MADYMO COMPUTER MODELLING
OF ENERGY ABSORBING REAR UNDERRUN
BARRIERS FOR HEAVY VEHICLES
- A PILOT STUDY
By
George Rechnitzer
Accident Research Centre
Roger Zou
Raphael Grzebieta
Department of Civil Engineering
March 1997
Report No. 112
·
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MONASH UNIVERSITY ACCIDENT RESEARCH CENTRE
REPORT DOCUMENTATION PAGE
Report No.
Date
112
1997
ISBN
0732606926
Pages
44
Title and sub-title:
Madymo Computer Modelling Of Energy Absorbing Rear Underrun Barriers For Heavy Vehicles
- A Pilot Study
Type of Report & Period Covered:
Author(s)
George Rechnitzer, Roger Zou
and Raphael Grzebieta
General engineering
Sponsoring Organisation(s):
This project was funded through the Centre's baseline research program for which grants have been
received from:
Department of Justice
Royal Automobile Club of Victoria (RACV) Ltd
Roads Corporation (VicRoads)
Transport Accident Commission
Abstract:
Simulations of test crashes has been carried out using two dimensional and three dimensional models
using the MADYMO computer program. These simulations have included seat-belted Hybrid III
dummies in the vehicle. Output includes the vehicle acceleration, velocity and force characteristics as
well as those of the Hybrid III dummy.
Comparison of the MADYMO results with the crash test results shows that the initial model
development provides very useful and reliable insight into the performance of the underrun barrier and
'occupant' response. The results also confirmed the significant benefits attainable in terms of occupant
protection (significantly reduced vehicle peak deceleration and occupant loading), though the use of
energy absorbing rear underrun barriers on heavy vehicles.
As with all model development it is also clear that improvements to the vehicle model itself are required,
in particular that of the vehicle's front end deformation characteristics (the crash pulse) to ensure more
accurate and realistic modelling.
The study has enabled the development of expertise in the use of MADYMO as a tool for the analysis
and design of crashworthiness systems, and has demonstrated the usefulness of this tool. This type of
program does require, however, the commitment of sufficient resources to maintain and strengthen the
experience and expertise in its use. This expertise would form an important resource for enhancing
Monash's and Victoria's vehicle safety and other injury research programs
KeyWords:
(IRRD except when marked*)
MADYMO*, safety, accident, injury, heavy
vehicle, design, vehicle occupants, under-ride
protection, energy absorption*
Reproduction
Monash University Accident Research Centre,
Wellington Road, Clayton, Victoria, 3168, Australia.
Telephone: +61399054371,
Fax: +61399054363
of this page is authorised
2
TABLE OF CONTENTS
EXECUTIVE
SUMMARy •.••.••....•........•.......•.....•.....•......•....•.•...........•............•...•.•.....•.....•....•....•.•...................•......•
1. INTRODUCTION
•.•.•.•..•.•..•.......•..•..•.•...•..•...•..•....•.•..•.•.•..................•.•.......•.•..•.•......................................•.............
2. MAD YM 0 MOD E LLIN G ................................................................•...............................................•.•................•.
3. DEVELOPMENT
OF THE MADYMO MODEL ...........................••.....................................•.......•.............•....
5
7
9
11
3.1 THE 'ELLIPSOID' MODEL
3.2 DEVELOPMENT OF HYBRID Ill, CAR, AND TRUCK INTERACTION MODEL
11
18
4. 2D MADYMO SIMULATION
22
4.1
4.2
4.3
4.4
INTRODUCTION
MODEL DESCRIPTION
ANALYSES CONDUCTED
RESULTS
5. 3D MADYMO SIMULATION
5.1
5.2
5.3
5.4
OF CRASH TEST .......................•.......•....................•.......................................
22
22
24
24
OF CRASH TEST ................................•..................•........................................
INTRODUCTION
MODEL DESCRIPTION
ANALYSES CONDUCTED
RESULTS
33
33
33
34
34
6. CON CL USI ON ......................................................................•.•..•........•..........•...•.•.•............•....•.•..•.•.•.•....•.•...•.....
43
7. RE CO MMEND ATI 0 NS ..........•.......•.•...•.•..•............................................................................•.................•...•.....
44
8. ACKN 0 WLEDG ME NTS .............................•.........•..........•.......•...•............•.........••..•.......•......•....•...•................•.
44
9. RE FE REN CES .....•....•........................................•.•..................................................................................•.•...........
44
3
n
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______
n.
__
._ •••
_
___
-
nO.
__ n
••
""
•
_
LIST OF FIGURES
1-1 -
FIGURE
ILLUSTRATION
OF ENERGY ABSORBING
REAR UNDERRUN
BARRIER SYSTEM ON REAR OF TRUCK, BEFORE AND
7
AFTER IMPACT
1-2 -
FIGURE
PHOTOGRAPH
OF THE CAR IN A CENTRED 48KPH IMPACT WITH THE ENERGY ABSORBING
WALL (REF. RECHNITZER
3-1
3-2
3-3
3-4
FIGURE
FIGURE
FIGURE
FIGURE
- STEP AI:
- STEP A2:
- MADYMO
- STEP A3:
(50KMIH),
FIGURE
FIGURE
FIGURE
13.9M/s,
VERIFICATION
=
CAR MASS
JOM/s (36KM1H),
CAR MASS
(Y-DlRECTION)
FIXED TO A
8
11
11
12
OFFICE OF ROAD SAFETY)
= JOOOKG,
= JOOOKG
CAR IMPACT INTO RIGID BARRIER
=
Vo
36KM/H
(V=36KM1H)
FOR RIGID BARRIER IMPACT;
VO
=
I3.9M/s
13
14
16
17
:
VERIFICATION
STEP A3:
VERIFICATION:
STEP A4
HYBRID
CAR IMPACT INTO RIGID BARRIER
CAR IMPACT INTO ENERGY ABSORBING
BARRIER.
(V=50KM/H)
V= 13.9M/s,
III RESULTS FOR CAR IMPACT WITH ENERGY ABSORBING
M= 1000KG
REAR UNDERRUN
BARRIER;
VO =
1OOOKG
3-9 -
MAD
FIGURE
3-10
- MADYMO
YMO
REAR UNDERRUN
3-11 -
VO
STEP A2:
= 1000KG
- STEP A4:
FIGURE
FIGURE
FIELD (Y-DlRECTION);
INPUT AND OUTPUT RESULTS
=
MCAR
FROM A PROJECT FOR THE FEDERAL
ACCELERATION
RIGID BARRIER IMPACT;
CAR MASS
3-5 - MADYMO
3-6 - MADYMO
3-7 -RESULTS
3-8 - STEP A5:
FIGURE
1996 (2);
ET AL,
ApPLIED
BARRIER
MODEL FOR STEP A5.
CAR IMP ACTING ENERGY ABSORBING
MODEL FOR: STEP A6.
CAR IMPACTING
STATIONARY
18
19
BARRIER
TRUCK FITTED WITH ENERGY ABSORBING
20
BARRIER
STEP A6:
SELECTED
RESULTS FOR CAR IMPACT WITH ENERGY ABSORBING
REAR UNDERRUN
BARRIER
FITTED
21
23
TRUCK; Vo = 13.9M/s,
CAR MASS = 1000KG;
TRUCK MASS = 10,000
KG
4-1- CRASH PULSES (Y-DECELERATION VS TIME) TAKEN FROM TWO 48KPH CRASH TESTS (REF (2»
FIGURE 4-2 - CAR PULSE OBTAINED FROM THE RIGID BARRIER TEST SHOWN IN FIGURE 4-1, AND USED IN THE
MADYMO ANAL YSES
TO STATIONARY
FIGURE
4-3 -
FIGURE
MADYMO
CAR MODEL:
O? VERSES DEFORMATION (STIFFNESS)
4-1, AND GIVEN IN FIGURE 4-2
FORCE
CAR PULSE DERIVED FROM FIGURE
4-4 - AxIAL LOAD -DEFORMATION CURVE FOR ENERGY ABSORBING
4-5 MADYMO MODEL FOR SIMULATION 1, ATT=O (CAR IMPACTING
FIGURE
FIGURE
FIXED TO CONCRETE
4-6
FIGURE
MADYMO
4-7
MADYMO
(4
MODULES
4-9
MADYMO
ATTACHED
FIGURE
4-10
4-11 -
1 AT
T= 140MS
(CAR IMPACTING
ENERGY ABSORBING
ABSORBING
FIGURE
1:
FIGURE
FIGURE
FIGURE
FIGURE
FIGURE
UNDERRUN
UNDERRUN
5-3 - RESULTS5-4- RESULTS5-5- RESULTS5-6 - 3D MAD
2D
FROM
KINEMATIC
2,
SEQUENCE
FROM T=O TO T=200MS.
