adaptive vibration control by a variable-damping dynamic absorber using er fluid

Shoshi Hidaka Isuzu Advanced Engineering Center, Ltd., 8 Tuchidana, Fujisawa 252-8501 JAPAN

Young Kong Ahn

Shin Morishita

Department of IVlechanical Engineering, Yokohama National University,

79-5 Tol<ivi/adai, Hodogaya-ku, Yokohama 240-8501 JAPAN

Adaptive Vibration Control by a Variable-Damping Dynamic Absorber Using ER Fluid This paper describes a variable-damping dynamic absorber applying Electrorheological (ER) fluid to the damping element of a conventional-type dynamic absorber. A prototype of variable-damping dynamic absorber was constructed and its performance was verified with a three-story structural model. The special ability of the present dynamic absorber is to reduce the vibration amplitude at .several frequencies by a single dynamic ab.wrber. ER fluid is functional fluid whose yield shear stress can be changed by the applied electric field strength. Because of its peculiar property, ER fluid has been applied to various mechanical components such as shock absorbers and engine mounts for vehicles, clutches, valves, etc. One of the practical ways in applying ER fluid to mechanical components may be to expand the performance of conventional mechanical components by combining ER fluid effectively with them. In this sense, this paper shows a successful application of ER fluid to a conventional-type dynamic absorber. An adaptive neural network control system composed of a forward model network for system identiflcation and a controller network was introduced to control the variable-damping element of the dynamic absorber. The numerical simulations show good agreements with the experimental results.

1 Introduction Vibration control devices are generally classified into three

types: passive, semi-active and active actuators. Passive actuators have reliable performance but have some limitations due to fixed system parameters. Though active ones show the highest performance of the three types, they are the most expensive and cannot exhibit their ability without some control systems. On the contrary, semi-active vibration actuators characterized as possessing variable-damping and/or variable-stiffness show good performance with control systems, and may keep its reliable performance even if some trouble occurs in the control systems.

Many researchers working on vibration reduction in structures have introduced dynamic absorbers as actuators (Sciulli and In-man, 1997; Sun et al., 1995), which should be tuned corresponding to the frequencies of vibration to be reduced. Because it is generally known that one dynamic vibration absorber (or dynamic absorber) can reduce the amplitude of vibration at a single frequency (Den Hartog, 1983), the number of dynamic absorbers should be the same as that of the frequencies of external force. Other recent researches on dynamic absorbers have included the investigation of vibration reduction performance when random excitation is applied to a structure (Asami et al., 1993; Nishimura et al., 1988), or on the study of optimized design methods for a structure subjected to oscillation with more numbers of frequencies than that of dynamic absorbers (Morishita et al., 1992).

In this paper, ER fluid is applied to the damping element of a conventional dynamic absorber to realize a variable-damping dynamic absorber, which may reduce the amplitude at several frequencies of vibration with a single dynamic absorber. The variable-damping dynamic absorber was constructed and its performance was investigated with a three-story structural model. An adaptive neural network control system was introduced for tuning the damping property of the dynamic absorber corresponding to the vibration frequencies to be reduced.

Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 1998; revised Dec, 1998. Associate Technical Editor; D. J. Inman.

2 Experimental Setup 2.1 Variable-Damping Dynamic Absorber. A variable-

damping dynamic absorber using ER fluid was designed to reduce vibrations at several frequencies as shown schematically in Fig. 1. The present dynamic absorber was planned to work in the horizontal direction. The mass of the dynamic absorber was connected to four coil springs, which were fixed to the housing of the dynamic absorber, and supported by several spherical ruby balls. A pair of electrodes were set up between the mass and the floor, whose gap filled with ER fluid was kept constant to 1.0 mm by the ruby balls. The principal size of the dynamic absorber was 150 mm long, 90 mm wide and 45 mm high.

The performance of the variable-damping dynamic absorber was examined experimentally with a three-story structural model mounted on a shaking table, as shown in Fig. 2. Three floors were fixed at both ends to plate springs, and the variable-damping dynamic absorbers were installed on each floor. The height of structural model was 660 mm, and the floor plates of 100 mm long, 200 mm wide and 20 mm thick were placed at intervals of 200 mm. Total weight of the model was 7.5 kg.

Three dynamic absorbers were prepared corresponding to the natural frequencies of the structural model, which were 4.0, 11.0 and 16.5 Hz for the first, second and third natural frequencies, respectively, including the masses of dynamic absorbers. The dynamic absorber for the first natural frequency was placed on the third floor, the one for the second natural frequency on the first floor and the one for the third on the second floor. The masses of the dynamic absorber were 100 g for the first natural frequency, and 50 g for the second and third ones. The total weight of the masses of dynamic absorbers were planned to be less than 2% of the total weight of the structural model.

