Engineering Engineers, Part D: Journal of Automobile

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering http://pid.sagepub.com/

Development of a new lumped-parameter model for vehicle side-impact safety simulation A Deb and K C Srinivas Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2008 222: 1793 DOI: 10.1243/09544070JAUTO801 The online version of this article can be found at: http://pid.sagepub.com/content/222/10/1793

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Development of a new lumped-parameter model for vehicle side-impact safety simulation A Deb* and K C Srinivas Centre for Product Design and Manufacturing, Indian Institute of Science, Bangalore The manuscript was received on 30 December 2007 and was accepted after revision for publication on 9 June 2008. DOI: 10.1243/09544070JAUTO801

Abstract: The current paper describes a simple and yet comprehensive lumped-parameter model (LPM) for simulating the National Highway Traffic Safety Administration (NHTSA) sideimpact safety tests for passenger vehicles. The LPM includes new lumped masses, not previously reported in a single multibody model, for key vehicle side-structure systems identified with the help of an energy-based study conducted using explicit finite element analysis of two passenger vehicles. In addition to the vehicle side structure, lumped masses for the NHTSA side-impact barrier and ‘rest of vehicle’, the latter implying the mass of the vehicle minus the combined mass of the side-structure subsystems considered in the LPM, have been incorporated so that the total mass of the system corresponds to that of an actual vehicle– barrier system in a NHTSA side-impact test (Lateral Impact New Car Assessment Program (LINCAP) or FMVSS 214). The lumped masses are interconnected with elastic–plastic springs. A unique feature of the present model is the inclusion of two lumped side-impact dummies for obtaining predictions of the front and rear (thoracic trauma index (TTI)). The validity of the present LPM is established by performing LS-DYNA-based LINCAP simulations of two realworld vehicles, namely the Dodge Neon and Dodge Intrepid, and obtaining a reasonably good correlation of the computed structural and occupant responses as well as TTI (front and rear) with the corresponding test results reported by the NHTSA. Keywords: vehicle side impact, lumped-parameter model, finite element model, simulation, thoracic trauma index

1

INTRODUCTION

Various idealized lumped-parameter models (LPMs) used in simulations of front, side, and rear crashes of vehicles have been reported in the literature [1–10]. In 1970, Kamal [1] developed a relatively simple but powerful model for simulating the crashworthiness response of a vehicle in full frontal impact. This model, known as a lumped mass–spring (LMS) model (equivalent to the LPM in the present study), came to be widely used by crash engineers because of its simplicity and relative accuracy. The vehicle in this model was approximated by a one-dimensional LMS system, an oversimplification that is quite acceptable for modelling the basic crash features in *Corresponding author: Centre for Product Design and Manufacturing, Indian Institute of Science, Bangalore, 560012, India. email: [email protected] JAUTO801 F IMechE 2008

frontal impact. The spring characteristics were determined experimentally in a static crusher. The LPM of a vehicle impacting a rigid barrier head-on at 35 mile/h was reported in reference [2]. This configuration of the model was arrived at from the study of an actual barrier test by identifying the relevant masses and springs and their modes of collapse. This model was tuned by adjusting the load–deflection characteristics of the springs to achieve the best agreement of acceleration with corresponding test results in terms of peak acceleration and timing of a crash event. The one-dimensional front impact LPM reported in reference [3] is an example where finite element models were used to extract the spring properties. This model contained a number of lumped masses (e.g. barrier, bumper, radiator, engine, cradle, shock tower, and firewall) and springs which were defined in reference [3]. A comparison [3] Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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A Deb and K C Srinivas

between test and LPM-based normalized deceleration histories showed good correspondence. However, Cheva et al. [3] did not describe how the finite element method was used to extract the spring properties. Additionally, LPMs for frontal offset impact simulation have been reported in references [3] and [4]. The LPM for frontal offset impact simulation in reference [3] has a changed barrier configuration and its connecting springs when compared with the symmetric LPM for simulating full frontal impact against a rigid barrier, also reported in reference [3]. In this model again, Cheva et al. had obtained the spring properties using finite element simulation; however, the details of the approach were not reported. A simpler frontal offset model was reported in reference [4]. This model was developed at the National Highway Traffic Safety Administration (NHTSA) and the vehicle’s structural properties are extracted directly from crash test data using the structural impact simulation and model extraction system identification methodology. In addition to simulating front impact, LPMs have been employed perhaps to a lesser extent for analysing vehicle side impact [5–10]. A side-impact LPM, shown in Fig. 1, for a bullet vehicle impacting a target vehicle’s side at 50 km/h has been discussed in reference [5]. The LPMs for side-impact safety analysis used in references [7] and [8] are shown in Figs 2 and 3. Thomas and Joseph [7] and Tomassoni [8] have discussed the need and importance of LPM for side impact. However, as in other cited studies on LPM, no systematic approach for obtaining the spring parameters is outlined. A drawback of the reported LPMs for side impact is that these do not include all the relevant components of the side structure of a vehicle. Data-based models for automobile side-impact analysis were reported in references [9] and [10]. In reference [9], the analytical model was made up of

