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1Associate Professor, Department of Mechanical Engineering, Tokyo Metropolitan College of Industrial Technology, Japan.

Ph. +81(3)34716331, Fax. +81 (3) 3471 6338, Email: [email protected], Department of Mechanical Engineering, Tokyo Metropolitan College of Industrial Technology, Japan.

Ph. +81 (3) 3471 6331, Fax. +81 (3) 3471 6338, Email: [email protected] Emeritus, Tokyo Metropolitan College of Industrial Technology, Japan.

4Professor, Department of Production Systems Engineering, Tokyo Metropolitan College of Industrial Technology, Japan.

Ph. +81 (3) 3471 6331, Fax. +81 (3) 3471 6338, Email: [email protected] t.ac.jp.5President, Kanazawa Seisakusho Co. Ltd. Japan. Ph. +81 (3) 3491 6147, Fax. +81 (3) 3490 9297.

A small base isolation system using a new device that used friction force was developed. In thispaper, dynamic characteristics of the system were investigated by an experiment using artificialseismic wave. The bearing combination of three cases, four spherical metal bearings, two sphericalmetal and two marble plate bearings, four marble plate bearings, was done in the experiment. Thepeak acceleration amplitude and the root mean square amplitude on the base isolation system havedecreased to 50-90 % and to 76-90 %, respectively, compared to the input wave. The best bearingcombination of reduction rate was the combination of two marble plate and two spherical metal

bearings. This system is useful to prevent overturning of equipments by seismic ground motion.

Keywords:base isolation system; friction bearing; dynamic characteristics; seismic response.

1. INTRODUCTION

In order to protect building structure from seismic ground motion, it is necessary to reinforce thestructure. However, seismic response of structure does not decrease remarkably, even if the strengthof structure is increased for anti-earthquake reinforcement. Equipments such as computer serverand office automation equipment that are set inside building will overturn during an earthquake,because they are higher than their width and depth. Therefore, small base isolation systems thatcan be installed inside building to decrease seismic response have been extensively developed [1-

3]. A new device has been developed using friction force to reduce seismic response [4]. Thebearing consists of two plates having spherical concaves and oval-type metal (marble plate) orspherical metal.

In this study, dynamic characteristics of the small base isolation system that consisted of this deviceare investigated by excitation experiments using artificial seismic wave.

DYNAMIC CHARACTERISTICS OF SMALL BASE ISOLATION SYSTEM FOREQUIPMENTS USING NEW DEVICE BASED ON FRICTION FORCE

NED UNIVERSITY JOURNAL OF RESEARCH, THEMATIC ISSUE ON EARTHQUAKES, 2012 87

Katsumi Kurita1, Shigeru Aoki2, Yuuji Nakanishi3, Kazutoshi Tominaga4, Mitsuo Kanazawa5

Manuscript received on 13thJanuary 2012, reviewed and accepted on 16th April 2012 as per publication policiesofNED University Journal of Research.

ABSTRACT


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NED UNIVERSITY JOURNAL OF RESEARCH, THEMATIC ISSUE ON EARTHQUAKES, 201288

Katsumi Kurita is an Associate Professor in the Department of Mechanical Engineering atTokyo Metropolitan College of Industrial Technology, Japan. He received his Bachelors andMasters from Tokyo Gakugei University, Japan, respectively, in 1991 and 1994. He receivedhis PhD in Engineering from Tokyo Institute of Technology, Japan in 2001. His research interestsinclude seismology and earthquake engineering.

Shigeru Aoki is a Professor in the Department of Mechanical Engineering at Tokyo MetropolitanCollege of Industrial Technology, Japan. He received his Bachelors and PhD in Engineeringform Tokyo Metropolitan University, Japan, respectively, in 1976 and 1985.

2. FRICTION BEARING

An example of friction bearing developed for this study is shown in Figure 1. It consists of twoplates with spherical concaves and a marble plate bearing. The spherical concaves plate and themarble plate bearing are made of stainless steel and cast iron, respectively. The size of the plate is344 x 344 mm (13.5 x 13.5 in.), and the thickness of this device is 62.4 mm (2.5 in.). Also, theradius of concave changes from 500-600 mm (19.7-23.6 in.), continuously. In this system, the marbleplate bearing slides between two plates, and vibration of the shaking table is transmitted to the upperplate via the marble plate bearing. Since the restoring force is generated when the marble platebearing uplifts, two plates return to original position.