AT T=OMS (CAR IMPACTING
28
29
1
ENERGY ABSORBING
KINEMATIC
BARRIER ATTACHED
SEQUENCE
FROM T=O TO T=280MS
TO INITIALLY STATIONARY
UNDERRUN
BARRIER
ATTACHED
TO INITIALLY STATIONARY
1, CAR
FROM T
REAR UNDERRUN
3D MADYMO
= 0-200MS
TRUCK,
IMPACTING
31
(CAR IMP ACTING ENERGY
V= 48KM/H
MODEL,
REAR UNDERRUN
SIMULATION
1,
BARRIER.
SIMULATION
OF CRASH TEST, SIMULATION
SIMULATION
OF CRASH TEST, SIMULATION
3D MADYMO
SIMULATION
OF CRASH TEST, SIMULATION
OF CRASH TEST, SIMULATION
32
37
CAR IMPACTING
38
39
40
41
42
BARRIER FIXED TO WALL.
3D MADYMO
SIMULATION
2
ENERGY ABSORBING
FOR 3D MADYMO
(CAR IMPACTING
TRUCK)
MAD YMO SIMULA TION OF CRASH TEST - SIMULA T10N
SEQUENCE
YMO
(CAR IMPACTING
30
2:
MODEL FOR 3D SIMULATION
ENERGY ABSORBING
BARRIER
TRUCK)
MODEL FOR SIMULATION
5-1 - MADYMO
5-2 - KINEMATIC
UNDERRUN
27
MODEL FOR SIMULATION
TO STATIONARY
RESULTS
BARRIER
WALL)
MODEL FOR SIMULATION
ENERGY ABSORBING
FIGURE
UNDERRUN
26
MODEL FOR SIMULATION
- MADYMO
23
23
STRUTS COMBINED)
ENERGY ABSORBING
ENERGY ABSORBING UNDERRUN BARRIER FIXED TO CONCRETE WALL)
FIGURE 4-8 - RESULTS FROM 2D MADYMO SIMULATION OF CRASH TEST - SIMULATION
FIGURE
BASED ON THE
WALL)
FIXED TO CONCRETE
FIGURE
OF VEHICLE ELLIPSOID
23
1
1
1
2
LIST OF TABLES
TABLE
TABLE
4-1 4-2 -
MADYMO
SUMMARY
MODEL
CONTACT
24
INTERACTIONS
OF KEY RESULTS FOR MADYMO
2D SIMULATION
1 AND 2
AND COMPARISON
WITH CRASH TEST
25
RESULTS
TABLE
5-1 -
SUMMARY
EXPERIMENTAL
OF KEY RESULTS FOR 3D SIMULATION
1 AND 2,
AND COMPARISON
WITH 2D SIMULATION,
AND
35
CRASH TESTS
4
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EXECUTIVE SUMMARY
The project aim was to develop a mathematical (computer) model of a car impacting an energy
absorbing rear underrun barrier on a heavy vehicle. This type of model will assist in the
development of prototype designs of energy absorbing underrun barrier systems (rear and front)
for heavy vehicles and reduce the cost of physical testing. A secondary aim was the development
of expertise in the use of this type of tool and explore further applications in terms of enhancing
our injury research capabilities. The project has drawn on the extensive design, testing, and crash
test work carried by Monash University for VicRoads and Federal Office of Road Safety on rigid
and energy absorbing underrun barriers.
MADYMO (MAthematical DYnamic MOdel) is a general purpose engineering computer
program using multibody and finite element (FE) analysis techniques. MADYMO is used
worldwide in industry and research for analysis of non-linear dynamic responses of the human
body and mechanical systems, and in particular for use in simulating vehicle collisions for
vehicle crashworthiness design, as well as for other injury prevention research such as in sport.
Analyses conducted and results
Crash tests of cars impacting energy absorbing rear underrun barriers were simulated using two
dimensional and three dimensional models created within the MADYMO program. These
simulations included seat-belted Hybrid III dummies placed in the vehicle. Output includes
vehicle acceleration, velocity and force characteristics as well information from the Hybrid III
dummy model.
The MADYMO analyses gave significantly reduced vehicle peak deceleration and occupant
loading, as seen by comparing the results from the MADYMO simulations for the energy
absorbing rear underrun barrier system and those for impacts with the rigid concrete barrier:
• the car deceleration is reduced to 30G from 46G (c/w 48G for rigid barrier crash test)
• peak head acceleration is reduced to 34G from 58G
• HIC is reduced to 167 from 483 (c/w 699 for a rigid barrier crash test).
The actual equivalent crash tests into the energy absorbing barrier attached to a rigid wall show
even greater reduction in the car's peak deceleration down to 20-25G from 48G and a passenger
HIC of271 compared with 699.
The total force on the energy absorbing struts of 470kN obtained from the 3D Madymo analyses
(for the energy absorbing underrun barrier attached to the rigid wall) compared very closely to
the total of 490kN obtained from the actual crash tests.
Conclusion
Overall the results from the 3D MADYMO simulations are in good agreement with actual crash
test results. Comparison of the MADYMO results with the crash test results shows that the
models developed provide very useful and reliable insight into the performance of the underrun
barrier system and occupant response with respect to the Hybrid III results.
The results also confirmed the significant benefits in terms of occupant protection, attainable
though the use of energy absorbing rear underrun barriers on heavy vehicles.
5
As with all model development it is also clear that improvements to the vehicle model itself (the
crash pulse) are required, in particular that of the front-end deformation characteristics to ensure
more realistic modelling.
Of particular value and interest was the ability to obtain comparative dummy response measures
for variations in crash parameters and design changes to the underrun barrier, using a vehicle
model with the Hybrid III ATD.
The study has enabled the development of expertise in the use of MADYMO as a tool for the
analysis and design of crashworthiness systems, and has demonstrated the usefulness of this tool.
To enable full use of this type of program does require, however, the commitment of sufficient
resources to maintain and further strengthen the experience and expertise in its use. This type of
expertise could form an important resource for enhancing Monash's and Victoria's vehicle safety
research as well as being useful for other injury research programs.
Recommendations
• That the use of computer modelling and analysis programs such as MADYMO be recognised
as a relatively low cost and significant tool which can be used to enhance Monash's
crashworthiness, accident research and injury prevention research .
• That sufficient resources be provided via the Department of Civil Engineering, Accident
Research Centre and key agencies, to support an ongoing program of research, development
and training of key personnel in the use ofMADYMO for research purposes.
6
_______
•
__ ••
n
_
1. INTRODUCTION
Improving vehicle crashworthiness design often requires crash testing to determine the actual
performance characteristics. It has long been recognised that computer modelling and simulation
can be an effective and relatively low cost tool to provide an initial consideration and analysis of
design alternatives. The use of suitable computer models to assist in the development of
prototypes can reduce the amount of costly physical testing.
MADYMO (MAthematical DYnamic MOdel) is a general purpose engineering program using
multibody and finite element (FE) analysis techniques. MADYMO is used worldwide in
automotive and industrial engineering, research laboratories and universities, for analysis of nonlinear dynamic responses of the human body and mechanical systems. Although originally
developed for studying occupant behaviour during car crashes, the MADYMO program is
sufficiently flexible to be used for modelling and· analysing collisions, vehicle crashworthiness,
crash victim safety, vehicle dynamics, and accident reconstruction involving many other vehicles
such as trains, aeroplanes, motor cycles, and even bicycles. It also provides for the assessment of
various restraint systems including seat belts and airbags. Because a number of models have been
developed relating to the response of the human body to impact injury, Madymo is also being
used to assess injury risk in sports and other activities. Simulations in both two and three
dimensions are possible with the 2D and 3D versions ofMADYMO respectively.
