Experimental Study of Ride-Down Effect in Automotive Head ...

Journal of Environmentand Engineering

Vol. 5, No. 3, 2010

498

Experimental Study of Ride-Down Effect in Automotive Head-on Collisions*

Koro UENISHI**, Hiroshi MATSUHISA***, Hideo UTSUNO*** and Yuki TAKAHASHI***

**Daihatsu Motor Co., Ltd., 2-1-1, Momozono-cho, Ikeda-shi, Osaka 563-8651, Japan

E-mail: [email protected] ***Kyoto University,

Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Abstract In automobile head-on collisions, some part of occupant's kinetic energy is transferred to the vehicle through a seat belt. The high ratio of the transferred energy is advantageous in protecting the occupant. This phenomenon is called “ride down effect”. In order to design a car body structure with consideration of the ride down effect, the dynamic relation between the occupant deceleration, which is an important injury criteria, and the automotive body structure must be investigated. This paper intends to clarify the dynamic theory of the ride down effect by means of an experimental model with two degrees of freedom consisting of a vehicle and an occupant. In addition, the relationship between the index of the ride down effect and the occupant deceleration was experimentally investigated. The experimental results show good coincidence with the theoretical predictions. It was found that a car body structure with stiffness featured in “hard in the initial stage of collision and soft later” is able to reduce the maximum occupant deceleration.

Key words: Automobile, Shock, Collision, Safety, Ride-down, Occupant Behavior

1. Introduction

In the automobile head-on collision, an occupant moves forward by inertia force as the car body rapidly decelerates. After the slack of the seat belt disappears and the tension in the seat belt is generated, the occupant begins to decelerate. When the occupant collides with the steering wheel or the elongation of the seat belt reaches the critical limit, the occupant deceleration becomes maximum. This maximum deceleration is one of the important occupant injury criteria (3ms-chest acceleration). During a car frontal collision, especially before the elongation of the seat belt reaches limit, some part of the occupant's kinetic energy is transferred to the car structure through the restraint system such as a seat belt. A higher ratio of the transferred energy is more advantageous in protecting the occupant. This phenomenon is called “ride-down effect”(1)-(5).

Theoretical analyses have been performed in our previous researches on the relationship between the index of the ride-down effect and the occupant’s deceleration caused by a car crash(6),(7). These researches showed that the maximum occupant deceleration could be reduced by setting load stiffness of the car body hard in the initial stage of collision and soft in the later stage. The profile of this stiffness was given in a rectangular shape and a ride-down shape of force-displacement curve. They also showed that the maximum occupant deceleration became small for the case that the occupant was moving backwards by the restorative force from the seat belt at the moment when the car

*Received 7 June, 2010 (No. T1-07-1053) Japanese Original : Trans. Jpn. Soc. Mech.

Eng., Vol.74, No.740, C (2008), pp.904-911 (Received 19 Nov., 2007)

[DOI: 10.1299/jee.5.498] Copyright © 2010 by JSME

Journal of Environment and Engineering

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velocity became zero. On the other hand, a crash simulator test, called “sled”, installed with a real-size dummy on it was carried out to confirm the validity of the car body load stiffness that was hard in the collision’s initial stage and soft later. However, in this real crash test, since the seating posture of the dummy and characteristics of the vehicle component were not constant, it was very difficult to investigate the ride-down effect quantitatively.

In order to solve this problem, a simplified experiment model with less degree of freedom is proposed in this paper. A experimental model with two lumped masses, representing the car body and the occupant respectively, is fabricated. A non-linear springs is installed to represent car body load stiffness. The relation between the ride-down effect and the body load stiffness as well as the occupant behavior are experimentally and theoretically investigated.