A 50 mm (2 in.) diameter spherical metal bearing is prepared instead of a marble plate bearing.Comparing the bearing between a marble plate and a spherical metal, the spherical metal generateslarge restoring force. On the other hand, the marble plate generates high damping ratio because ofsliding friction.

The small base isolation system composed of this device is shown in Figures 2and 3. The devicewas set up at each corner. To investigate effects of the bearing combination on reduction, the bearingcombination shown in Table 1is done in this experiment, and the same type bearing was installedat the line of diagonal.

3. NATURAL PERIOD AND DAMPING RATIO OF SYSTEM

As the friction bearing consists of a pendulum mechanism, this system has a natural period. Asthe bearing slides on the spherical concaves, friction force related to damping occurs between them

Yuji Nakanishi is a Professor Emeritus at Tokyo Metropolitan College of Industrial Technology,Japan. He received his Bachelors from Nippon University, Japan in 1968. He received his PhDin Engineering from Himeji Institute of Technology, Japan in 2002.

Kazutoshi Tominaga is a Professor in the Department of Production Systems Engineering atTokyo Metropolitan College of Industrial Technology, Japan. He received his Bachelors andMasters from Sophia University, Japan, respectively, in 1984 and 1986.

Mitsuo Kanazawa is the President of Kanazawa Seisakusho Co. Ltd, Japan.

Figure 1. Friction bearing with marble plate (mm).


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(Figure 4). Therefore, the natural period and the damping ratio of this system are very importantfactors to understand its dynamic characteristics. First, these parameters are estimated by freevibration test. The damping ratio is calculated by logarithmic decrement.

Free vibration is generated when the upper plate of this system that added some displacement fromoriginal position is released. Signal from acceleration sensors (Kyowa AS-2GA) installed on theupper plate of the small base isolation system was recorded to the PC through the interface (KyowaPCD-300A). The sampling rate is 0.01 sec/points.

Acceleration waveforms of free vibration at each condition are shown in Figure 5. Natural periodand damping ratio evaluated by this experiment are shown in Table 2. Natural period in case 1 islongest in this experiment; in case 2 and case 3, it becomes shorter. The damping ratio, when thespherical metal bearing was used, is small. As a number of the marble plate bearings increase, thedamping ratio becomes large. It means that large friction force is generated when the marble plate

bearing slip on the spherical concave plate.

Figure 2. Size of the small base isolation system using friction bearings (mm).

Figure 3. Photograph of the real small base isolation system (left) and its inside appearance(Right).

Case 1Case 2Case 3

Bearing combinationspherical metal: 2spherical metal: 2 + marble plate: 2marble plate: 4

Table 1. Bearing combination in the study

Figure 4. Moving mechanism of friction bearing by vibration; (top) spherical metal; (bottom)marble plate.


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4. EXCITATION EXPERIMENT USING ARTIFICIAL SEISMIC WAVE

In order to understand the dynamic characteristics of this system, the excitation experiment is doneby artificial seismic wave. The small base isolation system that installed a computer server rackwith 1850 x 860 x 1000 mm (73 x 34 x 39 in.) size and 100 kg (220 lb) of mass is put on the shakingtable (Figure 6). The natural frequency and the damping ratio of this server evaluated by micro-vibrations that were measured on the bottom and the top of this server at the same time, are 4.15Hz and 0.01, respectively. Acceleration sensors are installed on the shaking table, in the upper plateof the base isolation system and in the top of a computer server rack. The direction of excitationis unidimensional horizontally.

The waveform of artificial seismic wave as input wave is shown in Figure 7and its Fourier spectrum

is shown in Figure 8. The predominant frequency of the input wave is about 10 Hz, which is thenatural frequency of the general mechanical structure. The Fourier amplitude of the input wave isdecreased at a frequency under 0.3 Hz.

Figure 5. Waveforms of free vibration experiments on the small base isolation system.

Case 1Case 2Case 3

Natural period T0(sec)2.2812.0061.333

Damping ratio0.0090.1980.302

Table 2. Natural period and damping ratio evaluated by free vibration test

Figure 6. Setup of excitation experiment.

Figure 7. Waveform of artificial seismic wave as input wave.


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5. DISCUSSION ON RESULTS

5.1 Acceleration Response Waveforms

Acceleration response waveforms on the small base isolation system and on the top of the computerserver are shown in Figure 9. Amplitude of acceleration waveform in case 2 that used two of themarble plate and of the spherical metal bearings is smallest in this experiment. However, in case

1, although the response amplitude decreases up to 15 sec, large response amplitude with thefrequency of around 0.5 Hz band is identified from 25-35 sec.

