Calculation of vehicle-lumped model parameters ...

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Calculation of vehicle-lumped model parameters considering occupant deceleration in frontal crash a

Javad Marzbanrad & Mostafa Pahlavani a

a

School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran

Available online: 15 Sep 2011

To cite this article: Javad Marzbanrad & Mostafa Pahlavani (2011): Calculation of vehicle-lumped model parameters considering occupant deceleration in frontal crash, International Journal of Crashworthiness, 16:4, 439-455 To link to this article: http://dx.doi.org/10.1080/13588265.2011.606995

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International Journal of Crashworthiness Vol. 16, No. 4, August 2011, 439–455

Calculation of vehicle-lumped model parameters considering occupant deceleration in frontal crash Javad Marzbanrad∗ and Mostafa Pahlavani School of Automotive Engineering, Iran University of Science and Technology, Tehran, Iran

Downloaded by [Javad Marzbanrad] at 22:33 15 September 2011

(Received 23 January 2011; final version received 19 July 2011) In this study, two types of lumped parameter models (LPMs) are introduced for a vehicle to study frontal crash. A fourdegree-of-freedom (DOF) LPM Hybrid (LH) model is proposed and analysed as a full car model during crash status, which is compared with a serial 4-DOF model. In addition, a 5-DOF LH model is proposed and compared with a serial 5-DOF model. In this investigation, two parameters, including spring and damper coefficients, have been determined so that the proposed models have similar deceleration with the experimental data. These determined parameters have been calculated on the basis of difference minimisation between simulated and experimental results as occurred for occupants in the frontal crash. A genetic algorithm (GA) is implemented for defining a value function to optimise parameters. In other words, the GA is used for system identification to determine the spring and damper parameters for LPMs. Absolute decelerations along with their frequencies due to external load excitation are also studied here. Keywords: vehicle crash; lumped parameter model; genetic algorithm; optimisation

1.

Introduction

Historically, the considerations about the manner of decorating materials and necessities about physical structure of a vehicle have resulted in designing structure and its body. Generally, final design of a vehicle is the product of a longterm process, being derived by several tests and supported by simple linear stiffness modes. By developing software and hardware, it is possible to use more analytical facilities, making several tools, for analytical designing of modern structure of a vehicle. Therefore, engineers are able to meet their growing needs and better performance of crashworthiness and safe driving. These tools include lumped parameters models (LPMs), beam element models (BEMs), hybrid models and finite elements models (FEMs). Although these tools differ in complexity, each is based on the principles of structural mechanics that satisfy conservation of mass, momentum and energy. The selection of a particular analysis tool depends on the task at hand and on the particular design phase according to considered performance. For example, initially, a simple BEM is the most desired one, but FEM analysis is better than others during design phase of model. Therefore, on the basis of model complexity, time needed for developing a model and amount of information provided are different things. During recent years, automotive industry has confronted with maximum requests of customers, lawmakers and media for production of safe vehicles. This progress includes improving crashworthiness of structure ∗

Corresponding author. Email: [email protected]

ISSN: 1358-8265 print / ISSN: 1754-2111 online C 2011 Taylor & Francis DOI: 10.1080/13588265.2011.606995 http://www.informaworld.com

in crashes according to, for example, Federal Motor Vehicle Safety Standards (FMVSS), New Car Assessment Program (NCAP), Insurance Institute for Highway Safety (IIHS), consistency tests and insuring for keeping children and short adults. In other words, it is needed to use a vast picture from crashworthiness of vehicle. In 1970, Kamal [9] presented a simple and strong LPM for simulation of crashworthiness in frontal crash as shown in Figure 1. As such, for providing acceptable results, data were widely used by crash engineers. Spring characteristics were experimentally determined in a static crusher. In 1988, Magee [12] presented a model for crashing with a barrier. This study used actual crash information for determining properties of springs, masses and breaking models. This model was designed while considering the load displacement properties of springs for obtaining best consistency of accelerations, its peak and crash scheduling. Cheva et al. [3] presented one-dimensional LPMs. They used simulations of finite elements for determining spring properties. Also, recorded normalised acceleration in test and simulation of LPM had desired consistency with each other. Carrera et al. [1] presented an LPM in frontal/offset crash in national Highway Traffic Safety Administration (NHTSA), being directly extracted from structural properties of vehicle from data related into crash test. Lim and Paluszny [11] presented an LPM in side crash. This model was designed on the basis of a crash test at a velocity of


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J. Marzbanrad and M. Pahlavani

Figure 1. LPM stated by Kamal in frontal crash [9].