2. Dynamic model for automotive head-on collision

Schematic dynamic model of the system with a car body and an occupant is shown in Figure 1. m1 and m2 are the masses of the car body and the occupant, x1 and x2, and v1 and v2

are corresponding displacements and velocities, respectively. Springs A and B represent the body load stiffness of car’s front structure and the stiffness of seatbelt, respectively. The equations of motion are given as

BA11 FFxm +−= , (1)

B22 Fxm −= , (2) where, FA and FB are the force produced by spring A and B, respectively. Although both the front structure and the seat belt are characterized with non-linear stiffness in general, FB is assumed to be linear for the sake of simplicity. Then it is expressed as the following equation

( )12B xxkF −= , (3) where k is the spring constant of the seat belt. The initial displacements and velocities at the moment (t = 0) when the car body begins to collide with the wall are assumed as x1 = x2 = 0 and v1 = v2 = v0.

A

Bm2

m1

x1 x2

v1 v2

FA

FBFB

Fig. 1 Dynamic model of the system of a car body and an occupant for a head-on collision.

Some part of the occupant's kinetic energy that is transferred to the car body through the seat belt is equal to the work W1 that FB applies to the car body. By making use of the energy conservation law during the time period of the car velocity decreasing from initial v0 to zero, the index R of the ride-down effect is expressed as

( )2

02

pk202

202

1

21

21

21 vm

EEvm

vm

WR+−

== , (4)

where, 22h2k 2

1 vmE = , (5)


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2h2hp )(

21 xxkE −= , (6)

and xh is the maximum value of car deformation and v2h and x2h are the occupant velocity and displacement, respectively, at the time when the car velocity reaches v1 = 0 (t = th). It is assumed that the car does not rebound. Eq. (5) represents occupant’s kinetic energy at the moment when the car velocity becomes zero and Eq. (6) the potential energy accumulated in the seat belt at the same moment. Consequently, in order to increase the ride-down effect, Ek + EP in Eq. (4) must be minimized.

In the following sections, we will experimentally verify two types of body load stiffness for the purpose of occupant protection which we proposed in our previous research (6). Figure 2 shows the profile of the rectangular load stiffness and the ride-down load stiffness which have characteristics hard in the initial stage of collision and soft later.

0Displacement x1

Forc

e F

A

Rectangular load stiffness

Ridedown load stiffness

Fig. 2 Rectangular and ride-down stiffness characteristics.

3. Experimental verification of the rectangular stiffness

3.1 Experimental apparatus The schematic diagram and photograph of the experimental system are shown in Figs. 3

and 4, respectively. The car body is made of acrylic resin and the wheels made of aluminum are attached. On the front-end of the car body, a coil spring is installed for simulating a buckling component in a collision. An aluminum block represents the occupant which is connected to the car body by a coil spring imitating the seat belt. The mass of the car body is 0.595kg and the occupant 0.069kg. The spring constant of the seatbelt k is 133N/m. In order to make up the nonlinearity of body load stiffness, the spring A is made of two springs A1 and A2 separated with a gap. A1 is attached to the body side and A2 to the wall side. A dropping weight set through a pulley is used for driving the car body, which falls down and reaches ground before the springs A1 contacts with the spring A2. The collision speed in this experiment is set to 0.61 m/s. The decelerations of the car body and the occupant are measured by accelerometers and the motion is filmed by a high-speed camera with 500FPS.


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Weight

WallA1 A2

B

Rail

Occupant Car bodyHigh speed camera

Datalogger

IN

IN

OUT(Signal)ININ Contact signal

Accelerometer

Fig. 3 Experimental system of a head-on collision.

Fig. 4 Picture of the experimental apparatus.

3.2 Spring structure for rectangular load stiffness The schematic diagram and photograph of the spring device, which provides a

quasi-rectangular force-displacement characteristic, are shown in Fig 5 and 6, respectively. As seen in Fig 5, this structure arranges spring A1 and A2 in series with pre-load f0 given to the spring A2. Using spring constants A1k and A2k for A1 and A2, respectively, the force FA is expressed as

>+−+⋅

=

≤=

)()(

)(

01001A2A1

A2A1A

011A1A

xxfxxkkkkF

xxxkF, (7)

where, x0 is the critical displacement given by

1A

00 k

fx = . (8)