two parts: a differential equation part consisting of mass, stiffness, and damping characteristics, and a transfer function part, consisting of an autoregressive moving average of white noise. The lumped parameters used in the model were time varying and were estimated recursively by minimizing the quadratic criterion of the one-step-ahead prediction errors. In reference [10], uncoupled LPMs for vehicle structure and occupant injury prediction were developed on the basis of a study of the distribution of crash energies. The lumped structural parameters were estimated directly from test data using a Kalman filter estimator in a constrained environment. The above discussion on side-impact LPMs shows that none of the reported LPMs comprehensively represents a vehicle side structure together with dummies. The LPM developed in the current study is unique in terms of having representations of all important side structural systems such as the front door (FD), B pillar (BP), rear door (RD), and rocker (R); in addition, the ‘rest of vehicle’ (implying the mass of the vehicle minus the combined mass of the side-structure subsystems considered in the LPM), moving deformable barrier (MDB), and two sideimpact dummies (SIDs) are included. It has been shown in the context of validation of the Dodge Neon and Dodge Intrepid finite element models that the structural subsystems included in the current LPM are the main energy absorbers in NHTSA side impact. Apart from deciding the configuration of masses and springs, a major challenge in the usage of an LPM lies in realistic characterization of the behaviours of springs. In the LPM proposed here, elastic–perfectly plastic springs are assumed. The properties of these springs are developed for two cases by studying section forces in a component as well as interactions (i.e. contact forces) between relevant parts in the LS-DYNA-based Lateral Impact New Car Assessment Program (LINCAP) analyses

Fig. 1 An LPM for vehicle-to-vehicle side-impact simulation [5] Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


JAUTO801 F IMechE 2008

New model for vehicle side-impact safety simulation

Fig. 2

A simplified LPM for side-impact simulation [7]

of the validated Dodge Neon and Dodge Intrepid models already mentioned. The effectiveness of the present LPM is established by obtaining good correlation with test results on performing simulations of LINCAP tests of the Dodge Neon and Dodge Intrepid with the aid of the explicit LS-DYNA solver (version 960).

deformation curve obtained through analysis is compared in Fig. 6 with the corresponding test result [12] for normal impact of the barrier at 25 mile/h (11.1 m/s) against a rigid wall and good correlation is seen especially after 60 mm of barrier crush. Some discrepancy between simulation and test results is observed in the beginning; however, the measured barrier force rises in an abrupt manner initially and appears to be questionable. Assuming that the test-based barrier force in Fig. 6 would have most probably risen along an inclined path immediately after impact with the rigid wall, it can be concluded that the present finite element model of NHTSA MDB is an acceptable representation of the actual MDB. However, it may be instructive to verify the MDB model further in future if different test data of an MDB crash are available.

3 2

VALIDATION OF NHTSA MDB

In the present study, the sacrificial part of MDB detailed in Fig. 4 is verified by simulating with LSDYNA its impact against a rigid wall at 25 mile/h. The finite element model of the NHTSA MDB without cart is shown in Fig. 5. As can be seen in Fig. 5, solid elements (of hexahedral type with eight nodes) are employed to model the main honeycomb block as well as the protruding bumper. Since the voids in honeycomb cells are not modelled for computational efficiency, equivalent properties are used for the block as well as the bumper. The material type used in LS-DYNA for the block as well as the bumper is identified by the keyword MAT_HONEYCOMB (material type 26). The force–

Fig. 3

An LPM with one occupant for side-impact simulation [8]


