Damped Dynamic Vibration Absorber Research Articles

High-frequency disturbance force suppression mechanism of a flywheel equipped with a flexible dynamic vibration absorber

Flywheels generate speed-related disturbances and induce micro-vibrations that influence the performance of high-sensitivity instruments on board. This study addresses dynamic modeling and disturbance force suppression of the flywheels due to its inherent characteristic structural modes. The disturbance force transmission of a rotating flywheel due to a unit radial force applied at the rim of the wheel body is reported using the three-dimensional finite element method and frequency response function–based substructuring method. The characteristic structural modes for the radial and axial disturbance forces are identified. The axial deformation–dominated flapping mode and the radial deformation–dominated transverse mode will contribute most to the axial and radial disturbance forces, respectively. A flexible ring structure, which is rested on the arms of the wheel body through independent viscoelastic pads and simultaneously in contact with the inner rim of the wheel body by independent resilient cushion members, is proposed to function as a damped dynamic vibration absorber. The modes of the dynamic vibration absorber and the modes of the flywheel equipped with the dynamic vibration absorber are analyzed. It is shown that the dynamic vibration absorber is effective to suppress both the radial and axial disturbance forces at the characteristic structural modes under different rotational speeds, provided that the loss factor of the complex elastic modulus for the viscoelastic pads is larger than 0.2 and the proportional damping constant for the stiffness matrix is larger than 6 Ns/m. Experimental analyses are conducted on a flywheel with a well-designed dynamic vibration absorber to validate the theoretical findings. Modal tests and disturbance force measurements are carried out for the flywheel with/without the dynamic vibration absorber. It is shown that the identified characteristic structural modes will contribute remarkable peaks for the radial and axial disturbance forces. The proposed dynamic vibration absorber is capable to suppress the high-frequency disturbance forces efficiently under different rotational speeds.

Optimal Design of a Hysteretic Damped Dynamic Vibration Absorber Based on Stability Maximization Criterion

Optimal Design of a Hysteretic Damped Dynamic Vibration Absorber Based on Stability Maximization Criterion

Optimization of Response of a Dynamic Vibration Absorber Forming Part of the Main System by the Fixed-point Theory

In the classic form of the Dynamic Vibration Absorber (DVA), a damped DVA is attached to an undamped primary mass, and the main tuning objective is to minimize the dynamic response of the primary mass. Recently proposed structural systems with the selfcontrol ability such as controlled mega-substructure and core tubes with suspension systems use part of the main structure as a dynamic vibration absorber. Because the DVA in the self-control structural systems is a part of the main structure, the control objective of these kinds of systems is dual not only to limit the motion of the primary system but also to reduce the vibration of the DVA. In the present study, the simplified classic model of the DVA with the primary mass under the harmonic excitation is studied and the fixed-point theory is used to derive the optimum parameters of the DVA to minimize the maximum displacement and acceleration responses of the DVA. The effects of different design parameters such as the mass and stiffness ratios of the DVA on the response of the system are investigated. It is shown that the coordinates of one of the fixed points in both displacement and acceleration responses of the DVA are independent of the natural frequency and damping ratios. This point plays an important role in the optimization procedure. For a specific range of the mass ratios of the DVA, the maximum response of the DVA is larger than that of the primary mass; therefore, optimization based on the response of the DVA yields a better result for the self-control structural system.

Optimization of damped dynamic vibration absorber to control chatter in metal cutting process

This paper deals with finding the optimum parameters of a damped dynamic vibration absorber (DVA) to control chatter in metal cutting systems. The performance of conventional damped DVA is compared with the proposed skyhook damper in which the damper of the absorber system is connected between the absorber mass and an inertial reference in the sky, referred to as a skyhook damper. The damped DVA is optimized by reducing the magnitude in the positive side and increasing it in the negative side of the real part of the frequency response function of the main system. The optimum frequency ratio and the damping ratio of the damped DVA for the undamped and damped main system are obtained using analytical solutions and a numerical optimisation technique, viz genetic algorithm, respectively. The performance of the proposed skyhook damper is marginally better than the conventional type of damped DVA in controlling the vibration of the main system. This is verified by analyzing both the proposed and conventional models using finite element method-based commercial software ANSYS.

