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13th World Conference on Earthquake Engineering Vancouver, B.C., Canada
August 1-6, 2004 Paper No. 3362
EXPERIMENTS AND ANALYSIS OF ROLLER TYPE ISOLATION DEVICE
Satoshi UEDA 1 Takao ENOMOTO2 Takafumi FUJITA3
SUMMARY Japan is the country where seismic isolation is most widely used for civil engineering structures and equipment. Since the Hanshin-Awaji earthquake of 17 January 1995, in which works of art in several museums in this area were damaged, seismic isolation in Japan that include seismic isolation of museum buildings, display cases, and individual works of art, together with seismic isolation of floors in conservation rooms. This paper also describes a roller type isolation system for the individual showcases and individual works of art. The isolation system consists of two layers that form a XY-motion mechanism for two-dimensional horizontal motion; each layer consists of rails having a circular-linear-combined shape in the vertical cross-section to produce a restoring force, wheels, and fiction dampers comprising the wheels and the axles. Because the effective natural period of the system is independent of the mass, a long effective natural period can be achieved even for light equipment such as showcases. Shake table tests were carried out, showing good isolation performance of system and confirming validity of the analytical method.
INTRODUCTION Recently many kinds of seismic isolation systems for showcases of works of art or computer systems are under research and development. Especially showcases of works of art require higher performance against earthquake in order to protect valuable work of art from any damages. This paper describes a roller type isolation system which utilizing two layers of a XY-motion mechanism having a circular-linear-combined shape in the vertical cross section. Results of three-dimensional shaking table test by earthquake wave and validity of the analytical model.
1 ADVANCED SYSTEM CO., LTD Tokyo, Japan. E-mail: [email protected] 2 ADVANCED SYSTEM CO., LTD Tokyo, Japan. E-mail: [email protected] 3 Professor, Institute of Industrial Science, University of Tokyo, JAPAN. E-mail: [email protected]
CONSTRUCTION
Roller type isolation system consists of rail having circular-linear combined 1st and 2nd stiffness, wheel and axles and plane bearing with PTFE coating. X-Y rail motion mechanism enable to absorb impact of horizontal X-Y direction when acceleration applied by earthquake by pendulum motion with friction between axles and bearing. After earthquake wheel will return to center of rail by restoring force. Fig.1 shows schematic drawing of roller type isolation device. 1 shows top plate,2 shows wheelframe,3 as base plate,4 as wheel,5 as bearing,6 as axles and 7 shows rail. Natural period of system, 1st and 2nd stiffness, break load and friction co-efficient can be determined by bellow formula. Here T shows natural period of the system, r1 is radius of circular rail, k1 is spring constant (1st stiffness), Pv is vertical load, Qd is breaking load, d is diameter of axle, D is diameter of wheel, µ is friction co-efficient of bearing is friction co-efficient of system and θ is inclination of linear rail. Fig.2 shows concept model of characteristic of isolation device.
grT 12 π= ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(1)
11 rPk v= ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(2)
µ⋅= vd PQ ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(3)
( ) 0µµ ⋅= Dd ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(4)
２
３
４
５
６
７
１
vP
θ
d
1r
θ
D
Figure.1 Schematic drawing of roller type isolation device
Figure.2 Concept model of isolation device
SHAKING TABLE TEST (CASE 1) Analytical Model Shaking table test has been conducted on roller type isolation system supporting museum showcase with appropriate weight. Analytical model has been settled that total mass of moving mass of the system and weight is considered as one-mass model as Fig.3 Here x0 shows amplitude against the ground, m0 shows total mass of moving weight of the isolation system and weight., z is acceleration of earthquake, k0 is spring constant of the system (1st stiffness), ks is 2nd stiffness, c0 is damping co-efficient, xc1 shows changing point of 1st/2nd stiffness.
Roller type isolation system Isolation system which designed for museum high-showcase has size of 2600 mm length x 1090 mm width x 236 mm height. Isolation system is designed for experiment as the natural period is 2.68 sec, inclination of strait part of rail is 0.03rad, friction co-efficient is 0.036, allowable amplitude of system as ±275 mm. Weight of 833 kg is loaded on 1200 kg weigh isolation system. Fig.4 shows drawings of the system and Fig.5 photo of the system installed three-dimensional shaking table.
k0, ks c0 μ
Xxz&&
X0
m0
１４６０
５５０ ５５０
６０
０
５５
０５５
０
１０
９０
２６００
３３７
２３
６
Figure.3 Analytical model
Figure.4 Drawings of the system Figure.5 Test using three-dimensional shaking table
Dynamic Equation The equation of isolation device shall be descried when no rolling ( phase 1) and rolling at 1st stiffness（phase 2） also rolling at 2nd stiffness(phase 3) . Phase 1 (in case no rolling occur)
0,0, 000 === xxconstx &&& ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(5)
Phase 2 (in case rolling occur at 1st stiffness)
zmgmxxkxcxm &&&&&& 000000000 )sgn( −=⋅⋅⋅+++ µ ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(6)
Phase 3 (in case rolling occur at 2nd stiffness)
0000 xcxm &&& + { } )sgn()( 000 xxxkkx clscl −++ )sgn( 00 xgm &⋅⋅⋅+ µ zm &&0−= ‥‥‥‥‥‥‥(7)
Switching condition is described as follows.
