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International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 166
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
Design and Modeling of Hydraulic Crash Damper in
a Racing Electric Vehicle
Ahmad Syuhri Department of Mechanical Engineering, Faculty of Engineering, University of Jember, Jember, Indonesia
E-mail: ahmad.syuhri@unej.ac.id
Abstract— Since racing vehicle has greater risk of injury
and vehicle damage than any others urban vehicle, this paper
presents the design, modeling and performance study of crash
damper in a racing electric vehicle. Using lumped parameter
model (LPM) as analytical approach, the development model of
hydraulic crash damper is used to absorb or to dissipate the
kinetic energy on frontal crash. The mathematical model
between initial model and development model is derived to
obtain responses of both vehicle and occupant. Plot 3D surface
from numerical simulation is used to obtain optimum value of
development model. The results in time response are also plotted
to compare both initial model and development model.
Development model also claimed that can reduce in vehicle
deceleration, occupant deceleration and vehicle deformation in
the range of 25% to 28.1% than initial model.
Index Term— hydraulic crash damper, lumped parameter
model, vehicle occupant deceleration, deformation vehicle.
I. INTRODUCTION
Nowadays, student competitions in the racing vehicles are
growing rapidly. The competition itself encourages students to
design and to build their own vehicle. The product must be
compact and well calculated due to many risks in both driver
and vehicle. The greater velocity that occurs in racing
competitions can make driver injury and vehicle damage [1].
Mostly the damage is coming from a frontal crash that directly
affected on steering systems. Figure 1 shows the front bumper
has been reformed due to frontal crash in an electric vehicle
competition. Before it reformed, the right bumper displaced
and forced the tire. So the steering system can’t be actuated
until the bumper is well repaired. Unfortunately, the
repairment process needs to be welded. This situation is time
consuming, that’s why there must be any add-ons in a bumper
design to absorb energy, masses and overall lengths of
colliding vehicles.
Fig. 1. Front bumper has been reformed after frontal crash
To obtain the best bumper design, it must meet and fulfill
five requirements as follows, (1) be replaceable without
cutting or welding, (2) absorb energy and restrict damage to
the bumper system only, (3) be attached to the body via
energy absorbing structure that are inexpensive to repair or
replace, (4) be stable during impact and (5) prevent damage to
the structure [2]. Recently, there are two categories in the
development of bumper to absorb energy, either deformation
elements (“crash boxes”) or a reversible type (“shock
absorber”) [3]. The primary disadvantages of deformation
element is opposite with the best bumper design point (1) and
(5) such as it needs longer time to be replaced after the crash
and the deformation can destruct the shape of structures. In the
other hand, the reversible type or known as shock absorber,
which is mentioned as hydraulic crash damper in this paper,
has more advantages than crash boxes. It gives easily to re-
stretched or re-extended after crash which can save some
times during the competition, and this device also claimed to
generate a constant deceleration [4].
There are several analytical models to analyze the
behaviors between bumper, vehicle structure and occupant
under impact mode such as lumped parameter models (LPM),
beam element model (BED) and finite element models (FEM)
[5]. LPM is reported as the simplest and efficient tools to
analyses vehicle structures and concepts in energy absorbing
elements at design stages [6]. The responses of crash in a
vehicle can also be compared with a range of performance
such as optimal vehicle deceleration crash pulse where
contained of time acceleration history in three intervals based
on the occupant interactions with the vehicle [4]. Moreover,
the deformation of frontal vehicle body must not be exceeded
than 0.7 m [6], and the occupant performance in crash mode
also obtained at the peak deceleration of the occupant mass
[7].
This paper attempts to design the optimal bumper in
a racing electric vehicle using shock absorber respected to the
frontal crash. The body structure of electric vehicle is shown
in Fig. 2. There are three steps to create the optimal design.
First, derive the mathematical model and LPM to obtain the
dynamic behavior of structure occurred in frontal crash.
Second, address hydraulic crash damper in the mathematical
model and taken numerical simulation to find optimal value in
the specification of hydraulic crash damper. And the last,
compare initial model and development model with optimal
crash pulse.