In case that FA is smaller than f0, the upper formula of Eq. (7) is applied and only the spring A1 shrinks. On the other, in case that FA is larger than f0, the springs A1 and A2 work in series as shown in the lower formula of Eq. (7). In this case, the spring constant is kA1 kA2 /(kA1+kA2) that is smaller than kA1. Then, assuming kA1>>kA2, the combined spring A is able to have a quasi-rectangular load-displacement characteristic. Four kinds of combination of kA1, kA2 and f0 used in this experiment are listed in Table 1. L1 is the case without the spring A2, and f0 is set out so that the body’s maximum displacement during the collision is to be 0.012m. The force-displacement characteristics of L1-L4 calculated by using Eq. (7) are shown in Fig. 7. The spring constants are set such that the energy absorption of the spring A is equal to each other at the time of the maximum body displacement.


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A1 A2

Pre-Loadf0

Car body Wall side

x1

Fig. 5 Structure of the spring system with quasi-rectangular load stiffness.

Fig. 6 Picture of the quasi-rectangular load stiffness structure.

Table 1 Spring load stiffness of the quasi-rectangular structure.

kA1　　(N/m)

2A1A

2A1A

kkkk

+⋅

f0　（N)

L1

kA2　　(N/m) (N/m)

L2

L3

L4

1700

2430

2990

8750

587

587

587

491

549

473

10.3

7.77

11.5

Case code

0.000 0.002 0.004 0.006 0.008 0.010 0.0120

5

10

15

20

25

L4L3

L2L1

Forc

e F

A [

N]

Displacement x1 [m]

Fig. 7 Characteristics of the quasi-rectangular load stiffness system.

3.3 Results of experiment The time histories of the body and occupant decelerations measured from an

experiment are plotted in Fig. 8. It is confirmed that the rapid initial rise of the car body deceleration (L4) coincides with the reduction of the occupant deceleration. This phenomenon agrees well with the result of the theoretical analysis(6).


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0.00 0.02 0.04 0.06 0.08 0.10-20

-10

0

10

20

30

40

50

L4L3

L2L1

Occ

upan

t dec

eler

atio

n [m

/s2 ]

Time [s]

-20

-10

0

10

20

30

40

L4

L3L2 L1

Car d

ecel

erat

ion

[m/s2 ]

Fig. 8 Effect of quasi-rectangular load stiffness on the decelerations.

-0.04

-0.02

0.00

0.02

0.04

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5

1.0Relative occupantdisplacement

Disp

lace

men

t [m

]

Occupantvelocity

Car velocity

Vel

ocity

[m

/s]

Time [s]

(a) L1

-0.04

-0.02

0.00

0.02

0.04

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5


Disp

lace

men

t [m

]

Occupantvelocity

Car velocity

Vel

ocity

[m

/s]

Time [s] (b) L4

Fig. 9 Velocities of the car and the occupant during the collision.

In order to investigate the motions of the car body and the occupant in detail, their velocities of case L1 and case L4 and their relative displacement are shown in Fig. 9. The car body velocity of case L1 takes 0.028 second to become zero, at that time the occupant keeps moving forward by inertia force. This difference in velocity causes a large relative displacement of 0.022m at 0.062 second and also the maximum occupant deceleration becomes large. Meanwhile, in case L4, the car velocity becomes zero at 0.031 second. The


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maximum relative occupant displacement is 0.017m at 0.065 second. This relative displacement is smaller than that of case L1. Moreover, case L4 has the lowest maximum occupant deceleration among the four specifications. High speed camera images of case L1 and case L4 are shown in Fig. 10. The maximum occupant deceleration takes place at 0.06 second. A and B in this figure show the relative distance at that time of case L1 and case L4, respectively. Since B is shorter than A, case L4 is judged having better performance in terms of the reduction of impact to an occupant.

L1

0.10 sec

0.08 sec

0.06 sec

0.04 sec

0.02 sec

0.00 sec

A B

L4

0.10 sec

0.08 sec

0.06 sec

0.04 sec

0.02 sec

0.00 sec

Fig. 10 Car and occupant motions with quasi-rectangular stiffness cases L1 and L4 (High speed camera photo 500FPS).

