Numerical Simulation of Tram Collision with Pedestrian

. This paper is focused on the field of traffic passive safety. The main point of this research is to reduce the severity of the consequences of a collision between tramway and pedestrian. The collision scenario is based on statistical data of local research in Czech Republic. For the first assessment of influence of tram geometry, it is necessary to investigate in the numerical simulations with different shapes of tram face. For this purpose the Multibody simulations are carried. Then the detail finite element simulations are prepared. The explicit finite element code Virtual Performance solution (VPS) and human body model Virthuman where used for the simulations. The approval process and standards were prepared for trams in last years (e.g Technical Guide Tramway front-end design) and already today it is visible significant contrast with automotive industry. The main complications in design process are connected with other requirements for tram front-end construction. These requirements are from other passive and active safety field (requirement for collision tram-tram, collision tram-road vehicle, active safety eg. visibility) and from another fields (durability, design, aerodynamics). The new construction safe for pedestrian is different in more ways. Therefore it is difficult to propagate the changes in construction.


Introduction
The selected collision scenario consists of the tram with the initial velocity equaling to 20 km/h, initial position of the pedestrian with respect to the front-end of tram is the standing medium-sized adult male (50 th percentile) without initial velocity. Head Injury Criterion (HIC) is evaluated for the pedestrian with the maximum threshold value equal to 1000. The simulation phenomena is connected with structural dynamics, large deformations and contact definitions. The material behavior must be considered as nonlinear with rapture definition. The key point of this model is a proper definition of plastic material used as a cover sheet for tram front-end and the front windshield with two layers of glass and PVB foil. The numerical model also contains basic definition of glued joints (between polymer cover sheet and steel body frame) with rupture criterion. The main goal of this study is to provide the information about safety performance in specific scenario for new developed tram vehicle.The rail Industry has been significantly affected by the passive safety technology in the last few years. The tram front-end design must fulfil the new requirements for pedestrian passive safety performance in the near future. The requirements are connected with a newly prepared technical guide "Tramway front end design" prepared by Technical Agency for ropeways and Guided Transport Systems [1]. This guide describes the requirement for the design of rail vehicle front-end in to the context of railway vehicles operating in urban environments.

Collision description and influence of new standards
In terms of passive safety, the structures were partially included into the standard ČSN 12663 in advance, and they particularly relate to the calculations of housing stock. However, a new standard ČSN EN 15227 [3] has been introduced recently. The referring measures in this document represent the last resort of protection on condition of all options fail to prevent the accidents. These standards describe the requirement for the interiors only partly. The legislative which can summarize all requirements for the safe rail interior still does not exist. Another legislation is connected with rail vehicles interiors. The collision with pedestrian was not regulated by legislation up to now. The requirements for tram front-end safe for pedestrian are based on previous research [1]. For the first collision scenario the pedestrians involved in the collision are specified to be mid-size male (175 cm, 78 kg -50th percentile) and 6 years old (YO) child (110 cm, 24 kg). The report also defines possible impact area and impact zones, with respect to the shape of the vehicle, for more specification, see [1]. The collision scenario for evaluation of the first impact considers the tram moving with the initial velocity equals to 20 km/h and pedestrian standing still, left side to the vehicle, one step forward (not specified which leg to be forward) and the lateral position relative to the vehicle has two specifications (H-point with respect to the tram). The vehicle does not stop (not loaded with any deceleration pulse) only energy lost due to the impact. The pedestrian injury risk is monitored only with the Head Injury Criteria (HIC) [8], which should not exceed threshold 1000 [2].

Model of human body "VIRTHUMAN"
The model ("VIRTHUMAN") is suitable for the evaluation of the safety risk in common crash scenarios. The shape of the model is based on the real data from a scanned human body (database CAESAR) with parameters close to 50th percentile male [12]. The model is developed by using a Multibody approach. The biggest advantage of this approach is a short computing time and easy positioning [11]. The individual parts of the body are usually created as a single rigid body, or are created as a conglomerate of few rigid bodies. Thank to Multibody Structure it is quite simple to place the body model and prepare a crash scenario. The new model has all parts segmented individually. This model is described in literature with general use [9,10,12].

