Active Adaptive Vibration Absorbers And Fts Sibration -PDF Free Download

Active adaptive Vibration Absorbers and fts sibration

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Active-adaptive Vibration Absorbers and fts sibration Attenuation Performance Chao Peng, Xinglong Gong CAp hey Laboratory of Mechanical Behavior and Design of Materials, aepartment of Modern MechaniI rniversity of pcience and Technology of ChinaI eefei 230027I China [email protected], [email protected]



Applied Mechanics and Materials Vol 312 263
The aim of this research is to improve working frequency band and vibration attenuation
performance of a vibration absorber Towards this end a mechanical AAVA was designed This
paper is split into four sections Following the introduction section the principle and the vibration
attenuation performance of the AAVA are analyzed in Section 2 Section 3 describes the prototype
of the AAVA and its dynamic property testing Section 4 presents the experiments of the vibration
attenuation effect of AAVA based on a clamped clamped beam The conclusions are summarized in
the final section
Analysis on AAVA
The Principle of the AAVA
To illustrate the working principle a single degree of freedom primary system with the AAVA is
described in Fig 1 The active element is placed between the absorber mass and the primary
system The m p c p k p are the mass damping and stiffness of the primary system respectively
The ma ca k a are the mass damping and stiffness of the AAVA respectively The x p xa are the
displacements of the primary system and the absorber mass respectively The f act is the active
force The f is the harmonic excitation force applied on the primary system
According to the references 7 different values of the parameters in Fig 1 represent different types
of vibration absorbers as shown in Table 1
Fig 1 Schematic view of the primary system Fig 2 Vibration attenuation effect of different
with a tuned vibration absorber types of vibration absorbers
Tab 1 Several typical vibration absorbers
TYPE ka ma f act
TVA constant 0
AVA constant ka ma 2 xa ca x a
AAVA 2 ca x a
The is the frequency of excitation force The and are control efficient of AVA and
AAVA respectively According to Newton s law the equations of motion can be expressed as
ma xa ca xa x p k xa x p f act
m p x p c p x p ca x p xa k p x p k x p xa f f act
From Eq 1 the amplitude magnification coefficient of the primary system with different type
vibration absorbers attached can be obtained as follows
Z m Z k F Z m Fact
Zm Z p Zm Zk Z p Zk
264 Applied Research and Engineering Solutions in Industry
Z k 2 jma a a ma a
Z p m p 2 jm p p p m p p
Where p k p mp p c p 2mp p a ka ma a ca 2ma a The p and p are
the natural frequency and damping ratio of the primary system respectively The a and a are
the natural frequency and damping ratio of vibration absorber respectively For the AAVA and
ATVA a tracks the frequency of excitation force For the TVA and AVA a is fixed at the
natural frequency of the primary system
Comparison of vibration reduction performance
The vibration attenuation effect of the vibration absorbers is defined as the ratio of the amplitude
magnification coefficient of the primary system with and without vibration absorber the dB
expression of the effect is
X p without
Where the X p with and X p without are the amplitude magnification coefficient of the primary
system with and without vibration respectively According to the following parameters
ma mp 0 1 0 8 a 0 04 p 0 08 the effect of vibration absorption capacity can be
calculated
The comparison of four types of vibration absorbers with the same mass ratio and damping ratio
is shown in Fig 2 For the TVA the best vibration attenuation effect occurs at its natural frequency
When the excitation frequency is away from this frequency the effect decreases quickly The AVA
has better effect than TVA close by the natural frequency but the effect also becomes bad For
ATVA its vibration attenuation effect is equal to that of the TVA at its natural frequency and it has
better effect than TVA in the whole adjustable frequency band Nevertheless the superiority of the
ATVA compared with the TVA is not evident because of the large damping At the whole
frequency range the curve of AAVA s attenuation effect is below that of the other types of
vibration absorbers which indicates that the AAVA has the best vibration attenuation effect
The design and dynamic property of AAVA
The prototype of AAVA
According to previous analysis the AAVA has the best vibration attenuation effect compared
with other types of vibration absorbers It means that the AAVA is more suitable for engineering
application In this paper a mechanical AAVA is designed Fig 3 a shows a scheme of the
prototype and Fig 3 b shows a photograph of the prototype
Fig 3 The prototype of AAVA a Scheme b Photograph
Applied Mechanics and Materials Vol 312 265
The absorber mass of the prototype is a closed configuration which is composed of four
individual masses There are two horizontal guides mounted on the absorber mass Four horizontal
sliders can move in horizontal direction along the two horizontal guides This configuration can
make the best use of the space and reduce the size of the AAVA The leaf spring is chosen as the
spring pole because of the large bear load and lateral rigidity The stiffness element of the AAVA is
composed of four leaf springs The span between leaf springs can be changed which causes the
natural frequency of the AAVA changed If the span keeps at a fixed value the AAVA can be
regarded as ATV Four vertical guides mounted on the base are used to make the absorber mass to
move only in vibration direction The mass of the absorber mass is about 4 kilograms and the other
mass is about 1 kilogram
The active force is provided by a small voice coil motor The motor consists of a magnet and
motor coil The magnet is fixed to the absorber mass and the motor coil is fixed to the base When
a current flows through the motor coil an ampere force will be generated between the magnet and