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 167
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
Fig. 2. Structure of racing electric vehicle
II. DESIGN AND MODELING
A. Initial Model
In this section, mathematical models that associated with
equations of motion are developed to predict the dynamic
response of vehicle crash. As shown in Fig. 1, the frontal
structure of vehicle in the interaction with barrier collision can
be modeled as initial model (IM) of Two-DOF LPM [8]. The
vehicle body in above model is presented by a rigid mass, mv,
as shown in Fig. 3 and the bumper structure is described as
linear spring, kL. The occupant, mo, is coupled with vehicle
structure and presented as additional DOF. Effect of seat belt
in the occupant is also reported as damping, co, and stiffness,
ko, where attached with vehicle structure called restraint
system. There is slack in the initial work of seat belt, oc, and
make a dead zone in the force-deflection curve of stiffness
occupant [9].
Fig. 3. Initial model of Two-DOF LPM
Free body diagrams that associated with lumped
parameter model have been developed and shown in Fig. 4.
The differential equations describing the motions of the
vehicle and the occupant mass can be written as,
)( ocvoovLvv xxkxkxm
0)( voo xxc
(1)
0)()( vooocvoooo xxcxxkxm (2)
Fig. 4. Free body diagram of initial model
where vx , vx , and vx represent acceleration, velocity and
displacement of vehicle, ox , ox , and ox is acceleration,
velocity, and displacement of occupant respectively.
B. Development Model
The initial model is developed using hydraulic crash
damper as a bumper to reduce deceleration and deformation of
vehicle and mentioned as development model (MD).
Hydraulic crash damper is assigned as extended energy
dissipator and placed in the structure as shown in Fig. 5. From
that system, LPM such system is developed and given in Fig.
6. Damping force, FD, developed by hydraulic crash damper
installed in series model with stiffness of the body and the
interaction of these models is noted as displacement of
bumper, xb.
Fig. 5. Bumper development model
Fig. 6. Vehicle-occupant model with hydraulic crash damper
Mathematical model of vehicle-occupant model with
extendable bumper is taken from implementation of free body
diagram in Fig. 7 and presented as,
)()( ocvoobvLvv xxkxxkxm
0)( voo xxc
(3)
DbvL Fxxk 2)( (4)
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 168
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
0)()( vooocvoooo xxcxxkxm (5)
Fig. 7. Free body diagram of vehicle-occupant and extendable bumper
where FD represents damping force that caused by differential
pressure (P) in chamber of hydraulic cylinder. The
maximum operation of hydraulic cylinder is 0.3 m. After
reached it, there is no FD work.
In this work, hydraulic crash damper is created from
hydraulic cylinder and damper valve to fulfill force needed in
order to dissipate energy. Schematic diagram of working
principle of damper system can be seen in Fig. 8. AC1, AC2 and
Ad defined as cross section in chamber 1, cross section in
chamber 2 and cross section of damper valve, respectively.
From figure, hydraulic cylinder contains a piston rod and two
chambers that make different size in cross section of each
chamber. When vehicle crashed with a barrier, hydraulic
cylinder is forced and displaced along xb. It makes oil in
chamber 1 passed damper valve and flowed through pipe to
chamber 2.
Fig. 8. Hydraulic cylinder with damper valve
Assuming difference pressure in hydraulic cylinder can be
obtained using Bernoulli principle based on difference in
velocity and given by [10],
lddd
CCC hzg
vPzg
vP .
2.
2
2
1
2
11
(6)
where P, , v, g, z and hl are described as pressure, density,
fluid velocity, gravity acceleration, height differences and
head loss, respectively. Subscript C1 and d are mentioned as
chamber 1 of hydraulic cylinder and damper valve,
respectively.
Since there is no difference in height between chamber 1
and damper valve due to installation in series model (zC1 equal
with zd), zC1 and zd can be neglected. Head loss is particularly
consisted of head loss major and head loss minor. In this case,
both head loss major and head loss minor are neglected due to
short and simple pipe. Moreover head loss has little effect to
produce such a damping force [11]. So Eq. (6) can be
simplified to obtain differential pressure (P) in hydraulic
cylinder and expressed as,
22)(
2
1
2
11cd
dCdC
vvPPP (7)
In this case, continuity system is used in the following
condition where flow rate in chamber 1 is equal with flow rate
in damper valve or flow rate through cross section chamber 1,
A1, is equal with flow rate through cross section of valve, Ad.
Then the relation between velocity in chamber 1 and damper
valve can be obtained,
11
C
d
Cd v
A
Av (8)
where velocity in cylinder hydraulic is equal with velocity of
extendable damper (vC1 = bx ). Then substituted Eq. (8) to Eq.