Figure 1-1 - Illustration of energy absorbing rear underrun barrier system on
rear of truck, before and after impact
The objective of this pilot project is to explore the modelling capabilities of MADYMO and to
develop a MADYMO model which can reproduce the physical characteristics of the impact
between a car and an energy absorbing rear underrun barrier as shown in Figure 1-1. The model
must be flexible enough to vary the car mass and speed, the truck mass and speed, and the
stiffness of the underrun barrier. This work has drawn on the extensive design testing and
experimental work carried out to date on rigid and energy-absorbing rear underrun barriers at
Monash University for VicRoads (3,5) and the Federal Office of Road Safety (2).
7
-
-
__ 0
_0
••
•
0.-
_
0
••
.0
0
_
Analyses conducted
The following analyses were carried out:
• Development and verification of MAD YMO model:
Using a simplified car model, a number of crash scenarios were investigated:
1) car in a deceleration field;
2) car impact into rigid barrier, at 36km/h;
3) car impact into rigid barrier, at 50km/h;
4) car impact into energy absorbing underrun barrier fixed to a wall;
5) Hybrid III ATD's restrained by lap-sash seatbelts added to the car model. Car impact
with the energy absorbing underrun barrier fixed to a wall, modelled; at 50km/h;
6) Hybrid III ATD's restrained by lap-sash seatbelts added to the car model. Car impact
with the energy absorbing underrun barrier attached to an initially stationary truck .
• 2-Dimensional MADYMO simulation of a car (including Hybrid III ATDs with seatbelts), in
a central impact into an energy absorbing underrun barrier attached to a wall, and secondly to
a truck .
• 3-Dimensional MADYMO simulation of a car (including Hybrid III ATDs with seatbelts), in
a central impact into an energy absorbing underrun barrier attached to a wall.
Figure 1-2 - Photograph of the car in a centred 48kph impact with the energy
absorbing barrier fixed to a wall (re! Rechnitzer et ai, 1996 (2),'from a project for the Federal
Office of Road Safety).
8
2. MADYMO MODELLING
Model development
MADYMO utilises both multibody analysis, which simulates the gross motion of systems of
bodies connected by complicated kinematical joints, and finite element techniques, used for the
simulation of structural behaviour.
The finite element method divides the actual continuum into finite volumes, surfaces or line
segments. Each element deforms according to specified load-deformation relationship. The
continuum is then analysed as a complex system, composed of relatively simple elements where
continuity is ensured along all boundaries between elements. These elements are interconnected
at a discrete number of points, or nodes. The data required for the simulation include initial nodal
positions and velocities, the nodes corresponding to each element, the connectivity, as well as the
properties and behaviour of the materials.
MADYMO offers a set of standard force models including seatbelts, airbags and interactions of
bodies with each other and their surroundings. User-defined subroutines can be added to the
program for special modelling purposes.
File creation
To create a MADYMO input data file the user first selects the number of multibody systems and
(for MADYMO 3D) finite element structures to be included in the simulation model. For
instance, a simulation model can consist of one multi body system for a dummy, one for a
deformable steering column and one for a child restraint system, and finite element structures
(MADYMO 3D) for the driver, passenger side airbag and the kneebolster. For crash dummies,
standard databases are available. Next, for each multibody system the number of bodies and their
configuration and for each structure, the finite element mesh, the element types and the material
properties must be specified.
An input data file is then set up which specifies the configuration, the mass distribution and the
general properties of the multibody systems Goint characteristics) and the finite element
structures.
Object and system modelling
The acceleration field model calculates the forces at the centres of mass of bodies or finite
elements due to a homogeneous acceleration field. This model is particularly useful for the
simulation of the acceleration forces on a vehicle occupant during an impact. It is not necessary
to apply the acceleration field to all bodies.
Planes and ellipsoids (lines and ellipses in MADYMO 2D) can be used to model a body and
represent its shape. These planes and ellipsoids are also used to model contact with other bodies
or with finite elements. Each ellipsoid has associated kinematic properties, such as mass,
stiffness, volume, inertial properties etc. The contact surfaces are of major importance in the
description of the interaction of the occupant with the vehicle interior. The elastic contact forces,
including hysteresis, are a function of the 'penetration' of the contact surfaces. In addition to
9
elastic contact forces, damping and friction can be specified. When Madymo simulations are
viewed, ellipsoids appear to 'penetrate' beyond the contact surface (see Fig. 3.3). The distance
the ellipsoid penetrates beyond the contact surface represents the deformation of the ellipsoid.
Madymo uses this deformation to calculate the associated contact forces etc.
For modelling energy absorbing systems of the type used in the underrun barrier, MADYMO has
three types of massless spring-damper elements available. The Kelvin element is an uniaxial
element which simulates a spring parallel with a damper. The Maxwell element is an uniaxial
element which simulates a spring and damper in series. Non-linear spring characteristics as well
as velocity dependent damping can be defined.
The seatbelt model accounts for initial seatbelt slack or pre-tension and rupture of seatbelt
segments. Elastic characteristics can be specified separately for each seatbelt segment and slip of
seatbelt material from one segment to another is accounted for. Sliprings, retractors and, in
MADYMO 3D, pretensioners can be applied.
In MADYMO 2D an empirical airbag model is available. The geometry of the airbag is
represented by an ellipsoid, elliptical cylinder or a cylinder having an arbitrary shape in the plane
of simulation. This force model generates contact forces between airbag and impacting objects.
Output
A large number of standard output parameters is available, such as accelerations, forces, torques
and kinematic data. MADYMO offers in addition to standard output quantities, the possibility to
calculate injury criteria like femur and tibia loads, Head Injury Criterion (HIC), Gadd Severity
Index (GSI), Thoracic Trauma Index (TT!) and Viscous Injury Response (VC).
Results of the simulation are stored in a number of output files, which are accessible by
postprocessing programs. Programs are available for the visualisation of the kinematics, time
histories and cross plots.
10
3. DEVELOPMENT OF THE MADYMO MODEL
3.1 THE 'ELLIPSOID' MODEL
In order to gain expertise in the use of MADYMO, and to aid in the verification of the model
used in the subsequent full 2D and 3D simulations, simplified analyses were conducted. The
verification was done in two stages. Stage 1 (Steps AI-A4) is to verify the ellipsoid model, and
stage 2 (Steps A5 & A6) is to verify the dummy, car and truck interaction. A simplified car pulse
is assumed for the verification.
Step A1: A simplified car pulse as shown in Figure 3-1 (A) below, was assumed and input as an
acceleration field acting on the vehicle. With a given mass (lOOOkg), initial velocity
(lOm/s or 36km/h), the equivalent stiffness of the vehicle front end (modelled by an
ellipsoid) was determined (refer Figure 3-1 (B)).
1--
Input: acceleration
(-m/5"Z)
--
I
Output: acceleration
vs ctisp (rn)
(Tn/SUZ)
50
o
-50
-100
-150
-200
50
100
200
150
0.1
0.2
0.3
Displacement
Time (ms)
0.4
0.5
(m)
(B) Output acceleration v. vehicle crush
(A) Input car pulse (assumed)
Figure 3-1 - Step AI: Applied acceleration field (Y-direction); car mass = IOOOkg, Vo = 36km1h
Figure 3-1 (B) shows the displacement (crush) of the front of the vehicle and the resultant
deceleration. At a crush of 0.42 metres the deceleration is 20g, matching the input pulse.
Step A2: With the same mass and initial velocity used in Step AI, the equivalent car frontal
stiffness determined from step Al (see Figure 3-1 (B)), was input into the vehicle model
to determine if the acceleration pulse in Fig. 3.1 (A) would be obtained. The car was
impacted into a rigid barrier at 10-m/s (36km/h).
