Explicit dynamic analysis of the roll cage using rigid element Ayush Anand Student (Production) BIT Mesra, Ranchi,India-835215 ayush.aand@gmail.com Keywords: Roll cage, Dynamic analysis, Hypermesh Abstract The most important aspect of the vehicle design is the frame part or roll cage. The frame has the operator, engine, brake system, fuel system, and steering system, it must be of adequate strength to protect the driver in the event of a rollover or impact. BAJA SAE roll cage is generally constructed of steel tubing, with minimum dimensional and strength requirements dictated by Society of Automotive Engineers (SAE). The dynamic analysis is, therefore, an important analysis to perform after getting desirable stress in static analysis. In the present paper, explicit dynamic analysis had been performed with (on) all the components and sub-components being properly replaced by rigid elements. Introduction In mechanics, the static system is the state of a system that is in equilibrium with the action of balanced forces and torque so that they remain at rest. But to get a real case value, dynamic analysis has to be performed. Considering, this is a crash analysis with short duration impact, explicit dynamic analysis had been performed using HyperMesh 13.0. This analysis had been performed for the particular case of impact. Here the case considered is, Impact with the same vehicle: - The vehicle had to make a head-on collision with the same vehicle which had been at a particular distance from the extreme point of the roll cage. Process Methodology Meshing The 2D meshing had been done as shown in fig.1. The quality index had been used to ensure that the fail elements are minimal. Also, it was taken care that the element with a size less than 3 mm is minimal in order to avoid any unnecessary solver time. The meshing element was selected as mixed as per the scenario. Fig.1. Meshing Component Primary and secondary tubes were of different thickness and so, they were assigned with different component as shown in fig 2. 1
Fig.2: Red color denotes primary tubes while green denotes secondary tube Properties Thickness had been decided in this card. Other than that, some important parameters were also decided such as Ishell=24 (QEPH formulation) which reduces the hourglass energy & N=5 (number of integration points) Material M2 PLAS JOHNS ZERIL material had been taken considering the ductile material and the specification of the material had been shown in table 1. Table 1: Material specification SPECIFICATION VALUES Density(Rho_initial) 7.89e+9 ton/mm 3 Young's modulus ( E ) 210000 N/mm 2 Poisson ratio(nu) 0.3 Yield stress (a) 720 N/mm 2 Hardening parameter (b) Hardening coefficient (n) 0.21 230 MPa UTS (Sig._max) 810 N/mm 2 Assembly Fig.3: Centre of mass of each component (move up below the image) 2
Considering dynamic analysis, a rigid connection had been made for each of the components using RBE2, and the approximate center of mass for each component had been decided in CATIA as shown in fig. 3, which was bolted to the chassis members as they have to be. Adding rigid mass gave us a clear picture of doing the dynamic analysis as it could be seen in fig. 4. Fig.4: Rigid mass added for each component Mass was added using card ADMAS with element type M-ADV1 on the master node so as to divide the forces equally among the nodes as per their proportion as shown in fig. 5. Fig.5: Mass being given to each independent node The total mass comprising all the components comes out to be 224 kg. 3
Fig 6: Total mass of the system Contact and reflect Type 7 contact is created so that the components can interact in the event of impact. Reflect card was used to make an identical vehicle at a particular distance from our vehicle. Load collector Two load collectors were needed in our case: 1. Velocity: - Initial velocity of 54 kmph was imparted to our vehicle using card INIVEL collector and they were made to collide with the same vehicle which is at a distance of 23 mm from the front most part of the vehicle. 2. Constraints: -The second vehicle is constrained using card BCS_collector. Cards Several cards were made in order to optimize the whole simulation. Some of them were:- A. ENG_RUN: T stop had been calculated and decide here, which is basically total run time for the simulation. For this, the total time taken to hit the second vehicle and coming back to its original position has been taken. Considering the second vehicle at a distance 23mm from the first vehicle, and vehicle moving at speed of 54kmph, the total time would be 0.006 seconds. B.ENG_TFILE: The frequency of time after which the animation file would be generated is mentioned here which is taken as 6e-07. C. ENG_ANIM_ELEM: Those parameters which had to be evaluated other than displacement (default) had been taken here. Result and discussion The post processing had been performed on HyperView. Two results had been inferred from the analysis, Von Mises stress and total displacement. The maximum stress comes out to be 711 MPa. The maximum displacement comes out to be 2.97 mm. 4
Fig.7 Stress Fig.8 Displacement Fig 9: Total energy curve An energy curve was also plotted for this analysis on HyperGraph to ensure that the total energy remains constant throughout the process. 5
Conclusion The stress and the displacement value comes out to be under the desired value with a factor of safety coming out to be greater than 1 for this analysis. Also, the total energy remains constant for the entire process with the hourglass energy (Hourglass modes are non-physical), zero energy modes that do not generate any stress or strain but can affect solution accuracy by interfering with the structure s true response [13] coming out to be zero. Acknowledgement I sincerely thank the production department of BIT Mesra, Ranchi, India for funding this project work.the author would like to express their gratitude to Altair Engineering India Pvt. Ltd. for helping in carrying out all the work. References [1]. Milliken, D., Kasprak, E., Metz, L. and Milliken W.. Race Car Vehicle Dynamics: Problems, Answers and Experiments. Society of Automotive Engineers, Inc.,2003. [2]. Gillespie, T. Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Inc., 2001. [3]. Fenton, J. Handbook of Vehicle Design Analysis, Society of Automotive Engineers, Inc., 1996. [4]. Erjavec, J. Automotive Technology: A Systems Approach. Delmar Cengage Learning., 2009. [5]. Huang, M. Vehicle crash mechanics. CRC press,2002. [6]. Wu, C.F.J. Experiments planning, analysis, and parameter design optimization. 2nd ed. New York: John Wiley, 2012. [7]. E. Onate, C. Recarey, F. Zarate, J. Miquel, J. Rojek, Characterization of micro macro parameters in discrete element ~ formulation, CIMNE, Barcelona, 2004. [8]. http://geosim.engr.mun.ca/pipesoil.htm [9]. E. Onate, M. Manzan, A general procedure for deriving stabilized space time finite element methods for advective diffusive ~ problems, Int. J. Numer. Methods Fluids 31 (1999) 203 221. [10]. E. Onate, M. Manzan, A general procedure for deriving stabilized space time finite element methods for advective diffusive ~ problems, Int. J. Numer. Methods Fluids 31 (1999) 203 221. [11]. O.C. Zienkiewicz, R.C. Taylor, The Finite Element Method, fifth ed., Butterworth-Heinemann, Oxford, 2000 [12]. E. Onate, J. Rojek, R.L. Taylor, O.C. Zienkiewicz, Linear triangles, and tetrahedra for the incompressible problem using a finite ~ calculus formulation, in Proc. 2nd European Conference on Computational Mechanics ECCM-2001, Cracow, 26 29 June 2013 (on CD- ROM). [13]. https://caeai.com/blog/why-worry-about-hourglassing-explicit-dynamics-part-i 6