In case Phase1 –Phase 2
gmzmxk ⋅⋅>+ 0000 µ&& and clxx <0
‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(8)
In case Phase2 –Phase 3
clxx >0 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(9)
In case Phase3 –Phase 2
clxx <0 ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(10)
In case Phase2 –Phase 1
gmzm ⋅⋅< 00 2µ&& and 00 =x& ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(11)
In case Phase3 –Phase 1
gmzm ⋅⋅< 00 2µ&& and 00 =x& ‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(12)
In case Phase1 –Phase 3
gmzmxks ⋅⋅>+ 000 µ&& and clxx >0
‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥‥(13)
4th accuracy Runge-Kutta-Gill method has been used for digital analysis of this equation.
Input wave of earthquake 3 kinds of earthquake wave as EL Centro (Imperial Valley, 1940), Taft(Kern Country,1952) and JMA Kobe(1995) recorded at Hyougo Nanbu earthquake are used for three-dimensional shaking test. Input level has been leveled at 50 [cm/s] level at horizontal and 25 [cm/s] at vertical of EL-Centro and Taft wave , Original wave of JMA Kobe has been used . Maximum value of acceleration of each earthquake is listed at Table.1.
Result of experiments and analysis Fig .6 shows comparison of maximum acceleration and amplitude between input, measured and analysis results, it is confirmed input acceleration has decreased to level of 1/4 to 1/5. Fig.7 shows time histories of calculated and measured.
Input Wave
Horizontal Input level
Input Direction
Horizontal Acc. MAX[m/s2]
Vertical Acc. MAX[m/s2]
EW 3.14 El Centro NS 5.10
2.06
EW 4.90 Taft
0.50[m/s]
NS 4.25 1.03
EW 6.17 JMA Kobe
Original NS 8.18
3.32
88.9
89
77.9
76.6
82.5
85.8
66.7
66.7
66.7
66.7
66.7
66.7
809
636.6
452.5
535.1
552.6
316.9
0 200 400 600 800 1000
JM A Kobe NS
JM A Kobe EW
Taft NS
Taft EW
El Centro NS
El Centro EW
Acc. x 10-2 [m /s
2]
Input
C alculated
M easured
25.2
18.7
15.1
13.4
17.3
19.4
24.1
18.5
14.1
14.8
14.8
19.3
0 5 10 15 20 25 30
JM A Kobe NS
JM A Kobe EW
Taft NS
Taft EW
El Centro NS
El Centro EW
Disp. [cm ]
Figure.6 Response accelerations and displacements
Table .1 Caption for table 1
SHAKING TABLE TEST (CASE 2)
0 5 10 15 20 25 30 35 40-500
0
500
Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-20
-10
0
10
20
Disp.
tim e [sec]
Disp [cm]
0 5 10 15 20 25 30 35 40-600
-400
-200
0
200
400
600
Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-20
-10
0
10
20
D isp.
tim e [sec]
Disp [cm]
El Centro EW El Centro NS
0 5 10 15 20 25 30 35 40-600
-400
-200
0
200
400
600
Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-20
-10
0
10
20
Disp.
tim e [sec]
Disp [cm]
0 5 10 15 20 25 30 35 40-500
0
500
Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-20
-10
0
10
20
Disp.
tim e [sec]
Disp [cm]
Taft EW Taft NS
0 5 10 15 20 25 30 35 40-1000
-500
0
500
1000
Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-20
-10
0
10
20
D isp.
tim e [sec]
Disp [cm]
0 5 10 15 20 25 30 35 40-1000
-500
0
500
1000Input E.Q .
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40-100
-50
0
50
100
Acc.