Optimal design of vibration absorber using minimax criterion with simplified constraints

In this paper, a minimax design of damped dynamic vibration absorber for a damped primary system is investigated to minimize the vibration magnitude peaks. Moreover, to reduce the sensitivity of the primary system response to variations of the forcing frequency for a two-degree-of-freedom system, the primary system should have two equal resonance magnitude peaks. To meet this requirement, a set of simplified constraint equations including distribution characteristics of the resonant frequencies of the primary system is established for the minimax objective function. The modified constraint equations have less unknown variables than those by other authors, which not only simplifies the computation but also improves the accuracy of the optimal values. The advantage of the proposed method is illustrated through numerical simulations.

Min-max criterion to the optimal design of vibration absorber in a system with Coulomb friction and viscous damping

In this paper, an optimal design of damped dynamic vibration absorber using minimax method for a primary system with Coulomb friction and viscous damping is presented. Meanwhile, to reduce sensitivity of the primary system response to the variations of the forcing frequency, a set of constraint equations that include the distribution characteristic of the resonant frequencies of the primary system is established for the optimal design. Effectiveness of the proposed design is illustrated through numerical simulations. The formulations and results in this paper extend previous results given by Den Hartog and Pennestri.

2009 動吸振器系の不動点を用いた質量測定 : 第4報 : 質量の測定(G05-2 振動低減技術,G05 機械力学部門)

The performance of a mass measurement system with a damped dynamic vibration absorber was studied xperimentally. The measurement system utilizes the fixed point of a mass-spring system with a dynamic vibration absorber so that mass is estimated independently of damping in the absorber. It is characterized by using the phase-looked loop to achieve the tuning condition. The principle of measurement was described based on a mathematical model. A measuring apparatus was designed and fabricated. Several basic characteristics were studied experimentally. The average error of measurement was within 0.2%.

The Effect of Mass Ratio and Air Damper Characteristics on the Resonant Response of an Air Damped Dynamic Vibration Absorber

In this paper, it is shown that, a road vehicle 2DOF air damped quartercar suspension system can conveniently be transformed into a 2DOF air damped vibrating system representing an air damped dynamic vibration absorber (DVA) with an appropriate change in the ratio µ of the main mass and the absorber mass i.e. when mass ratio µ >> 1. Also the effect of variation of the mass ratio, air damping ratio and air spring rate ratio, on the motion transmissibility at the resonant frequency of the main mass of the DVA has been dis- cussed. It is shown that, as the air damping ratio in the absorber system increases, there is a substantial decrease in the motion transmissibility of the main mass system where the air damper has been modeled as a Maxwell type. Optimal value of the air damping ratio for the minimum motion transmissibility of the main mass of the system has been determined. An experimental setup has been designed and developed with a control system to vary air pressure in the damper in the absorber system. The motion transmissibility characteristics of the main mass system have been obtained, and the optimal value of the air damping ratio has been determined for minimum motion transmissibility of the main mass of the system

Design and Dynamic Response Analysis of Rail with Constrained Damped Dynamic Vibration Absorber

Rail traffic noise is mainly caused by the vibration of wheel and rail. Pasting the constrained damped dynamic vibration absorber on the rail is a common vibration and noise reduction measure. To analyze the effect of rail with constrained damped dynamic vibration absorber, we use the finite element software to establish single and multi-layered rail model with constrained damped dynamic vibration absorber, with the consideration of irregularity effect. We use the moving load to load and transient dynamic response to analyze. The results show that: the rail installed with constrained damped dynamic vibration absorber has a good vibration-reducing effect. Compared to the rail and track where the constrained damped dynamic vibration absorber is not installed, the maximum vertical displacement and acceleration of the rail and track where a single-layered constrained damped dynamic vibration absorber is installed was reduced by 65% to 68%; the maximum vertical displacement and acceleration of the rail and track where a three-layered constrained damped dynamic vibration absorber is installed was reduced by 70% to 72%.