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VALIDATION OF A DODGE NEON FINITE ELEMENT MODEL

In order to validate the new LPM to be discussed in a subsequent section, the properties of non-linear springs defining interactions between relevant subsystems (such as the MDB and vehicle body components) are necessary. These properties can be obtained from finite element simulation of fullvehicle side impact with an MDB. A prerequisite for this approach, however, is ensuring that the analysis of a vehicle finite element model with a striking MDB as in a LINCAP test generates responses that correlate well with corresponding test-based responses. To this end, confidence is gained in a finite element model of Dodge Neon (model year 1998) [13] shown in Fig. 7 for side-impact analysis by comparing computed structural responses against corresponding data for LINCAP test 2715 reported by the NHTSA. It may be noted that the finite element of a second vehicle, i.e. Dodge Intrepid, subject to LINCAP test is considered in the next section to corroborate further the applicability of the LPM concept to be discussed shortly. As the vehicle in Fig. 7 is of unibody construction, its body is made principally from stamped steel panels which are mutually joined along flanges with spot welds. Most of the body components including those belonging to the vehicle side structure, i.e. the FD, BP, RD, and R are meshed with Belytschko–Lin– Tsay shell elements with an averge size of 15 mm. The sheet metal panels are made of mild steel for which the properties (in LS-DYNA material type 24) adopted in the finite element model are as follows: density, 7890 kg/m3; Young’s modulus, 210 GPa; Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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Fig. 4

Details of the NHTSA MDB [11] for side-impact tests (all dimensions are in millimetres)

yield strength (true), 250 MPa; failure strain, 0.33; ultimate strength (true), 433 MPa; Cowper–Symonds strain rate parameters C 5 80 s21 and p 5 4.5. The values of the Cowper–Symonds parameters C and p were originally suggested as 40 s21 and 5 respectively for low strain rates for mild steel [14]. In reference [15], for four varieties of steel grades, C and p were chosen in the ranges 115–63 250 s21 and 3–7 respectively. It appears that the value of C can vary considerably based on the range of strain rates used and the type of steel (i.e. mild, high strength, etc.). The value of C (i.e. 80 s21) chosen here for mild steel is on the lower side compared with citations in literature; however, it is still twice that of the original suggestion, which is consistent perhaps with the moderate range of strain rates likely in automotive crashes. The value of p (i.e. 4.5) adopted here

compares favourably with the original suggestion of Cowper and Symonds [14] as well as the mean value of the range quoted above from reference [15]. It may be mentioned that the values of both C and p used here were given in the finite element model of the Dodge Neon obtained from reference [13]. A summary of the elements in the present model of Dodge Neon is given in Table 1. Deformed views of the Dodge Neon model without the barrier in the course of analysis using LSDYNA are shown in Fig. 8 and appear as qualitatively realistic compared with damage witnessed in a physical LINCAP test of a car. The consistency of simulation is revealed in Fig. 9 in which the total energy is nearly constant during analysis with minimal mass addition for restricting the time step for explicit computation to a minimum value. The

Proc. IMechE Vol. 222 Part D: J. Automobile Engineering




Fig. 5

Fig. 6

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Finite element model of MDB: (a) side; (b) front; (c) isometric views

Comparison of the force versus deflection curves in reference [12] and current simulation

Fig. 7


A finite element model of the Dodge Neon with a NHTSA MDB



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Table 1

Details of the finite element model for the Dodge Neon

Number Number Number Number Number Number

parts nodes solids beams shells elements

of of of of of of

336 283 859 2852 122 267 786 270 768

simulation-based velocity–time histories of the FD, BP, RD, and R in the struck side of the vehicle are compared with the corresponding LINCAP test results given by NHTSA in Figs 10 to 13 and good correlation is observed. It may be noted that the velocities from simulation results are taken at nodal locations equivalent to the accelerometer locations specified by NHTSA. In Fig. 10, the FD velocity is the average for three nodal locations corresponding to the test accelerometer locations and is compared with the average of corresponding test velocities. In the remaining velocity comparisons in Figs 11 to 13, only nodal responses of simulation are compared with corresponding test results. The computed gross energies absorbed by various subsystems such as MDB, FD, BP, RD, rocker R, and ‘rest of vehicle’ are shown in Fig. 14(a). It is noticed that the sum of energies absorbed by FD, BP, RD, and R is more than half of the energy absorbed by the vehicle; thus these subsystems are important in occupant protection in vehicle side impact. The specific energy (i.e. energy per unit mass) absorbed

Fig. 8

Deformed vehicle side structure through analysis at (a) 20 ms and (b) 60 ms

by each subsystem under consideration is given in Fig. 14(b) and the dominant roles played by these vehicle side-structure subsystems is sharply brought into focus. The energy absorption bar charts in Fig. 14 provide crucial guidelines in choosing the lumped masses in the development of the present side-impact LPM.

