Experiencias de Aprendizaje

In the mid-1960’s Raymond McHenry at the Cornell Aeronautical Laboratory was actively involved in automotive safety analysis, design and optimisation including

for the seatbelt in 1951 (CALSPAN History, 2006)). In 1966 McHenry published a paper describing the validation of computer simulation of vehicle occupants and the effectiveness of different restraint systems (McHenry, 1966). The mathematical model developed in this research was an articulated multibody model with 10 degrees of freedom described using non-linear equations.

In 1967 McHenry and Norman DeLeys published the first of a series of papers on the simulation of single-vehicle accidents and vehicle dynamics modelling (McHenry, 1971). Meanwhile, at the University of California, Richard Emori (1968) published a paper on the mathematical modelling of either single or two-vehicle automobile collisions using vehicle masses, spring constants and the equations of motion. This is one of the first instances of vehicle crash analysis based on crush energy.

Further development of the models by McHenry, DeLeys and Emori lead to the creation of the SMAC (Simulation Model of Automobile Collisions) computer program (McHenry, 1973). By this stage the Cornell Aeronautical Laboratory had been spun off to form the corporate entity CALSPAN (Calspan History and Timeline, 2006). Funding for the SMAC computer program was provided by the National Highway Traffic Safety Authority (NHTSA), USA, indicating that the potential of computer simulation was well recognised over 30 years ago despite the relatively limited computing capabilities available at the time.

With computers being slow and expensive (by modern standards) development and execution costs for SMAC were relatively high with the software run on time-share mainframe computers. Each application run cost approximately US$25 (McHenry, 1997).

SMAC has been further developed by a number of companies (McHenry Software, Rectec, HVE by Engineering Dynamics and others) and is still in use today with a purchase price of between US$750 and US$10,000 depending on the degree of sophistication.

brakes, acceleration) and environmental factors (coefficient of friction). Outputs include vehicle kinematics, tyre tracks and vehicle damage. An iterative approach is usually required when using SMAC; an initial guess is needed with respect to vehicle velocities and driver inputs. Modern versions can perform the iteration automatically but in the 1970’s, when computing power was limited, a more basic automotive accident simulator, CRASH (Computer Reconstruction of Automobile Speeds on the Highway), was developed by McHenry to enable users to quickly evaluate a number of scenarios prior to using the SMAC program.

The CRASH program conducts a relatively simple trajectory analysis based on conservation of energy and linear and angular momentum. The user has the choice of a ‘damage-only’ option based on vehicle mass, deformation and principle direction of force (PDOF) and a ‘trajectory’ option which applies conservation of momentum using vector algebra. CRASH is based on the following assumptions and limitations (Smith, 1982; Nash, 1987):

• two-dimensional analysis only

• simplified vehicle characteristics

• simplified damage analysis

• simplified tyre-ground contact forces

• an instant of common velocity between impacting vehicles

• no driver input during post-impact trajectory

• subsequent impacts involving a previously damaged portion of a vehicle

The net effect of these assumptions and limitations varies considerably depending on the scenario analysed.

In comparison to CRASH, SMAC has a greater range of inputs and outputs and the original version was influenced by a generally more complex set of assumptions and limitations (McHenry, 1988 and 1997, Warner, 1978)

• two-dimensional analysis only

• sensitivity to integration time-step and rounding/truncation errors

• uniform linear crush stress rates do not adequately account for the vehicle structure and are incompatible with SMAC’s implementation of coefficient of restitution

• poor fidelity in side-swipe and rigid-barrier collisions

• poor fidelity in vehicle side-slip motion due to calculation method of tyre-ground forces

Many of these assumptions and limitations have been corrected to some extent in subsequent versions of SMAC.

3.3.2 Multibody Analysis

McHenry (See preceding section on SMAC and CRASH) also developed a multibody model for the analysis of vehicle occupants in 1963 (Du Bois, 2004) Validation with crash test data was demonstrated for pelvis displacements, chest acceleration and restraint loadings. This work led to the development of MVMA2D (Motor Vehicle Manufacturers Association 2-Dimensional) computer simulation program. The multibody occupant model employed in MVMA2D consists of 10 segments and nine masses. The equations of motion for the linkages were derived using the explicit Langrangian technique (Prasad, 1984). Contact between the model and the vehicle interior was determined using ellipses attached to the body links. Joint stiffness was determined to be initially linear with non-linearly increasing stiffness as the limits of travel were approached.

Around 1970 CALSPAN (see section 3.3.1) developed the CAL occupant simulation model, based on the MVMA2D model (Cheng, 1987). Initially only 2-dimensional analysis was permitted, however in 1972 a 3-dimensional version was released (Prasad, 1984). Many different versions of CAL2D/3D and MVMA2D have been produced over the years and are generally referred to as CVS (Crash Victim Simulator) programs. The most current and common version CVS is the ATB (Articulated Total Body) Simulator. It is often incorporated into other software packages, such as HVE (Human Vehicle Environment) by Engineering Dynamics (Grimes, 1997) where it is used in conjunction with HVE’s version of SMAC (see Section 3.3.1).

