Journal of Physics: Conference Series Related content PAPER • OPEN ACCESS Characterization and performance evaluation of a vertical seismic isolator using link and crank mechanism To cite this article: N Tsujiuchi et al 2016 J. Phys.: Conf. Ser. 744 012232 - Experimental performance evaluation of heat pump-based steam supply system T Kaida, I Sakuraba, K Hashimoto et al. - Fluid-Structure interaction analysis and performance evaluation of a membrane blade M. Saeedi, R. Wüchner and K.-U. Bletzinger - Optimization and performance evaluation for nutrient removal from palm oil mill effluent wastewater using microalgae Raheek I Ibrahim, Z H Wong and A W Mohammad View the article online for updates and enhancements. This content was downloaded from IP address 168.151.1.23 on 24/09/2017 at 19:28 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 Characterization and performance evaluation of a vertical seismic isolator using link and crank mechanism N Tsujiuchi1, A Ito2, Y Sekiya 3, C Nan 3,and M Yasuda 4 1 Professor, Doshisha University Dept. of Mechanical Engineering, Tataramiyakodani1-3, Kyotanabeshi, Kyoto, 610-0394 Japan 2 Associate Professor, Doshisha University Dept. of Mechanical Engineering 3 Student, Doshisha University Dept. of Mechanical Engineering 4 Professor, Setsunan University Dept. of Mechanical Engineering, Ikedanakamachi17-8, Neyagawashi, Osaka, 572-8508 Japan E-mail: ntsujiuc@mail.doshisha.ac.jp Abstract. In recent years, various seismic isolators have been developed to prevent earthquake damage to valuable art and other rare objects. Many seismic isolators only defend against horizontal motions, which are the usual cause of falling objects. However, the development of a seismic isolator designed for vertical vibration is necessary since such great vertical vibration earthquakes as the 2004 Niigata Prefecture Chuetsu Earthquake have occurred, and their increased height characteristics are undesirable. In this study, we developed a vertical seismic isolator that can be installed at a lower height and can support loads using a horizontal spring without requiring a vertical spring. It has a mechanism that combines links and cranks. The dynamic model was proposed and the frequency characteristics were simulated when the sine waves were the input. Shaking tests were also performed. The experimental value of the natural frequency was 0.57 Hz, and the theoretical values of the frequency characteristics were close to the experimental values. In addition, we verified this vertical seismic isolator’s performance through shaking tests and simulation for typical seismic waves in Japan. We verified the seismic isolation’s performance from the experimental result because the average reduction rate of the acceleration was 0.21. 1. Introduction In recent years, to prevent art objects and valuable, accurate instruments from falling and sustaining damage during an earthquake, various provisions of seismic isolation have been developed. The cost to prepare for seismic isolation, however, is high [1]. In addition, although seismic isolators for small objects have been put into practical use [2], many seismic isolators are only efficient for horizontal motion because horizontal vibration is most often the cause of falling objects [3, 4]. However, development of seismic isolators that are effective for vertical vibration is necessary to cope with great vertical-vibration earthquakes, such as the 2004 Niigata Prefecture Chuetsu Earthquake. Previous studies developed vertical seismic isolators that combine a vertical spring and a link mechanism to maintain the horizontal position while using a negative stiffness mechanism to reduce the natural frequency [5, 6]. However, when the natural frequency decreases, which is caused by low rigidity so that enough seismic isolation’s performance is obtained, its static deflection of the spring increases since the soft spring absorbs the weight. So, the stroke decreases and the seismic isolator. When using negative stiffness to reduce the spring’s static deflection, the natural frequency is reduced Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd 1 