Effects of Container Size, Stroke and Frequency on Damping Properties of a Damper Using a Steel Particle Assemblage

Transcription

1 Advanced Experimental Mechanics, Vol.1 (2016), Copyright C 2016 JSEM Effects of Container Size, Stroke and Frequency on Damping Properties of a Damper Using a Steel Particle Assemblage Yasushi IDO 1, Makoto HANAI 1, Takuma KAWAI 2, Koichi HAYASHI 3 and Atsushi TOYOUCHI 4 1 Department of Engineering Physics, Electronics and Mechanics, Nagoya Institute of Technology, Nagoya , Japan 2 Toyota Motor Corporation, Toyota , Japan 3 Department of Electric Mechanical Engineering, National Institute of Technology, Toba College, Toba , Japan 4 New Business Development Department, Stationed at Kumagaya Plant Engineering Division, KYB Corporation, Kumagaya , Japan (Received 26 November 2015; received in revised form 24 May 2016; accepted 17 June 2016) Abstract: A damper using a particle assemblage is a damper using particles instead of a working oil in a standard oil damper. Two kinds of container size for double-rod type damper using a steel particle assemblage were prepared. Effects of container size of the damper, stroke and frequency of forced vibration on the damping force were investigated experimentally. The damping force of the damper depends on both the frequency of forced vibration and the length of the container of the damper, however, basic property of the damping force is almost independent of the stroke of forced vibration. Keywords: Damper, Damping Force, Particle Assemblage, Stroke, Frequency, Double-Rod Type, Vibration Control 1. Introduction Dampers are useful devices for restraining and attenuating vibrations of structures, machines, and so on. A viscosity damper, a friction damper and a hysteresis damper are typical examples of the dampers and a particle impact damper is another example. The particle impact damper comprises a container filled with particles. When vibration is applied to the particle impact damper, it absorbs kinematic energy through frictional collisions of both between particle and particle and between particle and wall in the container [1-6]. The behaviors of particles in the particle impact dampers were computed using the discrete element method [6-10] to study damping processes. Another way to use a group of particles in a damper is using a spherical particle assemblage instead of a working fluid in a standard oil damper [11]. Oil is not used in the damper using a particle assemblage, so the structure of the damper becomes simple and environmental load due to oil leakage is reduced. Effects of both packing fraction and material of particles on the damping properties of the damper utilizing the spherical particle assemblage was reported by Ido and Hayashi [11]. The damping force of the damper using the magnetic particle assemblage in the presence of magnetic field was investigated experimentally by Ido, et al. [12]. Basically, the damping force depends on the installation angle of the damper due to the gravity. When the particles are magnetic particles, effect of installation angle on the damping force can be reduced by applying magnetic field [13]. However, effects of stroke and container size of the damper had not been reported yet. In this study, influences of stroke and container size of the damper on the damping force were investigated experimentally. We prepared two kinds of container with different length for the damper using a steel particle assemblage, because the distance between the dead center of the piston and the end wall is also considered to be an important factor to characterize the damping force of the damper. 2. Experiments 2.1 Damper using a particle assemblage Figure 1 shows the schematic of the damper using a steel particle assemblage. We used the double-rod type damper in our experiments. The space of the container which consists of the cylinder, the end cover and the spacers is filled with spherical steel particles and the piston is reciprocated in the container. The piston is a circular cylinder with tapers of angle of 45 degrees. So, the piston promotes the motion of particles with its moving. The rods are attached on both sides of the piston so as to maintain the capacity inside the damper constant. The rods are supported by the bearings at the exit of the container of the damper. The friction of the damper at slide parts is very small and we can ignore it. The length of the container of the damper can be changed by attaching spacers of different length in front of the end covers. 2.2 Experimental apparatus Figure 2 shows the schematic of the experimental apparatus. The damper was installed in the horizontal direction. The damper was forced to vibrate using the motor (Mitsubishi Electric Co., Ltd., HA-LP801) with the reciprocating block slider crank mechanism. The displacement of the piston was measured using the laser Fig.1 Schematic of the double-rod type damper using a particle assemblage. 1: Cylinder, 2: end cover, 3: ball bearing, 4: rod, 5: piston, 6: particles, and 7: spacer 105