OPTIMAL DESIGN OF DAMPED DYNAMIC VIBRATION ABSORBER FOR DAMPED PRIMARY SYSTEMS

This study focuses on the optimum design of the damped dynamic vibration absorber (DVA) for damped primary systems. Different from the conventional way, the DVA damper is connected between the absorber mass and the ground. Two numerical approaches are employed. The first approach solves a set of nonlinear equations established by the Chebyshev’s equioscillation theorem. The second approach minimizes a compound objective subject to a set of the constraints. First the two methods are applied to classical systems and the results are compared with those from the analytical solutions. Then the modified Chebyshev’s equioscillation theorem method is applied to find the optimum damped DVAs for the damped primary system. Various results are obtained and analyzed.

Optimal design of a damped dynamic vibration absorber for vibration control of structure excited by ground motion

Optimum parameters of a dynamic vibration absorber of non-traditional form have been derived for suppressing vibration of a single degree-of-freedom system due to ground motion. The reduction of transmission of motion from the support to the mass of the structure is compared for the cases of using the traditional and the proposed dynamic absorbers. Under the optimum tuning condition of the absorbers, it is proved analytically that the proposed absorber provides a larger suppression of resonant vibration amplitude of the primary system excited by ground motion than the traditional absorber.

APPLICATION OF A TUNABLE ELECTROMAGNETIC DAMPER IN SUPPRESSION OF STRUCTURAL VIBRATION

An electromagnetic damper is developed to construct a tunable damped dynamic vibration absorber. The developed vibration absorber can suppress vibration of a structure subjected to a harmonic force with variable frequency. The damping of the vibration absorber can be adjusted on-line to cope with variation in the exciting frequency. The electromagnetic damper is composed of an electromagnet and a copper plate attached to the absorber mass. The relationship between the damping ratio and the damper current is discussed analytically. An experiment is conducted to determine the damping coefficients. A clamped-clamped beam is used as a primary system. The damper is connected between the absorber mass and the ground. This setup is referred to as skyhook dynamic vibration absorber in this study. The performance of a skyhook dynamic vibration absorber is compared with that of a groundhook dynamic vibration absorber where a damper is connected between the primary mass and the absorber mass. Two algorithms are proposed to tune the damper on-line. The first algorithm is FFT-based while the second one is rms-based. The control algorithms are tested against three frequency varying scenarios: multi-step change, linear change, and single-step change plus impact disturbance. Merits of each of the control algorithms are demonstrated.

Application of a Dynamic Vibration Absorber to a Piecewise Linear Beam System

This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.

Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response. 2nd Report. Hysteretic Damped Absorber.

For a large number of engineering problem, we may encounter hysteretic damped systems. Internal damping in the viscoelastic materials and structural damping at a joint, support, bearing, or other assembly are considered to be the hysteretic damping. The principal difference between the viscous damping and the hysteretic damping is that for the viscous damping the energy dissipated per cycle depends linearly on the frequency of vibration, whereas for the hysteretic damping it is independent of the frequency. In this paper, we derive the exact algebraic solutions for design of a hysteretic damped dynamic vibration absorber attached to undamped or damped primary systems for various performance indexes. The absorber is designed on the basis of the H∞ optimization, that is, minimization of the maximum amplitude response of the primary systems to periodic excitation. The solutions obtained here are compared with the approximate ones based on the classical method familiarly called the fixed-points theory.

Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model

In this paper, we propose a dynamic vibration absorber (DVA) with an air damper consisting of a piston and a cylinder. First, it will be shown that the air damper can conveniently be represented by the Maxwell model where a spring element and a dashpot are connected in series. The air damper has no ability to return the piston to its original position. For this reason, it is necessary for the piston to be supported by a spring which is placed in parallel with the damper. The air damped DVA can then be modeled by the three-element model. Many studies have been done on the Voigt type of DVA, and the accurate expressions of optimum tuning and damping parameters have already been derived by Hahnkamm and Brock et al. However, only a few papers have been published on the three-element type of DVA, and reliable expressions for it have not been derived until now. Therefore, we began our work by trying to derive expressions for optimum parameters of the three-element type of DVA. It was clear that the optimized three-element type of DVA is superior to the conventional Voigt type of DVA. The optimum parameters which we obtained from our expressions were tested on a vibratory model. The experiments showed that the our expression is very useful for designing the air damped DVA.

