Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 SAE TECHNICAL PAPER SERIES Dynamical Simulation and Structural Analysis of Light Vehicles Chassis Marco A Cardoso Rogbrio J Marczak UFRS- GMA-GRUPO MECANICAAPL~CADA L , ~ A a- - , Affiliated with The Engineen'ng Society EAeForAdvancing hfobilify J r r b n d r r i r m d s p c e I N T E R N A T I O N A L Mobility Technology Conference & Exhibit SBo Paula, Brasil October 2-4, 1995 400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A Tel: (412)776-4841 Fax:(412)776-5760 Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 The appearance of the ISSNcode at the bottom of this page indicates SAE's consent that copies of the paper may be made for personal or internal use of specific clients This consent is given on the condition,however that the copier pay a $7.00 per article copy fee through the Copyright Clearance Center Inc Operations Center 222 Rosewood Drive, 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Automotive Engineers, Inc Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE The author is solely responsible for the content of the paper A process is available by which discuss~onswill be printed with the paper if it is published in SAE transactions For permission to publish this paper in full or in part, contact the SAE Publications Group Persons wishing to submit papers to be considered for presentation or publication through SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Activity Board SAE Printed in USA 93 203offi Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Dynamical Simulation and Structural Analysis of Light Vehicles Chassis Marco A Cardoso Rogbrio J Marczak - UFRS GMA-GRUPO MECANICA APUCADA Some critical regions were selected after a detection of the points with greatest load level The results show that is possible to reproduce realistic situations, allowing the use of real security levels on the most requested points This methodology can be easily extended to other structural elements ABSTRACT The present paper shows some of the results obtained for service simulation and structural analysis of a small size vehicle with tubular structure The results are presented after the successfbl use of the presented methodology in a practical case All simulations in time domain were camed out by computer programs, which used terrain profiles compatible to the purpose of the vehicle The dynamic loads obtained were applied to finite element models, allowing the evaluation of nominal stress concentration factors, necessary for reability evaluation The proposed methodology showed t o be quite effective, allow the evaluation of security factors in critical points and can be easily extended to general automotive structural elements SERVICE SIMULATION The service simulation of the vehicle, representing any traffic situation, is necessary to estimate the loads acting on the component From this simulation procedure, in the present paper context, the variables of interest are the reactions at the suspension's support points of the chassis These reactions can be used as primary loads on a detailed finite element model NUMERICAL MODEL In order to proceed the service simulation, the vehicle was modeled with the following basic components: chassis, engine, transmission, axle shaft, hel reservoir, accessories and pilot MI geometric properties of each component was ~alculated, resulting in the evaluation of translational and rotational inertia moments for hanging mass and the wheelhires masses This is a lengthy calculation step and requires some knowledge of all relevant subsystems of the vehicle, as well as its dimensions, mass and assembly points The vehicle model was accomplished by the Rigid Baty Spring Model (RBSM) illustrated in figure The main mass mo has tree degrees of freedom i.e longitudinal rotation (P), lateral rotation (a)e translation (Zo) on the axis Z The only degree of freedom considered for each wheelhires masses is the vertical displacement on axis Z This model is used only for excitation came fiom the irregularities of the track Further vibration sources was considered in the present paper - INTRODUCTION The growing research for development of ultimate quality products and the worldwide automotive industry has clearly led the disrepair of some obsolete project techniques Nowadays world tendency is to reach acceptable levels of reliability for S ~ N C ~components, U ~ without hrther implications as, for example, over dimensioning The use of safety factors based on empirical recommendations (in some cases even arbitrary), has no place at the modem methodology of industrial products' project This context has been led to a great development of mechanical components analysis techniques in the aerospace industry in a first moment and, more recently, in the automotive industry Among them are the analysis methods like the finite element method and time transient dynamics analysis Such development has allowed the dimensioning of structures with given safety levels, and the experience with prototypes has confirmed good results, which generally allows a estimate of the life time with good reliability The present papers presents an analysis of some of the steps of service simulation and the structural behavior of a small size vehicle with tubular chassi The simulations in time domain are executed with the vehicle driving over an irregular road track, and the dynamic loads obtained can be applied to finite elements models, in order to obtain the nominal stress concentration factors for components As an illustrative example, only the chassis is here analyzed Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Figure 1: Simplified layout of the RBSM used The equilibrium equations for the RBSM used are represented by its angular and translational acceleration with respect to each degree of freedom They were obtained from the dynamic equilibrium of each mass, on the directions of each degree of freedom: Figures and present the side views of the RBSM, for a complete understanding of all degrees of freedom used The figure shows the longitudinal rotation P with the respective displacement and referential axes overlapped the right and left sides The lateral counterparts of these variables are illustrated in the figure zo=- kd.61+h-62+kt-63+ktS4+ lmo (2.e) C d & + C d & + ~ t - & + ~ + m O ~ ~ t -. t b+ Figure 2: RBSM - Side view When a tire does not touch the road, only the gravitational action should be considered The gravity was considered acting only on the main mass m, while the wheel's masses ml, md, m3 e m4 had this effect not considered So, this effect acts on the main mass leading to the following modification in eq.