PRACA ORYGINALNA
Nonlinear method of determining the vehicle pre-crash speed based on B-spline with propabilistic weights - subcompact car class
Przemyslaw Kubiak 1  
,  
Ewa Sys 1  
,  
Lukasz Goslawski 1  
,  
Maria Manko 2  
,  
Jacek Gralewski 3  
,  
Mateusz Krukowski 4  
,  
Adam Mrowicki 1  
,  
Tiefang Zou 6  
 
 
Więcej
Ukryj
1
Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, Polska
2
Institute of Polymer and Dye Technology, Faculty of Chemistry, Lodz University of Technology, Polska
3
Institute of Social Sciences and Management of Technologies, Lodz University of Technology, Polska
4
Institute of Mathematics, Lodz University of Technology, Polska
5
TEMA–Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, Portugal
6
School of Automobile and Mechanical Engineering, Changsha University of Science and Technology, China
AUTOR DO KORESPONDENCJI
Przemyslaw Kubiak   

Department of Vehicles and Fundamentals of Machine Design, Lodz University of Technology, 1/15 Stefanowskiego Str.,, 90-924, Lodz, Polska
Data publikacji: 30-09-2019
Data nadesłania: 19-02-2019
Data ostatniej rewizji: 24-03-2019
Data akceptacji: 12-09-2019
 
The Archives of Automotive Engineering – Archiwum Motoryzacji 2019;85(3):5–18
SŁOWA KLUCZOWE
DZIEDZINY
STRESZCZENIE ARTYKUŁU
A new non-linear method utilizing the work W of car deformation is considered in this study. The car deformation is defined as an algebraic function of deformation ratio Cs. The method of variable correlation is exploited in order to develop experimental data. To determinate mathematical model parameters, data from the NHTSA database including frontal crash tests are used. Such database is comprised of substantial number of crash cases and main focus was put on frontal impacts. In the non-linear method used so far, the so-called energetic approach, collisions are considered non-elastic. The speed threshold defining the elastic collision was set to be 11 km/h. This simplistic approach is used to determine the linear relation of energy loss during deformation on deformation coefficient Cs. Deformation points C1-C6 are taken into account while calculating a mean value that defines this coefficient. A more accurate non-linear method as well as more complex form of deformation coefficient is suggested to determine the work of deformation in this paper. The focus of those methods is to establish the value of nonlinear coefficient b_k which is the slope factor of precrash velocity Vt and deformation ratio Cs function.
 
REFERENCJE (37)
1.
Axler, S. J. Linear algebra done right. Springer, 1997.
 
2.
Campbell, B. J. The traffic accident data project scale. In Proceedings of Collision Investigation Methodology Symposium, 1969, 675-681.
 
3.
Cheney E.W., Kincaid D. Numerical analysis: mathematics of scientific computing. Brooks/Cole, 2003.
 
4.
Cromack J.R., Lee S.N. Consistency study for vehicle deformation index. SAE Technical Paper, 1974, DOI: 10.4271/740299.
 
5.
Faraj R., Holnicki-Szulc J., Knap L., Seńko J. Adaptive inertial shock-absorber. Smart Materials and Structures, 25, 2016, DOI: 10.1088/0964-1726/25/3/035031.
 
6.
Foret-Bruno J.Y., Trosseille X., Le Coz J.Y., Bendjellal F., Bendjella F., Steyer C., Phalempin T., Villeforceix D., Dandres P., Got C. Thoracic injury risk in frontal car crashes with occupant restrained with belt load limiter. SAE Transactions, 1998, 2955-2975, DOI: 10.4271/983166.
 
7.
Geigl B.C., Hoschopf H., Steffan H., Moser A. Reconstruction of occupant kinematics and kinetics for real world accidents. International journal of crashworthiness, 8, 2003, 17-27, DOI: 10.1533/ijcr.2003.0217,.
 
8.
Gidlewski, M., Żardecki, D. Linearization of the lateral dynamics reference model for the motion control of vehicles. Mechanics Research Communications, 82, 2017, 49-54, DOI: 10.1016/j.mechrescom.2016.09.001.
 
9.
Gidlewski M., Żardecki D. Simulation investigations of lane change process with automatic steering system. InProceedings of 25th ESV’2017 Conference in Detroit, USA, available on the Internet 2017.
 
10.
Gidlewski, M., Prochowski, L. Analysis of motion of the body of a motor car hit on its side by another passenger car. In IOP Conference Series: Materials Science and Engineering, 148, 2016, DOI: 10.1088/1757-899X/148/1/012039.
 
11.
Gidlewski M., Żardecki D. Simulation Based Sensitivity Studies of a Vehicle Motion Model. InProc. of the 20th Int. Scientific Conf. Transport Means, 2016, 236-240.
 
12.
Grolleau V., Galpin B., Penin A., Rio G. Modelling the effect of forming history in impact simulations: evaluation of the effect of thickness change and strain hardening based on experiments. International journal of crashworthiness, 13, 2008, 363-373, DOI: 10.1080/13588260801976120.
 
13.
Han I., Kang H., Park J.C., Ha Y. Three-dimensional crush measurement methodologies using two-dimensional data. Transactions of the Korean Society of Automotive Engineers, 23, 2015, 254-262, DOI: 10.7467/KSAE.2015.23.3.254.
 