Multibody numerical model
For assessment of influence of tram geometry, it is necessary to investigate in the numerical simulations with different shapes of tram face. To avoid some unpredictable stochastic phenomena, it would be best to provide simulations with maximum number of possible geometries. One possible approach is to simplify the tram front-end design to the discreet description. The tram face can be divided to the finite number of linear flats with the finite number of positions [4]. Each flat has its own stiffness, damping and slope (inclination angle) definition. This approach is not as perfect as continuous reality, because the number of variants increase rapidly (1), but it can evaluate the safety of most geometries, where some of them are quite unpredictable (see Fig. 1).
Where the constant n is number of bodies and r is number of possible positions for each body. From this simple formula (1) it is obvious then the computations cannot be provided manually although this approach leads to the fast rigid body simulations.This definition of simulation allows us to use another code for creating and running all possible variants of tram design. The first fast solution was prepared in Matlab which runs specific multibody computations on Linux based cluster through shell bash script (*.sh). The Matlab was selected cause its suitable and known possibilities to format text correctly and readable for Pam-Crash (close to Fortran syntax). Although the multibody is not much suitable for parallelization, solving more of multibody simulations allows very simply parallelism. Each simulation can run in separate thread or node of cluster.

The explicit FEM modeling in pedestrian collision
The commercial codes are influenced by intensive research in the past. The HEMP program, whose code was freely accessible, became the basis for today's software packages. Explicit time integration is suitable for simulating processes which involve large strains and changes in shape. It offers the better representation of the nonlinear behavior of materials and failures. Explicit solvers are generally better suited for problems with complex contact situations. Therefore, they are a good choice for solving collision problems, crashes, bullet penetrations, and similar tasks.

The essence of an explicit code is Newton's second law of motion. It is an equation of motion in the matrix form (2). This equation is defined for the given time instant.
To maintain equilibrium between dynamic forces, the relationships below must be met [5].
Once the internal forces have been defined and some fundamental elements added, an equation for the numerical solution can be obtained in the following form (2). The element {Fhoug} was added to prevent the hourglassing effect, and {Fcnt} is a vector of contact forces. Furthermore, {σn} is an internal stress matrix, and [B] is a strain matrix.
A great advantage of the explicit method is the use of elements with a single integration point. A downside is the reduced stability of computation. If an element deforms symmetrically, no corresponding change in internal energy takes place. Eventually, the computation leads to an imbalance between the kinetic and the internal energy of the system. This numerical error is known as hourglassing. The total energy must be controlled by dynamic calculations. The recognized critical threshold is an increase in the hourglassing energy above 5 % of the total energy of the system.

Detail FE numerical model
When the rough shape of tram front-end design is finished, the next logical step is to prepare more detail model.The model of the frame is modeled as standard steel S355 and only the parts with better crashworthiness are created from the steel 1.4003. The standard explicit numerical simulation use only few material models, which are not much typical [14].

Isotropic nonlinear viscoelastic element of Maxwell type
This model is used for windshield glass PVB foil definition and is also suitable for ABS shell of tram behavior description [16].
Where ԑ ̇ is the plastic strain rate, ԑ _ref is the reference strain rate, and k, w, m, h 1 , h 2 are material constants. The general material behavior is quite similar to another plastic with numerical description [5,6].

Rankine Criterion for fracture definition
The glass is modelled as linear elastic material with a brittle failure criterion. For the fracture definition the Rankine Criterion is used and the fracture occurs when the maximum principal stress exceeds the critical value [15].

(5)
Where σ is the damaged stress tensor, σ_11,σ_12,..,σ_23 are components of undamaged tensor, d1 and d2 are damage values in two directions and dmax is maximum of d1 and d2. The approach si similar for brittle material behavior [13].

The glue connection between ABS and steel part
As the critical time step (and computational costs) are connected with the element size, it is necessary to avoid definition of connection with small thickness elements. The penalty algorithm as TIED node to segment connection is god choice. As a rapture model the stress criterion is used.
Where is the normal stress is the shear stress is the failed surface and 1 2 are exponents (usually equal 2). The approach is in contrast with known approach with energy criterion [7].

Discussion of results
The very first shape of tram was get as a result of Multibody simulations (Fig. 2). Here is visible the rough structure of future front-end design as shape created by rigid multibody plates connected to base body with spring. The stiffness and damping of the structure in not much precious although the estimated shape provide quite good crashworthiness. The kinematic of pedestrian movement is visible from the next figures. The first impact to the soft ABS plates mounted with soft steel (1.4003) structure is positioned in pelvic region of human body (Fig. 3). Then the impact of the pedestrian head to the tram windshield is quite safe with HIC=327. After the first impact the movement in the vertical direction is feasible. The human body is moving up thanks to the inclination of the geometry (Fig. 4). Therefore the probability of fall under the tram wheels is lower.

Conclusion
The simulations for tram front-end design crashworthiness improvement where finished. The tram design must fulfils more regulations (not only from the field of passive safety) and is very difficult to propagate changes. The design based on Multibody and FE simulations fulfills (with significant reserves) the requirements of pedestrian passive safety (which will be published in final form in next future). The next logical step will be the production of a first full-scale tram front-end. The experimental testing of design inspired by simulation is now prepared. It is supposed the feasible behavior of the new tram design.