2 Y. IDO, M. HANAI, T. KAWAI, K. HAYASHI and A. TOYOUCHI 3. Experimental Results and Discussions Fig.2 Schematic of the experimental apparatus. 1: Damper, 2: motor, 3: motor controller, 4: load cell, 5: strain amplifier, 6: laser displacement sensor, 7: amplifier unit, and 8: oscilloscope displacement sensor (LB-040 and LB-1000, Keyence) and the amplifier unit (Panasonic Industrial Devices SUNX Co., Ltd., SUNX ANR1226). The damping force of the damper was measured using the load cell and the strain amplifier (Kyowa Electronic Instruments Co., Ltd., LUX- A-20kN and DPM-751A). The displacement and damping force were recorded using the oscilloscope (Yokogawa Electric Corp., DL1620). The frequency of forced vibration was changed by adjusting the motor controller. 2.3 Experimental conditions The particles were steel balls (SUJ2) and the density of SUJ2 is g/mm 3. The diameter of particles was 1.5 mm and the packing fraction of the particles in the container was The packing fraction is defined by the total mass of the packing particles divided by the product of the packing volume and the density of particles. The frequencies of forced vibration were 0.1, 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 Hz and the strokes of the piston were 10, 50, and 80 mm. In our experiments, we prepared two kinds of container whose inner lengths were 200 mm and 150 mm as shown in Fig.3. The length of the container was adjusted by inserting the spacers of different size in both sides in front of the end cover. Fig.3 Schematic of the dampers and the inner lengths of the container are 200 mm and 150 mm 3.1 Effect of the frequency of forced vibration Figure 4 shows the damping force vs. displacement curves and Fig. 5 shows the damping force vs. velocity curves, when the frequencies of forced vibration are 0.1 Hz, 1.0 Hz, 3.0 Hz and 5.0 Hz with constant stroke of 50 mm in the container whose inner length is 200 mm. Clockwise rotation of the damping force vs. displacement curve is corresponding to the time development.from Fig.4, we have found quite interesting results that the damping force characteristics clearly depend on the frequency of forced vibration and the damping force vs. displacement curves are drastically changed with the frequency. That is, the damping force vs. displacement curve of the frequency of 0.1 Hz indicates the typical hardening type property, and the damping force vs. displacement curve of 1.0 Hz is slightly different from the curve of the frequency of 0.1 Hz. The damping force vs. displacement curves of 3.0 Hz and 5.0 Hz are extremely different from the curves described above. The damping force takes maximum value little after the piston reaches the dead centers, and then after that, the damping force decreases with the displacement. When the frequency of forced vibration is low (0.1 or 1.0 Hz), acceleration of the piston is small and the force acting on the particles in front of the piston are also small. Then the particles move into the front space without strong restoring and frictional forces. In the first stage, just after the piston passing through the dead centers, the damping force mainly comes from inertial force of the particles in the damper, because some empty space exists in front of the piston in the direction of the movement and the local packing fraction is smaller than the average value. In this stage, most of the particles which are pushed by the piston move into such space in front of the piston. In the second stage, the damping force increases because of increase of the compression stress of the particles. Number of the particles in front of the piston increases and the stress force of the particles also increases. In the third stage, the damping force is almost constant, because the increase of stress force due to the compression of the particles is balanced with the decrease of stress force due to the movement of the particles to the opposite direction of the displacement of the piston. On the other hand, when the frequency of forced vibration is relatively high (3.0 and 5.0 Hz), behaviors of the particles in the damper can be explained as follows. In the first stage, just after the piston passing through the dead centers, the damping force increases rapidly, because empty space decreases because of increase of the particles moving to the opposite direction of motion of the piston before the dead centers with increase of the frequency. In this stage, the particles in front of the piston are compressed rapidly because the particles move into empty space in front of the piston. In the second stage, the damping force decreases gradually, because the particles start to move in the opposite direction of the displacement of the piston after the empty space is almost filled with particles. 106

3 Advanced Experimental Mechanics, Vol.1 (2016) Fig.4 The damping force vs. displacement curves. The frequencies of forced vibration are 0.1 Hz, 1.0 Hz, 3.0 Hz, and 5.0 Hz. The stroke of forced vibration is 50 mm and the inner length of the container of the damper is 200 mm. Time history is corresponding to the clockwise direction on the curves Fig.5 The damping force vs. velocity curves. The frequencies of forced vibration are 0.1 Hz, 1.0 Hz, 3.0 Hz and 5.0 Hz. The stroke of forced vibration is 50 mm and the inner length of the container of the damper is 200 mm 107

4 Y. IDO, M. HANAI, T. KAWAI, K. HAYASHI and A. TOYOUCHI 3.2 Effect of the stroke of forced vibration Figure 6 shows the damping force vs. displacement curves and it shows the effect of the stroke of forced vibration on the damping force, when the inner length of the container is 200 mm. Figure 7 shows the maximum damping force and the damping energy, when the packing fraction is The damping energy is obtained by calculating the area of the loop of the damping force vs. displacement curves. From Fig.6, basic damping force characteristics are independent of the stroke of forced vibration, because the basic feature of the curve shapes is the same. Furthermore, the maximum damping force does not depend on the stroke. The increase of damping force due to the compression of the particles in front of the piston and the kinematic frictional force with the movement of particles is small negligibly, because the stroke of forced vibration (10 mm, Fig.6 The damping force vs. displacement curves describing effect of the stroke of forced vibration on the damping force. The frequencies of forced vibration are 0.1 Hz, 1.0 Hz, 3.0 Hz, and 5.0 Hz. The inner length of the container of the damper is 200 mm. Time history is corresponding to the clockwise direction on the curves Fig.7 Effects of the stroke on the maximum damping force and the damping energy. The packing fraction of the particles is The stroke of forced vibration is indicated in the graph 108