14.
Han I. Analysis of vehicle collision accidents based on qualitative mechanics. Forensic science international, 291, 2018, 53-61, DOI: 10.1016/j.forsciint.2018.08.004.
 
15.
Han I. Vehicle collision analysis from estimated crush volume for accident reconstruction. International Journal of Crashworthiness, 24, 2019, 100-105, DOI: 10.1080/13588265.2018.1440499.
 
16.
Hight P.V., Fugger T.F., Marcosky J. Automobile damage scales and the effect on injury analysis. SAE Technical Paper 920602, 1992, DOI: 10.4271/920602.
 
17.
Iraeus J., Lindquist M. Pulse shape analysis and data reduction of real-life frontal crashes with modern passenger cars. International journal of crashworthiness, 20, 2015, 535-546, DOI: 10.1080/13588265.2015.1057005.
 
18.
Krukowski M., Kubiak P., Mrowicki A., Siczek K., Gralewski J. Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights—Intermediate Car Class. Forensic science international, 293, 2018, 7-16. DOI: 10.1016/j.forsciint.2018.10.011.
 
19.
Kubiak P. Work of non-elastic deformation against the deformation ratio of the Subcompact Car Class using the variable correlation method. Forensic science international, 287, 2018, 47-53, DOI: 10.1016 / j.forsciint.2018.03.033.
 
20.
Lindquist M., Hall A, Björnstig U. Real world car crash investigations–A new approach. International journal of crashworthiness, 8, 2003, 375-384, DOI: 10.1533/ijcr.2003.0245.
 
21.
Mackay G.M., Hill J., Parkin S., Munns J.A. Restrained occupants on the nonstruck side in lateral collisions. Accident Analysis & Prevention, 25, 1993, 147-152, DOI: 10.1016/0001-4575(93)90054-Z.
 
22.
Mannering F.L., Bhat C.R. Analytic methods in accident research: Methodological frontier and future directions. Analytic methods in accident research, 1, 2014, 1-22, DOI: 10.1016/j.amar.2013.09.001.
 
23.
McHenry B.G. The algorithms of CRASH. InSoutheast Coast Collision Conference, 2001, 1-34.
 
24.
McHenry R.R. Computer program for reconstruction of highway accidents. SAE Technical Paper No. 730980, 1973, DOI: 10.4271/730980.
 
25.
Nelson W.D. The History and Evolution of the Collision Deformation Classification SAE J224 MAR80. SAE Technical Paper No. 810213, 1981, DOI: 10.4271/810213.
 
26.
Neptune J.A. Crush stiffness coefficients, restitution constants, and a revision of CRASH3 & SMAC. SAE Technical Paper No. 980029, 1998, DOI: 10.4271/980029.
 
27.
Norros I., Kuusela P., Innamaa S., Pilli-Sihvola E., Rajamäki R. The Palm distribution of traffic conditions and its application to accident risk assessment. Analytic methods in accident research, 12, 2016, 48-65, DOI: 10.1016/j.amar.2016.10.002.
 
28.
Sharma D., Stern S., Brophy J., Choi E. An overview of NHTSA’s crash reconstruction software WinSMASH. InProceedings of the 20th International Technical Conference on Enhanced Safety of Vehicles, 2007.
 
29.
Siddall D.E., Day T.D. Updating the vehicle class categories. SAE Technical Paper No. 960897, 1996, DOI: 10.4271/960897.
 
30.
Vangi D., Cialdai C. Evaluation of energy loss in motorcycle-to-car collisions. International journal of crashworthiness, 19, 2014,361-370, DOI: 10.1080/13588265.2014.899072.
 
31.
Vangi D. Simplified method for evaluating energy loss in vehicle collisions. Accident Analysis & Prevention, 41, 2009, 633-641, DOI: 10.1016/j.aap.2009.02.012.
 
32.
Wach W., Unarski J. Determination of vehicle velocities and collision location by means of Monte Carlo simulation method. SAE Technical Paper No. 2006-01-0907, 2006, DOI: 10.4271/2006-01-0907.
 
33.
Wach W., Gidlewski M., Prochowski L. Modelling reliability of vehicle collision reconstruction based on the law of conservation of momentum and Burg equations. In 20th International Scientific Conference TRANSPORT MEANS, 2016, 693-698.
 
34.
Wang W., Sun X., Wei X. Integration of the forming effects into vehicle front rail crash simulation. International journal of crashworthiness, 21, 2016, 9-21, DOI: 10.1080/13588265.2015.1091170.
 
35.
Wasik M., Skarka W. Simulation of Crash Tests for Electrically Propelled Flying Exploratory Autonomous Robot. In ISPE TE, 2016, 937-946.
 
36.
Wood D.P., Simms C.K. Car size and injury risk: a model for injury risk in frontal collisions. Accident Analysis & Prevention, 34, 2002 , 93-99, DOI: 10.1016/S0001-4575(01)00003-3.
 
37.
Żuchowski A. The use of energy methods at the calculation of vehicle impact velocity. Archiwum Motoryzacji, 68, 2015,85-111,197-222.
 
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