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 but the seismic isolator’s height increases since a link mechanism is added to the seismic isolator. It is therefore difficult to achieve both reducing the natural frequency and downsizing the seismic isolator. In this study, we propose a vertical seismic isolator of which the natural frequency is reduced and which is downsized by a mechanism that combines a link and crank, and can support a vertical load with just a horizontal stiff spring, reducing the amount of expansion and contraction, without a vertical spring. The mechanism also increases the stroke of the seismic isolator and reduces its height. We verify this seismic isolator’s performance by experiment and numerical simulation. 2. Vertical seismic isolator 2.1. Mechanism of vertical seismic isolator Our proposed vertical seismic isolator is shown in figure 1 and its schematic diagram is shown in figure 2. It is composed of a top plate, a bottom plate, a center shaft, links, cranks, and connecting rods. This seismic isolation system consists of a compound link and crank mechanism. The horizontal spring force acts vertically through the link and crank mechanism. The top and base plates, which are fixed on the link, maintain a horizontal position because the center shaft and the link retain a parallelogram shape. Damping is obtained by friction that arises in moving parts. The seismic isolator can be downsized because stiff spring was installed horizontally and the spring’s expansion and contraction length are reduced. Additionally, the initial tension may be adjusted to correspond to the mass of mounting objects because both ends of the horizontal spring are connected by a bolt that adjusts the spring’s initial length. Therefore, the height in equilibrium condition can be maintained by adjusting the initial tension. The limit for mounting object’s mass is 3.0 kg and the limit for the vertical stroke is 156 mm (±78mm). Figure 1. Proposed vertical seismic isolator with a link and crank mechanism. Figure 2. Schematic diagram of seismic isolator. 2 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 2.2. Equivalent spring constant Figure 3 shows a simplified figure of the link, the crank, and the connecting rod. la is the link length, lb is the crank length, lc is the connecting rod length, xd is the displacement of the spring head from the equilibrium condition, θa is the link angle, θb is the crank angle, and θc is the rod angle. When ld is the distance from the link hinge to the spring head, it is (1) l d = lb cos θb + lc cos θc Then ld0 is ld in the equilibrium condition, and spring displacement xd is xd  l d  l d 0 From lbsinθb = lcsinθc , rod angle θc is (2)  lb  sin  b   lc   c  sin 1  (3) where fh is the horizontal spring force, and fc is the force acting on the rod. Torque Tb acting on the crank is, from fh = fccosθc: Tb  f c lb sin( b   c )  f h lb sin( b   c ) cos  c (4) To support seismic isolator load f on the link, necessary torque Ta is Ta  2l a f cos  a (5) Since torque Ta, which is acting on the link, is equivalent to torque Tb that is acting on the crank, from equation (4) and (5), seismic isolator load f becomes f  fh lb sin( b   c ) 2l a cos  a cos  c (6) Using equation (3) and (6), and θb =θa +α, compression rate β of the spring displacement and the top plate displacement is written as equation (7):   l lb sin  a    sin 1  b sin( a   )   l sin  b   c    lc   b  2l a cos  a cos  c  l  2l a cos  a cos sin 1  b sin( a   )    lc   (7) Furthermore, the relation between vertical displacement xa of the seismic isolator’s top plate from initial state and spring’s displacement xd is xa = β-1xd. Thus, when the seismic isolator’s displacement is xa, potential energy is stored in the spring constant of spring k as equation (8). 