Rollover Analysis of a Bus Using Beam and Nonlinear Spring Elements

Transcription

1 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) Rollover Analysis of a Bus Using Beam and Nonlinear Spring Elements SU-JIN PARK, WAN-SUK YOO, YUEN-JU KWON School of Mechanical Engineering Pusan National University Jangjeon-dong Geumjeong-gu Busan, SOUTH KOREA Astract: - In case of us rollover, the ody structure of a us should e designed to ensure the survival space for passengers. So, this study focused on evaluating the rollover strength through a computer simulation using the commercial code, LS-DYNAD at the initial stage of vehicle development. For this purpose, section structure of the us frame was first ed using simple eam elements, and the impact oundary conditions required y ECE regulation No. 66 were applied. In order to validate the eam element, the simulation results were compared to those of shell element. Since the analysis error with eam element was mainly caused y the difference in strain energy at the T-shaped connecting joint, the joint connection was modified with nonlinear springs to account for the local uckling. With the improved eam, the results were in a good agreement to shell element, ut the simulation times were much reduced. Key-Words: - Rollover strength, Survival space, Beam element, Nonlinear spring, Collapse theory Introduction Many types of uses have een used for commercial traffic transportation, and life span of a us is longer than that of a passenger car. Also, a us have een operated with much more passengers than a small passenger car, however, the research and interest related on its safety seemed relatively low. Since there are many seriously wounded passengers in traffic accidents of uses, more careful analysis and simulation for impact accidents should e investigated. Since the understanding and knowledge of automoile consumers for their safety had een growing up, the related official rules have come into effect. In many us manufacturers and research institutes, new designs and various researches are in progress to match new regulations. In Australia, ADR 59 (Australian Design Rule 59) had specified the deformation of us ody in rollover accidents [], and ECE 66 (Economic Commission for Europe 66) controls the same sustance presently []. Bus structure designs that ensure the survival space of passengers are indispensale, and for these purposes, the rollover analysis and design y using explicit finite element method are useful [,4]. Takagi [6] has numerically simulated rollover occurrence and occupant ehavior according to the rollover initiation types with commercial computer program. The physical test method for rollover accident has recently developed y Richardson [5] and Larson [7], and Moffatt [8] used the controlled rollover impact system for rollover impact investigation. In this study, the commercial code LS-DYNAD [] was used for the rollover analysis of us structure, and the eam analysis was modified with nonlinear spring characteristics for the advanced exactness of its solution. Rollover Test The rollover test of real section structure was executed y a us manufacturer [5] according to the conditions which were defined y ECE. The ody section was located on a rotational platform, and the platform was lifted up y a crane as shown in Fig.. The ody section structure has the weight of 8 kgf, and the free dropping egins after the center of gravity moves out of the hinge point. As the results of rollover test, a deformed ody section is shown in Fig.. Plastic deformation occurred near the welding point of side ody eams, and also the local reak-down appeared on the open section of the eams. The ending collapse took place at the joining area of lower part of window frame and side eams as shown in Fig.. The strength of this area dominates deformation of the whole ody, and this connection is the most

2 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) important to ensure the survival space of passengers in rollover accidents. Fig. 4 Rollover analysis of shell element Numerical Rollover Simulation Fig. Rollover test apparatus. Analysis with Shell Element Model The ody section structure is a skeleton set which is composed of frame-type pillars. This structure is a framework of the whole ody which asors 6~7 % of the impact energy when impact takes place [9,]. The exterior panels and leads were neglected for their small capacity of impact energy asorption. Shell elements were used to estalish the ody section structure as shown in Fig. 4, and concentrated mass elements were arranged to adjust the weight of the structure. The material properties of elasto-plastic steel were employed, and the nonlinear region of material property curve was piece-wise linearly approximated. Fig. Rollover test of the ody section structure. Analysis with Beam Element Model In the design stage of a us, the numerical evaluation of rollover features with a simple eam has the advantages of its low cost and quick response []. Moreover, the reduction of effort to generate the analysis is also possile. The Belytschko-Schwer eam elements [] with the material properties of resultant plasticity, which was adequate for ox-tue type structures, were selected as shown in Fig. 5. The cross-sectional area, moment of inertia, torsional modulus, and the properties of shear area were considered without discrimination with the previous []. Also, the concentrated mass elements and the same oundary conditions were applied. Fig. Side pillar frame under ending collapse Fig. 5 Rollover analysis of eam element. Comparison of the Two Results