Peak amplitude of acceleration response waveforms is shown in Table 3. And, from a wave energyreduction point of view, root mean square (RMS) amplitude of acceleration response waveformsis shown in Table 4. Generally, intensity of ground motion uses the peak amplitude. However, ifthe peak amplitude consists of high frequency and appears a moment, it may not be effective foroverturning equipments. And it is important to evaluate the reduction of wave energy, the RMS wasused as a value of evaluation. The peak amplitude of acceleration response waves on the small baseisolation system and on the top of computer server decreases 15-57% compared to the input waves.Also, the RMS amplitude decreases 10-24%.

Figure 8. Fourier spectrum of the input wave.

Figure 9. Acceleration seismic waveforms on the small base isolation system and on the topof computer serve.

Table 3. Peak amplitude of acceleration response waveforms

Case 1Case 2Case 3

Input (gal)

146913771360

Isolation (gal)

836203574

Top (gal)

980270558


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The case of good reduction at the frequency between 1 and 10 Hz is case 2 from the integrated valueof spectral ratio shown in Table 5. As the acceleration response waveforms are shown in Figure 9,some sharp pulses in waveforms from 25-35 sec are identified in case 1. Since motion of the smallbase isolation system by resonance has exceeded the clearance displacement, a collision occurredbetween two spherical concaves plates in case 1. So the reduction rate at the frequency between 1and 5 Hz is not so good compared to case 2. In case 3, the value of a spectral peak by resonance isrestrained using the marble plate bearing that may generate high friction force. However, the decreasingrate at the high frequency band is getting worse.

6. COMPARISON OF THE THEORETICAL TRANSFER FUNCTION

The simulation model for evaluation consisted of a single degree of freedom system with a springand a damper shown in Figure 12. The equation of motion is

Table 5. Integrated value of spectral ratio

Case 1Case 2

Case 3

0.1-20 Hz6.962.67

6.09

1-10 Hz3.821.27

3.62

Figure 12. Analytical model for calculating a theoretical transfer function.

(1)

where c/2Smk is the damping ratio; n =Sk / mis the natural angular frequency; aredisplacement, velocity and acceleration on this base isolation system;yandyare displacement andvelocity of the input motion; cis the damping coefficient; and kis the spring constant. Therefore,the transfer function of this system is given as Eq. (2)

(2)

where is the angular frequency; and i is the imaginary unit.

Comparison between the spectral ratio and the theoretical transfer function in case 2 using parametersevaluated by free vibration is shown in Figure 13. The location of a peak at the frequency of 0.5Hz between them is a little bit different. Fitting the transfer function for the spectral ratio by aforwarding model, the natural period and the damping ratio are re-evaluated. The shape of thetransfer function, natural period, and damping ratio are shown in Figure 14and Table 6. Thedamping ratio evaluated by this method is larger than the one evaluated by free vibration. Although

the shape of the transfer function can express the spectral ratio at the frequency band between 0.2Hz and 1-2 Hz, it is impossible to explain a spectral peak at the frequency of 7.5 Hz.

Therefore, using 2DOF system (Figure 15), a theoretical transfer function as shown in Figure 16is calculate. The parameters in Table 2were used. Further, since the mass of computer server m1and the upper plate mass of the base isolation system m2were 100 kg (220 lb) and 35 kg (77 lb),respectively, the mass ratio was 2.85. The shape of the theoretical transfer function indicates two


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Table 6. Natural period and damping ratio evaluated by fitting theoretical transfer functionto spectral ratio using 1DOF

Case 1Case 2

Case 3

Natural period T0(sec)2.2222.381

1.667

Damping ratio 0.0650.17

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Figure 13. Comparison between the spectral ratio and the theoretical transfer function usingparameters evaluated by a free vibration test.

Figure 14. Comparison between the spectral ratio and the fitting transfer function on thespectral ratio.

Figure 15. Two degrees of freedom analytical model for calculating a theoretical transferfunction.

Figure 16. Comparison between the spectral ratio and the theoretical transfer function usingtwo degrees of freedom. The parameters evaluated by a free vibration test were used.


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resonance peaks and an anti-resonance valley. If the valley of spectral ratio at the frequency of 5Hz is considered to be an anti-resonance point (Figure 17), although locations of peaks are a littlebit different, it is possible to explain the shape of spectral ratio. Since the computer server with largemass was put on the small base isolation system, it is assumed that this system hold a motion oftwo degrees of freedom. However, the natural period evaluated by fitting the transfer function forspectral ratio (Table 7) is quite lower than the one by free vibration. Also it is difficult to explainthe valley of anti-resonance point. It is assumed that this motion do not explain only vibration of2DOF but also non-linier motion by friction force.