3 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 1 1 2 kxd  k 2 xa2 2 2 (8) In fact, the relation of k and equivalent spring constant ka is written as ka   2 k (9) Figure 3. Simplified figure of link-crank mechanism. In this way, the system’s natural frequency can be reduced by adjusting β and reducing equivalent spring constant ka even though a stiff spring is used. Figure 4 shows the vertical restoring force on vertical displacement xa of the seismic isolator’s top plate, where ka is the gradient. The theoretical values are close to the experimental values. The stroke was 156 mm, which was relatively long to have effect for earthquakes having large displacement although it was enough. Therefore, the stroke is maintained by adjusting the initial tension to the limit of mounting object’s mass of 3.0 kg. Restoring force [N] 35 30 25 Simulation Experiment 20 15 10 0 20 40 60 80 100 120 140 160 Relative displacement [mm] Figure 4. Vertical restoring force on vertical displacement of seismic isolator. 4 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 2.3. Equation of motion Figure 5 shows a dynamic model of our vertical seismic isolator. The sum of the mounting object’s mass and the top plate’s mass is M. The link-crank mechanism expresses the mass point on the links and this mass, which is the seismic isolator’s mass after deduction of the top plate’s mass and the bottom plate’s mass, is m. The link length is l / 2, the equivalent spring constant is ka, the link angle in the equilibrium condition is θ0, the link angle is θ0+θ, the displacement from the equilibrium condition is z0 on the base plate, the displacement from the equilibrium condition is z1 on the top plate, the vertical displacement of the link-crank mechanism is z2, its horizontal displacement is x, and the relative displacement of the top plate with respect to the base plate is z. In this regard, the mass and rotary inertia are ignored on the link, and θ is the plus direction when relative displacement z increases. The device’s internal damping is considered by replacing a dash pot and the damping constant is c. The following are the relations among z0, z1, z2, and z: z1  z  z 0 z2  (10) 1 ( z  z0 ) 2 (11) Using link angleθ0+θ and link length l / 2 , relative displacements z and x are z  l sin 0     sin  0  (12) x (13) l cos 0     cos  0  2 By substituting equation (12) for equation (10) and (11), they become z1  z 0  l sin 0     sin  0  z2  z0  (14) l sin 0     sin  0  2 (15) By differentiating equation (13)-(15) with respect to the variable of time, kinetic energy T of this system becomes T 1 1 1 2 2 Mz1  mz 2  mx 2 2 2 2   2 l 1 1    1  l  M z0  l cos  0     m z0   cos  0     m   sin  0    2 2  2   2  2 2 2 (16) And by obtaining potential energy U of this device from equation (12), it becomes U 1 1 1 2 k a z 2   2 kz 2   2 kl 2 sin  0     sin  0  2 2 2 Since equation (16) and (17) are obtained, Lagrangian L is 5 (17) MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232  IOP Publishing doi:10.1088/1742-6596/744/1/012232  2 l 1  l 1  1   L  M z 0  l cos 0     m z 0   cos 0     m   sin  0    2  2 2  2 2   1 2   2 kl 2 sin  0     sin  0  2 2 By obtaining dissipation function F, F 1 2 1 2 2 cz  cl  cos 2  0    2 2 2 (18) (19) By substituting equation (18) and (19) for the Lagrange equation and rearranging this equation, the motion equation is    m  M cos( 0   )  l  cl cos( 0   )   2 klsin( 0   )  sin  0  4 cos( 0   )   (20) m    M  z0 2  Here,  is ignored because it is a negligible term. The relations between θ and z are found from equation (12): 2 z l     sin 1   sin  0    0 m  * m   * 2  M cos    L z z  cL z z cos    klsin   sin  0    M  z0 4 cos   2   z     0    sin 1   sin  0  l  l L*z  2 l 2  z  l sin  0  (21) By substituting equation (21) for equation (20), it becomes (22) Here, z 2 is ignored because it is a negligible term. In addition, a friction term is approximated below:  s i (g)zb n (23) The friction term written in equation (23) is added to equation (22). Thus, equation (24), which is the motion equation of this seismic isolator, is obtained and used in the following numerical simulation: m  *  * 2  M cos    L z z  cL z z cos    klsin   sin  0  4 cos    m    M  z0  sign( z)b 2  6 (24) MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 M z1 l/2 c z2 ka m z x l/2 z0 θ Figure 5. Dynamic Model of proposed vertical seismic isolator. 