3 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) It was cleared that the survival space for passengers was secured via computer simulations. Deformation of window pillars were similar to the results of ody section test, and the survival spaces were otained during rollover procedures as shown in Fig. 4 and Fig. 5. The displacement of window pillars measured from the rain rails and deformation angles from the waist rails are summarized in Tale. The displacement and deformed angle in eam element were smaller than those of shell element, and the differences were 9 % and % of the results in shell element, respectively. The strain energy asored y the ody section in deformation processes is shown in Fig. 6. The asored energy of eam element was higher than that of shell element. These differences come from the over-estimated stiffness of eam element. In the eam element, no local uckling at the area of plastic hinge was considered, and as the result, plastic deformation was not sufficiently estimated. Therefore the eam element ing with the consideration of the stiffness of pillar joint area is needed to otain more exact simulation results. Tale Comparison of displacements and deformed angles measured at window pillar Test 9 mm Shell element 97 mm Displacement Simulation Beam element 6 mm Test 4.9 Shell element Deformed 5.6 Angle Simulation Beam element.5 Asored energy (J) 5 eam Time (sec) Fig. 6 Comparison of asored energy 4 Simulation with Modified Models Nonlinear spring elements were supplemented to improve the disadvantages of eam element us. Nonlinear spring elements were added at the joining area of eam elements to consider the local uckling and the adequate structural stiffness. 4. Collapse Theories The scheme for nonlinear spring input is descried in Fig. 7. The characteristics for axial crush, ending collapse, and torsional collapse are required to import nonlinear spring elements, and the curves of force-displacement, moment-rotational angle, and torsion-twisting angle should e computed in advance to the simulations, respectively. The following equations were adopted to represent the axial crush and the average crush force []. a Pasm = 6π mp t, () σ y t mp =, 4 () P = f P, () adm d asm.56 f d =. v. (4) The maximum ending moment and post-uckling ehavior are important factors to descrie the ending collapse of structural frames. The relations on the ending collapse defined y Kecman and Wierzicki were used as followings [4,7]. M r H M ( α ) = sin 8I I α t r H ( η) η 4 sinα t H / η ( ) H H, (5) H =.76 t, (6) r =.795 t, (7)

4 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) α β I = cos dφ, (8) cos φ I = cos α sin α, (9) ( ) tan β = tan α. () In the joint area, the eccentric loading is applied, and torsional deformation occurs. The ehavior of thin-walled eams under the torsional loading is effectively treated using initial twisting moment T i, twisting moment in steady-state T s, critical twisting angle θ c, and the final twisting angle θ f as shown in Fig. 8, and the following equations were used to calculate the torsional energy EA [6]. Fig. 8 Torsion-twisting angle curve Fig. 9 Modified for T-shaped joint EA Tsθ f θ c =, () T T i T =.7σ, () i s.5.75 y t.4..6 t T s = 5.58σ l, () where σ denotes the stress value that corresponds to the average strain. Force (kn) eam eam-nonlinear spring Time (msec) Fig. Reaction force curves against ending Fig. 7 Scheme for nonlinear spring input Torsional moment (Nm) eam eam-nonlinear spring Rotetional angle (radian) Fig. Reaction torsion curves against twisting 4. Verification with Simple Joint Model

5 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) To verify the effect of nonlinear spring attachment, T-shaped simple joint was investigated as shown in Fig. 9. Nonlinear springs were located on the joining point and its oth sides. As previously mentioned, the collapse conditions y Wierzicki and Santosa were applied to activate the added spring elements [,6]. Reaction properties against the ending and torsional load are plotted in Fig. and Fig., and the asored energy curves are in Fig. and Fig., respectively. It was verified that the modified represented well the nonlinear characteristics of joint area. e reasonale in the previous section. The joining areas etween window pillars and side eams, at which the local uckling and plastic hinge had originated in the previous test and simulations, were reed as shown in Fig. 4. The resultant deformed shape from the rollover simulation with the modified us is in Fig. 5. Bending at the modified joint area was increased, and the resultant difference was reduced to % of shell element us. The asored energies are plotted in Fig. 6, and this comparison shows the improved result which contains the difference of. % in their energy values. Internal energy (kj) eam eam-nonlinear spring Time (msec) Fig. 4 The locations of modified joints Fig. Asored ending energy curves Internal energy (kj) eam eam-nonlinear spring Fig. 5 Deformed shape of modified us Time (msec) Fig. Asored twisting energy curves 4. Modified Bus Model and Improved Results The eam element us was modified with the nonlinear spring elements which were verified to Asored energy (J) eam eam-nonlinear sproing Time (sec)

