magneto-rheological damper hysteresis characterization for sas systems
DESCRIPTION
MR damperTRANSCRIPT
Magneto-Rheological Damper hysteresis characterization for
SAS systems
D. Ghorbany, H.R. Karimi, Y. Iskandarani
Department of Engineering, Faculty of Engineering and Science, University of Agder,
N-4878 Grimstad, Norway
E-mails: [email protected], {hamidrk, yousef.iskandarani}@uia.no
Abstract
A semi-active control of vehicle suspension system with
magneto-rheological (MR) damper is studied for the vibration
suppression in this paper. Subsequently several mathematical
models are used to simulate and analyze hysteresis behavior
of MR brake. The second part of this work is devoted to
derivation of the dynamic model equation of the experimental
setup. The last part presents the evaluation of the dynamic
simulation modeling results with the full-scale experimental
data. Simulation results show effects of the semi-active
control on the vibration of suspension system.
1. INTRODUCTION
In recent years, the manufacturing of magneto-rheological
(MR) dampers is an important subject for engineers. Some
has used magneto-rheological dampers as control devices for
engineering applications to dissipate the energy in civil
structures (e.g. during an earthquake). Those instruments
have many advantages such as small power requirement,
reliability, and low price to manufacture [1]-[4]. Recently the
military has shown interest to using MR dampers to control
gun recoil on naval gun turrets and field artillery.
Vibration control of vehicle suspension systems has been a
very active subject of research, since it is of great importance
for drivers and passengers. There are various mechanical
systems in the world which provide isolation of a structure
from the effect of disturbances (e.g. vibrations). One example
of such a device is a rotational magneto-rheological brake
(MR brake) which creates braking torque by changing the
viscosity of the MR fluid inside the brake. The magneto-
rheological brakes are used in many applications including
prosthetics, automotive, vibration stabilization.
In this paper, there is presented examination of the
mechanical system equipped with MR brake. The main aim
of this work is to obtain the hysteresis plot by finding the
torque in MR brake dependent on different input current.
2. MR DAMPER AND EXPERIMENTAL SETUP
2.1 MR ROTARY DAMPER (brake)
In order to reduce vibration of the mechanical system as a
kinetic and potential energy it has done built MR brake with
the waveform boundary of rotary disk. The kinetic and
potential energy which is generated in the mechanical system,
are been saving in the MR brake, and then by re-cycling,
some of the energy lost in braking into electrical energy.
Rotary brakes based on controllable fluids are passive devices
with an excellent torque to weight ratio and excellent control
capability [2]. As such, they offer a strong potential to be
used in semi active suspension system like a quarter of car as
well as to decrease the vibration of the car body. Higher
torque to volume ratio, lower voltage and less sensitivity to
impurity are the some advantages of this device. MR dampers
consist of two categories:
Linear damper.
Rotary damper.
The proposed MR brake mechanism utilizes a hybrid concept
of magnetic circuit in using both axial and radial magnetic
flux to generate braking force. MR actuators provide
controlled torque through control of an applied magnetic
field. Therefore knowledge of the relationship between the
applied current and output torque is required. The measured
torque shows hysteresis effects as the current increases and
decreases [4]-[5]
3. DESIGN OF EXPERIMENTAL SETUP
The prototype of experimental setup (e.g. of a vehicle
suspension) works as shown in Fig. 1. Vibration control of
vehicle suspensions systems has been an active subject of
research, since it can provide a good performance for drivers
and passengers. Recently, many researchers have investigated
the application of MR fluids in the controllable dampers for
semi-active suspensions; it means control with the current.
Fig 1 Design of experimental setup.
Advances in Computer Science
ISBN: 978-1-61804-126-5 485
This work has the purpose of characterizing, identifying the
mathematical model and simulating the behavior of a MR
fluid in car suspension systems. The MR device designed in
this research is a rotational damper through which an electro-
magnet rotates MR fluid. The semi-active suspension system
consists of a rocking lever that emulates the quarter of car
body, whereas a spring and an MR damper simulate the semi
active vibration control. A DC motor coupled to an eccentric
wheel due to the same shaft is used to simulate the vibrations
induced to the vehicle.
3.1 DYNAMIC MODEL
Based on Newtonβs second law the following two dynamic
equations describe the vehicle suspension system - see Fig 2.
π½2π2πΌ2
ππ‘2β π2
ππΌ2
ππ‘+ π2 π π2 πππ πΌ2
β π2ππ π0π
β π2πππ πΌ2 β π1πππ πΌ1 2 + π2π πππΌ2 β π1π πππΌ1
2
= ππΌ1
ππ‘βππΌ2
ππ‘ πππ π
(1)
Fig 2 Geometrical diagram of experimental setup.
J1d2Ξ±1
dt2 β k1dΞ±1
dt+ m1 g1 r1 cos Ξ² β Ξ±1 +
r1ks(l0s β r2cosΞ±2 β r1cosΞ±1
2 + r2sinΞ±2 β r1sinΞ±1 2
)
βkg R cos Ξ² β Ξ±1 l0g + R sin Ξ² β Ξ±1 + r β Dx + ukin
βfg d Dx β ukin
dtβ
dΞ±1
dtR cos Ξ² β Ξ±1
= dΞ±1
dtβ
dΞ±2
dt MMR i
(2)
3.2 METHODOLOGY OF PARAMETERS
ESTIMATION
In the following, a set of equations describe the torque of the
experimental setup.