--
Input:
ELastic
Force
eN)
vs deformation
1--
(m)
Outpu.t: acceleration
(m/s"2)
I
*le3
250
200
150
100
50
-250
0.1
0.2
0.3
Displacement
0.4
0.5
0.6
o
50
lOO
150
200
250
Time (ms)
(m)
(B) Output acceleration v. time
(A) Input car pulse (stiffness)
Figure 3-2 - Step A2: Rigid barrier impact; Vo = IOm/s (36km1h), car mass = IOOOkg
11
l/l
E
1.0
C\J
l/l
ooE
T""
It::""
-
0
Concrete barrier
00
E
/J /J
l/l
~II~
-
/
>-
N
Figure 3-3 - MADYMO Verification: Step A2: Car impact into rigid barrier (V=36km/h)
The output shows the vehicle position at t=O, 25, 50 and lOOms. Note the ellipsoid's apparent
'penetration' of the barrier. This apparent penetration represents the deformation of the
ellipsoid - that is, the crush of the car's front section.
12
Comparison of Figure 3-2 (B), which is the output (acceleration versus time) from the car
impacting the rigid barrier, with Figure 3-1 (A), which is the original definition of the car pulse,
indicates the same peak acceleration of 20g at 50ms was obtained with the two curves having
similar shape.
Step A3: Step A3 (see Fig. 3-5) increases the car speed to 50km/h (13.9m/s), from the 36km/h
used in Steps A2 and A3. This required extending the car's crush characteristics to
beyond O.5m as shown in Figure 3-2 (A) to that shown in Figure 3-4 (A), with a crush up
to 2.0m at a load of 290kN. Results of the simulation are shown in Figure 3-4 (B), (C)
and (D). These show a maximum deceleration of 24g, corresponding to the resultant force
of 240kN and maximum crush of O.66m, values which are confirmed by independent
calculation 1.
••
g
..
..l
150000
300000
....
0 100000
200000
50000
0
250000
0.5
1.5
Deformation
2
(m)
(A) Input - car front end stiffness
1---50
Ellipsoid:
~
0
Y-com.p. acceleration
-
~~
(m./snZ)
0
1I~
00
Iba
l~O
1---
I
Rnull~nt
Forr;;~ (N)
1---
1
RliIsuUant
Force
(H)
I
41eJ
250
~~
~
200
150
100
50
0.1
Time (ms)
Time (ms)
(C)
(B)
Output:-
resultant
car acceleration
v. time
Impact force v. time
0.2
0.3
0.4
Displacement
0.5
0.6
0.7
(m)
(D)
Impact force v. displacement
Figure 3-4 - Step A3: Input and output results (Y-direction) for rigid barrier impact; Vo =
13.9m/s (50km/h), car mass = 1000kg
I
By equating the kinetic energy of the car (O.5my2) to the work done in crushing the car front (Fs), and using the
stiffness relationship from Fig. 3.5(A), the deformation's'
can be calculated. These calculations confirm the
Madymo results.
13
(fl
E
10
C\I
(fl
ooE
T""
I<:'"
Concrete barrier
/J
~\
m
-~
//1;
~ (~Il~
>-
N
Figure 3-5 - MADYMO Verification: Step A3: Car impact into rigid barrier (V = 50km/h)
The output shows the vehicle position at t=O, 25, 50 and lOOms. The apparent
penetration of the barrier by the ellipsoid represents the deformation of the
ellipsoid - that is, the crush of the car's front section.
14
Step A4: Using the same ellipsoid stiffness (ie. front of car) used in step A3, the vehicle was
modelled to impact an energy absorbing underrun barrier which was in-turn attached to a
concrete barrier (Figure 3-6). The energy absorbing module on the barrier was modelled
as a Maxwell element. The result of the simulation is presented in Fig. 3-7.
The following main points are noted from Figure 3-7:
• Figure 3-7 (A) shows the resultant force-displacement response for the energy absorbing
module2 (Maxwell element) on the underrun barrier. This shows a build up of force to 120kN
and remaining constant up to a crush of O.5m, at which point the module becomes a rigid
strut. As the analysis is two-dimensional, the force-displacement relationship represents the
total for all four struts on the barrier.
• Figure 3-7 (B) shows the resultant force-time response for the energy absorbing module on
the underrun barrier, over an impact duration of 200ms. The average force value per strut is
nominally 1/4 of that shown, as there are 4 struts.
• Figure 3-7 (C) shows the resultant force on the car from the impact, with a peak of around
180kN .
• Figure 3-7 (D) shows the car crushes O.65m.
• Figure 3-7 (E) shows the for the car the Y-acceleration component peaks at 12g.
• Figure 3-7 (F) shows the change of velocity of the car with time during impact.
It should be noted that the interaction of the ellipsoid model used for the rear face of the barrier
with the ellipsoid model for the front of the car (refer Figure 3-6) results in a force vector which
changes in direction at this interface due to the displacement of the barrier and deformation of the
car front. Thus, the horizontal (Y) acceleration of the car shown in Figure 3-7 (E), cannot be
directly compared with the resultant forces shown in Figure 3-7 (C) and (D) as these need to be
resolved in the appropriate direction. Similarly, the resultant force in the Maxwell element shown
in Figure 3-7 (A) needs to be resolved in the X and Y direction for any direct comparison with
the other output parameters.
2
This is based on the material properties and test results for the energy absorbing system presented in ref. (2).
15
en
en
oE
E
Lt)
Lt)
(\J
..-
IC'"
Concrete barrier
en
en
E
E
Lt)
Lt)
(\J
,.....
>-
J!
N
\
Figure 3-6 - MAD YMO Verification: Step A 4
Car impact into energy absorbing underrun barrier (Vo = 13.9 m/s, m = 1000kg)
16
ResuLta.nt Force (N) I
Ma.xweLl. ete77\.ent:
50
-50
-50
-100
-100
-150
-150
-200
-200
-250
-250
Displacement
-----
50
(B)
(A)
(m)
Car - Barns".:
150
200
250
300
350
Time (ms)
-----
Force (N) I
ResuLtant
CaT
-
BarT'i.or: Ro.ulta.nt
FOTct;l
CN) I
*1.,3
*1e3
200
200
150
150
100
100
50
50
o
100
~O
o
100
l~O
200
200
300
300
0.1
(D)
(C)
Time (ms)
----
:SOk.ta.c
-
EUipsoic::t:
Y-comp.
0.2
0.3
0.4
0.5
Displacement
acceleration
----
(1n/s .•.•Z)
~OAl.l",1-
0.6
0.7
(m)
'V.toc«" (tn/.)
e«r ",.loe,",,: Y-eom.p.
12
-20
10
-40
-60
-60
-100
-120
o
50
100
150
200
250
300
350
~o
50
100
100
200
250
~
3~
(F)
(E)
Time (ms)
Ti~
(ms)
Figure 3-7 -Results - Step A 4: Car impact into energy absorbing barrier. V=13.9m/s, m= 1OOOkg
17
3.2 DEVELOPMENT OF HYBRID Ill, CAR, AND TRUCK
INTERACTION MODEL
Two further analyses were performed to examine:
Step A5: the incorporation of the Hybrid III ATD and seatbelts into the vehicle model;
Step A6: attaching the energy absorbing barrier onto a stationary but movable truck.
Step A5: The 2D Hybrid III A TD and belts were merged with the vehicle model to form an
integrated dummy and vehicle model. The simulation involved impacting the vehicle into
an energy absorbing underrun barrier fixed to a concrete wall. The car stiffness, car mass
and initial velocity were the same as in step A4. Output from this model includes HIC
values and chest acceleration over 3ms. Figure 3-9 shows the Madymo model and
simulation. Figure 3-8 shows a small sample of the results that can be obtained using the
Hybrid III ATD.
Head: Y-comp.
acceLerat'ion
Cm/s·"2)
Upper
I
20
TDrso:
Y-cornp.
(m/s .•...
Z)
acceleration
2°1
o
o
-20
-40
-60
60
-:~j
-80
-100
-120
:~
-140
::1
-160
o
50
100
150
200
250
300
350
o
Time
(A) Hybrid
III Y-component
,
50
100
150
"
200
250
300
350
Time
accel. for head
(B) Hybrid
III V-component
accel. for upper torso
Figure 3-8 - Step A5: Hybrid /11results for car impact with energy absorbing rear underrun
barrier; Vo = 13.9m/s, mcar = 1000kg
Figure 3-8 (A) shows the peak Y-component head acceleration of 14g and overall impact
duration of over 250ms; Figure 3-8 (B) shows the peak Y-component upper torso acceleration of
around 16g and overall impact duration of over 250ms.