the motor coil The amplitude and direction of the force can be controlled by the current If the
voice coil motor stop working the AAVA can be regarded as a translational ATVA
Dynamic characteristics of the prototype
Using the approaches have been proposed in references 8 9 the dynamic characteristics of the
prototype can be obtained Fig 4 shows the frequency shift property curves and damping property
of the prototype
Fig 4 The experimental results of dynamic property
a The frequency shift property b The damping property
As described in this figure for either the ATVA or AAVA the natural frequency of prototype is
from 19 25Hz to 31 25Hz when the span changes from 26mm to 58mm The damping ratios are
obtained by using the half power bandwidth method It is shown that the average damping ratio of
ATVA are 0 04 and this value is 0 02 for AAVA As the AAVA introduces the active force it can
reduce the damping
Experimental evaluation of the vibration attenuation performance of the AAVA
To evaluate the vibration attenuation effect of the prototype of AAVA a clamped clamped beam
with a pullback weight attached was used as the primary system Fig 5 shows the schematic of the
experimental set up for evaluation of the vibration attenuation performance of the AAVA The first
mode of the beam is bending vibration and the natural frequency of mode is about 26Hz The
AAVA was mainly used to control this mode vibration so it was placed at the center of beam where
the vibration is the largest
As shown in Fig 5 an impedance head connects with the beam and the exciter and it measures
the force signal and the acceleration signal which is used as the input of the controller The ratio of
the force signal and the acceleration signal is the acceleration admittance of the beam With an
absorber attached the dynamic property of the beam changes and hence the admittance of the beam
changes Therefore the vibration attenuation effect of an absorber can be represented by comparing
the admittance of the beam with and without absorber
266 Applied Research and Engineering Solutions in Industry
Fig 5 Experimental set up a Scheme b Photograph
1 Prototype 2 Control box 3 Clamped clamped beam 4 Accelerometer
5 Charger amplifier 6 Dynamic signal analyzer 7 Power amplifier 8 Computer 9 Exciter
Fig 6 Experimental results of the vibration attenuation effect
Fig 6 shows the experimental results of the vibration attenuation effect If the prototype is not
controlled and its resonant frequency is fixed at 26Hz the resonant frequency of the beam it can
be regarded as a TVA While the prototype is only controlled to trace the excitation force
frequency it can be looked as an ATVA As shown in Fig 6 for TVA the best vibration attenuation
effect occurs at its natural frequency The effect goes down when the excitation frequency is far
from this frequency At some frequencies the values of the effects are even larger than 0 indicating
that the vibration of the system is increased by the TVA For ATVA whose natural frequency is
tuned to trace the excitation frequency its vibration attenuation effect is better than that of the TVA
within the entire adjustable frequency band except at 26 Hz Nevertheless the superiority of the
ATVA compared with the TVA is not evident because of the large damping The AAVA has the
best vibration attenuation effect It can result in a reduction of vibration of the beam by up to
average 15 dB which is better than that achieved with the ATVA
Conclusions
In this work we developed a mechanical AAVA whose natural frequency can be tuned from 19 25
Hz to 31 25 Hz by adjusting the span between the ends of two spring poles from 26cm to 58cm The
damping of the prototype is rather small and the average damping ratio was reduced to 0 02 from
0 04 by the active force Experimental studies were conducted to evaluate the vibration attenuation
performance of the AAVA on a clamped clamped beam The results show that the AAVA has
better vibration attenuation performance than ATVA and TVA
Acknowledgments
Financial support from the National Natural Science Foundation of China Grant No 11125210
and the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering
Grant No KJCX2 EW L02 are gratefully acknowledged
Applied Mechanics and Materials Vol 312 267
References
1 Jalili N Knowles D W IV Structural Vibration Control Using an Active Resonator
Absorber Modeling and Control Implementation Smart Materials and Structures 13 5 998
2 Olgac N Hansen B H Design Considerations for Delayed Resonator Vibration Absorber
Journal of engineering mechanics 121 1 81 89 1995
3 Franchek M A Ryan M W Bernhard R J Adaptive Passive Vibration Control Journal
of Sound and Vibration 189 5 565 585 1995
4 Liu J and Liu K A Tunable Electromagnetic Vibration Absorber Characterization and
Application Journal of Vibration and Acoustics 295 3 5 708 724 2006
5 Rustighi E Brennan1 M J Mace B R A Shape Memory Alloy Adaptive Tuned Vibration
Absorber Design and Implementation Smart Materials and Structures 14 1 19 28 2005
6 Kidner M R F Brennan M J Real time Control of Both Stiffness and Damping in an
Active Vibration Neutralizer Smart Materials and Structures 10 4 758 769 2001
7 Sun H L Zhang P Q Gong X L Chen H B A Novel Kind of Active Resonator
Absorber and the Simulation on Its Active force Journal of Sound and Vibration 300 12 117
8 Xu Z B Gong X L Liao G J Chen X M An Active damping compensated
Magnetorheological Elastomer Adaptive Tuned Vibration Absorber Journal of Intelligent
Material Systems and Structures 21 10 1039 1047 2010
9 Gong X L Peng C Xuan S H Xu Y L Xu Z B A Pendulum like Tuned Vibration
Absorber and Its Application to Multi mode System Journal of Mechanical Science and
Technology 26 11 3411 3422 2012
Applied Research and Engineering Solutions in Industry
10 4028 www scientific net AMM 312
Active Adaptive Vibration Absorbers and its Vibration Attenuation Performance
10 4028 www scientific net AMM 312 262


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