5 Advanced Experimental Mechanics, Vol.1 (2016) 50 mm and 80 mm) is shorter than the length of the damper (200 mm). However, when the frequency of forced vibration is 5.0 Hz, the maximum damping force of the stroke of 80 mm is greater than those of the stroke of 10 mm and 50 mm. The amount of movement of the particles is larger than that in any other conditions, because the maximum velocity of the piston takes the largest value. So, the increase of damping force due to the compression stress of the particles and the kinematic frictional force with the motion of the particles is not negligible, therefore, the damping force becomes strong. 3.3 Effect of the inner length of the container Figure 8 shows the damping force describing the effect of the inner length of the container of the damper. From Fig.8, the damping force of the length of 200 mm is larger than that of the length of 150 mm. Because the number of particles in the damper is different, that is, the number of particles in the container of 200 mm is approximately , on the other hand, the number of particles in the container of 150 mm is approximately Therefore, the number of particles in the container of 200 mm is approximately 1.4 times, so the damping force of the length of 200 mm becomes larger because the compressive stress of the particles and the kinematic frictional force increase due to the increase of the contacts both between particleparticle and between particle-wall. Figure 9 shows the maximum damping force and the damping energy, when the stroke of forced vibration is 50 mm. The damping energy is derived by calculating the area of the closed loop of the damping force vs. displacement curves. Therefore, the damping energy indicates the expending energy per one cycle. From Fig.9, the damping energy of the container length of 200 mm is larger than that of the container length of 150 mm, because the number of contacts between both particle-particle and particle-wall becomes larger with increase of the number of particles in the container. 4. Conclusions In this paper, the damping properties of the damper using the steel particle assemblage were investigated experimentally, especially, effects of the stroke, the frequency of forced vibration and the inner length of the container of the damper on the damping force were examined. It was shown that the damping force depends on the frequency of forced vibration, while the difference between the maximum damping forces of different strokes of forced vibration is small. The damping force characteristics of low frequency is quite different from that of relatively high frequency of forced vibration. The damping force and the damping energy of the damper utilizing the long container is larger than that of the damper using the short container. Acknowledgment This work was partially supported by KAKENHI Grant Number 15K Fig.8 The damping force vs. displacement curves showing effect of the inner length of the container on the damping force. The frequencies of forced vibration are 0.1 Hz, 1.0 Hz, 3.0 Hz, and 5.0 Hz. The stroke of forced vibration is 50 mm 109

6 Y. IDO, M. HANAI, T. KAWAI, K. HAYASHI and A. TOYOUCHI Fig.9 Effects of the length of the container of the damper on the maximum damping force and the damping energy. The stroke of forced vibration is 50 mm. The length of the container of the damper is indicated in the graph References [1] Panossian, H.V.: Structural damping enhancement via non-obstructive particle damping technique, ASME J. Vibration and Acoustics, 19 (1992), [2] Dehghan-Niri, E., Zahrai, S.M. and Rod, A.F.: Numerical studies of the conventional impact damper with discrete frequency optimization and uncertainty considerations, Scientia Iranica A, 19-2 (2012), [3] Zahrai, S.M. and Rod, A.F.: Shake table tests of using single-particle impact damper to reduce seismic response, Asian Journal of Civil Engineering, 16-3 (2015), [4] Sanchez, M., Rosenthal, G. and Pugnaloni, L.A.: Universal response of optimal granular damping devices, J. Sound Vibration, 331 (2012), [5] Du, Y., Wang, S., Zhu, Y. and Li, L.: Performance of a new fine particle impact damper, Advances in Acoustics and Vibration, 2008 (2008), Article ID [6] Lu, Z., Masri, S.F. and Lu, X.: Studies of the performance of particle dampers attached to a twodegrees-of-freedom system under random excitation, Journal of Vibration and Control, 17 (2011), [7] Saeki, M.: Energy dissipation model of particle dampers, 50th AIAA/ASME/ASCE/ASC Structures, Structural Dynamics, and Materials Conference, (2009), AIAA, [8] Zahrai, S. M. and Rod, A. F.: Effect of Impact Damper on SDOF System Vibrations under Harmonic and Impulsive Excitations, Journal of Physics: Conference Series, 181 (2009), [9] Inoue, M., Yokomichi, I. and Hiraki, K.: Particle damping with granular materials for multi degree of freedom system, Shock and Vibration, 18 (2011), [10] Takahashi, Y. and Sekine, M.: Examination of Particle Behavior in Container on Multi-Particle Collision Damper, Machines, 3 (2015), [11] Ido, Y. and Hayashi, K.: Damping force of a damper utilizing a spherical particle assemblage, Proc. 15th International Conference on Experimental Mechanics, (2012), [12] Ido, Y., Hayashi, K. and Kawai, T.: Damping Force of a Semiactive Damper Utilizing Magnetic Particles under Applied Magnetic Field, International Journal of Applied Electromagnetics and Mechanics, 39 (2012), [13] Kawamoto, R., Ido, Y. and Hayashi, K.: Influence of Installation Angle of a Damper Using a Magnetic Particle Assemblage on Damping Force under Applied Magnetic Field, Journal of the Japan Society of Applied Electromagnetics and Mechanics, 23 (2015),