50 km/h. Thomas and Joseph [15] designed a model as illustrated in Figure 2. Also, Tomassoni [16] considered a model presented in Figure 3. Kim and Arora [10] studied linear and nonlinear systems for vehicle crash. It was performed, theoretically, for the purpose of stating the importance of numerical ways in modelling and analysing crash. In 1991, Bennet et al. [2] considered an LPM for dynamic simulation and analysing occupants. Generally, a crash condition, including car to barrier, car to car, side crash, frontal/offset crash and so on, could be simulated via an LPM. Analysts and designers, such as Hollowell [5,6], gave more attention to hybrid models of finite element and LPMs except FEMs, which are time-consuming and difficult. In

Figure 2. LPM stated by Thomas and Joseph in side crash [15].

1986, Ni and Song [13] described three methods for simulating vehicle structures in crashes. The first method was called the hybrid method, which used an LPM for the structure. The structural components were represented by non-linear spring elements whose force–deformation characteristics were obtained by static crush tests in the laboratory. The second method was called the analytical method, which was based on either the limit analysis of the automotive structure modelled as a space frame or the FE analysis of the structure using beam and shell elements. The third method, called the mixed method, combined the hybrid and the analytical methods. This approach was demonstrated on two example problems where some structural components were modelled as non-linear spring elements and others were modelled using finite elements. The primary aim of the crashworthiness design process is to secure dummy response results that measure below or at acceptable injury risk values. The crash pulse, typically generated from the frontal crash of a vehicle into a rigid barrier, is the essential feature in the design process. It is used as an input to occupant models. Currently, the design process relies on calculating the crash pulse from either LPMs or FEMs. In 2003, Ruan and Yu [14] conducted their research on mass–spring systems. In their study, the equations of LPM


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of introduced lumped model relate to the parts of vehicle such as engine, suspension system and fire wall. The method for system identification of linear systems was validated through a 2-DOF serial model. Furthermore, 4-DOF and 5-DOF models were introduced in this paper as could be considered for a vehicle model in frontal crash. Kinematic analysis, including velocity and acceleration, was accomplished and compared the results with serial models as well as with the tests. The parameters for the lumped model of a vehicle were determined such that the deceleration of occupant during a crash corresponds very closely in agreement to the experimental test. The LPMs developed here could 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 frontal impact safety. In conclusion, the lumped model presented here gives accurate occupant deceleration, which is enough to represent the car dynamic behaviour during frontal crash. However, more DOF may be required to capture the behaviour of other types of cars. It is concluded that the enhancement of engine mass could increase relative displacement of occupant in the vehicle crash, whereas the enhancement of body mass could decrease relative displacement of occupant. It is also concluded that the enhancement of engine or body mass causes decrease in occupant deceleration. A continuation of the current work would include coupling of model parameters in a more DOF; i.e. divide the global car into the smaller parts. This would provide information on how the model parameters could be adjusted based on information from experimental test of vehicle crash. References [1] A.C. Carrera, S.G. Mentzer, and R.R. Samaha, Lumped parameter modeling of frontal offset impacts, International Society of Automotive Engineering (SAE International) Technical Paper, 1995, doi: 10.4271/950651. [2] J.A. Bennett, R.V. Lust, and J.T. Wang, Optimal design strategies in crashworthiness and occupant protection. Crashworthiness and occupant protection in transportation systems, ASME, AMD 126/BED 19 (1991), pp. 51–66.