Comparing the damping ratio between evaluated by excitation experiment test and by free vibration

test, the results are different depending on the method used. In excitation experiment test, continuoussignal was used. Supplying the signal to the small base isolation system, the system should attenuatethe signal continuously. It seems that the energy of signal does not attenuate. On the other hand,in free vibration test, a step signal was used. The energy of signal attenuate rapidly, because theinput signal is a pulse. So it can be assumed that the damping ratio evaluated by excitation experimenttest was larger than by free vibration test.

7. CONCLUSIONS

In order to protect the overturning of equipment installed inside the building by seismic groundmotion, a new device was developed using friction force, and a small base isolation system that canbe installed inside the building was produced by this device. Besides, dynamic characteristics of

this system were investigated by excitation experiment. As a result,

1) From a free vibration experiment, natural period Toand damping ratio were evaluated. Inthe case of a small friction force using four spherical bearings, = 0.004 and To= 2.281 sec.In the case of a high friction force using four marble plate bearings, the damping ratio becamelarger and the natural period was smaller, = 0.105 and To=1.333 sec.

2) The peak acceleration amplitude and RMS amplitude of response wave decreased 15-57%and 10-24% to the input wave. The best bearing combination of reduction rate was thecombination of two marble plate and two ball bearings. From the spectral ratio point of view,this combination indicated a good result from 1-10 Hz.

3) In the case of a low damping ratio, the spectral peak at the frequency of 0.5 Hz generated

by resonance became big. On the other hand, it became small in the case of a high dampingratio. As damping ratio became larger, a spectral peak at the frequency of 10 Hz was identified,and its value became gradually large.


Figure 17. Comparison between the spectral ratio and the fitting transfer function on spectralratio calculated by two degrees of freedom.

Table 7. Natural period and damping ratio evaluated by fitting theoretical transfer functionto spectral ratio using 2DOF

Case 1Case 2Case 3

Natural period T0(sec)Base isolation system1.1111.1761.234

Server0.4160.2700.269

Damping ratio Base isolation system0.140.351.50

Server0.0020.030.03


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4) A natural period and a damping ratio were evaluated by fitting a theoretical transfer functionto a spectral ratio by a forwarding model using a model of a single degree of freedom. Thedamping ratio was higher than the one evaluated by a free vibration experiment. However,it is difficult to explain that there is a spectral peak at the frequency of 10 Hz.

5) Although locations of peaks are a little bit different, it is possible to explain the spectral shapeusing two degrees of freedom model. However, if two peak locations of the transfer function

are fitted for spectral ratio, the natural period evaluated by fitting is smaller than the parameterby free vibration. Also, it is difficult to explain the valley of anti-resonance point. It is assumedthat this motion does not explain only a vibration of two degrees of freedom but also non-linier motion by friction force.

ACKNOWLEGEMENTS

The comments by two anonymous reviewers are quite helpful for improving this manuscript. Theauthors are grateful to them.

REFERENCES

[1] Fujita S, Morikawa Y, Shimoda I, Nagata S. Shimosaka H. Isolation System for Equipment

Using Friction Pendulum Bearings (1stReport, Shaking Tests and Response Analysis onIsolated Equipment). Trans Jap Soc Mech Eng, Series C 1993;59(557):11-16 (in Japanesewith English abstract).

[2] Ueda S, Akimoto M, Enomoto T, Fujita T. Study of Roller Type Seismic Isolation Device forWorks of Art. Trans Jap Soc Mech Eng, Series C 2005;71(703):807-812 (in Japanese withEnglish abstract).

[3] Fujita S, Yamamoto H, Kitagawa N, Kurabayashi H. Research and Development of the FrictionPendulum Isolation Device with Poly-Curvature (Investigation of Isolation Performance onShake Test and Response Analysis Using Vending Machine Model). Trans Jap Soc Mech Eng,Series C 2003;69(684):1990-1996 (in Japanese with English abstract).

[4] Aoki S, Nakanishi Y, Nishimura T, Kanazawa M, Otaka T, Inagaki M. Reduction of SeismicResponse of Mechanical System by Friction Type Base Isolation System. In: Third Asian

Conference on Multibody Dynamics. Tokyo, Japan:2006. CD-ROM A00705.

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Kurita (Final)