Acc. x10-2 [m/s2]
0 5 10 15 20 25 30 35 40
-20
-10
0
10
20
D isp.
tim e [sec]
Disp [cm]
JMA KOBE NS
Measured
Calculated
JMA KOBE EW
Figure.7 Histories of calculated and measured
Results of 3D shaking test with real museum showcase and isolation system is described here. Monetization of showcase and isolation system has been studied for simulation of response. Isolated equipment (Museum showcase) Isolated showcase has 900 mm square x 2700 mm height size and 350 kg weight. Fig.8 shows photos of showcase and position of acceleration sensors. In order to confirm basic performance of showcase, showcase has been oscillated by random mode at fixed condition. From this random oscillation test, natural frequency of showcase (first mode) has been determined as 6.9 Hz. Fig.9 shows transfer function of acceleration from shaking table to display point and one from shaking table to top of showcase.
Top of Case
Display Location
Shaking Table Accelerometer
X
Z
Y
X
Figure.8 Show case (□900x900x2700h)
100
101
102
-20
-10
0
10
20
30
40
Frequency(H z)
Gain [dB]
T402R N D 100X 振動台 X(2C h) --> 展示位置 X(8C h) 伝達関数
100
101
102
-200
-100
0
100
200
Frequency(H z)
Phase [deg]
6.9[H z]
35[H z]
100
101
102
-20
-10
0
10
20
30
40
Frequency(H z)
Gain [dB]
T402R N D 100X 振動台 X(2C h) --> ケース頂部 X(11C h) 伝達関数
100
101
102
-200
-100
0
100
200
Frequency(H z)
Phase [deg]
7[H z] 10.7[H z]
35[H z]
100
101
102
-20
-10
0
10
20
30
40
Frequency(H z)
Gain [dB]
T402R N D 100Y 振動台 Y(3C h) --> 展示位置 Y(9C h) 伝達関数
100
101
102
-200
-100
0
100
200
Frequency(H z)
Phase [deg]
6.9[H z]
32[H z]
100
101
102
-20
-10
0
10
20
30
40
Frequency(H z)
Gain [dB]
T402R N D 100Y 振動台 Y(3Ch) --> ケース頂部 Y(12C h) 伝達関数
100
101
102
-200
-100
0
100
200
Frequency(H z)
Phase [deg]
6.9[H z]
X-direction Shaking Table → Display Location X-direction Shaking Table → Top of Case
Y-direction Shaking Table → Display Location Y-direction Shaking Table → Top of Case
Figure.9 Show case (□900x900x2700h)
Roller type isolation system Isolation system used for this test has 900 mm square x 1900 mm height, 2.68 seconds natural time period of rail, 0.03 inclined strait rail and allowable maximum amplitude of ±220mm.It has 400 kg weight and is shown at photo of Fig .10. Statistic load test Statistic load test with appropriate weight has been conducted to determine friction co-efficient and performance of the system. Testing equipment shown at Fig.11 has been used to survey horizontal performance of each X,Y direction. Friction co-efficient has been calculated from measured horizontal load, deflection and vertical load. Here co-efficient at zero horizontal deflection is calculated using bellow equation.(4.1)(4.2) Co-efficient of μ=0.032 is calculated for X direction at total moving weight of 1.9 kN and μ=0.031 for Y direction at total weight of 1.6 kN. Fig.12 shows performance of X and Y direction.
Figure.10 Isolation device (□900x900x190h) for show case
ｌｏａｄ ｃｅｌｌ
ｍｏｔｏｒ ｓｅｉｓｍｉｃ ｉｓｏｌａｔｉｏｎ
ｄｉｓｐｌａｃｅｍｅｎｔ ｍｅｔｅｒ
ｔｅｎｓｉｌｅ ｔｅｓｔ ｄｉｒｅｃｔｉｏｎ
Figure.11 Test apparatus for isolation device
-150
-100
-50
0
50
100
150
-20 -15 -10 -5 0 5 10 15 20
cm
N
F1
F2
-150
-100
-50
0
50
100
150
-20 -15 -10 -5 0 5 10 15 20
cm
N
F1
F2
X direction Ｙ direction
Figure.12 Restoring force vs. horizontal displacement
Analytical Model Analytical model is considered as 2 degree of freedom as Fig.13 when the showcase is supported by isolation system.
Result of experiments and analysis Fig.14shows comparison of maximum acceleration and amplitude between input, measured and analysis results, it is confirmed input acceleration has decreased to level of 1/4 to 1/5. Fig.15 shows time histories of calculated and measured.