3. Experiment and numerical simulation 3.1. Experimental device Figure 6 shows the experimental set up for the shaking test. The vibration exciter used in this study consisted of two hydraulic actuators, a 1.2 × 1.2 m shaking table, and hydraulic units and operates in both the horizontal and vertical directions. The frequency and acceleration of the input vibration were controlled by a PC connected to this two-dimensional shaker. The experiment was run by attaching the vertical seismic isolator to this vibration exciter. The experimental scenery is shown in Figure 7. A three-dimensional acceleration pickup sensor (Wireless Technologies, Inc. WAA-006) was used in order to measure acceleration. Figure 6. Experimental setup. Figure 7. Vertical seismic isolator attached to vibration exciter. 3.2. Frequency characteristics We verified the frequency characteristics of the vertical seismic isolator by inputting a sinusoidal wave of acceleration’s amplitude a0 through experiments and numerical simulation. The mounting object’s mass was 2.5 kg. Table 1 details the specifications of the material parameters and this numerical simulation uses the Runge-Kutta method for the motion equation. The difference time was 0.01 s. C was found using a half-power method from the experimental frequency response. Friction force b in simulation was determined so that the peak of the amplification ratio of acceleration was equal to the experiment peak and its value was 0.69 N. Table 2 shows input acceleration’s amplitude a0. Here, a0 is not always constant because of the limits of the capacities of the shaker and the seismic isolator in the experiment. 7 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 Table 1. Material parameters. Table 2. Input acceleration. . a0 [m/s2] f [Hz] f [Hz] Parameter M m k Value 3.6 kg 1.1 kg 10396 N/m la 0.12 m lb 0.023 m lc c θ0 0.07 m 2.8 N･s/m 30 deg 0.35 0.40 0.45 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.20 0.20 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 0.40 a0 [m/s2] 0.63 0.64 0.65 0.70 0.80 0.90 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 0.40 0.40 0.40 0.40 0.40 0.40 0.45 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 In this case, Figure 8 (a) shows the time history of acceleration response in the experiment when the input wave frequency is 0.7 Hz as an example and Figure 8 (b) shows the time history in the numerical simulation. Here, low pass filter was applied when the waves had heavy noise. The curve shape in the simulation was similar to the shape in the experiment. The input wave was amplified and frequency was in the resonance area. Figure 9 shows the frequency characteristic of the acceleration’s amplification ratio. In the range of more than 2 Hz, the acceleration was reduced considerably. The frequency in the range of more than 1 Hz was in the seismic isolation area. The experimental value of the natural frequency was 0.57 Hz and the theoretical value was 0.62 Hz. Although this seismic isolator used a stiff spring, the natural frequency was low because of the low vertical equivalent spring constant. In addition, the theoretical values of the amplification ratio of the acceleration were close to the experimental values. Therefore, the validity of the proposed dynamic model (Figure 5) was confirmed. 1.5 Input Response 1 Acceleration [m/s2] Acceleration [m/s2] 1.5 0.5 0 -0.5 Input 1 Response 0.5 0 -0.5 -1 -1.5 -1 -1.5 0 5 Time [s] 10 0 5 Time [s] (a) Experiment. (b) Numerical simulation. Figure 8. Time history of acceleration response ( f=0.7 Hz). 8 10 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 Acceleration amplification ratio 3.5 Experiment 3 Simulation 2.5 2 1.5 1 0.5 0 0 2 4 6 Frequency [Hz] 8 10 Figure 9. Frequency characteristic of acceleration amplification ratio. 