Step A6: In this case the model from Step A5 includes attaching the barrier to a stationary but
movable truck (see Fig. 3-10). Interaction between the ATD, car and barrier is
determined, with HIC and chest G's given. Figure 3.11 presents a sample ofthe results.
Figure 3-11 (A) and (B) show very similar results to Figure 3-8 for the Hybrid III head and torso
acceleration
Figure 3-11 (D) indicates that the truck post-impact speed was 1.4m/s. Figure 3-11 (F) shows the
peak axial force on the four energy absorbing elements was 350kN (an average force of
88kN/strut). The Madymo result for the post impact truck speed of the truck can be compared to
the theoretical calculation, based on the principle of conservation of momentum, as follows:
As the car is stationary after impact, all the momentum is transferred to the truck, then:
mtVl=m2V2; 1000x13.9 = 10,000xV2;
hence V2 = 1000x13.9/10,000 = 1.39m1s
i.e.
V 2 = 1.4m/s, which corresponds to the Madymo result.
18
en
oE
en
ooE
LO
C')
en
E
oo
o
en
E
8
,.....
Figure 3-9 - MADYMO Model for Step A5. Car impacting energy absorbing barrier
19
en
oE
Lt)
•....
en
ooE
C')
en
ooE
o
en
E
o
Lt)
en
oE
Lt)
C\I
Figure 3-10 - MAD YMO Model for Step A 6: Car impacting stationary truck fitted
with energy absorbing rear underrun barrier
20
Head: Y-com.p.
acceLeration
Upper Torso: Y-C0171p.
(m.~
acceleration
(m/sU2)
50
40l
201
o
o
-20
-40
-60
-50
-BO
-100
-lOO
-120
-150
-140
-160
o
-200
50
100
150
200
250
300
350
o
50
100
150
Time
250
300
350
Time
III Y-component
(A) Hybrid
200
acceI. for head
Car: Res.
(m/s)
velocity
III Y-component
(B) Hybrid
acceI. for upper torso
Truck: Res. vetocity
I
14
1.6
12
1.4
(1TL/s)
I
1.2
10
8
0.8
0.6
6
0.4
4
-----,
200
0.2
T
T
1
250
300
350
lOO
50
150
Time
Body
-
250
300
350
Time
(C) Car velocity v. time
Ellipsoid
200
Barrier:
ResuUant
(D) Truck velocity v. time
Force
(N)
Maxwell
ELe: ResuLtant
Force
(N)
I
50
'le3
0
-200
-50
500
-lOO
-300
-250
-150
-350
*le3
150
200.
loo-I
I
50
o
o
50
100
150
200
250
300
350
100
Time
150
200
250
300
350
Time
(E) Car ellipsoid resultant force v. time
(F) Maxwell element resultant force v. time
Figure 3-11 - Step A6: Selected results for car impact with energy absorbing rear underrun
barrier fitted to stationary truck; Vo = 13.9m1s, car mass = 1000kg; truck mass = 10,000 kg.
21
4. 2D MADYMO SIMULATION OF CRASH TEST
4.1 INTRODUCTION
In Section 3, a simplified car pulse was utilised (Figure 3-1 (A) & Figure 3-4 (A)) in order to
understand how MADYMO models can be developed and used to simulate vehicle impacts,
including incorporation of seatbelted Hybrid III ATDs and energy absorbing underrun barriers.
In this section, the car pulse shown in Figure 3-4 (A) is replaced with the actual crash pulse of a
Ford Falcon obtained from an experimental barrier crash test at 48km/h, shown in Figure 4-1.
The 2D MADYMO simulations are for a car in a centred impact into an energy absorbing
underrun barrier attached to a fixed wall, and for the same system attached to a truck. Figure 1.2
shows one of these crash tests (described by Rechnitzer; 2; 1996), with the crash pulse also
shown in Figure 4-1.
4.2 MODEL DESCRIPTION
The model consists of three systems: the Hybrid III model as system 1; the vehicle model as
system 2, and the truck underrun barrier and stationary truck as system 3. The energy absorbing
modules which connect the barrier cross-beam and chassis are modelled using Maxwell
elements. The Madymo model and initial position of all three systems is illustrated in Figure 4-5.
Vehicle model
The vehicle model represents a Ford Falcon and is a separate one-body system. Planes and
ellipses are connected to this body to represent the vehicle geometry. The seat and the floor are
modelled by rigid planes and they both are connected to vehicle system. In this model the car has
an initial velocity of 48 km/h and a mass of 1830kg, mass moment of inertia about the x-axis of
3200kgm2. The equivalent stiffness of the vehicle ellipsoid (used in MADYMO to model the
front of the car) is given in Figure 4-3 and is derived from Figure 4-1 (for impact with a rigid
wall). This load-deformation characteristic is assumed to be the same when modelling the car
crash into the truck underrun barrier.
Dummy model
A 50th percentile Hybrid III dummy is seated in the vehicle and restrained by a separate shoulder
and lap seatbelt. The dummy interaction is only with the seat and seat belt system. This dummy
model is for a 'passenger' and is part of the MADYMO database. A 'driver' dummy is also
available in Madymo but was not used in these analyses. For details on dummy model refer to
the database described in the MADYMO Databases manual (Part I, Chapter 2). The Hybrid III
50th percentile male dummy was used to calculate the injury parameters: HIC for the head
resultant acceleration, and the upper torso resultant acceleration over 3ms.
Underrun barrier and moveable truck
The energy absorbing underrun barrier and truck are modelled in the same system. The truck has
a mass of 10,OOOkg,and a mass moment of inertia about the x-axis of 20,OOOkgm2.The truck is
stationary but unrestrained.
22
c',
10
~
r!ZIRBrt
=
/
.rA;::
-400 011
rrI5J802.~
r:.,..
_____ .0 __ , ••••
" «'ll'::"5
-300
'f" -200
••
I
9
I012 100
for
0
-100 0·r5
r ~
I
I\
G',
:::Vy,',,':";
~ii
F121
RH B/J?IL
-40f----------·------·':1!-------m----------i--,·
\[
0.05
LONG
-.-....--...--,-------
0.1
Time
0.2
0.15
-500
secs
Ture (s)
Figure 4-1- Crash pulses (y-deceleration vs time)
taken from two 48kph crash tests (rei (2))
Figure 4-2 - Car pulse obtained from the rigid
barrier test shown in Figure 4-1. and used in the
MADYMO analyses
The solid line is for impact with the energy absorbing
rear underrun system; the dashed line is from a
standard rigid barrier test
••
~
"
.~.- .....................................................................................................................................................
..
'"'
400000
900000
300000
600000
700000
800000
200000
100000
500000
••
I .,
...............
--
..........
1'1
~
III
to.
o
o
0.5
2
1.5
DefolllUltion (m)
Figure 4-3 - Madymo car model: Force m verses deformation (stiffness) of vehicle ellipsoid
based on the car pulse derivedfrom Figure 4-1, and given in Figure 4-2
Modelling the energy absorbing strut (Maxwell element model)
Energy absorbing modules which connect the barrier cross-beam and chassis are modelled using
Maxwell elements. The stiffness is determined experimentally (ref (2» and is shown (simplified)
in Figure 4-4. The energy absorption capacity of the system is 45kJ over an initial 400mm of
compression; and around 65kJ at a deformation of 450mm. In comparison the kinetic energy of
car (mass = 1800kg) travelling at 48km/h is 160kJ.
600000
f
500000
/
I
400000
z
:;
..
o
300000
..J
200000
100000
o
o
100
200
Displacement
300
400
500
(mm)
Figure 4-4 - Axial load -deformation curve for Energy Absorbing Modules (4 struts combined)
23
Contact interactions
The interactions between the Hybrid III ATD and the vehicle interior are represented by planeellipse contacts. The interaction between dummy parts is represented by an ellipse-ellipse
contact. The interaction between car and underrun barrier is represented by an ellipse-ellipse
contact. The interactions between car wheels and road surface are represented by plane-ellipse
contacts. All contact interactions are summarised in Table 4-1.