The index of R of the ride down effect, the kinetic energy Ek of an occupant and the

potential energy Ep of a seat belt at the time when the body velocity becomes zero were calculated with the measured data and Eqs. (4)-(6). The relations among R, Ek, Ep and the maximum occupant deceleration αp are shown in Fig. 11. The correlation r2 between R and αp is 0.983. Consequently, it is confirmed experimentally that the rectangular body deceleration characteristic results in a high index of the ride-down effect and provides advantage in regard to the occupant's protection. As shown in the lower graph of Fig. 11, when R increases, Ek decreases and Ep increases. However, since the increase in Ep is small compared with the decrease in Ek, their sum of Ek+EP decreases.


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18 20 22 24 26 280.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

L2

Ek Ep Ek+Ep

Ener

gy

[J]

Index of ride down effect R [%]

30

32

34

36

38

40

L4

L3

L3L1

L2

L4

r2=0.983L1

Occ

upan

t dec

eler

atio

n α p [m

/s2 ]

Fig. 11 Relationships among the ride-down index R, αp, Ek and Ep.

4. Experimental verification of the ride-down load stiffness

The ride-down load stiffness is embodied by combining two coil springs as shown in Figs. 12 and 13. The springs A1 and A2 are arranged in parallel with pre-load f0A2 on the spring A2. A plate with hinge is arranged in front of the spring A1 and this plate looses contact with the piston when the piston moves more than x1rd. At the beginning of collision, the car body pushes the piston of spring A2, and both springs A1 and A2 are compressed. Then, after piston moves more than x1rd, the reaction force of the spring A1 diminishes, as a result, only spring A2 continues to be compressed and it gives lower force. Therefore, the force-displacement characteristic becomes ride-down shape. The force-displacement characteristic of FA is expressed as

>+=≤++=

)()()(

1rd1A201A2A

1rd12A01A2A1A

xxfxkFxxfxkkF , (9)

where f0A2 is set up in order to have the maximum body displacement during a collision become 0.012m. In this experiment, maintaining the inclination of the force-displacement characteristic FA in early stages constant, the variation of time response of the occupant deceleration caused by the change of x1rd is observed. Spring constants of A1 and A2 are fixed as kA1=8750 N/m and kA2=587 N/m, respectively, and x1rd has 6 specifications (D1: 0.00272, D2: 0.00367, D3: 0.00383, D4: 0.00431, D5: 0.00465, D6: 0.00485m). As shown in Fig.14, for all specifications the force-displacement characteristics is designed so that the total amounts of energy absorption by the spring A are same when the maximum body displacement is 0.012m. The masses of the body and the occupant, the spring constant of a seat belt and the collision velocity are set as same as those for the quasi-rectangular experiment in the last section.


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A1

A2

Pre-Loadf0A2

Car body

Wall side

Hinge

(a)　Structure for Ridedown

x1rd

(b)　Hinge system Fig. 12 Structure of the spring system with ride-down load stiffness system.

Fig. 13 Picture of the ride-down load stiffness structure.

0.000 0.002 0.004 0.006 0.008 0.010 0.01205

1015202530354045

D5D6

D4D3

D2D1

Forc

e F

A [

N]

Displacement x1 [m] Fig. 14 Characteristics of the ride-down load stiffness system.


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4.1 Results of experiment The time responses of the body and the occupant decelerations measured from the

