inertia mass damper and its...

Inertia Mass Damper and its application

Katsuaki Sunakoda1 and Issei Yamazaki2

1 Akita University, Akita, Japan

2Research and Development, Sanwa Tekki Corporation, Tochigi, Japan

The Seventh　Kwang-Hua Forum December 9-11, 2016, Shanghai

Summary1) Historical Background of I.M.D.

2) Mechanical Model of I.M.D. & E.I.M.D. (Dynamic stiffness, Negative stiffness.)

3) Dynamic response of the system with I.M.D. & E.I.M.D. (Two degree of freedom system and

simulation, Frequency Response).

4) Introduction of experimental test in NCREE (The outline of E.I.M.D of 30kN , Three story structure seismic test analytical model, Frequency response spectrum, Seismic Excitation Response .

1: Ear2: Ball nut3: Ball screw4: Angular bearing

5: Case6:Flywheel7: Key and keyway8: Piston

Primitive I.M.D

Detail of ball nut

x Ball screw, the relationship displacement and angle

Mechanical model of I.M.D. and E.I.M.D.

2lx

22

21

21 xmI'T

Kinetic energy expressed as,

Where I: moment of inertia of rotating part , m: straight movement parts. consist of ball nut, load column, cover and ear, but second term is usually negligible small compared with first term of right hand side.

22

21

21 xmIT e

Introduction of the idea of equivalent mass

Il

Ix

me22

2

Equivalent mass can be expressed as

Detail of ball nut

Spring rate and damping coefficient　　　　Spring rate : determined by testing　　Damping : determined by testing

Mechanical model of I.M.D. & E.I.M.D.

Il

me

2

24I: Rotating inertia moment

x2x1

ce

ke

x2 x1

ce

keme

ce

me

x1

x2

F

x1

F

Mechanical model of I.M.D. / E.I.M.D.(ii) MORE REALISTIC MODEL

Mechanical model of I.M.D. / E.I.M.D.(i) SIMPLE MODEL

x1

F

x2

F

ω： low ω: high

ω： low ω: high

tax sin1

0)( 1222 xxkxcxm eee

Dynamic Stiffness

12 xxx

222

222

11

)()()()(

eee

eee

e

cmkcmk

xxk

xFK

DYNAMIC RESPONSE OF THE SYSTEM WITH I.M.D. or E.I.M.D.

ce me

ke

mck

x0x2

x1

022

011

xxXxxX

022011

021111

1222

,where

)(

0)(

xxXxxX

xmXXkkXXcXm

XXkXcXm

e

eee

　　

0

iii xQ

xU

xT

dtd

221

221 )(

21)(

21 xxkxxkU e

201

202 )(

21)(

21 xxcxxcQ e

　　122

02 21)(

21 xmxxmT e

mass main of frequency angular natural :/

I.M.D. of frequency angular natural:/

mk

mk

x

eee

2/1

2

22

2

2

2

222 411

2 e

xe

e

xe

e

xe

mm

mm

012224

e

x

e

e

e

x

e mm

2/1

22

2

2

2

2

2

2

2

2

0

1

141

ee

xe

x

e

eee

e

x

e

e

hmmh

mm

mm

xX

1

2

XX

22

2

2

2

022

011

41

)2/()2/(

ee

e

xx

eeee

h

mchmchxxXxxX

★Parameter of beamm [kg] = 100k [N/m] = 86,672h = 0.01

★Parameter of I.M.D.me [kg] = 1500ke [N/m]= 3,500,000he = 0.005

★Natural frequency of I.M.D.

　　　　　　　　　　= 7.688

★Natural frequency of single beam

= 4.686

★Primary and secondary natural frequency of beam + I.M.D. = 1.159 = 31.0085

★Natural frequency of beam + spring

= 30.142

e

ee m

kπ

f21[Hz]

mk

πf

21 [Hz] nth

mkk

πf e

21 [Hz] spr

[Hz] 1f[Hz] 2f

★Parameter of beamm [kg] = 500k [N/m] = 693.42h = 0.01

★Parameter of I.M.D.me [kg] = 1500ke [N/m]= 3,500,000he = 0.005

★Natural frequency of I.M.D.