Interaction
23 711
4,5
6,
10,
8,9
12,
14,
13
15
Ellipsoid-Ellipsoid
Plane-Ellipsoid
seat
cushion
torso
seat
back
lower
torso
car
front
end
barrier
head
seat
back
-- plane
upper
torso
foot
plane
--heel
shoe,
left
and
chin
floor
road
-Identifier
plane
upper
plane
--torso,
-lower
car
heel
front
rear
left
shoe,
wheels
and
wheels
left
right
andright
right
stop
left
-and
right
shoe
11,2
..
Table 4-1- MADYMO Model Contact Interactions
Integration parameters
This simulation uses the 5th order Runge-Kutta
timestep. The initial time step is lOE-3 ms.
Merson integrator method with a variable
Output parameters
Kinematic output is stored every 2ms. Time history data are stored every 1ms. The time data
selected is comprised of decelerations; the Hybrid III head, upper torso and lower torso
decelerations; the relative displacement between the car and barrier head; relative compression of
Maxwell elements; linear and angular velocity of the car; forces between the car and the barrier
head; and forces in the Maxwell elements and seatbelt. Furthermore, the head injury criterion
(HIC 36 ms) and the maximum acceleration (3MS) of the upper torso were determined.
4.3 ANALYSES CONDUCTED
• Simulation 1 comprises the vehicle impacting at 48km/h an energy absorbing rigid barrier
attached to a concrete wall .
• Simulation 2 comprises the vehicle impacting at 48km/h an energy absorbing barrier attached
to the rear of an initially stationary truck.
4.4 RESULTS
The results of this simulation are comprised of deformation, accelerations, velocities, interaction
forces, peak values and injury parameters. A sample of results are presented in Figure 4-8 for
Simulation 1; and in Figure 4-11 for Simulation 2. Figure 4-5 to Figure 4-7, and Figure 4-9 &
Figure 4-10 show the vehicle and Hybrid III motions at various time intervals during the impact,
24
•
for Simulations 1 & 2, respectively. The key results and a comparison with the experimental
crash test are summarised in Table 4-2 below.
Car peak acceleration
Resultant car- barrier force
Simulation 1
Simulation 2
Crash test
Eng-abs. underrun
barrier attached to
Eng-abs. underrun
barrier attached to
wall
Eng-abs. underrun
barrier attached to
truck
30g
575kN
30g
575kN
20-25G
wall (ref2)
Maximum Acceleration of Upper
Torso - 3ms
Table 4-2 - Summary of key results for Madymo 2D Simulation 1 and 2 and comparison with
crash test results
From Table 4.2 the Madymo model car peak deceleration of 30G compared moderately well with
the 20-25G measured in the actual crash tests. Similarly the HIe value of 123, considering the
modelling approximations, were surprisingly close to the value of 271 (for the passenger)
measured in the crash; as was the 'maximum acceleration of Upper Torso - 3ms' of 225
compared with 264 in the crash test.
It is important to note that the vehicle's front structure stiffness characteristics used in the
Madymo analyses are those derived from a full frontal barrier impact, and this stiffness would
most likely be greater than for the interaction with the underrun barrier. This higher stiffness
would result in higher vehicle decelerations, as found in the Madymo analyses.
It is also noteworthy that the acceleration and force results for Simulation 2 (where the barrier is
attached to a moveable truck) are slighter higher than for Simulation 1 (where the barrier is fixed
to a wall), contrary to initial expectations. It is probable that in such a dynamic system, actions
become a complex function of the particular combination of stiffness characteristics and masses.
Further exploration of this effect would require a series of analyses with varying parameters,
which though of interest was beyond the scope of this study.
3 The peak forces on the underrun barrier in the crash test can be calculated from the peak deceleration
measured
on the car, and using Newton's formulae F=ma. This gives F=1800x25x9.8 = 441kN. Resolving this horizontal
force to the angle of the MaxweIJ elements gives F= 490kN which is very similar to the value of 460kN from the
Madymo model.
25
Figure 4-5 MADYMO modelfor Simulation 1, at t=O (car impacting energy
absorbing underrun barrier fixed to concrete wall)
26
11
Q)
.§
~
Figure 4-6 MADYMO modelfor Simulation 1, at t=140 (car impacting energy
absorbing underrun barrier fIXed to concrete wall)
27
\...,_
r-~'-
fc'
',""
- ):J
t-;:
-1,-",·
'\'1<-:'JJ
f'+---r'"
~. \
ri}>
-
-'~~
I
7"1,._'\
.
,','.~
{m~ -
(/)
oE
CO
T""
Figure 4-7 MADYMO modelfor Simulation 1: kinematic sequence from t=O to t=200ms.
(car impacting energy absorbing underrun barrier fixed to concrete wall)
28
Figure 4-8 - Results from 2D Madymo simulation of crash test - Simulation 1
(car impacting energy absorbing underrun barrier fixed to concrete wall, v= 48km/h.
-----
baTT'i.IBr2:.f"rc
-
Car
-
Barr'ier:
Res-utta.-nt FOTce
eN)
1
250
150
lOOJ
Time (ms)
Time (ms)
(A) Car resultant
.---
barr';u .•..Z.frc
_ Att.
(B) Resultant
acceleration
Shoo Part:
Rgs-u-Lta'n.t
Fore""
eN)
I
car-barrier
barr'i.G1rZ.£ac - Hea.d.: Res.
I ------
force
a.cc .••t.Q~a.t":'on (m/s·-Z)
1
100
L
0-1
o
250
50
Time (ms)
Time (ms)
(C) ATD resultant
(D) ATD head resultant
belt force (sash)
Max-uJeLl element:
Resultant
Force
eN)
-----
I
~le3
Maxwelt
element:
acceleration
ResuLta.nt Force eN) I
'"le3
100
tOOl
I
I
oh
L~,
-100~
:::1
-100
~200
'I
-300
-400
-400j
-500
I
o
"
50
100
150
"
200
250
-500
Time (ms)
(E) Resultant
0.1
0.2
0.3
0.4
0.5
0.6
(F) Resultant force - Maxwell elements (F v D)
force - Maxwell elements (F v T)
29
Figure 4-9 MADYMO modelfor Simulation 2, at t=Oms (car impacting energy
absorbing underrun barrier attached to stationary truck)
30
,--
un
--- -
---
n
_
(/)
oE
ex)
C\l
ill
~
:::iE
(/)
oE
ill
~
ex)
(/)
(/)
E
o
o
ill
~
oE
C\l
:::iE
:::iE
~
ill
~
:::iE
Figure 4-10 MADYMO modelfor Simulation 2: kinematic sequence from t=O to t=280ms.
(car impacting energy absorbing underrun barrier attached to initally stationary truck)
31
Figure 4-11 - Results from 2D Madymo simulation of crash test - Simulation 2 (car impacting
energy absorbing underrun attached to initially stationary truck, v= 48km/h.
-----
(T71./",··2) I
ReS'. acceLerat;.o'n.
EU'i.pso'ict:
Fa.cM
Res"t..LLtaTLt
I
eN)
3>0
500
250
200
300
150
100
50
100
150
200
250
300
350
Time (ms)
Time (ms)
(A) Car resultant acceleration
-----
"ea-et: Res. a.cce~era.t;'on
(B) Resultant car-barrier
(TT\./s~~2)
-----
1
truck.Ire
force
- Att. Shoo Part: Re:ndta:n.t
Force
eN)
·loe3
250
200
150
100
50
o
o
150
200
250
300
350
300
Time (ms)
Time (ms)
(C) ATD head resultant acceleration
----
Ma.%'UJeLt
350
IIl.nnllnt: ResuLta.nt Force
eN)
(D) ATD resultant belt force (sash)
I
-----
Truce:
Y-COTn.;p.
vetoci.tv
(TT1./s) I
2.5
1.5
-200
-400
".j
-500
o
,
D.l
,
0.2
,
0.3
Displacement
,
0.4
,
50
O.S
100
150
200
250
300
350
Time (ms)
(m)
(F) Truck Y-component velocity
(E) Resultant force - Maxwell elements (F v D)
32
I
5. 3D MADYMO SIMULATION OF CRASH TEST
5.1 INTRODUCTION
Following on from the 2D Madymo simulation set out in the preceding Section 4, the 3D version
of Madymo was used and the vehicle models developed to be three-dimensional. This is
particularly useful and important for crash analyses as the systems are usually non-linear
(principle of superposition, as used in linearly elastic analyses, can not be used), geometrically
asymmetric (offset impacts) and not isotropic in material properties. The 3D simulation enabled
each of the four energy absorbing struts on the barrier to be modelled separately, allowing
individual strut loads to be obtained rather than average values as from the 2D analysis.