3.3. Performance for seismic waves We evaluated the seismic isolator’s performance for following nine previous seismic waves that occurred in Japan through numerical simulations and experiments: the Niigata Prefecture Chuetsu Earthquake in Kawaguti Town, the Niigata Prefecture Chuetsu Earthquake in Ojiya city, the Miyagioki Earthquake, the Tohoku Earthquake (the Great East Japan Earthquake), the Fukuoka Earthquake, the Miyagi Earthquake, the Chuetsuoki Earthquake, the Noto Earthquake, and the Tottori Earthquake [7]. Here, only vertical directional component of the input waves was used. For example, Figure 10 shows the time history of the acceleration response in Tohoku earthquake. The response was considerably reduced in regards to the input acceleration. In addition, the theoretical values were relatively close to the experimental values. (a) Experiment. (b) Numerical simulation. Figure 10. Time history of acceleration response inTohoku earthquake. Figure 11 also show the maximum acceleration of the top and base plates on the nine seismic waves and the acceleration’s reduction rate on the nine seismic waves. The average reduced rate of acceleration in our experiment was 0.21 for the nine seismic waves and the average reduced rate in simulation was 0.11, confirming the effect of seismic isolation. However, experimental results had 9 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 larger acceleration than simulation. It is assumed that this reason is that systems having play tend to have high acceleration [8]. Figure 11. Comparison of maximum acceleration in nine earthquakes. 4. Conclusion We proposed a vertical seismic isolator that used link and crank mechanism and reduced the vertical seismic isolator’s height and its natural frequency because it could support a vertical load with just using a horizontal stiff spring without a vertical spring. The stroke was 156 mm, which was relatively long to have effect for earthquakes having large displacement. When mounting object’s mass changed, the stroke was maintained by adjusting the initial tension to the limit of 3.0 kg. The dynamic model was proposed and the frequency characteristics were calculated when the sine waves were the input. Then, shaking tests were also performed. The natural frequency value in experiment was 0.57Hz, which was considerably low. The theoretical values of the frequency characteristics were close to the experimental values. Therefore, the validity of the proposed dynamic model was confirmed. We evaluated the seismic isolator’s performance for nine previous seismic waves that occurred in Japan through numerical simulations and experiments. We verified the seismic isolation’s performance from the experimental result because the average reduction rate of the acceleration was 0.21. 10 MOVIC2016 & RASD2016 Journal of Physics: Conference Series 744 (2016) 012232 IOP Publishing doi:10.1088/1742-6596/744/1/012232 References [1] [2] [3] [4] [5] [6] [7] [8] Fujita T, Suzuki S and Fujita S 1990 High damping rubber bearings for seismic isolation of buildings: 1st Report Hysteretic restoring force characteristics and analytical models vibrations and stability Transactions of the Japan Society of Mechanical Engineers(C) 56 658-66 (in Japanese) Shintani M, Hattori Y and Kotera T 2006 Study on isolation device by friction Transactions of the Japan Society of Mechanical Engineers(C) 72 388-93 (in Japanese) Ueda S, Akimoto M, Enomoto T and Fujita T 2005 Study of roller type seismic isolation device for works of art Transactions of the Japan Society of Mechanical Engineers(C) 71 807-12 (in Japanese) Takahashi Y, Matsuhisa H, Utsuno H and Yamada K 2009 A study on a three dimensional seismic isolator with a tilt prevention system Transactions of Lecture Meeting in Regular Meeting of the Japan Society of Mechanical Engineers Kansai Branch 84 502 (in Japanese) Matsumura H, Matsuhisa K, Utsuno H, Yamada K, Sawada K and Yasuda M 2007 A study on lowering natural frequency of the three dimensional seismic isolator under high load Transactions of CD-ROM of the Japan Society of Mechanical Engineer at D&D2007 108 (in Japanese). Ashida R, Matsuhisa H, Yasuda M, Yamada K and Sawada K 2012 Three dimensional seismic isolator by using a differential non-circular pulley The Japan Society of Mechanical Engineers 1805(in Japanese). Japan Meteorological Agency Observation data of severe earthquakes (in Japanese) http://www.data.jma.go.jp/svd/eqev/data/kyoshin/jishin/index.html (accessed on 28 Jan. 2016). Nakajima T and Tsuda K 2005 Nonlinear response phenomenon in vibration test Osakafuritsu Industrial Technology Research Institute report 19 39-44 (in Japanese). 11