　　　　　　　　　　= 7.688

★Natural frequency of single beam

= 0.187

★Primary and secondary natural frequency of beam + I.M.D. = 0.094 = 15.377

★Natural frequency of beam + spring

= 13.317

e

ee m

kπ

f21[Hz]

mk

πf

21 [Hz] nth

mkk

πf e

21 [Hz] spr

[Hz] 1f[Hz] 2f

ra

TEgfs Fuu

RRKK

Lα

ηuIαII

LηF sign2121 2

22

whereF: total resistance forceη: rotating conversion efficiency of ballscrew & nut(≈0.9 to 1)L: lead of ball screwIs: moment of inertia of ball screwIf: moment of inertia of rotating flywheelIg: moment of inertia of rotating shaft of generatorα: increasing speed ratioKE: electromotive force constantKT: torque constantRa: internal resistance of generatorR: outer electrical resistanceFr: experimental friction force

INTRODUCTION OF EXPERIMENTAL STUDY IN NCREE

E.I.M.D.

Inertia mass 12000 [kg]，Resistance (open circuit) []

Amp.3[mm]

Amp.6[mm]

-6 -3 0 3 6-20000

-10000

0

10000

20000R=[]Exp.

0.3Hz0.5Hz1.0Hz1.5Hz2.0Hz2.5Hz

-6 -3 0 3 6-20000

-10000

0

10000

20000R=[]Cal.

-6 -3 0 3 6-20000

-10000

0

10000

20000R=[]Exp.

0.3Hz0.5Hz1.0Hz1.5Hz2.0Hz

-6 -3 0 3 6-20000

-10000

0

10000

20000R=[]Cal.

Displacement x [mm]　

Forc

e F

[N]　


Forc

e F

[N]　


Forc

e F

[N]　


Forc

e F

[N]　

Inertia mass 12000 [kg]，Resistance (short circuit) 0 []

Amp.3[mm]

Amp.6[mm]

-6 -3 0 3 6-20000

-10000

0

10000

20000R=0[]Exp.

0.3Hz0.5Hz1.0Hz1.5Hz2.0Hz2.5Hz

-6 -3 0 3 6-20000

-10000

0

10000

20000R=0[]Cal.

-6 -3 0 3 6-20000

-10000

0

10000

20000R=0[]Exp.

0.3Hz0.5Hz1.0Hz1.5Hz

-6 -3 0 3 6-20000

-10000

0

10000

20000R=0[]Cal.


Forc

e F

[N]　


Forc

e F

[N]　


Forc

e F

[N]　


Forc

e F

[N]　

Three story structure in NCREE

3[m]

3[m]

3[m]

Analytical model without/with E.I.M.D.(i) without E.I.M.D. (ii) with E.I.M.D.

cV1

mV1

m1

k1

c1

x1

x0

cV2

mV2

m2

k2

c2

cV3

mV3

m3

k3

c3

m1

k1

c1

m2

k2

c2

m3

k3

c3

x2

x3

x1

x0

x2

x3

Mass [kg]m1 6000m2 6000m3 6000

Damping coefficient [Ns/m]c1 0.988×104

c2 1.712×104

c3 1.084×104

Stiffness [N/m]k1 1.211×106

k2 1.148×106

k3 1.366×106

Inertia mass [kg]mV1 6000 or 12000mV2 6000 or 12000mV3 6000 or 12000

Damping coefficient [Ns/m]cV1 0 or 1.000×105

cV2 0 or 1.000×105

cV3 0 or 1.000×105

Indentified parameters of three story structure

Parameters of E.I.M.D.