(7), the differential pressure (PC1-d) can be expressed as,
2
2
11 1
2b
d
CdC x
A
AP
(9)
Damping force generated by differential pressure of
hydraulic cylinder is multiplication between pressure and
cross section.
1
2
2
111 .1
2. Cb
d
CCdCD Ax
A
AAPF
(10)
It can be seen from Eq. (10) that the damping force, FD, is
quadratic function. Substitute Eq. (10) to Eq. (4) and now the
interaction of hydraulic cylinder as damping force and
stiffness of body structure of vehicle can be obtained.
2
2
11 1 b
d
CCbvL x
A
AAxxk
(11)
The energy absorbed by hydraulic crash damper is
defined as integral of damping force due to displacement of
extendable bumper and given by,
bDD dxFE (12)
C. Parameters
Due to limitation in space and dimension, the diameter of
hydraulic cylinder in chamber 1 (bore diameter) and piston
diameter is 3.2 cm and 1.8 cm, respectively. So the cross
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 169
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
section of chamber 1, AC1, and chamber 2, AC2, can be taken
into account. Parameters used in this numerical simulation are
given below in Table I. For damper valve, dd, will be
determined using optimal algorithm in numerical simulation
where the range of damper valve diameter is 1x10-3
m to
10x10-3
m.
TABLE I
PARAMETERS AND VARIABLES OF HYDRAULIC AND VEHICLE-OCCUPANT
Parameter Value Unit
dC1 0.032 m
846 kg/m3
mo 65.7 kg
ko 98.1x103 m
co 2.54x103 Ns/m
oc 0.005 m
mv 156 kg
kL 554325 N/m
III. RESULTS AND DISCUSSIONS
A. Optimal Damper on the Development Model
To reduce both deceleration pulse and deformation,
optimal numerical simulation of DM has been conducted to
achieve better responses. Figs. 9-11 represent 3D surface of
variation in different damper valve diameter in the range from
1x10-3
m to 10x10-3
m (X-axis) and impact velocity range
from 20 km/h to 100 km/h (Y-axis). The results shown in Z-
axis are vehicle deceleration, occupant deceleration and
deformation of vehicle. The optimum value of damper valve
diameter can be obtained at the lowest slope of those 3D
surfaces.
Fig. 9. Deceleration response of vehicle on 3D surface
Fig. 10. Deceleration response of occupant on 3D surface
Fig. 11. Deformation response of vehicle on 3D surface
As it is clearly seen in Fig. 9, the minimum slope on 3D
surface for deceleration response of vehicle noticed on damper
valve diameter of 3.5x10-3
m (referred as optimum value) with
three examples in different velocities such as 20 km/h, 65 km/h
and 100 km/h that produced deceleration 16.59 g, 68.33 g and
111.3 g, respectively. Occupant deceleration in Fig. 10 and
deformation of vehicle in Fig. 11 are also followed by a very
similar pattern over impact velocity and damper valve
diameter. From Fig. 11, using example in data cursor of
3.5x10-3
m for damper valve diameter with three different
velocities, the deformation of vehicle is 0.4056 m whenever
impact velocity is reached 100 km/h.
Overall, it can be seen that the response of deceleration
and deformation increases sharply respected with increasing
of damper valve diameter until 6x10-3
m and shown nearly
constant at rest. It must be caused by the relation between
damping force and damper valve diameter shown in Eq. (10).
The smaller ratio between cylinder cross section (AC1) and
damper valve diameter (Ad), the less hydraulic system
produced sufficient damping force.
Figure 12 illustrates a plot surface percentage energy
absorbed by hydraulic system in different impact velocities
and damper valve diameters. The percentage of energy
absorbed is defined by ratio of the total absorbed energy and
the total kinetic energy of vehicle [6]. The percentage of
energy absorbed in damper valve diameter of 3.5x10-3
m is
reported at 88.03%, 72.9% and 64.7% in velocity of 20 km/h,
65 km/h and 100 km/h, respectively. As an example, 88.03%
means ability of hydraulic cylinder to absorb or to dissipate
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 170
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
energy and the rest 12.97% is absorbed by structure of body
vehicle. The trend line of percentage energy absorbed is
shown quadratic function respected with impact velocity. It
caused by quadratic equation in the development of
mathematical model on hydraulic damper.