2.2 ER Fluid. ER fluid is known as a functional fluid whose yield shear stress can be varied by the applied electric field strength, and this unique fluid was known to the world through the patent obtained by W. Winslow in 1948. Since then, not a few researchers have tried to develop various types of ER fluid with higher performance and better stability (Block and Kelly, 1988; Jordan and Shaw, 1989), and have tried to apply ER fluid to mechanical components such as variable dampers, clutches,

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350 O 1.6

(a) sohemalic view

Coil spnnfl

(b) Side view

Fig. 1 Variable-damping dynamic absorber

brakes, valves, etc. (Morishita and Ura, 1993; Stanway et al., 1996).

ER fluids are classified into two types: colloidal suspension and homogenous liquid type. ER suspension is a dispersion of semiconducting particles in dielectric oil, and the particles are aligned in chain structures being polarized under electric field. The tensile force of the chain structures may produce the increment of yield shear stress when ER suspension is subjected to shear flow or pressure flow. In case of homogeneous ER fluids, the direction of molecules or the direction of cluster of molecules is mainly governed by the direction of electric field, and the viscosity itself can be controlled by the applied field strength. Liquid crystal is known as one of the homogeneous ER fluids. In this study, ER suspension was selected because it showed wide variation of yield stress compared with homogeneous type ER fluids, and because fluid of varying zero-field plastic viscosity could be easily prepared.

Figure 3 shows the yield shear stress variation due to the applied electric field strength. The ER fluid used in the present experiment

Dynamic absorbers

Plate ~ spring

) 100 200 300 400 500 600 700

Shear rate [s'^]

Fig. 3 Siiear stress variation under eiectric fieid

was the suspension of sulfonated polystyrene-co-divinylbenzene particles in silicone oil (Asako et al., 1995). These characteristics were measured by a rotational viscometer under AC electric field of 50 Hz. As the applied electric field was strengthened, the yield shear stress increased, while the post-yield plastic viscosity exhibited as the slope of each line was not affected by the electric field, which means that ER suspension can be characterized as Bingham plastic model. The Bingham plastic model is expressed by

T = To(E) sign (v) + /J,7 (1)

where, T is shear stress, y is shear rate, TO(E) is yield shear stress under the applied electric field strength, E, and fx is Newtonian viscosity.

2.3 Typical Characteristics of tlie Dynamic Absorber. After the three variable-damping dynamic absorbers were placed on each floor of the structural model, the frequency response of the structure was measured to know the typical characteristics of the present dynamic absorber. The absorbers on the third, second and first floors were designed to reduce vibration amplitude of the first, third, and second natural frequencies, respectively. The experiments were conducted under three conditions:

(I) The mass of dynamic absorber was fixed on the floor. (II) The dynamic absorber was actuated without ER fluid.

(Ill) The dynamic absorber was actuated with ER fluid in the gap of electrodes.

Figure 4 shows the frequency response when the shaking table

Fig. 2 Experimental setup

6 8 Frequency [Hz]

Fig. 4 Frequency responses of the structural model witti dynamic absorbers

374 / Vol. 121, JULY 1999 Transactions of the ASME


11 12 Frequency [Hz]

13

Fig. 5 Response curves of the structural model with the variable-damplrig dynamic absorber at various electric field strengths

was excited at an amplitude of 0.1 mm by swept-sine signal from 2.0 to 20.0 Hz. When all the masses were fixed (Condition (I)), three natural modes appeared around 4.0, 11.0 and 16.5 Hz. Under the Condition (II), the response peaks were divided into two at both sides of each of these natural frequencies, between which it showed low responses as deep notches as shown in Fig. 4. Introducing ER fluid to each of the dynamic absorbers (Condition (III)), the peak value of the response curve decreased because of the damping effect of ER fluid without electric field.

Next, the effect of applied electric field on the response of the structure was examined for each dynamic absorber. An example of response variation is shown in Fig. 5 around the second natural frequency, when the electric field to the dynamic absorber was strengthened up to 400 V/mm. As the electric field was increased, the response varied markedly as shown in Fig. 5 because of the friction damping change between the mass and the floor.