000

233233323333

3231223233122232312222

2120112122011121201111

xxkxxccxxmxmxxkxxkxxccxxccxxmxxmxmxxkxxkxxccxxccxxmxxmxm

VV

VVVV

VVVV

233122011 ,, xxuxxuxxu 　　

03333333332313

0233223332223322212

01221122211122111

xmukuccummumumxmukukuccuccumummumxmukukuccuccumumm

VV

VVVV

VVVV

3

2

1

0

uuu

wherex ubKuuCuM ，

3333

3222

211 0

V

VV

VV

mmmmmmmm

mmmM

33

3322

2211

000

0

V

VV

VV

cccccc

ccccC

3

32

21

000

0

kkk

kkK

3

2

1

mmm

b

Equation of motion

tm

tm

tm

UU

UU

UU

j33

j22

j11

e

e

e

3

2

1

0

UUU

X UbKUUCUM ，

022 j X bUCMK

3

2

1

212

0

j

GGG

X

G

bCMKU

tmXX j

00 e

303

202

101

GXU

GXU

GXU

mm

mm

mm

tmAX j

00 e

tm

tm

tm

AXAXAX

j33

j22

j11

e

e

e

3210

210

10

32

21

10

3

2

1

UUUXUUX

UX

UXUXUX

XXX

X

030201

0201

01

0 111

XUXUXUXUXU

XU

X

X 0

22 j X bUCMK

3

2

1

00 GGG

XXGUU

321

21

1

0 111

GGGGG

G

XX

32103

2102

101

1

1

1

GGGAA

GGAA

GAA

mm

mm

mm

0.001

0.01

0.1

1

10

WithoutWith_1With_2With_1DWith_2D

8.218917.451166.802821.463331.42808

91% 83%18%17%

A1m

/A0m

コピー領域の設定L: 10T: 7.5R: 150B: 220100%チェックなし

0.1 1 10 1000.001

0.01

0.1

1

10


18.056616.210915.06112.148082.04201

12%11% 90% 83%

A3m

/A0m

f [Hz]

0.001

0.01

0.1

1

10


14.934313.455312.55231.902631.82419

90% 84%13%12%

A2m

/A0m

0.01

0.1

1

10 WithoutWith_1With_2With_1DWith_2D 8.21891

7.451166.802821.463331.42808

91% 83%18%17%

U1m

/X0m

コピー領域の設定L: 10T: 7.5R: 150B: 220100%チェックなし

0.1 1 10 1000.01

0.1

1


16.210915.06112.148082.04201

12%11% 90% 83%U

3m/X

0m

f [Hz]

0.01

0.1

1


13.455312.55231.902631.82419

90% 84%13%12%

U2m

/X0m

Magnification of amplitude response

• Without: structure without E.I.M.D • With_1: structure+ mass ratio* 1+damping zero* of E.I.M.D • With_2: structure+ mass ratio 2+damping zero of E.I.M.D. • With_1D: structure+ mass ratio 1+ damping max*. of E.I.M.D • With_2D: structure+ mass ratio 2+ damping max. of E.I.M.D

Test conditions

*: where, mass ratio means (inertia mass)/(structure mass of each story), and damping zero and max (1.000×105 Ns/m ) mean in case of terminal resistance is infinity and short-circuit, respectively.

-4

0

4

x 0 [m

/s2 ]

:

コピー領域の設定L: 7.5T: 5R: 147.5B: 217.5100%チェックなし

-4

0

4

x 1 [m

/s2 ]

:

-4

0

4

x 2 [m

/s2 ]

:

-4

0

4

x 3 [m

/s2 ]

:

-30

0

30

u 1 [m

m]

-30

0

30

u 2 [m

m]

0 10 20 30 40-30

0

30

u 3 [m

m]

Exp. Cal.

t [s]

-4

0

4

x 0 [m

/s2 ]

:

コピー領域の設定L: 7.5T: 5R: 147.5B: 217.5100%チェックなし

-4

0

4

x 1 [m

/s2 ]

:

-4

0

4

x 2 [m

/s2 ]

:

-4

0

4

x 3 [m

/s2 ]

:

-30

0

30

u 1 [m

m]

-30

0

30

u 2 [m

m]

0 10 20 30 40-30

0

30

u 3 [m

m]

Exp. Cal.

t [s]

Hachinohe 1.5m/s2without

Hachinohe 1.5m/s2with_2D

El Centro 1.5m/s

0 1 2 3 4 51

2

3

Floo

r Num

ber

Peak value of absolute acc. [m/s2]

Without　 With_1　 With_2　 With_1D　 With_2D

Hachinohe 1.5m/s2

　　　

0 10 20 30 401

2

3

Floo

r Num

ber

Peak value of relative disp. [mm]

Kobe 1.5m/s2

0 1 2 3 4 51

2

3


Floo

r Num

ber

0 1 2 3 4 51

2

3


Floo

r Num

ber

　

0 10 20 30 401

2

3

Peak value of relative disp. [mm]　

Floo

r Num

ber

0 10 20 30 401

2

3

Peak value of relative disp. [mm]

Floo

r Num

ber

Thank you !

inertia mass damper and its...

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