



0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













1[8]

(a)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 0045 0038 0028 00126119864 = 25 kVmm 891 557 246 04

(b)

119879 (∘C) 20 40 60 80119864 = 0 kVmm 086 0861 0873 0957119864 = 25 kVmm 0057 0129 0256 0551


Governingequation

119864 = 0 kVmm 119864 = 25 kVmm120574 (sminus1)


1205780

005322 004383 12899 3489871119861 001324 000839 00512 0018498

Arrheniusequation

1205780

002405 002650 05983 115023119861 105892 670760 40944 1479864







0

0005

001

0015

002

0025

003

0035

004

0045

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)




0

05

1

15

2

25

3

35

4

45

5

0 20 40 60 80

Appa

rent

visc

osity

120578ap

p(P

as)








0

05

1

15

2

25

3

0 20 40 60 80 100

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

E = 0kVmm 120574 = 2 sminus1



(a)


0

50

100

150

200

250

300

350

0 20 40 60 80

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

) E = 25 kVmm 120574 = 2 sminus1


(b)


0

005

01

015

02

025

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(a)

0

5

10

15

20

25

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(b)



0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm



(b)



0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)



0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

05

1

15

2

25

3

0 20 40 60 80 100

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)

E = 0kVmm 120574 = 2 sminus1



(a)


0

50

100

150

200

250

300

350

0 20 40 60 80

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

) E = 25 kVmm 120574 = 2 sminus1


(b)


0

005

01

015

02

025

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(a)

0

5

10

15

20

25

0 20 40 60 80

Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)



(b)



0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm



(b)



0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)



0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

0005

001

0015

002

0025

003

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)



(a)

0

05

1

15

2

25

3

35

0 20 40 60 80

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm



(b)



0

0005

001

0015

002

0025

003

0035

004

0045

0 2 4 6 8 10

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(a)

0

05

1

15

2

25

3

35

4

45

5

0 2 4 6 8 10 12

Appa

rent

visc

osity

120578ap

p(P

as)


T = 20

T = 40

T = 60

T = 80

∘C∘C

∘C∘C

(b)



0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

12

14

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 20∘C

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 20∘C

(b)

0

01

02

03

04

05

06

07

08

09

0 2 4 6 8 10 12

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 0kVmm T = 60∘C


(c)

0

20

40

60

80

100

120

0 2 4 6 8 10

Dire

ct st

iffne

ss co

effici

entK

ds(M

Nm

)


E = 25 kVmm T = 60∘C


(d)









0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

005

01

015

02

025


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 0kVmm T = 20∘C

(a)

0

5

10

15

20

25


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 20∘C

(b)

0

002

004

006

008

01

012

014


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m) E = 0kVmm T = 60∘C


(c)

0

1

2

3

4

5

6

7

8


Dire

ct d

ampi

ng co

effici

entC

ds(M

Ns

m)

E = 25 kVmm T = 60∘C


(d)






0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

0002

0004

0006

0008

001

0012

0014


E = 0kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(a)

0

05

1

15

2

25

3

35

0 2 4 6 8 10


E = 25 kVmm T = 20∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)

(b)

0

0001

0002

0003

0004

0005

0006

0007

0008

0009


E = 0kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(c)

0

02

04

06

08

1

12


E = 25 kVmm T = 60∘C

Cros

s-co

uple

d da

mpi

ng co

effici

entC

rts

(MN

sm

)


(d)



7 Conclusions





Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Nomenclature

















References













RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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