3 Adaptive Control of Structures

3.1 Control Scheme. The purpose of this paper is to investigate the performance of the variable-damping dynamic absorber using ER fluid. The damping property should be controlled by some control system so that the vibration response of the multi-degree-of-freedom system subjected to external forces with more than two frequencies may be decreased by a single variable-damping dynamic absorber. The control scheme carried out here is as follows;

(a) The vibration response of the structure at the lowest natural frequency should be decreased by the basic function of the tuned dynamic absorber.

(b) For the vibration reduction at higher natural frequencies, the mass movement in the dynamic absorber might be constrained by changing the applied electric field to ER fluid. When the mass velocity is reduced by the "brake" of ER fluid during oscillation, the corresponding reaction force should be transmitted to the floor where the dynamic absorber is installed. Because the reaction force has a direction contrary to the external force, it may reduce the external force and the structural response may be decreased to some degree.

3.2 Neural Network Control System. Due to learning and nonlinear input-output transformation capability, neural networks are successfully applied in the field of pattern recognition, system identification and control, and they are found to be a very promising tool for next generation technology. Neural networks are also known to be applicable as an adaptive control system with multi-input and multi-output system capabilities. In the selection proce

dure of the control system for the variable-damping dynamic absorbers using ER fluid, a neural network was chosen because it might have high adaptability for the change of property of ER fluid with the passage of time and for the change of dynamic characteristics of structures, in addition to the capabilities of neural networks mentioned above.

A block diagram of the adaptive neural network control system is shown in Fig. 6. The present control system was composed of a forward model network for structural identification and a controller network. Each network was a two-layered network to reduce the computing time in the experiment. The forward model network identified the displacements of the floors at each time step using the external force, the control signals, the identified displacement and their time history. On the other hand, the control signal was produced by the controller network using the external force, the identified displacement from the forward model network, the displacement of mass of the dynamic absorber and their time history. 10 signals in the past time steps were used as the time history of each input signal, concerning accuracy as well as operation time. A sigmoid function was used as the transfer function of each neuron, and the parameters to be updated were connecting weight, threshold value and slope of the transfer function. The steepest descent method was used as learning algorithm, where the learning constants in the forward model network were 0.2, 0.1 and 0.1 for the connecting weight, the threshold value and the slope of the transfer function, respectively, and 0.5, 0.25 and 0.1 in the controller network.

3.3 Numerical Simulation. The numerical simulations were conducted to estimate the performance in vibration reduction of the structural model by changing the damping property of a single dynamic absorber. The dynamic absorber set on the third floor, which was tuned for the first natural frequency, was assumed to activate as an actuator. The masses of other two dynamic absorbers on the first and second floor were fixed on the floor so that no contribution might be produced on vibration reduction by these dynamic absorbers. The target to be controlled was set to the displacement of the third floor. Then, the structural model in Fig. 3 is simplified into a four degree-of-freedom system including the mass of the dynamic absorber as shown in Fig. 7. Introducing coordinates in Fig. 7, Eq. (1) is expressed as.

T = To(£:) sign (7) -H h (2)

External force Forward model

Structural system

Dynamic absorber disp.

Fig. 6 Neural network control system

Journal of Vibration and Acoustics JULY 1999, Vol. 121 / 375


o VTZ^^^ i i-iESTt^.

1 M i

EIS V

A JC-]

M.

Fig. 7 Four degree-of-freedom system

and the total damping force, D, can be estimated by multiplying the area of electrode, S,

D = ToiE) sign iy)S + lJiS(xj - i s )

where h is the gap of the electrodes. The yield shear stress, expressed from the experimental investigation as

To= 1.51£' '*X 10" '

(3)

(4)

In the numerical simulations, the response of the structural model was calculated by integrating the equation of motion using the Newmark-/3 method as the teaching signal for the neural network control system. The time interval for the numerical integration was set to 1.0 X 10"' sec. The simulation was conducted under Conditions I-III, in Sec. 2.3, and also Condition III with the neural network control system.

The response of the structural model on the third floor is shown in Fig. 8, when the shaking table was excited by swept-sine signal from 2.0 to 18.0 Hz at the rate of 0.02 Hz/s. The response of the structural model was controlled efficiently at each natural frequency, and the applied electric field strength was varied adap-tively according to the frequencies of the external force by the neural network control system.

The displacements of the third floor and the mass of the dynamic absorber are shown in Fig. 9, when the structural model was excited at the second natural frequency. When the dynamic absorber was controlled, the amplitude of mass vibration was increased, whereas that of the response of structural model was controlled to some degree.