experiment are indicated in Fig. 15. The car deceleration shows a sharp peak soon after the collision. The peak value becomes larger as the ride-down shape becomes clearer in order from case D1 to case D6. However, the deceleration of occupant becomes smaller as the ride-down shape becomes clearer. In this condition, cases D5 and D6 show almost same minimal deceleration of occupant. The velocities and relative displacement of the car body and occupant in cases D1, D5 and D6 are shown in Fig. 16. The occupant velocity in case D1 reaches zero after the car body velocity becomes zero. While, the occupant velocity of case D5 reaches zero just before the car body stops, consequently, the maximum relative displacement becomes small. The occupant velocity of case D6 reaches zero before the car body stops. However, the relative occupant displacement has a slight large value compared with case D5. The motions in cases D1 and D5 taken by the high speed camera are shown in Fig. 17. The vertical solid line shows the maximum occupant displacement, and the vertical dashed line shows the maximum body displacement. At 0.04 second, the car body of case D1 has already rebounded and is moving backward. At this moment, the occupant is still moving forward. In case D5, low deceleration is maintained after the car body reaches xlrd. The time that the body velocity becomes zero is 0.057 second which is longer than that of case D1. Then, at this moment, the occupant has already moved backward. After 0.06 second, the rebound of the occupant is larger compared with that of the car body.

0.00 0.02 0.04 0.06 0.08 0.10-20

-10

0

10

20

30

40

D5D6

D4D3D2D1

Occ

upan

t dec

eler

atio

n [m

/s2 ]

Time [s]

-10

0

10

20

30

40

50

D5D4

D2D3

D6

D1

Car

dec

eler

atio

n [m

/s2 ]

Fig. 15 Effect of ride-down load stiffness on the decelerations.


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-0.04

-0.02

0.00

0.02

0.04

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5


Dis

plac

emen

t [m

]

Occupantvelocity

Car velocityVel

ocity

[m

/s]

Time [s]

D1

-0.04

-0.02

0.00

0.02

0.04

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5

1.0

Relative occupantdisplacement

Dis

plac

emen

t [m

]

Occupantvelocity

Car velocityVel

ocity

[m

/s]

Time [s] D5

-0.04

-0.02

0.00

0.02

0.04

0.00 0.02 0.04 0.06 0.08 0.10-1.0

-0.5

0.0

0.5

1.0

Relative occupantdisplacement

Dis

plac

emen

t [m

]

Occupantvelocity

Car velocityVel

ocity

[m

/s]

Time [s]

D6

Fig. 16 Velocities and displacement of ride-down stiffness cases D1, D5 and D6.


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D5

0.06 sec

0.07 sec

0.05 sec

0.04 sec

0.03 sec

0.02 sec

D1

0.06 sec

0.07 sec

0.05 sec

0.04 sec

0.03 sec

0.02 sec

: Maxmum car displacement: Maxmum occupant displacement

0.01 sec

0.00 sec

0.01 sec

0.00 sec

Fig. 17 Car and occupant motions with ride-down stiffness cases D1 and D5.

The correlation among the maximum occupant deceleration αp, the occupant kinetic

energy Ek, the seatbelt potential energy Ep, and the index R of the ride-down effect is shown in Fig. 18. αp decreases as R increases from case D1 to case D5. Regarding case D6, in spite of increase of R, αp increases. Case D5 has the minimum αp. R and αp are not related in linear as the case of rectangular load stiffness shown in Fig.11. From the relation among R, Ek and Ep described in the lower figure of Fig.18, as R increase, Ek tends to decrease but Ep increases from case D1 to case D4. Then from case D4 to case D6, Ek increases but Ep decreases. The reason for the increase of Ek is that the occupant reaches a negative velocity when the body velocity becomes zero. This agrees with the motion shown in Fig. 17.


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15 20 25 30 35 40 45 50 55-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

D2

Ek E

p Ek+Ep

Ener

gy

[J]


161820222426283032

D6D5

D6D5

D4

D3

D3D1

D2

D4

D1

Occ

upan

t dec

eler

atio

n α p [m

/s2 ]

Fig. 18 Relationships among, αp, Ek, Ep and the ride-down index R for various x1rd.

Theoretical analysis on this experiment was carried out. Fig. 19 shows the time history

of the decelerations of car body and the occupant. And, the correlation among the maximum occupant deceleration αp, Ek and Ep, and the index R of the ride-down effect is shown in Fig. 20. Comparing with experimental results shown in Fig. 18, it is seen that the time history and the correlation of this analysis agree well with the experimental results.