An overview of HVE’s human model based on the ATB can be found in SAE 950659 (Day, 1995). Injury parameters include HIC (Head Injury Criterion), HSI (Head Severity Index), CSI (Chest Severity Index) and chest acceleration.

MADYMO (MAthematical DYnamic MOdelling) 2-D and 3-D: Both 2-dimensional and 3-dimensional versions of MADYMO were developed simultaneously by TNO (Organisatie voor Toegepast-Natuurwetenschappelijk Onderzoek or, in English:

Organisation for Applied Scientific Research) Automotive in the Netherlands and first released in 1975. The coding for MADYMO-2D in the early 1980’s (Version 3) consisted of about 1800 lines of Fortran, compared to 2200 lines of code for the 3D version (Prasad, 1984).

MADYMO multibody models consist of joint-connected bodies with the equations of motion derived using Lagrangian methods. Force models included those resulting from acceleration and contact between bodies and planes. The greatest advantage held by MADYMO over competing software was the flexibility allowed in the number of bodies permitted and the ability to use user-defined constraints and conditions (Cheng, 1987). See Section 3.4 for more information on MADYMO.

One of the first academic papers that referred to MADYMO was Child Restraint Evaluation by Experimental and Mathematical Simulation, SAE 791017 by Wismans, Maltha, Melvin and Stalnaker (Prasad, 1984). The authors found that the mathematical model provided better correlation with cadaver testing than the results obtained from dummy testing.

One of the first papers on the use of MADYMO for pedestrian accident reconstruction was published in 1983 by Wijk et al. 2-dimensional pedestrian models were created that consisted of either 2, 5 or 7 segments. A 3-dimensional model consisting of 15 segments was also used. The 2 and 5 segment models consisted of 5 bodies (head, thorax, pelvis, upper leg and lower leg) whilst the 7-segment model had two legs (i.e.

head, thorax, pelvis and two each of upper leg and lower leg). The 15 segment model consisted of head, neck, upper thorax, abdomen, pelvis and two each of upper arm, lower arm, upper leg and lower leg. The vehicle bumper and bonnet were modelled

measured during simulated vehicle impacts occurring at 30 and 40 km/h. The results obtained using the mathematical models were compared with experimental results from dummy testing. The 3-dimensional model was found to provide the most realistic results but required three times the computational time of the 7-segment 2-dimensional model. This time penalty was not insignificant given the limited computing power available to Wijk in the early 1980’s.

Please see Section 4.2 for injury parameters in the current version of MADYMO.

Another multibody accident reconstruction program developed in the 1970’s was KRASH (Lockheed-California Company). KRASH was developed in 1971 by the U.S. Army to model the impact dynamics and mechanics of airframes with support from the FAA coming in 1974 (Fleisher, 1994). It is in current use for aircraft crash analysis and uses a semi-empirical modelling method of lumped-masses, beam elements and non-linear springs (Fasanella, 2001) in order to effect fast computation on modest computational facilities. With the advent of high-performance, low-cost computing KRASH is now being superseded by programs using finite-element analysis.

3.3.3 Finite Element Analysis

Finite Element Analysis is a discrete event modelling method entailing the reduction of structures, bodies and/or fluids into discrete elements. The physical properties of these elements are governed by a relatively simple set of mathematical equations. Any state-change imposed on any given element from an external source (eg physical, gravitational or thermodynamic loading) can be easily calculated. Not only can the changes within the element be determined, but any influence on the surrounding environment including neighbouring elements and other bodies can be calculated by the application of interface properties. This method permits the analysis of complex problems by breaking the problem down into solvable pieces. (Graillet, 1999)

The solvers used in Finite Element Analysis can be either implicit or explicit. Implicit solvers use a forward difference algorithm with the assumption of constant average

Explicit solvers typically use the central difference method. It is assumed displacements occur linearly and accelerations and velocities are calculated accordingly. Explicit solvers will tend to be unstable unless the time step is smaller than a value based on media stress wave velocity and smallest element dimension.

Implicit solvers are quicker (by two orders of magnitude) but are not appropriate for all problems.

FEA Program Developer Implicit/

Explicit

Implicit Both In common usage, best for quasi-static

Both Nonlinear In common usage.

Quasi-static and

Both Nonlinear LS-DYNA (commercial version by Livermore

MARC David Hibbitt, Brown University, Rhode Island, USA. 1972

Both Both 1^st commercial non-linear FEA software.

Both Both Combined multibody

and FEA analysis. research by the National Aeronautics and Space

In common usage for structural, thermal and

NONSAP Developed by K J Bathe at the University of California, 1973

? Nonlinear Has been superseded by ADINA (Bathe, 1997)

Bathe et al, 1974

RADIOSS Developed by Mecalog. Both Nonlinear Now licensed through Altair Engineering

Park et al, 1991

Finite element analysis advanced rapidly in the 1970’s and 1980’s. A comparative summary of some of the various Finite Element Software applications developed over this time can be seen in Table 3.1.

Finite element analysis requires a comprehensive understanding of the material properties being modelled. Whilst such knowledge is expected of automotive engineers it is unlikely that many accident reconstructionists have sufficient engineering knowledge to be able to obtain accurate results using finite element analysis.