Figure 10 also shows the performance of the dynamic absorber, which is the frequency response of the structural model excited by superpositioned sinusoidal external forces having both the first and the second natural frequencies. The power spectral density of acceleration (G,) was normalized by that of the acceleration (Go) under Condition I. The response at the first natural frequency was decreased remarkably under Condition III, without control. Because the response peaks at the first and second natural frequencies under Condition I were very large, the normalized amplitude was very small at these frequencies. And because the response at the other frequencies was small enough under Condition I, the normalized amplitude showed comparatively large variation.

When the dynamic absorber was controUed, the response at the first natural frequency showed less effectiveness, while the ampli-

1st mode With dynamic absorber

15 16 17 Frequency [Hz]

Fig. 8 Displacement responses of tlie structurai modei (numerical simulation, swept-slne)

tude ratio was decreased at the second natural frequency by controlling the applied electric field strength as shown in Fig. 10. The amplitude ratio at the first natural frequency was increased because the kinetic energy of the mass of the dynamic absorber tuned for the first natural frequency which was to be used for reduction of the amplitude was distributed to the other natural frequencies. Since velocities were used in neural networks, the controller produced the control voltage to reduce the larger velocity amplitude of the second mode than that of the first mode.

3.4 Experimental Verification. Figure 11 shows the vibration control system of a three-story structural model with the variable-damping dynamic absorber set up on the third floor. Displacements of the shaking table, the third floor, and the mass of

Absorber mass , 3rd Floor

Without controi

59.7 59.8

Time [s] 59,9

Fig. 9 Displacement responses of the absorber mass and the third floor, and time history of control signal (numerical simulation, at 2nd natural frequency)



-200 0.0 5.0 10.0 15.0

Frequency [Hz] 20.0

Fig. 10 without

Normalized power spectral density of the system with and control (numerical simulation)

4 6 8 10 12 14 16 18 20

Frequency [Hz]

Fig. 12 Time history of responce (experiment, swept-sine, without control)

dynamic absorber were measured by gap sensors and put into the computer through A/D converters. The sampling interval was set to 1 X 10"' sec. The signal from the gap sensor set up on the third floor was used as the teaching signal for the forward model network in the control system. The control signal was put into a function generator producing a sinusoidal wave of 50 Hz, whose amplitude was varied by DC control voltage. The AC voltage from the function generator were amplified and applied to the electrodes on the dynamic absorber.

The experimental results are shown in Figs. 12 and 13, when the shaking table, on which the structural model was set up, was excited by swept-sine signal from 2.0 to 20.0 Hz at the rate of 0.02 Hz/s. The amplitude was set to 0.1 mm at each frequency. The frequency range of exciting signal included the first, second and third natural frequencies of the structural model. When the structural model was excited around the first natural frequency, the dynamic absorber was set to be not controlled, and the structural model was controlled just passively by the dynamic absorber. Beyond 9.5 Hz of the exciting frequency, a little below the second natural frequency, the controller network started to make signals for the dynamic absorber.

Comparing the top figure of Fig. 12 with that of Fig. 13, the amplitude of the third floor was reduced around the second natural frequency. The amplitude around the third natural frequency.

A/D, D/A converter

Computer

Signal from gap sensors

V///////////A

V//////////M

Function generator

^ O 0 o-"

Shaking table

High-Voltage Power Supply

Exciter

Fig. 11 Experimental apparatus of vibration control system and the structural model

Journal of Vibration and Acoustics

however, showed little difference between the two. This might be caused by the capacity limitation of the neural network control system used in the present experiment. Though the parameters to be optimized in the neural networks had been tuned beforehand for the banded random excitations including the second and third natural frequencies of the structural model, the control system could not produce the control signal corresponding to the third natural mode. As shown in the bottom figure of Fig. 13, the control voltage was large enough to give restriction to the mass movement around the second natural frequency, while the control voltage was very small around the third natural frequency. This might be overcome by adding the number of input signals for the controller network or by increasing the number of layers of the networks, but it could not be conducted because of the lack of computer capacity used in the experiment.

The time histories of the response when the structural model was excited at the second and third natural frequencies are shown in Figs. 14 and 15. The control system achieved 67 percent reduction of amplitude at the second natural frequency and 36 percent reduction at the third natural frequency in five seconds by controlling the mass movement of the dynamic absorber. In both cases, the mass of the dynamic absorber was shifted from the equilibrium position, which means that the mass repeated to be restricted and to be released so that the phase difference between the mass and flie structure might produce the effect of amplitude reduction.