0.00 0.02 0.04 0.06 0.08 0.10-20

-10

0

10

20

30

40

D5D6

D4D3D2D1

Occ

upan

t dec

eler

atio

n [m

/s2 ]

Time [s]

-100

1020304050607080

D5D4

D2D3

D6

D1

Car

dec

eler

atio

n [m

/s2 ]

Fig. 19 Theoretical results of decelerations of the car and occupant for ride-down load stiffness.


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20 25 30 35 40 45 50-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

D2

Ek E

p Ek+Ep

Ener

gy

[J]


161820222426283032

D6D5

D6D5

D4

D3

D3D1

D2

D4

D1

Occ

upan

t dec

eler

atio

n α p [m

/s2 ]

Fig. 20 Theoretical results of relationships among αp , Ek and Ep and the ride-down index R.

5. Discussion

We discuss the above results by using the time history of the relative occupant displacement (x2 – x1) as indicated in Fig. 21. The occupant behavior when the car body stops can be classified into domain 1 and 2. Domain 1 is the time period that the occupant is moving forward before the car body stops. It is equivalent to L1 to L4 and case D1 to case D3 in the nonlinear spring of Figs. 7 and 14. Generally, since the spring characteristic of a car body is stiffer than that of the seat belt, the car body stops earlier than the occupant. Therefore, if the time of the car body stop is delayed by applying the nonlinear spring, the occupant’s kinetic energy after the car body stop decreases and the maximum occupant deceleration decreases. In this case, the index of the ride-down effect and the maximum occupant deceleration are linearly related as shown in Figs. 11 and Fig. 18.

On the other hand, domain 2 is the duration in which the occupant has already passed the maximum position and on the way of returning backward when a car body stops. It corresponds to the phenomena of case D4 to case D6 in Fig. 14. In this case, the relation between the occupant deceleration and the index of the ride-down effect is not linear. Case D5 has the minimum occupant deceleration that is the most desirable condition from the viewpoint of occupant protection.

0Time

Location to minimize themaximum deceleration ofthe occupant

x 2 -

x 1 Domain 2Domain 1

Fig. 21 Time history of relative occupant displacement.


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6. Conclusions

In order to clarify the relation between the ride-down effect and the behavior of the car body and the occupant by experiment, the models having the quasi-rectangular load stiffness and the ride-down load stiffness in the front-end of the car body were fabricated. Collision experiments were carried out and the following results were obtained.

1) The rectangular load stiffness of car body is effective to reduce the maximum occupant deceleration. Furthermore, the ride-down load stiffness, which is “hard in the initial stage and soft later” is recommendable. 2) The maximum occupant deceleration has smaller value in the case when the car velocity becomes zero, the occupant is already moving backwards by the restorative force of the seat belt. 3) The results of the experiment agree with the theoretical analysis.

References

(1) Martin, D. E. and Kroell, C. K., Vehicle Crush and Occupant Behavior, SAE paper, No.670034 (1967)

(2) Katoh, H. and Nakahama, R., A Study on the Ridedown Evaluation, 9th International Technical Conference on Experiment Safety Vehicles, pp.190-195 (1982)

(3) Evans, N. C., Furton, L. M. and David, A. C., Occupant Energy Management Technique for Restraint System Analysis and Design -Theory and Validation, SAE paper, No.922082 (1992)

(4) Bonello, K. J., Occupant Energy Management Technique for Restraint System Analysis and Design - Understanding the Physics of the System, SAE paper, No.922083 (1992)

(5) Huang, M., Laya, J. and Loo, M., A Study on Ride-Down Efficiency and Occupant Responses in High Speed Crash Tests, SAE paper, No.950656 (1995)

(6) Uenishi, K., Matsuhisa, H., Utsuno, H. and Park, J. G., Impact Reduction of an Automotive Occupant by "Ride Down" Effect in Head-on Collision, Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.70, No.697 (2004), pp. 2624-2630.

(7) Uenishi, K., Matsuhisa, H., Utsuno, H. and Park, J. G., Effects of the body and Seatbelt Design on Occupant Impact in car crash, Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.71, No.706 (2005), pp. 1877-1883.

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