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Semi-active implementation
of nonlinear damping for vibration isolation
By
Diala Uchenna
OutlineIntroduction.Aims and Objectives.Elements of a vibration isolation system.
Vibration isolation system with a linear damping characteristic .
Vibration isolation system with a Nonlinear damping characteristic.
Nonlinear (cubic) damping characteristic implementation with Magnetorheological damper (MR damper).
Results. Conclusion and Recommendation.
Vibration isolation deals with the control of unwanted vibrations to keep the adverse effects within acceptable limits (Z.Q. Lang et al., 2009).
Transmissibility is: a measure of the response of a vibration isolation system. also a measure it’s performance.
Viscous damping is incorporated to reduce vibration amplitude at resonance. However, if the effect of the viscous damper is linear, as
the damping level is increased to minimise the transmissibility in the resonant region, the transmissibility is increased in regions where isolation is desired.
Active vibration isolation system have been developed to resolve this problem but with limitations of cost and complexity.
Introduction
To study the effects of nonlinear viscous damping on a vibration isolation system.
To demonstrate it’s implementation using semi-active techniques with an MR damper. Nonlinear viscous damping measure is proposed
here using semi-active means to resolve the issue with active devices.
To design a controller to track the desired nonlinear viscous damping force.
Aims and Objectives
Vibration isolation system normally consists of a spring that offers stiffness to the system .a damping element (dashpot) to disperse input
energy.
Fig.1.0 : A mass-spring-damper system
Where, m = Mass of the objectk = Spring stiffnessc = Linear damper coefficient
Elements of a vibration isolation system
Vibration isolation system with a linear damping characteristic (Open loop)
The transmissibility is given as:
= nondimensional excitation freq ratio
= damping ratio
Fig.2.0: A mass-spring-damper system with linear damping characteristics
Vibration isolation system with a linear damping characteristic (Open loop) contd...
Transmissibility curves for freq ratio, r = 0:0.2:2 and damping ratio = 0.1, 0.2, 0.4 and 0.7 are shown in figure 3.0.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 240
45
50
55
60
65
70
75F
orce
tra
nsm
issi
bilit
y
freq ratio
E0.1__E0
E0.2__E0E0.4__E0
E0.7__E0
Fig. 3.0: Transmissibility curve for a vibration isolation system with linear damper
Region of desired isolation
Resonant region
Vibration isolation system with a nonlinear damping characteristic (Open loop)
The transmissibility is given as:
c1 = Linear damper coefficientc2 = Nonlinear damper coefficient
Fig.4.0: A mass-spring-damper system with nonlinear damping characteristics
Vibration isolation system with a nonlinear damping characteristic (Open loop) contd...Transmissibility curves for freq ratio, r = 0:0.2:2, zeta 1 = 0.1 and zeta
2 = 0, 0.2 and 0.4 are shown in figure 5.0.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 240
45
50
55
60
65
70
75
For
ce t
rans
mis
sibi
lity
freq ratio
E0.1__E0
E0.1__E0.2E0.1__E0.4
Fig. 5.0: Transmissibility curve for a vibration isolation system with nonlinear damper
Region of desired isolation
Resonant region
Vibration isolation system with a nonlinear damping characteristic (Open loop) contd...
Transmissibility curves for r = 0:0.2:2, zeta 1 = 0.2 and zeta 2 = 0, 0.2 and 0.4 are shown in figure 6.0.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 240
45
50
55
60
65
70F
orce
tra
nsm
issi
bilit
y
freq ratio
E0.2__E0
E0.2__E0.2E0.2__E0.4
Fig. 6.0: Transmissibility curve for a vibration isolation system with nonlinear damper
Region of desired isolation
Resonant region
Semi-active vibration isolation is realizable using mass control, stiffness control or damping control.
A spring in parallel with an adjustable damper (core of system) is used for this project.
Some controllable dampers include; • Magnetorheological dampers (MR dampers)• Electrorheological dampers (ER dampers)• Viscoelastic dampers etc.The MR damper was used in this project work.
Nonlinear (cubic) damping characteristic implementation with MR damper.
MR damper comprises a hydraulic cylinder containing ferromagnetic particles, of micron size, suspended in a fluid (often oil).
Exposure to electric or magnetic field, via a solenoid embedded inside, causes the MR material to modify from a free flowing viscous fluid to a semi-solid state in a few milli-seconds.
Fig.7.0: Schematic of an MR damper
Nonlinear damping characteristic implementation with MR damper contd...
-40 -30 -20 -10 0 10 20 30 40-3000
-2000
-1000
0
1000
2000
3000
Velocity (m/s)
mr d
ampe
r For
ce
1.5 A
1A
0A
0.25A
0.5A2A
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-3000
-2000
-1000
0
1000
2000
3000
Displacement (m)
mr d
ampe
r for
ce (N
)
0A
0.25A
0.5A1A
1.5A
2A
Fig.8.0: Simulation results for MR damper force versus (a.) Velocity (m/s) (b) Displacement (m) plots
Nonlinear damping characteristic implementation with MR damper contd...
Nonlinear damping characteristic implementation with MR damper contd...(Closed loop with Proportional Integral, PI controller)
Fig.9.0: Schematic of a nonlinear damping characteristic implemented using the MR damper
Nonlinear damping characteristic implementation with MR damper contd...
Fig.10: Schematic of a nonlinear damping characteristic practically implemented using the MR damper.
Nonlinear damping characteristic implementation with MR damper contd...
Fig.11: SIMULINK model of the vibration isolation system with nonlinear damping implementation using the MR damper.
[dot_x1(t)]^3
u(t)
x1(t) Nonlinear cubic damper
force
MR Damper force
x' = Ax+Bu y = Cx+Du
State-SpaceScope4
Scope3
Scope2
Scope1
Vel. (m/s)
Current (A)Fmr (N)
MR Damper
200
Gain
Disturbance force
Direction of force
du/dt
Derivative Cubic
Cntrl input Cntrl signal
Controller Subsystem
Add-ve force
correction
Results
0 5 10 15 20 25-15
-10
-5
0
5
10
15
20
Freq(rad/sec)
Fou
t/F
in2
(dB
)
Force Transmissibility (Cubic Damper)
E3rms = 0
E3 = 0E3
rms = 0.2
E3 = 0.2
E3rms = 0.4
E3 = 0.4E3
rms = 0.7
E3 = 0.7
0 5 10 15 20 25-15
-10
-5
0
5
10
15
20
Freq(rad/sec)F
out/
Fin
2 (d
B)
Force Transmissibility (MR Damper)
E3rms = 0
E3 = 0E3
rms = 0.2
E3 = 0.2
E3rms = 0.4
E3 = 0.4E3
rms = 0.7
E3 = 0.7
Fig.12: Simulation results for transmissibility plots using desired Cubic damper model and MR damper model
Conclusion and recommendations
•The results show the beneficial effects of nonlinear viscous damping. •This implies same effect is achievable as an active device. •This would have significant implications for the engineering design of passive vibration isolators in a wide range of practical applications.•More investigations on the effect of more complex nonlinear viscous damping characteristics on vibration isolation could be carried out to improve on the results achieved in this study.
Thank you
Appendices