3rd Floor

2.5 4 6 8 10 12 14 16 18 20

Frequency Hz]

Fig. 13 Time history of responce (experiment, swept-sine, with control)

JULY 1999, Vol. 121 / 377


Control start

is (0 c c O O)

Ow

0.5

0.0

l^H SHI

niT^ « • • •

H H H H

^ ^

n • mfWTrrTTti'-n-

nilULbuuL -10 10 20

Time [s] * 30

Fig. 14 Time iilstory of responce (experiment, at 2nd naturai frequency)

4 Conclusions In this study, ER fluid was applied to the damping element of a

conventional-type dynamic absorber, and its performance was

Control start

,—, h E +-< c 0) E 0) ^ a.

Q

5" ^

p c c Q D)

C M

0,3

0.0 -0.3 -0.6 2.0 1,0 0.0

-1.0 -2.0 1.5

1 0

0.5

nn

•

•

- - •

V

1

•*#**»• pHN'v'Hrv

Fig. 15 Time tiistory of responce (experiment, at 3rd naturai frequency)

investigated with a three-story structural model. It is shown experimentally that the damping property of the dynamic absorber using ER fluid can be controlled by applying electric field, which may cause variation in the response of the structure when it is setup on a structural model. Furthermore, in the case when a dynamic absorber is tuned for the first natural frequency and a structure is subjected to an excitation by the first and upper natural frequencies, it is shown that the vibration response at the first and second natural frequency of the structure can be reduced by controlling the damping property of the variable-damping dynamic absorber by an adaptive neural network control system.

Acknowledgment

This research was partly supported by Grant-in-Aid for Scientific Research (No. 1(3650235) from the Ministry of Education of Japan.

References Asako, Y., Ono, S., and Aizawa, R., 1995, "Properties of Electrorheological Fluids

Containing Sulfonated Poly(Styrene-co-Divinylbenzene) Particles," Proceedings of the 5th International Conference on Electro-Rheological Fluids, Magneto-Rheological Suspensions and Associated Technology, pp. 342-349.

Asami, T., Momose, K., and Hosokawa, Y., 1993, "Approximate Expression for Design of Optimal Dynamic Absorbers Attached to Damper Linear Systems (Optimization Process Based on the Minimum Variance Criterion)," Transactions of the Japan Society of Mechanical Engineers, Vol. 59, No. 566, Series C, pp. 2962-2967.

Block, H., and Kelly, J. P., 1988, "Electro-rhology," Journal of Physics D: Applied Physics. Vol. 12, No. 12, pp. 1661-1677.

Den Hartog, J. P., 1985, Mechanical Vibrations, 4th ed., McGraw-Hill Book Company, pp. 87-105.

Jordan, T. C , and Shaw, M. T., 1989, "Electro-rheology," IEEE Transactions on Electrical Insulation, Vol. 24, pp. 849-879.

Morishita, S., and Ura, T., 1993, "ER Fluid Applications to Vibration Control Devices and an Adaptive Neural-Net Controller," Journal of Intelligent Material Systems and Structures, Vol. 4-July, pp. 366-372.

Morishita, S,, Kuroda, Y., and Ura, T., 1992, "Adaptive Vibradon Control System with Control Dynamic Damper," Transactions of the Japan Society of Mechanical Engineers, Vol. 58, No. 550, Series C, pp. 1748-1754.

Nishimura, H., Yoshida, K., and Shimogo, T., 1988, "Optimal Dynamic Vibration Absorber for Multi-Degree-of-Freedom Systems (Theoretical Considerations on the Case of Random Input)," Transactions of the Japan Society of Mechanical Engineers, Vol. 54, No. 501, Series C, pp. 1066-1072.

Sciulli, D., and Inman, D. D., 1997, "Active Isolation Design for a Flexible Base," Proceedings of DECT'97, 1997 ASME Design Engineering Technical Conferences, September 14-17, Sacramento, California, DETC97/VIB-4117.

Seto, K., Iwanami, K., and Takita, Y., 1984, "Vibration Control of Multi-Degree-of-Freedom Systems by Dynamic Absorbers (1st Report, On The Design Method for Dynamic Absorbers)," Transactions of the Japan Society of Mechanical Engineers, Vol. 50, No. 458, Series C, pp. 1962-1969.

Stanway, R., Sproston, J. L., and El-Wahed, A. K., 1996, "Applications of ER Fluids in Vibration Control: A Survey," Smart Materials and Structures, Vol. 5, pp. 464-482.

Sun, J. Q., Jolly, M. R., and Norris, M. A., 1995, "Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey," Transactions of the ASME, 50th Anniversary of the Design Engineering Division, Vol. 117, pp. 234-242.



adaptive vibration control by a variable-damping dynamic absorber using er fluid

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