4

VALIDATION OF A DODGE INTREPID FINITE ELEMENT MODEL

In order to lend greater credibility to the side-impact LPM to be discussed in the next section, a finite element model of Dodge Intrepid (model year 1999) which is a substantially larger car than Dodge Neon is also considered. The original Dodge Intrepid model has been obtained from reference [13] and has been improved here for satisfactory correlation with results of LINCAP test 2999 reported by NHTSA. This finite element model is shown in Fig. 15. The material properties (in LS-DYNA material type 24) used in the present Dodge Intrepid model are as follows: density, 7890 kg/m3; Young’s modulus, 210 GPa; yield strength (true), 210 MPa; failure strain, 0.35; ultimate strength (true) 5 450 MPa. It is pointed out that the effect of strain rate has been ignored in the material properties of steel adopted from reference [13] and given above. The current model of the Dodge Intrepid containing 85 670 shell elements [16] is very coarse compared with the Dodge Neon model containing 267 786 shell elements (Table 1). Studies have shown that the artificial stiffness due to a coarser mesh apparently compensates for the reduced material strength resulting from not accounting for the strain rate effect on the material properties of the body sheet metal [17]; on the other hand, the Cowper–Symonds constitutive behaviour assumed in the Dodge Neon model in the previous section increases the strength of a relatively fine mesh to appropriate levels because of the strain-rate-hardening effect on the dynamic yield strength of steel. The consistency of the LINCAP simulation with the previously validated MDB is revealed in Fig. 16 in which the total energy is nearly constant during analysis with minimal mass addition for restricting time step for explicit computation to a minimum value. The constancy of the total energy also indicates that the sum of kinetic and internal energies of the MDB–vehicle system at any instant of time is approximately the same as its total energy. The simulation-based velocity–time histories of the FD, BP, RD, and R in the struck side of the vehicle are





Fig. 9

Global energies for the finite element analysis of the Dodge Neon

Fig. 10

Velocity–time history comparison for the FD of the Dodge Neon (FE, finite element)

Fig. 11

Velocity–time history comparison for the BP of the Dodge Neon (FE, finite element)


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Fig. 12 Velocity–time history comparison for the RD of the Dodge Neon (FE, finite element)

Fig. 13 Velocity–time history comparison for the R of the Dodge Neon (FE, finite element)

compared with the corresponding LINCAP test results given by NHTSA in Figs 17 to 20 and extremely good correlation is observed. It may be noted that the analysis-based velocities are for nodal locations corresponding to the positions of accelerometers in the LINCAP test. As in the case of the Dodge Neon, the computed gross energies absorbed by MDB, various sidestructure subsystems and ‘rest of vehicle’ are shown in Fig. 21(a). The specific energy (i.e. energy per unit mass) absorbed by each subsystem under consideration is given in Fig. 21(b). It is observed that the side-structure subsystems considered, i.e. the FD, BP, RD, and R, once again constitute a dominant group in terms of energy absorption during side impact. In terms of specific energy absorption, these side-structure components are actually the most

dominant subsystems not withstanding the fact that their orders are different for the cases of the Dodge Neon and Dodge Intrepid (as seen by comparing Figs 14(b) and 21(b)). The last observation provides a valuable guideline in the formulation of a generic LPM for NHTSA side impact enumerated in the following section.

5

TOPOLOGY OF A NEW LPM FOR NHTSA SIDEIMPACT SIMULATION

The powerful tools available for full-vehicle finite element simulation are often inconvenient for design iterations because of the time involved in modifying a model and performing a complete analysis. On the other hand, parametric studies can





Fig. 14

(a) Energies absorbed by various subsystems of the Dodge Neon as percentages of the total system energy absorption; (b) specific energies (kJ/kg) absorbed by the same subsystems

be made in an extremely efficient manner if an equivalent LPM can be formulated for a detailed finite element model of a vehicle for side-impact analysis. Furthermore, in the early stages of design of a new vehicle platform, it may not be feasible to create a representative finite element model owing to lack of geometric data. In such situations also, an

