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.

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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)

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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

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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

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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.

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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.

REFERENCES [1] Belingardi, G. and Obradovic, J. (2010). Design of the impact

attenuator for a formula student racing car: numerical simulation of the

impact crash test. Journal of the Serbian Society for Computational Mechanics. 4(1). pp 52-65.

[2] RCAR Paper. (2010). Bumper Test Procedure.

URL:http://www.rcar.org/Papers/Procedures/BumperTestProcedure.pdf [3] Agyei-Agyemang, A., Obeng, G.Y. and Andoh, P.Y. (2014)

Experimental Evaluation of the Attenuation Effect of a Passive Damper

on a Road Vehicle Bumper. World Journal of Engineering and Technology. 2. pp 192-200. DOI: 10.4236/wjet.2014.23021

[4] Witteman, W.J. (1999). Improved Vehicle Crashworthiness Design by

Control of the Energy Absorption for Different Collision Situations. Doctoral Dissertation. Eindhoven University of Technology.

Netherland.

URL: http://www.mate.tue.nl/mate/pdfs/5191.pdf [5] Marzbanrad, J. and Pahlavani, M. (2011). Calculation of vehicle-

lumped model parameters considering occupant deceleration in frontal

crash, International Journal of Crashworthiness, 16(4), pp 439–455. DOI: 10.1080/13588265.2011.606995

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:16 No:03 172

167003-8989-IJMME-IJENS © June 2016 IJENS I J E N S

[6] Khattab, A.A.R. (2010). Investigation of An Adaptable Crash Energy

Management System to Enhance Vehicle Crashworthiness, PhD Thesis, Concordia University, Canada.

URL:spectrum.library.concordia.ca/7234/1/PhDThesis_Khattab_Final.p

df [7] Elmarakbi, A. (2010). Analysis of a new front-end structure offset

impact: mass-spring-damper models with piecewise linear

characteristics. Int. J. Vehicle Systems Modelling and Testing. 5(4). Pp 292–311.

DOI: 10.1504/IJVSMT.2010.038035

[8] Elmarakbi, A. and Zu, J. (2007a). Incremental harmonic balance method for analysis of standard/smart vehicle-to-rigid-barrier frontal

collision. Int. J. of Vehicle Safety. 2(3). pp 288-315.

DOI: 10.1504/IJVS.2007.015545 [9] Elmarakbi, A. and Zu, J. (2007b). Mathematical modelling of a vehicle

crash with emphasis on the dynamic response analysis of extendable

cubic nonlinear dampers using the incremental harmonic balance method. Proc. IMechE Part D: J. Automobile Engineering. 221(2). pp

143-156.

DOI: 10.1243/09544070JAUTO296 [10] Fox, R.W., McDonald, A.T. and Pritchard, P.J. (2004). Introduction to

Fluid Mechanics. 6th Ed. John Wiley & Sons, Inc, USA

[11] Syuhri S.N.H. (2015). The Influence of Changing Mechanical Damping and Electrical Damping for Total Damping Force and Energy

Regeneration on Hydraulic Regenerative Suspension, Thesis, Institute

of Technology Sepuluh Nopember, Indonesia. (in Indonesian