6 Proceedings of the 9th WSEAS International Conference on Applied Mathematics, Istanul, Turkey, May 7-9, 6 (pp8-) Fig. 6 The comparison of asored energy 5 Conclusion In the rollover simulation of a finite element us, a eam element was successfully modified to save the analysis cost with little loss of its accuracy in comparison with a shell element. The stiffness of simple eam elements was overestimated, and the local plastic deformation was partially out of consideration. However, the modified, to which spring elements and its nonlinear characteristics were applied, estimated the structural stiffness properly, and showed the improved results of reaction forces and internal energy. The staility and effectiveness of joint modification technique was confirmed, and the approach was proved to e useful and advantageous in the vehicle rollover investigation and its development. Acknowledgements: This study was financially supported y Pusan National University in the program, Post-Doc. 6. The authors thank the Ministry of Science and Technology of Korea for its sincere support under the NRL project (M474-5J74). References: [] ADR 59, Australian Design Rule 59/, Omnius Rollover Strength. [] United Nation, Addendum 65: Regulation No.66, Uniform Provision Concerning the Approval of Large Passenger Vehicles with regard to the Strength of their Superstructure, 996. [] T. E. Chung, Rollover Analysis and Measurement of a Large-sized Bus, Transaction of KSAE, Vol.5, No.6, 997, pp [4] H. D. Kim, J. H. Song, C. Y. Oh, Development of a Finite Element Model for Crashworthiness Analysis of a Small-Sized Bus, Transaction of KSAE, Vol., No.,, pp [5] S. Richardson, R. H. Grzeieta, G. Rechnitzer, Proposal for a Dynamic Rollover Protective System Test, International Journal of Crashworthiness, Vol. 8, No.,, pp. -4. [6] H. Takagi, A. Maruyama, J. Dix, K. Kawaguchi, MADYMO Modeling Method of Rollover Event and Occupant Behavior in Each Rollover Initiation Type, SAE -6-7, Nagoya, Japan,. [7] R. E. Larson, J. W. Smith, S. M. Werner, G. F. Fowler, Vehicle Rollover Testing, Methodologies in Recreating Rollover Collisions, SAE --64, Troy, Michigan,. [8] E. A. Moffatt, E. R. Cooper, J. J. Crotean, K. F. Orlowski, D. R. Marth, J. W. Carter, Matched-Pair Rollover Impacts of Rollcaged and Production Roof Cars Using the Controlled Rollover Impact System, SAE --7, SAE World Congress, Detroit, Michigan,. [9] H. W. Lee, H. W. Shin, A Study on the Characteristics of Frontal and Olique Impact of a 4WD Vehicle, Autumn conference proceeding of KSAE, 997, pp [] C. S. Hong, C. Y. Oh, D. C. Lee, Development of a Finite Element Model for Frontal Crash Analysis of a Mid-Size Truck, Journal of KSPE, Vol. 7, No. 4,, pp. 6-. [] Livemore Software, LS-DYNA THEORETICAL MANUAL, 998. [] H. K. Min, T. Kim, An Analysis for Rollover Strength of a Medium Bus, SAE NO.9975, 999, pp [] T. Wierzicki and W. Aramowicz, On the Crushing Mechanics of Thin-Walled Structures, ASME Journal of Applied Mechanics, Vol. 5, 98, pp [4] D. Kecman, Bending Collapse of Rectangular and Square Section Tues, Int. J. of Mech., Vol. 5, No. 9-, 98, pp [5] Technical Report, E, The Analysis and Experiment on the Rollover Accident of a Bus, Daewoo Bus Corporation. [6] S. Santosa and T. Wierzicki, Effect of an Ultralight Metal Fillar on the Torsional Crushing Behavior of Thin-Walled Prismatic column, Int. J. Crashworthiness, Vol., No. 4, 997, pp. 5-. [7] S. H. Park, S. Y. Kang, H. Y. Kim, D. K. Min, D. C. Han, Development of Nonlinear Spring Element and Vehicle Crashworthiness Analysis, Proceedings of KSME Conference, 97865, 997, pp