LPM can be an effective tool for guiding design and developing a robust vehicle side structure (including key members such as doors, BP, and R) for meeting aggressive side-impact safety targets. The topology of the present LPM is as shown in Fig. 22. This topology is arrived at after studying various other LPM configurations whose study is not reported here. The current LPM is of a comprehensive nature as it includes for the first time the relevant lumped parameters for a complete NHTSA side-impact analysis with front and rear SIDs. Guided by the insight obtained in the previous sections, the LPM as shown in Fig. 22 includes the six structural subsystems indicated in Figs 14 and 21 and, in addition, two SIDs (each represented by ribs, lower spine, and pelvis) for front and rear thoracic trauma index (TTI) prediction. The values of the lumped masses are close to their actual values in the Dodge Neon and Dodge Intrepid finite element models discussed earlier. It may be noted that the lines 1 to 15 between the lumped masses in Fig. 22 represent the energyabsorbing elastic–plastic springs. The spring labels are given in terms of the masses that they connect in Table 2. Although not reported here, a number of other LPM configurations have also been investigated including those documented by earlier researchers [7–10]; however, the current LPM in Fig. 22 appears to yield the most consistent correlation with test results. An important feature of the present LPM is the incorporation of both front and rear dummies in the model with initial clearance between each dummy and the relevant door. The properties of the dummies in the LPM are independent of the vehicle and MDB spring characteristics. It may be noted that no distinction is made between the upper and lower ribs of a dummy in the current LPM. An enhancement that can be carried out in future is the incorporation of viscous damping parameters in the SID representations and velocity-sensitive spring properties [18] for the vehicle body subsystems.

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Fig. 15 A finite element model of the Dodge Intrepid JAUTO801 F IMechE 2008

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EXTRACTION OF LPM SPRING PROPERTIES

Two sets of spring properties for the proposed LPM are extracted from the results of the LINCAP simulations carried out earlier for validating the Dodge Neon and Dodge Intrepid side-impact models using the explicit LS-DYNA 960 solver. It is clarified here again that a spring in the LPM in Fig. 22 does not represent the behaviour of any individual lumped mass representing a subsystem; Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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Fig. 16

Fig. 17

Global energies of the finite element simulation of the Dodge Intrepid

Velocity–time history comparison of the FD of the Dodge Intrepid (FE, finite element)

Fig. 18 Velocity–time history comparison of the BP of the Dodge Intrepid (FE, finite element) Proc. IMechE Vol. 222 Part D: J. Automobile Engineering




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Fig. 19 Velocity–time history comparison of the RD of the Dodge Intrepid (FE, finite element)

Fig. 20 Velocity–time history comparison of the R of the Dodge Intrepid (FE, finite element)

however, it does define the interaction between a pair of subsystems. Thus, to obtain the required spring characteristics for a given vehicle side-impact scenario, a number of contact and sectional forces have been used. CONTACT_AUTOMATIC_SURFACE_ TO_SURFACE is defined between components where contact forces are needed for defining LPM springs; the components between which contacts are defined are MDB to FD, MDB to RD, MDB to R, FD to BP, RD to BP, FD to ‘rest of vehicle’, and RD to ‘rest of vehicle’. Section planes are defined for the BP and R for obtaining section forces in the direction of impact. Displacement–time histories of various components such as the FD, BP, RD, R, and MDB are obtained from the finite element analysis results for a given vehicle (i.e. the Dodge Neon or Dodge JAUTO801 F IMechE 2008

Intrepid). Contact and sectional force–time histories of relevant components are saved together with their displacement–time histories after analysis. The force–displacement characteristics are then obtained by eliminating the time column from both force–time and displacement–time histories. From the force–displacement characteristics described, spring behaviour is approximated with bilinear curves as shown in Figs 23 and 24 for spring 1 of Dodge Neon LPM connecting MDB to the FD and for spring 2 of Dodge Intrepid LPM connecting MDB to the RD respectively; a similar approach is followed in obtaining the remaining spring characteristics of the present LPM for a given vehicle. The bilinear approximations have been generated here through inspection by applying the criteria of maintaining the spring yield force at a mean value of the Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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Fig. 21

(a) Energies absorbed by various subsystems of the Dodge Intrepid as percentages of the total system energy absorption; (b) absorbed specific energies (kJ/kg) of the same subsystems

arbitrarily varying finite element analysis-based force, and the areas under the idealized and finite element analysis-based force–displacement curves to be nearly same. The partly heuristic approach followed here in obtaining the equivalent spring characteristics can be substituted in future by an automated robust approach such as a method based on the least-squares error approximation of finiteelement-based results. At present, utmost attention has not been paid to increasing the elegance of the spring property extraction procedure and no quantification of the deviation arising out of approximating finite-element-based load–displacement behaviours is presented as the final objective here has been to compare the LPM-based results with actual test data reported by NHTSA for LINCAP tests of the Dodge Neon and Dodge Intrepid of the relevant model years.