Although the 3D analysis provides for offset impacts to be modelled, this project was restricted
to centred impacts.
The 3D MADYMO simulation was for a car (based on a Ford Falcon) in a centred impact into a
energy absorbing underrun barrier attached to a fixed wall. This models an actual crash test
described by Rechnitzer (2; 1996). The car pulse from the standard barrier test (Figure 4-1) was
used to determine the characteristics4 of the load-deformation of the front end of the car as shown
in Figure 4-3. The Hybrid III 50th percentile male dummy is used to calculate the injury
parameters HIC for the head resultant acceleration and the upper torso resultant acceleration.
5.2 MODEL DESCRIPTION
As in the 2D simulation, the model consists of three systems: dummy model as system 1, vehicle
model as system 2, and truck underrun barrier as system 3. The underrun barrier cross-beam is
modelled as a flexible beam. The four energy absorbing modules which connect the barrier
cross-beam and chassis are modelled using Maxwell elements. The models of all three systems
are illustrated in Figure 5-1.
Vehicle model
The vehicle model represents a Ford Falcon and is a separate one-body system. Planes and
ellipses are connected to this body to represent the vehicle geometry. The seat and the floor are
modelled by rigid planes and they both are connected to the vehicle system. In this model the car
has an initial velocity of 48 km/h and a mass of 1830kg.
Dummy model
A 50th percentile Hybrid III dummy is seated in the vehicle and restrained by a separate shoulder
and lap seatbelt. Dummy interaction is only with the seat and seat belt system. This dummy
model is for a 'passenger' and is part of the MADYMO database. For details on the dummy
model refer to the database described in the MADYMO Databases manual (Part Il, Chapter 2).
This load-deformation characteristic is assumed to be the same when modelling the car crash into the truck
underrun barrier. The engagement of the car frontal structure with the underrun barrier can be quite different when
impacting a full face barrier.
4
33
Underrun
barrier
model
The underrun barrier model is based on the actual design used in the underrun crash tests
described in Rechnitzer et al (2: 1996). The barrier cross-beam is modelled using flexible beams,
with properties based on the steel 100mm x 100mm x 3mm square hollow section.
Maxwell element model
Energy absorbing modules which connect the barrier head and chassis are modelled using
Maxwell elements. The stiffness is determined experimentally, and is approximated in Figure 4-4
Note that this figure shows the load deformation characteristics for the four elements combined.
Thus for the 3D model, each element has one quarter of the stiffness determined from this curve.
Contact interactions
The interactions between dummy and vehicle interior are represented by plane-ellipse contacts.
The interaction between dummy parts is represented by an ellipse-ellipse contact. The interaction
between car and underrun barrier is represented by an ellipse-ellipse contact. The interactions
between car wheels and road surface are represented by plane-ellipse contacts. Refer to Table 4-1
for contact interactions.
Integration
parameters
This simulation uses the 5th order Runge-Kutta
timestep. The initial timestep is IOE-3 ms.
Merson integrator method with a variable
Output parameters
Kinematic output is stored every 2ms. Time history data are stored every Ims. The time data
selected is comprised of decelerations; the Hybrid III head, upper torso and lower torso
decelerations; the relative displacement between the car and the barrier head; relative
compression of Maxwell elements; linear and angular velocity of the car; forces between the car
and the barrier head; and forces in the Maxwell elements and seatbelt. The head injury criterion
(HIC 36 ms) and the maximum acceleration (3MS) of the upper torso were also determined.
5.3 ANALYSES CONDUCTED
• Simulation
1 models
the vehicle impacting an energy absorbing barrier attached to a fixed
wall, at 48km/h. The barrier cross-beam is represented by a flexible beam .
• Simulation 2 models the vehicle impacting a rigid wall at 48km/h, simulating the standard
48km/h rigid barrier impact test.
5.4 RESULTS
The results of this simulation comprise deformations, accelerations, velocities, interaction forces,
peak values and injury parameters. The Madymo model and kinematic sequence during the
impact are shown in Figures 5-1 & 5-2. The results for Simulation 1 are give in Figure 5-3; the
individual loads in each of the Maxwell elements is given in Figure 5-4 (force vs deformation)
34
and Figure 5-5 (force vs time). The results for Simulation 2, impact with the rigid wall is given in
Figure 5-6.
The key results and comparison with the 2D model and experimental test results are summarised
in Table 5.1 below.
(1)
(2)
(3)
(4)
Crash test-
2DMadymo
Simulation 1
3D Madymo
Simulation 1
3D Madymo
Simulation 2
Table 4-2
(Figure 5-3 &
5.4)
car impact with
Eng-Abs barrier
attached to wall
(Figure 5-6)
car impact with
rigid barrier
car impact with
Eng-abs
underrun barrier
attached to wall
(ref2)
Car resultant acceleration
Resultant car- barrier
force
Resultant force
- Maxwell element 1
- Maxwell element 2
- Maxwell element 3
- Maxwell element 4
Maxwell elements
- Total force
ATD head resultant
acceleration
car impact with
Eng-Abs barrier
attached to wall
20-25G
360 to 460kN
70 est.
175 est.
175 est
70 est
490kN
* estimated
44g
271
ATD Head Injury
Criterion, HIC (36 ms)
(passenger)
Maximum Acceleration
264m/s
of Upper Torso - 3ms
Table 5-1 - Summary o/key results/or 3D Simulation 1 and 2, and comparison with 2D simulation,
and experimental crash tests.
From Table 5.1 comparison of the 2D and 3D Madymo model for the energy absorbing underrun
barrier attached to the rigid wall, gave similar overall deceleration levels. The total force on the
energy absorbing struts of 470kN was a little higher than the 430 kN from the 2D model. This
result is expected as the 2D model is less stiff as it uses the average stiffness for all four struts: in
contrast the 3D model is much more realistic as the load between the inner and outer struts can
be discriminated (85kN for the outer struts and 150kN for the inner struts.). These loads compare
well with the estimated individual strut loads, and the total of 490kN from the actual crash test as
shown in Column 1 of Table 5-1.
The Madymo analyses for the energy absorbing underrun system also shows the benefits of the
system in terms of significantly reducing vehicle peak deceleration and occupant loading. This is
clearly seen by comparing the results from the Madymo simulations for the energy absorbing
system and those for impacts with the rigid barrier, as well as the rigid barrier crash tests:
• the car deceleration is reduced to 300 from 460
• peak head acceleration is reduced to 340 from 580
• HIC is reduced to 167 from 483
35
-_.--,,-----_._
•
•
._
•••
_ ••
•
•
_
._.
•••
~
• _ __"">"'O-.
un errun barrier attached to a rigid wall, show an even greater reduction in the car's peak
de eleration: down to 20-250 from 480, and a HIC of 271 compared with 6995. The Madymo
~e
the actual
equivalent
of thetestcarresult
impacting
energy absorbing
re ultresults
of 167from
for HIC
compare
very wellcrash
with tests
the crash
of 271,the
particularly
as these
re]lultsare very similar in terms of injury criteria and indicate a low probability of head injury.
results.
o lerall the results from the 3D Madymo simulations are in good agreement with actual crash test
5
Th~s HIe value is from Table 1 ofRef.2, and is for a full frontal barrier crash test at 48km/h for the vehicle.
36
Figure 5-1 - MADYMO model for 3D Simulation 1, car impacting energy absorbing rear
underrun barrier.
37
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t:a.
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,-E
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(/)t:
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,-(3
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'/
,~
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.'r, f
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;::
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.
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(/)
E
i=
i=
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i=
::2
::2
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iE
=
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.. t:
,...
11
(/)
."