TGravity β Tspring β Tviscous β TMR = J Ο (3)
where
πππππ¦ βΆ π½2π2πΌ2
ππ‘2
ππ£ππ πππ’π βΆ π2ππΌ2
ππ‘
ππΊπππ£ππ‘π¦ βΆ π2 π π2 πππ πΌ2
ππ πππππ βΆ
π2ππ π0π β
π2πππ πΌ2βπ1πππ πΌ12+π2π πππΌ2βπ1π πππΌ12
πππ βΆ π π + πΌ π§
The equations (3) describe the torque from the upper beam
due to the magneto-rheological damper. In this way the πππ
is the function of input to the simulink block diagram, to
estimating the mathematical model such as Bouc-Wen, Dahl
and Bingham models.
Fig 3 Scheme of the upper part of the experimental setup.
By comparing those three different mathematical models by
using the experimental graph (blue) in the last three figures, it
is concluded that the Bouc-Wen model gives the best
estimation for the hysteretic characteristic. The different
control current input from 0A to 1A shows that the vibration
of the body is reduced. For the 0A the bodies vibration goes
to the stable in around 11 seconds, and by changing the
current from 0A to the 0.2A as a input the system is going to
stable in 6 seconds. In another case by increasing the control
input of current, the damper friction in the magneto-
rheological (MR) rotary brake fluid is increasing. And also
the vibration of the body is going to be stabilized in the
shorter time.
Fig 4 Damping simulation of MR brake.
TMRΞ±1
Ξ±2X1
r2
r1
ks
α΅
Dx
Ukin
r
R
log
Kg
+
T body
T spring
TsT
TDT
fg
T unsrung mass
m1 g1
X
m2 g2
Spring
Ξ±2
Ξ±1 = 0
MR brake
Upper beam
Lower beam
Advances in Computer Science
ISBN: 978-1-61804-126-5 486
3.3 EQUATION OF MOTION
Fig 5 Quarter of car design.
πΉ0sin(ππ‘) is the external force that is the function of the road
oscillation. The general equation of motion of the eccentricity
is described of the model in figure above like a quarter a car.
π π + πΆ π + πΎ π = πΉ(π‘) (4)
where the M is the mass matrix, the C is the damping matrix,
and the K is the stiffness matrix for the system.
Based on equation of motion, the system is described in
below: [7]
ππ’π₯ 1 + πππ₯ 1 + πππ₯1 + ππ π₯ 2 β π₯ 1 + ππ π₯2 β π₯1 =
πΉ0 sin(ππ‘)
(5)
ππ π₯ 2 + ππ π₯ 2 β π₯ 1 + ππ π₯2 β π₯1 = 0 (6)
Fig 6 Torque (Nm) β Time(s)
4. PARAMETERS ESTIMATION AND
IDENTIFICATION
4.1 Bouc-Wen model and parameters identification
For application of MR brake in vibration control, the model
of the MR damper should be continuous in all the ranges and
be numerically tractable, and the BoucβWen model is
adopted here. The schematic model is shown in Fig. 7. The
torque in this system is given by [3]-[6]
Fig 7. Bouc-Wen model of MR damper
TMR = Ξ± i z + C i ΞΈ (7a)
z = βΞ³ ΞΈ z z n β Ξ²ΞΈ z n + δθ (7b)
with
πΆ π = πΆ0 + πΆ1(π)
πΌ π = πΌ0 + πΌ1(π)
where πΎ,π½, πΏ and n are parameters related to the shape of
hysteresis loop. By adjusting the parameters Ξ³, Ξ², Ξ΄ and n, of
the model it is possible to control the nonlinearity the size of
hysteresis graph. The simulation result is shown as figures
below.
Fig 8 Torque β Angle (Deg)
Fig 9 Torque β Angular velocity (Deg/sec)
mu
Cs Ks
Kg
ms
fg
x1 mu
ms
Tire
x2
xin
x1
x2
F0 sin(Οt)
Road oscillation T
Σ©
Bouc-WenC
Advances in Computer Science
ISBN: 978-1-61804-126-5 487
Table 1 Parameters identification of Bouc-Wen model
Parameters Value Unit
π½ 737 πΎ 1 πΏ 843 N 0,9 Coa 0,0015 Ns/m
Cob 0,07 Ns/m
Ξ±a 1 N/m
Ξ±b 0,07 N/m
Simulation results confirm that the higher current is applied,
the higher torque is generated, resulting in increasing
systemβs damping.
