ISSN: 2180-3811 Vol. 4 No. 1 June 2013 Validation and Experimental Evaluation of Magnetorheological Brake-by-Wire System
111
where it is coupled to the input shatrotor of MR brake via pulley and A-type V-belt. The speed from the motor is transmited to the MR brake
shat using belt tensional and well ited beside the electric motor. The pulley shat is connected to the MR brake shat using jaw coupling and
same concept also was applied at the load shat. The pulley shat and load shat used a pillow block bearing to support the rotating shat
where the inner bearing will allow the shat to rotate in free direction.
Figure 1. Mechanical assembly of the MR brake test rig
Figure 1. Mechanical assembly of the MR brake test rig
The MR brake housing is coupled to a load cell via an arm of length of 238 mm. In this equipment, the load cell is employed to measure the
braking torque. The load cell was calibrated at 1 V: 53.4 Nm and the maximum torque measured using this sensor is 534 Nm. Next, the load
cell is connected to the bridge ampliier which functions as the signal conditioning. Meanwhile, the rotational speed of the MR brake shat
was measured by using an ABS speed sensor. The MR brake test rig is equipped with an IO device for data processing. Next, the Integrated
Measurement and Control IMC device provides signal processing of the sensory system. The IMC device that is only capable to receive
analogue voltage signal. Then, the signals are digitally processed and
stored in a personal computer using FAMOS control sotware. IMC device is connected to a personal computer using NetBEUI protocol.
A DC power supply manufactured by GWINSTEK is used to supply electric currents to the MR brake electromagnetic coil. All the measured
data are displayed in Personal Computer PC for the further analysis.
3.0 mathEmatical modEl
The characteristics of MR luid can be described by using a simple Bingham plastic model Philips, 1969. The constitutive equation for a
Bingham plastic luid where the total shear stress τ is writen as:
ISSN: 2180-3811 Vol. 4 No. 1 June 2013 Journal of Engineering and Technology
112 total shear stress τ is written as below:
H p
1
where, is the yield stress due to the applied magnetic field, , is the constant
2
r dr
w h
k
k
T T
4
4
r w
where,
where,
H
is
plastic viscosit
is the yield stress due to the applied magnetic ield,
H
netic field,
,
p
H is
field viscosity of the
2
r dr
w k
k
T T
4
4
r w
is the constant plastic viscosity which is considered equal to the non- ield viscosity of the luid, and
total shear stress τ is written as below:
fluid, and
the friction
2
r dr
w h
k
k
T T
4
4
r w
is the shear strain rate. Based on the Eq. 1, the braking torque generated by the friction of the interface
between static and moving parts in the MR luid inside the MR brake can be writen as equations Park et al., 2006; Karakoc et al., 2008:
total shear stress τ is written as below:
2
2
o i
r s
b p
r
rw T
N kH
r dr h
2 w
h k
k
T T
4
4
r w
where r is the radius of the disk,
total shear stress τ is written as below:
the disk,
s
w is the fluid gap betwee
k
T
T
is the angular velocity of the rotating disk, h
is the thickness of the MR luid gap between rotor and enclosure, H
is the magnetic ield intensity corresponding with k and β . The values of k and
β are constant by considering the relationship between the magnetic ield intensity and the yield stress of the MR luid.
An integration of Eq. 2 will determine the two types of components of braking torque which are torque generated due to applied magnetic
ields
T
H
and torque due to friction and viscosity of the luids
total shear stress τ is written as below:
ated due to appli the fluids
T
. B oc et al., 2008.
T
. Both torque elements are expressed as follows Park et al., 2006; Karakoc et
al., 2008.
total shear stress τ is written as below:
4
4
2
p o
i s
T N
r r w
h
3
3 3
2 3
H o
i
T Nk
r r i
4
T T
J T
T N
r mgr
P w
T
J J
Therefore, the total braking torque produced by MR brake can be writen as follow
b H
T T
T
5
An effective MR brake torque generated when applied current to the magnetic coils. J
T T
N r
mgr
P
w
T
J J
An efective MR brake torque generated when applied current to the magnetic coils. This will decelerate the dynamics of all inertia
ted when applied c
ll inertia
all
J that c
the torque motor
m
T is c
T N
w mg
P w
T
J 4J
4cw
that coupled rigidly to the MR brake shat. The
will decelerate the dy
shaft. The
input
T term
T that is coupled rigidly
P
T
J J
P
term is the torque motor
ll inertia that c
nput
the torque motor
m
T is c
T brake shaft. The
N w
P w
T
J 4J
4cw
is combined with loading torque
L
T that is
based on
P
T
that is coupled rigidly on the MR brake shat. The loading torque is generated based on the
weight of the load N and the efective radius r
L
of the load. Then, the mathematical expression in terms of
the load N and the e
on in terms of
input
T can be
T
P
w
T T
J
T
J J
r T
can be writen in Eq. 6 as:
ISSN: 2180-3811 Vol. 4 No. 1 June 2013 Validation and Experimental Evaluation of Magnetorheological Brake-by-Wire System
113
input m
L m
m L
T T
T P
w mgr
6 where P = power of electric motor and w = angular speed of electric motor pulley.
T
J J
J
where P
m
= power of electric motor and W
m
= angular speed of electric motor pulley. Then, the equation motion of MR brake with a test rig is
derived and stated in Eq. 7 as follow:
input b
c all
s
T T
T J
7 T
J J
J
where T
c
= viscous damping of bearing and
c
T aring and
s
= a ake
all
J consists
J
T T
= angular acceleration of MR brake shat. Then, the total inertia of MR brake J
all
consists of rotor, shat, four bearing inner parts, a sprocket, a pulley and the load
can be writen in Eq. 8.
4
all disk
sprocket pulley
bearing Load
shaft
J J
J J
J J
J
8
The total inertia is approximately about 0.25 Nm
2
for 50 N, 0.45 Nm
2
for 100 N and 0.65 Nm
2
for 150 N respectively. By substituting Eq. 6 into Eq. 7, the Eq. 9 can be writen as follow:
4
m m
L H
all s
P w
mgr T
T cw
J
9
4.0 modEl Validation