1m
0x
1x
z&&
1c
1k0k
0c sk
µ
143.2
118.1
140.5
132.7
133.4
96.0
123.1
116.5
116.7
98.2
104.7
91.0
124.5
94.2
113.8
102.5
91.2
95.5
71.4
73.9
83.2
74.7
77.1
79.9
75.0
70.3
77.9
73.0
77.6
79.7
83.4
72.0
814.9
607.3
396.4
495.5
321.2
239.0
492.8
280.4
0 200 400 600 800 1000
Kobe NS m 0
Kobe NS m 1
Kobe EW m 0
Kobe EW m 1
Taft NS m 0
Taft NS m 1
Taft EW m 0
Taft EW m 1
Hachinohe NS m 0
Hachinohe NS m 1
Hachinohe EW m 0
Hachinohe EW m 1
El Centro NS m 0
El Centro NS m 1
El Centro EW m 0
El Centro EW m 1
Acc. x 10-2 [m /s2]
Input
C alculated
M easured
21.9
13.0
9.4
11.6
9.6
16.9
18.3
12.2
18.2
18.2
15.8
15.8
10.1
10.1
11.5
11.5
9.1
9.2
14.7
14.8
17.1
17.2
10.3
10.3
0 5 10 15 20 25
Disp. [cm ]
Figure.14 Response accelerations and displacement
Figure.13 Analytical model
0 5 10 15 20 25 30 35
-100
0
100
Acc
. x10
-2 [m/s
2]
m0 Acc.0 5 10 15 20 25 30 35
-100
0
100
Acc
. x10
-2 [m/s
2]
m1 Acc.
0 5 10 15 20 25 30 35-20
-10
0
10
20m0 Disp.
time [sec]disp
[cm
]
0 5 10 15 20 25 30 35-500
0
500Input E.Q.
Acc
. x10
-2 [m/s
2]
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 A cc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 A cc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 D isp.
Tim e [s]
Disp. [cm]
0 5 10 15 20 25 30 35
-200
0
200
Input E.Q .
Acc. x10-2 [m/s2]
El Centro EW El Centro NS
0 5 10 15 20 25 30 35
-100
0
100
Acc
. x10
-2 [m/s
2]
m0 Acc.0 5 10 15 20 25 30 35
-100
0
100
Acc
. x10
-2 [m/s
2]
m1 Acc.
0 5 10 15 20 25 30 35-20
-10
0
10
20m0 Disp.
Time [s]
Disp. [cm
]
0 5 10 15 20 25 30 35
-200
0
200
Input E.Q.
Acc
. x10
-2 [m/s
2]
Hachinohe EW
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 Acc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 Acc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 Disp.
time [sec]
disp [cm]
0 5 10 15 20 25 30 35-400
-200
0
200
400Input E.Q.
Acc. x10-2 [m/s2]
Hachinohe NS
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 A cc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 A cc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 D isp.
Tim e [s]
Disp. [cm]
0 5 10 15 20 25 30 35-500
0
500Input E .Q .
Acc. x10-2 [m/s2]
Taft EW
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 A cc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 A cc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 D isp.
tim e [sec]
disp [cm]
0 5 10 15 20 25 30 35-500
0
500Input E.Q .
Acc. x10-2 [m/s2]
Taft NS
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 A cc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 A cc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 D isp.
Tim e [s]
Disp. [cm]
0 5 10 15 20 25 30 35
-500
0
500
Input E.Q .
Acc. x10-2 [m/s2]
JMA Kobe EW
0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m0 A cc.0 5 10 15 20 25 30 35
-100
0
100
Acc. x10-2 [m/s2]
m1 A cc.
0 5 10 15 20 25 30 35-20
-10
0
10
20
m0 D isp.
tim e [sec]
disp [cm]
0 5 10 15 20 25 30 35-1000
-500
0
500
1000Input E.Q .
Acc. x10-2 [m/s2]
JMA Kobe NS
Measured
Calculated
Figure.15 Histories of calculated and measured
CONCLUSION
Shaking table tests were carried out, showing good performance of the system and confirming validity of the analytical method. Earthquake acceleration such as JMA Kobe original wave and 0.5 [m/s] level of El-Centro and Taft has decreased to about less than 1.0 [m/s2] at showcase. Although there is some difference between experiments and analysis, each time histories of accelerations and displacements showed good conformity which confirming validity of the analytical model.
EXAMPLE OF APPLICATION TO MUSEUMS
Fig 16(a),(b) Isolation systems have been installed bellow The Thinker and Burghers of Calais (Auguste Rodin) at National Western Art museum at Ueno/Tokyo. Fig 17(a),(b) Isolation system has been integrated bellow beautiful showcase at Gifu Modern Museum at Gifu prefecture.
REFERENCES 1. Akenori SHIBATA: Saishin Taishinnkouzoukiseki, Morikita Shuppan Co., Ltd. 2001 (in Japan)
Figure.16(a) The Thinker (Auguste Rodin) Figure.16(b) Burghers of Calais (Auguste Rodin)
Figure.17(a) Show case Figure.17(b) Show case