Figure 5-2 - Kinematic sequence from t = 0-200ms for 3D MADYMO model, Simulation 1, car
impacting energy absorbing rear underrun barrier fixed to wall.
38
Figure 5-3 - Results - 3D MADYMO Simulation of crash test, Simulation 1
Vehicle impacting energy absorbing underrun barrier attached to fixed wall, at 48km/h.
Cross-beam = flexible beam.
1---
X-<.mp
G"
1
'00
.00
300
'00
•
0.3
Time (ms)
O.3~
Displacement
(A) Car x-component acceleration
(m)
(B) Resultant car-barrier force v. displacement
1---
RuuUanJ. f'oru
CN) I
,..
"0
'50
Time (ms)
(C) Resultant car-barrier force v. time
1---
Ru.
Gcut..ra.hon
(•••1."2)
1-· ..··,,1
I
250
150
100
.
o
Time (ms)
Time (ms)
(D) Hybrid III upper torso acceleration
(E) Hybrid III resultant head acceleration
39
Figure 5-4- Results - 3D MADYMO Simulation of crash test, Simulation 1
(cont. from Figure 5-3)
Vehic1e impacting energy absorbing underrun barrier attached to fixed wall, at 48km/h.
Cross-beam = flexible beam.
Force versus displacement shown for Maxwell elements 1-4
1----
MaxweLL
et!!
1
Maxwelt
I
*te3
20
20
-20
~j\~l
-40
-60
-40
-80
-60
-100
-120
-80
-}40
-100 I
o
,
0.1
,
0.2
,
0.3
Displacement
,
0.4
,
- 160
0.5
o
(m)
1----
0.1
0.2
0.3
Displacement
MaxweLL
et!!
3
0.4
0.5
(m)
I
·le3
'"lc3
20
20
~\
-20
-40
-60
["
-40
-80
-100
-80
-120
-80
-140
I
-160J
o
,
01
,
0.2
,
0.3
Displacement
,
0.4
,
-100
0.5
(m)
I
o
,
0.1
,
0.2
Displacement
40
,
0.3
,
0.4
(m)
,
0.5
ete
2J
Figure 5-5- Results - 3D MADYMO Simulation of crash test, Simulation I
(cont. from Figure 5-4)
Vehicle impacting energy absorbing underrun barrier attached to fixed wall, at 48km/h.
Cross-beam = flexible beam.
Force versus time shown for Maxwell elements 1-4
1----
Maxwett
1----
de 1 I
Maxwett
de
21
20
20
-20
-20
-40
-BO
-40
-BD
-60
-100
-120
-BO
-140
-100
-160
o
50
100
150
200
250
o
50
100
150
200
250
Time (ms)
Time (ms)
1----
MaxweLL llie
1----
31
ltIaxwetL
"le3
20
-20
-40
-60
-BO
-100
-120
-140
-160
o
50
100
150
200
250
50
100
150
Time (ms)
Time (ms)
41
200
250
de 4 I
Figure 5-6 - 3D MADYMO Simulation of crash test, Simulation 2
Vehicle impacting fixed wall, at 48km/h.
-----
500
Res"U.lQ:n.t
forctZ
1
1000.,
400
\
3004
.001
~
1\
\
'""1 i
, l,-A--.,,~~_,
oll
o
50
100
150
,
.50
200
Displacement
Time (ms)
(A) Car resultant acceleration
(m)
(B) Resultant car-barrier force v. displacement
-----
R •• ~'a~t
fore.
I
~le3
1000
800
800
.00
150
200
250
Time (ms)
(C) Resultant car-barrier force v. time
----
Res. Q.cceterc:dicTL(Tn/s--Z) I
8001
0\
500l
400J
\
300-l
I
/
I
z001
1001
o~,
o
I
/
50
,
100
,
150
,
200
,
250
.50
Time (ms)
(D) Hybrid III head acceleration
Tilne (ms)
(E) Hybrid III resultant upper torso acceleration
42
6. CONCLUSION
Crash tests of cars impacting energy absorbing rear underrun barriers were simulated using two
dimensional and three dimensional models created within the MADYMO program. These
simulations included seat-belted Hybrid III dummies placed in the vehicle. Output includes
vehicle acceleration, velocity and force characteristics as well information from the Hybrid III
dummy model. Comparison of the MADYMO results with the crash test results shows that the
models developed provide very useful and reliable insight into the performance of the underrun
barrier system and occupant response with respect to the Hybrid III results.
The results also confirmed the significant benefits in terms of occupant protection, attainable
though the use of energy absorbing rear underrun barriers on heavy vehicles. The MADYMO
analyses gave significantly reduced vehicle peak deceleration and occupant loading. This is
clearly seen by comparing the results from the MADYMO simulations for the energy absorbing
rear underrun barrier system and those for impacts with the rigid concrete barrier:
• the car deceleration is reduced to 30G from 46G (c/w 48G for rigid barrier crash test)
• peak head acceleration is reduced to 34G from 58G
• HIC is reduced to 167 from 483 (c/w 699 for a rigid barrier crash test).
The actual equivalent crash tests into the energy absorbing barrier attached to a rigid wall show
even greater reduction in the car's peak deceleration down to 20-25G from 48G and a passenger
HIC of271 compared with 699.
The total force on the energy absorbing struts of 470kN obtained from the 3D Madymo analyses
(for the energy absorbing underrun barrier attached to the rigid wall) compared very closely to
the total of 490kN obtained from the actual crash tests.
Overall the results from the 3D MADYMO simulations are in good agreement with actual crash
test results.
As with all model development it is also clear that improvements to the vehicle model itself (the
crash pulse) are required, in particular that of the front end deformation characteristics to ensure
more realistic modelling.
Of particular value and interest was the ability to obtain comparative dummy response measures
for variations in crash parameters and design changes to the underrun barrier, using a vehicle
model with the Hybrid III ATD.
The study has enabled the development of expertise in the use of MADYMO as a tool for the
analysis and design of crashworthiness systems, and has demonstrated the usefulness of this tool.
To enable full use of this type of program does require, however, the commitment of sufficient
resources to maintain and further strengthen the experience and expertise in its use. This type of
expertise could form an important resource for enhancing Monash's and Victoria's vehicle safety
research as well as being useful for other injury research programs.
43
7. RECOMMENDATIONS
That the use of computer modelling and analysis programs such as MADYMO be recognised as
a relatively low cost and significant tool which can be used to enhance Monash's
crashworthiness, accident research and injury prevention research.
8. ACKNOWLEDGMENTS
Thanks to Dr Gray Scott of VicRoads for his review and comments of this work and report; and
to Jared Rechnitzer in assisting with the report preparation.
9. REFERENCES
(1) MADYMO 3D Users' Manual Volume 1 & 2, Version 5.1.1, 1994. TNO Road-Vehicles
Research Institute.
(2) Rechnitzer G., Powell C., Seyer K., Development and testing of energy absorbing Rear
underrun Barriers for Heavy vehicles. 15th International Technical Conference on the
Enhanced Safety of Vehicles, May 13- 16, 1996; Paper No. 96-S4-0-1O, World Congress
Centre. Melbourne.
(3) Rechnitzer, G., Scott G. & Murray, N.W., (1993). 'The Reduction of Injuries to Car
Occupants in Rear End Impacts with Heavy Vehicles'; 37th STAPP Car Crash
Conference, 8-10 Nov. 1993, San Antonio, Texas. paper 933123, SAE Inter.
(4) Rechnitzer, G. (1993) 'Truck Involved Crash Study: Fatal and injury crashes of cars and other
road users with the front and side of heavy vehicles'. Monash University Accident
Research Centre, Melbourne, Report 35.
(5) Rechnitzer, G .. and Foong Chee Wai. (1991), 'Truck Involved Crash Study: Fatal and Injury
Crashes of Cars into the Rear of Trucks'. Monash University Accident Research Centre,
Melbourne. Report No. 26.
(6) Horii M. & Tomura K., A Study Of Front Underrun Protectors For Heavy Vehicles, 14th
International Conference On Enhanced Safety Of Vehicles, Munich, May 1994, Paper o.
94-S 11-0-07.
[dltrueklbaseline/mdmo
I.doe]
44