4.2 Dahl model
Dahl model of MR damper is described as follows
TMR = kx i ΞΈ t + kw i z t (8a)
z = Ο (ΞΈ β ΞΈ z) (8b)
with
kx = kxa+ kxb
(i)
kw = kwa+ kwb
(i)
The Dahl model is the Coulomb friction element in the
change of friction of the force, when the direction of motion
is changed. The equations (8) explain that the spring stiffness
(kx and kw ) are current dependent, and also
(kwa, kwb
, kxa, kxb
) and Ο are parameters that control the
shape of the hysteresis loop, see simulation result of Dahl model
in Fig. 10. It means that the spring stiffness is a function of
current, and the parameters are estimated by the output of
experimental data response. [3]
Fig 10 simulation result of Dahl model
Fig 11 Torque β Angle (Deg)
Fig 12 Torque- Angular velocity (Deg/sec)
The simulation results of the Dahl parameters show that the
identification of parameters is correct. The hysteresis loop of
Torque- Angular velocity is increasing from 0A up to the 6A.
By increasing the current, the Magneto-rheological (MR)
brake generates more torque. The hysteresis loop of the
parameters explains that the estimation of parameters is
acceptable.
4.3 Bingham model
Bingham mechanical model is described as follows:
Tmr = fc β sgn ΞΈ + c0ΞΈ + f0 (9)
The Bingham model has been used to characterize MR and
ER fluids. The model consists of a Coulomb friction element
placed in parallel with a viscous damper, which is shown in
Table 2 Parameters identification of Dahl model
Parameters Value Unit
kxa 0,001 Ns/m
kxb 0,001 Ns/m
Ο 5
kwa 5 N/m
kwb 1,5 N/m
Advances in Computer Science
ISBN: 978-1-61804-126-5 488
Figs. 11 and 12. In this model the torque generated by the
device given by (eq. above) where π0 is the damping
coefficient and ππ is the friction force, π0 is non zero. [3]
The Bingham parameters are shown as in below. The goal of
the Bingham model is that to reproduce a hysteretic torque
with high velocity. The simulation results are plotted in the
different parameters for ππ as it is shown as in Figs. 13-15.
Fig 13 Torque β Angle (Deg)
Fig 14 Torque β Angle (Deg)
Bingham model parameters:
πΆ0 βΆ 0.002 ππ
π, ππ βΆ 0.1 π , 0.2 π, π0 βΆ 1
To identify the Bingham parameters, it has been used the
torque equation of the Magneto-rheological (MR) brake.
Torque-Angle hysteresis loop describes the displacement of
the body angle between the (-3.5, 3.5) deg. Torque-Angular
velocity hysteresis loop describes the rotational speed of the
body angular velocity in deg/sec.
5. Conclusions From the experiment investigation of the magneto-rheological
damper, it has been shown that the MR brake has a very
broad changeable damping force range under magnetic field
and the damping coefficient increases with the electric
current.
Fig 15 Torque - Angular velocity (Deg/sec)
The application of the physical device for the vibration
control is studied. The dynamic equation of the mechanical
SAS system is derived together with the geometrical and
graphical description of the system. Equations of motion are
established by using Newtonβs 2nd Law.
The flexibility of shaping the closed-loop road excitation
frequency responses of a quarter-car model by feedback
control was investigated. Physical torque equation of the MR
brake has been investigated, and then parameters of the
different mathematical models have been estimated. Also, the
parameters identification has been done for the real
experimental data. The estimated hysteresis loops were
compared in passive and semi active suspension with the real
experimental response of the damper.
References [1] Tran Hai Nam and Kyoung Kwan Ahn, A New Structure of MR
Brake with the Waveform Boundary of Rotary Disk, In Procc.
ICCAS-SICE, 2009, pp. 2997 β 3002.
[2] Jinung An and Dong-Soo Kwon, Modeling of a Magneto-
rheological Actuator Including Magnetic Hysteresis, Journal of
Intelligent Material Systems and Structures September 2003 vol.
14 no. 9 541-550
[3] Andre N. Vavreck and Ching β Han Ho, Characterization of a
commercial magnetorheological brake/damperin oscillatory
motion. Proc. SPIE 5760, 256 (2005); doi:10.1117/12.599156
[4] Jorge A. Cortes R., Leopoldo S. Villareal- Gonzales and Manuell
Martinez M., Characterization, modeling and simulation of
magneto rheological damper behavior under triangular
excitation. AZojomo (ISSN 1833-122X) Volume 1 November
2005, DOI: 10.2240/azojomo00164.
[5] Jastrzebski, Lukasz, Simulation of Magnetic Fields in a
Generator for an MR Rotary Damper Using COMSOL
Multiphysics. XXXIV. Seminar ASR '2009 βInstruments and
Controlβ, Babiuch, SmutnΓ½ & Ε kutovΓ‘ (eds) 2009, VΕ B-TUO,
Ostrava, ISBN 978-80-248-1953-2
[6] Mauricio Fabian Zapateiro De La Hoz, Semi active control
strategies for vibration mitigation in adaptronic structures
equipped with magneto rheological dampers. Universitat de
Girona, Spain, 2009, PhD Thesis, ISBN: 9788469255223
[7] Toni Liedes, Improving the performance of the semi active
Tuned mass damper, OULU UNIVERSITY PRESS, OULU
2009, ISBN 978-951-42-9124-1
Advances in Computer Science
ISBN: 978-1-61804-126-5 489