AN APPLICATION OF CHEBYSHEV'S MIN–MAX CRITERION TO THE OPTIMAL DESIGN OF A DAMPED DYNAMIC VIBRATION ABSORBER

In this paper an application of the Chebyshev's criterion to the optimal design of the damped dynamic vibration absorber is presented. The results are summarized in ready-to-use computational graphs. The reliability of the proposed method is demonstrated through a comparison of the numerical results obtained by different authors.

Vibration Control Using an Air Damped Dynamic Vibration Absorber. Theory of the Three-Element Type of Dynamic Vibration Absorber.

In this paper, we propose a dynamic vibration absorber (DVA) with an air damper consisting of a piston and a cylinder. The dynamic behavior of the air damper can conveniently be represented by the Maxwell model where a spring element and a dashpot are connected in series. The air damper has no ability to return the piston to its original position. For this reason, it is necessary for the piston to be supported by a spring which is placed in parallel with the damper. The air damped DVA can then be modeled by the three element model. Many studies have been done on the Voigt type of DVA, and the accurate expressions of optimum tuning and damping parameters have already been derived by Hahnkamm and Brock et al. However, only a few papers have been published on the three element type of DVA, and reliable expressions for it have not been derived until now. Therefore, we began our work by trying to derive expressions for optimum parameters of the three-element type of DVA. It was clear that the optimized three element type of DVA is superior to the conventional Voigt type of DVA. The optimum parameters which we obtained from our expressions were tested on a vibratory model. The experiments showed that the our expression is very useful for designing the air damped DVA.

Damped dynamic vibration absorber

First Page

Effectiveness of a two‐layer damping treatment partially covering a beam

A damping treatment for an elastic beam consisting of a layer of viscoelastic material beneath an elastic bar is considered. The treatment extends axially over a portion of the beam. Under the assumption of simple end supports and a point force excitation, the vibrational response of the damped structure is analyzed by expanding the beam displacement in a series of normal modes. The normal modes for the bar are taken to be those of a free‐free beam and are therefore coupled to each of the simply supported beam modes. A numerical procedure is used to calculate the modal response of the beam from the system of coupled equations. The damping effectiveness of the partial treatment is determined by evaluating the modal loss factor as a function of the extent of coverage. Several equivalent methods are examined to evaluate conveniently the modal loss factor. An efficient numerical scheme is to evaluate the loss factor using the real and imaginary parts of the damped resonance frequency. The results obtained are interpreted with the aid of asymptotic limits for the loss factor of the damped dynamic vibration absorber, and conclusions regarding sensitivity of damping effectiveness to extent of coverage are drawn.

Analysis of Parallel Damped Dynamic Vibration Absorbers

The analysis of parallel damped dynamic vibration absorbers is presented. The system considered is essentially a modification of the conventional damped vibration absorber and consists of adding, in parallel, a subsidiary undamped absorber mass in addition to the damped absorber mass. The analysis clearly shows that it is possible to obtain an undamped antiresonance in a dynamic absorber system which exhibits a well-damped resonance. While the bandwidth of frequencies between the damped peaks is not significantly increased, the amplitudes of the main mass are considerably smaller within the operational range of the absorber. The damped absorber mass and the main mass attain null simultaneously so that the vibratory force is transmitted directly to the undamped absorber. Numerical results are presented for the special case when the absorber masses have the same magnitude. Two cases of tuning have been considered: (a) when the absorber masses are tuned to the frequency of the main mass, and (b) when the absorber masses are tuned to the so-called favorable tuning frequency. Comparison of the results with those of the conventional absorber indicates that the parallel damped dynamic vibration absorber has definite advantages over the conventional damped vibration absorber.