RESULTS FROM LPM ANALYSES

For the reliability of results, the proven explicit LSDYNA solver has been employed in the present study for analysing the LPM of Fig. 22. Two cases are considered here corresponding to the LINCAP tests of the Dodge Neon and Dodge Intrepid for which the finite-element-based responses have already been correlated with test results in the previous sections. The values of the various lumped masses and the spring parameters used as input data for analysis are given in Table 3 and Table 4 respectively for the Dodge Neon and in Tables 5 and 6 respectively for the Dodge Intrepid. The material type MAT_ SPRING_GENERAL_NONLINEAR in LS-DYNA is used for defining the spring properties. The characteristics of the springs involving dummies have been adjusted initially using an iterative approach so that their responses correlate well with LINCAP test results of the Dodge Neon. The same dummy-related spring properties have been retained for the LPM analysis of the Dodge Intrepid. It may be noted that initial gaps are provided between the FD or RD and the corresponding springs attached to the relevant dummy. An appropriate initial velocity of 15.25 m/s is given to the MDB in the LPM to simulate the LINCAP test of each vehicle (i.e. the Dodge Neon or Dodge Intrepid). The LPM-based velocity responses are compared with actual test results (corresponding to LINCAP tests 2715 and 2999) in Figs 25 to 28 for the Dodge Neon and in Figs 29 to 32 for the Dodge Intrepid, and good correlation, especially of the final velocities, is seen considering the idealizations involved in the LPM abstraction. It has been observed in earlier studies [19, 20] that the final velocities of the doors and BP significantly influence the dummy injury parameters defined in terms of the TTI. A summary of test-based peak dummy responses for the Dodge Neon and the relevant TTIs is given in Table 7, and corresponding results obtained from LPM simulation are given in Table 8. The values of the front and rear TTIs obtained in LINCAP test 2715 are 94 and 84 respectively, which compare extremely well with the corresponding LPM-based predictions of 92 and 83. In a similar manner, a summary of testbased peak dummy responses for the Dodge Intrepid and the related TTIs are given in Table 9; the corresponding LPM-based results for SID responses and values of the front and rear TTIs are included in Table 10. It can be seen from Tables 9 and 10 that the LPM-based predictions of the front and rear TTIs for the Dodge Intrepid, namely 63 and 82 respectively, compare reasonably well with the corresponding





Fig. 22

A new side-impact LPM concept with front and rear SIDs

values of 65 and 87 reported by NHTSA for LINCAP test 2999. It is clear from the results reported above for two distinct passenger vehicles that the LPM configuration suggested here can be employed with confidence in representing NHTSA side impact. A degree of ‘tuning’ of the model is of course involved in choosing spring properties that are realistic and would yield responses matching well with the actual crash test or detailed finite-element-based results. Such calibration of a given LPM can be made efficiently by implementing an automated algorithm for performing a sensitivity analysis with respect to Table 2 Spring labels in Fig. 22 Line in Fig. 22

Masses that the line connects

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

MDB to FD MDB to RD MDB to R FD to BP RD to BP FD to ‘rest of vehicle’ RD to ‘rest of vehicle’ R to ‘rest of vehicle’ BP to ‘rest of vehicle’ FD to front SID, lower spine FD to front SID, ribs FD to front SID, pelvis RD to rear SID, lower spine RD to rear SID, ribs RD to rear SID, pelvis


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various spring properties and obtaining the best correlation with given target responses. On obtaining a satisfactory LPM representing a given vehicle, it can be applied as an effective tool for estimating, through an iterative approach, an optimal design with minimum values of front and rear TTIs. Since the current LPM is able to yield velocity responses of key side-structure components, it is expected to be able to predict well the average lateral intrusions in a side-impact event. In the cases considered, the LPM has been found to predict well the peak acceleration responses of front and rear SIDs, leading to good predictions of TTI as well as peak pelvis acceleration. However, in situations where a dummy can be subject to significant rotation about a vertical axis such as a rear dummy impacted partially by the leading part of the RD, the related spring properties will have to be chosen carefully. A similar observation applies to the case of a dummy that is hit by a raised barrier primarily in the thorax region, leading to a significantly high TTI and perhaps low pelvis g. It may be noted that, to simulate the case when a high-ride-height vehicle such as a sport utility vehicle laterally impacts a car, the spring representing the interaction between the MDB and R will have minimal strength or, in the worst case, no strength at all, resulting in increased structural and dummy responses. Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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Fig. 23

Idealization of the behaviour of spring 1 connecting the MDB to the FD in the LPM representing the Dodge Neon side impact

Fig. 24

Idealization of the behaviour of spring 2 connecting the MDB to the RD in the LPM representing the Dodge Intrepid side impact