[3] W. Cheva, T. Yasuki, and V. Gupta, Vehicle Development for Frontal/Offset Crash Using Lumped Parameter Modeling, International Society of Automotive Engineering (SAE International) Technical Paper, 1996, doi: 10.4271/960437. [4] A. Deb and K.C. Srinivas, Development of a new lumpedparameter model for vehicle side-impact safety simulation, J. Autom. Eng. 222 (2008), pp. 1793–1811. [5] W.T. Hollowell, Adaptive time domain, constrained system identification of nonlinear structures, Symposium on vehicle crashworthiness, including impact biomechanics, ASME, AMD 79/BED 1 (1986), pp. 105–123. [6] W.T. Hollowell, Adaptive time domain, constrained system identification of nonlinear structures, Ph.D. diss., The University of Virginia, 1986. [7] M. Huang, Vehicle Crash Mechanics, 2nd ed., SAE International, CRC Press, Boca Raton, FL, 2002. [8] P. Jons´en, E. Isaksson, and K.G. Sundin, Identification of lumped parameter automotive crash models for bumper system development, Int. J. Crashworthiness 14 (2009), pp. 533–541. [9] M.M. Kamal, Analysis and Simulation of Vehicle to Barrier Impact, International Society of Automotive Engineering (SAE International) Technical Paper, 1970, doi: 10.4271/700414. [10] C.H. Kim and J.S. Arora, Nonlinear dynamic system identification for automotive crash using optimization: A review, Struct. Multidisc. Optim. 25 (2003), pp. 2–18. [11] G.G. Lim and A. Paluszny, Side Impact Research, International Society of Automotive Engineering (SAE International) Technical Paper, 1988, doi: 10.4271/885055. [12] C.L. Magee, Design for crash energy management present and future developments, Proceedings of the Seventh International Conference on Vehicle structural mechanics, Detroit, MI (SAE International, Warrendale, PA), 1988. [13] C.M. Ni and J.O. Song, Computer-aided design analysis methods for vehicle structural crashworthiness, Proceedings of symposium on vehicle crashworthiness including impact biomechanics, ASME, AMD 79/BED 1 (1986), pp. 125–139. [14] H.H. Ruan and T.X. Yu, Collision between mass – Spring systems, Int. J. Impact. Eng. 31 (2005), pp. 267–288. [15] J.T. Thomas and N.K. Joseph, Occupant Response Sensitivity Analyses Using a Lumped Mass Model in Simulation of Car-to-Car Side Impact, International Society of Automotive Engineering (SAE International) Technical Paper, 1985, doi: 10.4271/856089. [16] J.E. Tomassoni, Simulation of a Two-Car Oblique Side Impact Using a Simple Crash Analysis Model, International Society of Automotive Engineering (SAE International) Technical Paper, 1984, doi: 10.4271/840858.

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Appendix Table A1. Calculated values of parameters.


Parameter c1 c2 c3 c4 c5 c6 c7 c8 c9 k1 k2 k3 k4 k5 k6 k7 k8 k9

Unit

4-DOF LH model

4 DOF serial model

5-DOF LH model

5 DOF serial Model

N.s/m N.s/m N.s/m N.s/m N.s/m N.s/m N.s/m N.s/m N.s/m N/m N/m N/m N/m N/m N/m N/m N/m N/m

0.08114 – 21, 321.7573 2158.7018 2, 992, 868.2638 354.8610 – – – 1, 144, 966.3425 5.1506 4.7522 7.4641 956, 675.5547 553, 891.4382 – – –

20, 621.1106 2, 480, 317.3400 8.5810 178.3963 – – – – – 78, 344.9782 1, 141, 520.3823 1, 011, 727.5060 681, 806.2138 – – – – –

– – –

19, 919, 388.2110 19, 917, 598.5614 0.18304 19, 777.1246 810.8301 – – – – 1, 341, 925.0874 1, 333, 105.2186 1, 117, 990.6919 1.91805 572, 047.2444 – – – –

0.8981 33, 114.2156 1.7284 6764.6574 8, 648, 277.6159 1595.5245 48.8660 915, 522.5864 1, 206, 875.4364 1, 178, 694.8422 36.7265 136.4661 38.6678 4, 761, 249.3940 389, 232.4263