Fig. 12. Percentage of energy absorbed in different velocities and damper
valve diameters
B. Compared Results
In this section, the numerical simulation in time response
is used to obtain the characteristics of each model. Using
optimal parameter of damper valve diameter at 3.5x10-3
m
with impact velocity of 65 km/h, the comparison results
between initial model (IM) and development model (DM) of
vehicle, occupant and deformation are shown in Figs. 13-15.
Figure 13 shows comparison between initial model and
development model on vehicle deceleration. Optimal crash
pulse in the range of 64 km/h to 80 km/h, developed by
Witteman [4], is also plotted to compare deviation on the
crash pulse. The peak of IM and DM can be obtained at 91.3 g
and 68.33 g, respectively. It can be concluded that DM can
reduce 25.16 % on the peak of vehicle deceleration in frontal
crash than IM. Whereas the response of occupant deceleration
is shown in Fig. 14, the peak of vehicle deceleration between
IM and DM is at 86.23 g and 63.51 g.
Fig. 13. Vehicle deceleration pulse between IM and DM in time response
compared with optimal crash pulse
Fig. 14. Occupant deceleration pulse between IM and DM in time response
Fig. 15. Vehicle deformation pulse between IM and DM in time response
The trend line on the deformation of vehicle as shown in
Fig. 15 also has the same pattern with occupant deceleration
where the IM response is stopped earlier than DM response
due to characteristics of hydraulic damper. The peak of
vehicle deformation between IM and DM is noticed at 0.32 m
and 0.24 m, respectively. DM model can reduce deformation
on vehicle exactly 25% compared with IM. Moreover,
percentage of energy absorbed by hydraulic damper also
obtained at 72.9%. It means that 72.9% of crash energy is
absorbed or dissipated by hydraulic damper, and the rest of
28.1% is absorbed by structure of body vehicle. It is worth
since IM absorbed 100% of crash energy to structure body of
vehicle.
The crash responses of vehicle-occupant models both IM
and DM are also evaluated in a wide range of frontal crash
impact velocity from 20 km/h to 100 km/h. Figs. 13-15 show
peak responses of vehicle deceleration, occupant deceleration
and deformation of vehicle in different impact velocities.
From those figures, the responses of DM are always lower
than IM.
International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 171
167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S
Fig. 16. Vehicle deceleration peak between IM and DM in a range of
velocity
Fig. 17. Occupant deceleration peak between IM and DM in a range of
velocity
Fig. 18. Deformation vehicle peak between IM and DM in a wide range of
velocity
Figure 19 illustrates the kinetic energy and the energy
absorbed on vehicle in different velocity. The characteristic of
energy absorbed by hydraulic crash damper, which is noted as
“blue line” in Fig. 19, is remarkably close with kinetic energy
of vehicle on low velocity range (20 km/h to 40 km/h). But it
decreases the ability to absorb energy as increasing of
velocity. This phenomenon can be linked with Fig. 12 where
damper valve diameter of 4x10-3
m to 5x10-3
m is the best at
absorbing energy in a high range velocity (80 km/h to 100
km/h), but worse at low velocity. It can be caused by the
length of displacement as shown in Eq. (12) where energy
absorbed in damper is integral of damping force to
displacement of extendable bumper.
Fig. 19. Peak of energy absorbed and kinetic energy of vehicle in different
crash velocity
IV. CONCLUSION
Considering the minimum deceleration of vehicle-
occupant and deformation of vehicle, the minimum slope or
optimum value of damper valve diameter is obtained at
3.5x10-3
m. The percentage energy absorbed in that diameter
is in the range of 88.03% to 64.7% parallel with increasing of
velocity from 20 km/h to 100 km/h. The time response of
vehicle-occupant deceleration and deformation vehicle also
compared between IM and DM. The results are shown that
DM has better response and has ability to dissipate 72.9%
crash energy than IM in impact velocity of 65 km/h.
The declining effect in the percentage of energy absorbed
as increasing impact velocity can be a further study since there
is lack of energy absorbed in a high range velocity.
Furthermore, stopper in the rest of displacement of hydraulic
cylinder must be added to contribute a smooth deceleration
curve in both vehicle and occupant.
ACKNOWLEDGMENT
The project presented in this article is supported by
Department of Mechanical Engineering, Faculty of
Engineering, University of Jember.
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