Table 4 Spring parameters for the Dodge Neon sideimpact simulation Table 3

LPM parameters used for the Dodge Neon side-impact simulation

Lumped mass

Value (kg)

MDB FD BP RD R Rest of vehicle

1365 18 4.5 15 6.5 1188

Spring number

Stiffness K (kN/mm)

Yield force FY (kN)

1 2 3 4 5 6 7 8 9

1.0 0.47 0.37 1 4.5 0.425 0.1 3.2 0.125

75 45 36 10.5 18 80 10 22.5 17





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Fig. 25

Comparison of the Dodge Neon BP velocities from the LPM and the corresponding NHTSA test

Fig. 26

Comparison of the Dodge Neon FD velocities from the LPM and the corresponding NHTSA test

Table 6 Table 5 LPM parameters used for the Dodge Intrepid side-impact simulation Lumped mass

Value (kg)

MDB FD BP RD R Rest of vehicle

1365 25 4.5 14 6.5 1430


Spring parameters for the Dodge Intrepid side-impact simulation

Spring number

Stiffness K (kN/mm)

Yield force FY (kN)

1 2 3 4 5 6 7 8 9

0.7 1.0 1.4 2.5 3.0 1.0 0.5 3.2 2.4

70 55 70 25 30 16 28 65 60



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Table 7


Fig. 27

Comparison of the Dodge Neon RD velocities from the LPM and the corresponding NHTSA test

Fig. 28

Comparison of the Dodge Neon R velocities from the LPM and the corresponding NHTSA test

Front and rear SID peak responses and TTI in the LINCAP test on the Dodge Neon Value for the following Front SID

Left upper rib acceleration (units of g) 94 Left lower rib acceleration (units of g) 87 Lower spine acceleration (units of g) 94 TTI 94 Pelvis acceleration (units of g) 102

Table 8

Front and rear SID peak responses and TTI in the LPM analysis of the Dodge Neon Value for the following

Rear SID 74 77 91 84 104

Rib acceleration (units of g) Lower spine acceleration (units of g) TTI Pelvis acceleration (units of g)



Front SID

Rear SID

86 97 92 106

74 92 83 94



8

Fig. 29

Comparison of the Dodge Intrepid BP velocities from the LPM and the corresponding NHTSA test

Fig. 30

Comparison of the Dodge Intrepid FD velocities from the LPM and the corresponding NHTSA test

CONCLUSION

In the present paper, a comprehensive LPM for vehicle side-impact safety design is presented. For the first time, to the present authors’ best knowledge, the LPM developed includes all relevant sidestructure components, i.e. the FD, BP, RD, and R; additionally, the remaining vehicle structure lumped as one mass, two SIDs (front and rear), and NHTSA MDB are included. Procedures for obtaining simplified spring properties from a validated finite element model of a real-world vehicle have been discussed. The LPM is analysed with the well-known explicit JAUTO801 F IMechE 2008

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LS-DYNA solver and yields reasonably good correlation with LINCAP test results of two vehicles, i.e. the Dodge Neon and Dodge Intrepid. Challenges to obtaining realistic dummy responses from the LPM for a given side-impact scenario have been pointed out. The LPM developed here can be a good tool for guiding the design of a new vehicle as well as conducting parametric studies for improving a given vehicle design for side-impact safety. The power of the present LPM lies in its effectiveness in conducting parametric studies efficiently as demonstrated in reference [16] with numerous analysis cases, and in being able to convert the gross stiffness and strength Proc. IMechE Vol. 222 Part D: J. Automobile Engineering


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Table 9


Fig. 31

Comparison of the Dodge Intrepid RD velocities from the LPM and the corresponding NHTSA test

Fig. 32

Comparison of the Dodge Intrepid R velocities from the LPM and the corresponding NHTSA test

Front and rear SID peak responses and TTI in the LINCAP test of the Dodge Intrepid Value for the following

Left upper rib acceleration (units of g) Left lower rib acceleration (units of g) Lower spine acceleration (units of g) TTI Pelvis acceleration (units of g)

Front SID

Rear SID

60 60 71 65 69

82 85 89 87 110

Table 10

Front and rear SID peak responses and TTI in the LPM analysis of the Dodge Intrepid Value of the following

Rib acceleration (units of g) Lower spine acceleration (units of g) TTI Pelvis acceleration (units of g)



Front SID

Rear SID

60 66 63 68

79 85 82 93



parameters into detailed geometric guidelines for relevant vehicle side-structure components using a knowledge-based approach [16].

ACKNOWLEDGEMENTS The authors would like to thank the General Motors Corporation, Warren, Michigan, USA, for sponsoring the work reported here. The authors are indebted to Dr Mark Neal and Dr J. T. Wang of the General Motors Research & Development Laboratories for their valuable advice and interaction.

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REFERENCES 1 Kamal, M. M. Analysis and simulation of vehicle to barrier impact. SAE paper 700414, 1970. 2 Magee, C. L. Design for crash energy management – present and future developments. In Proceedings of the Seventh International Conference on Vehicle structural mechanics, Detroit, Michigan, USA, 2–4 April 1988 (SAE International, Warrendale, Pennsylvania). 3 Cheva, W., Yasuki, T., Gupta, V., and Mendis, K. Vehicle development for frontal/offset crash using lumped parameter modelling. SAE paper 960437, 1996. 4 Alexandra, C. C., Stuart, G. M., and Samaha, R. R. Lumped parameter modelling of frontal offset impacts. SAE paper 950651, 1995. 5 Lim, G. G. and Paluszny, A. Side impact research. SAE paper 885055, 1988. 6 Green, J. E. Computer simulation of car-to-car collisions. SAE paper 770015, 1977. 7 Thomas, J. T. and Joseph, N. K. Occupant response sensitivity analyses using a lumped mass model in simulation of car-to-car side impact. SAE paper 856089, 1985. 8 Tomassoni, J. E. Simulation of a two-car oblique side impact using a simple crash analysis model. SAE paper 840856, 1984. 9 Gandhi, U. N. and Hu, J. S. Data-based approach in modeling automobile crash. Int. J. Impact Engng, 1995, 16(1), 95–118. 10 Gandhi, U. N. and Hu, J. S. Data-based models for automobile side impact analysis and design evaluation. Int. J. Impact Engng, 1996, 18(5), 517–537. 11 National Highway Traffic Safety Administration Federal Motor Vehicle Safety Standards; side impact protection; side impact phase-in reporting requirements (XII public participation), docket no. NHTSA-2004-17694, RIN 2127-AJ10. Available from http://www.nhtsa.dot.gov/cars/rules/rulings/ SideImpact/part12.html. 12 Samaha, R. R., Molino, L. N., and Maltese, M. R. Comparative performance testing of passenger cars


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relative to FMVSS 214 and the EU 96/EC/27 side impact regulations: phase I. In Proceedings of the 16th International Technical Conference on the Enhanced safety of vehicles (ESV), Windsor, Ontario, Canada, 31 May–4 June 1998, paper 98-5-0-08, pp. 1727–1759 (National Highway Traffic Safety Administration, Washington, DC). Vehicle Modelling Laboratory, applications, finite element model archive, FHNA/NHTSA National Crash Analysis Centre. George Washington University, 2002, available from http://www.ncac.gwu. edu/vml/models.html. Otubushin, A. Detailed validation of a non-linear finite element code using dynamic axial crushing of a square tube. Int. J. Impact Engng, 1998, 21(5), 349–368. Sato, K., Yoshitake, A., Hosoya, Y., and Mikami, H. FEM simulation to estimate crashworthiness of automotive parts. SAE paper 982356, 1998. Cheruvu, K. S. Development of a knowledge-based hybrid methodology for vehicle side impact safety design. PhD Thesis, Indian Institute of Science, Bangalore, India, November 2007. Kumar, M., Paul, L., and Jim, F. Effect of strain rate in full vehicle crash analysis. SAE paper 200001-0625, 2000. Deb, A., Biswas, U., and Chou, C. C. Effects of unloading and strain rate on headform impact simulation. SAE paper 2004-01-0738, 2004. Deb, A. and O’Connor, C. Prediction of front TTI in NHTSA side impact using a regression-based approach. SAE paper 2000-01-0636, 2000. Cheruvu, K. S., Deb, A., Mark, O. N., and Wang, J. T. Setting vehicle side impact design targets using a regression-based approach. Int. J. Veh. Safety, 2007, 2(1–2), 206–220.

APPENDIX Notation BP FD LINCAP LMS LPM MDB NHTSA R RD SID TTI

B pillar front door Lateral Impact New Car Assessment Program lumped mass–spring lumped-parameter model moving deformable barrier National Highway Traffic Safety Administration rocker rear door side-impact dummy thoracic trauma index



Engineering Engineers, Part D: Journal of Automobile

Engineering Engineers, Part D: Journal of Automobile

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