(2.e): Figure 3: RBSM - Front view The equations that describe the flexible elements displacement (suspension and tires) was obtained from a model described above In the numerical implementation the following convention was considered: when the is negative compression has occurred and displacement when it is positive traction occurred in the suspension system When the displacements of the tires +i is positive (traction), the equations are changed to represent the ballistic behavior of the vehicle, as will be detailed in the sequel The displacement equations are explicitly given by + The profile of the displacement of the masses in this situation is ballistic (quadratic) This model was numerically implemented using a commercial software that perfom the numerical time integration of the equations, allowing the evaluation of time histories for any variables (displacement, velocities, accelerations, forces, etc.) VALIDATION OF THE NUMERICAL MODEL - In order to validate the RBSM described, some typical situations were simulated for this kind of vehicle In figure one can be observe the displacement of the chassis when excited by a ramp profile acting identically over both sides of the vehicle (illustrated on the abscissa axis) After the contact of the vehicle with the ramp disappear, only gravity acts, and the displacement curve became quadratic This effect rarely is considered in simulation of this kind, and were was quite well reproduced in the present work This effect, specially in off-road vehicles, generally leads to wrong values of reactions acting over support points, in particular when the vehicle touches the ground again Figure illustrates the gravity center velocity time history during this test The increase of velocity as it enters the ramp and the effect of the return of the back wheels to the ground is clear Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Figure 4: Vertical displacement of the chassis Figure 7: Vertical acceleration of wheel I In figure the vertical velocity of the left front wheel can be observed The peak values occurred in the moment that the wheel touches the ramp The velocity acquire a constant value still over the ramp and has a linear decrease when the wheel is in the air The figure illustrates the acting force in the fiont left suspension system When the tire is on the ground, under compression, the force is negative becoming null when it is in the air, reproducing fairly what happens in reality Figure 5: Vertical velocity of chassis Analyzing the displacement of the wheels when excited by the ramp profile lead to the expected conclusion: in a first moment compression acts on the suspension which is followed by a small oscillation and then continue the slope profile In all wheels the same happens, being slightly greater for the front wheels In following the results obtained for the left front wheel are presented Figure illustrates the displacement time history for this wheel using the ramp test Figure illustrates the behavior of the wheel acceleration Two peaks of acceleration occurred, one as the vehicles enters the ramp and another when it touches the ground, as expected , -2 ,J, , , , , - -3.8880 8.8000 raw 13.8880 Figure 8: Velocity of wheel Figure 9: Vertical force on the tire Figure 6: Vertical displacement of wheel The figure 10 illustrates a comparison of the behavior of both wheels, for this test Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Figure 10: Comparison of displacement of the wheels To illustrate the dfierent behavior for each side of the vehicle, the ramp of both sides were delayed In figure 11 one can be observe the lateral rotation and the front left and back right wheels displacement for this test Figure 12: PSD of a non-paved terrain The spatial frequency S1 is the abscissa of the spectral frequency curve S(Q) in the bilogarithmic graphic of figure 12 The PSD is valid in a well defined band, L I f2 I am, characteristic of chosen terrain In the present case, the following values were used: &in = 0.12 &a= 1.10 Figure 11: Lateral rotation with delayed ramps on both sides SIMULATION OF THE TERJUIN PROFILE A random profile of typical terrain where the vehicle is used is essential to obtain the stresses that will be used in f i e r analysis The random excitation was evaluated by a composition of a finite.number of harmonic components, with amplitudes and frequencies evaluated fiom the terrain power spectral density hnction (PSD) @odds & Robson [1973]) To avoid that two or more components become in phase, different phase angles were used to each component, randomiy chosen (Pereira e Marczak [1989]): Where the amplitudeAiis given by: being S(0) the PSD used The figure 12 illustrates a typical PSD (Gillespe [1992]) Figure 13: PSD function The PSD was divided into 12 not multiple components, in order to reduce the possibility of occurrence of harmonics in phase For each discrete frequency a the correspondent amplitudes were evaluated The constants S(Q) and WI are properties of the terrain as defined by Dodds & Robson, [1973] The values used here are : The amplitudes and frequencies calculated were applied to both sides of the vehicle However, to ensure difrent profiles to each side of the vehicle the phase angles of the eq.(4) were set difrent The excitations that act on the back wheels are the same of the fkoa wheels, but delayed of time period corresponding to the distance between the axis, for a given vehicle speed (figure 14) Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Figure 14: Delay of the terrain profile Figure 17: Time history of the vertical displacement Figure 15 illustrates the obtained proiiles during seconds of simulation Figure 18: T i e history of the vertical acceleration Figure 15: Difference between profiles for the right and the left side The use of the described terrain profile allowed the evaluation of the time histories for forces acting on the four suspensions links These forces are integrally supported by the chassis Figure 16 illustrates a typical time history showing a mean value around -360 N, what represents a fourth part of the vehicle's weight, that means, the static force on the suspension The negative sign just indicates that the applied force is the compression, following the adopted convention The nominal force band embraces from -2.000 N up to 1.500 N The value adopted for fbther analysis was 2.000 N in compression, representing the worse situation Figure 19: T i e history of the suspension displacement IDENTIFICATION OF CRITICAL REGIONS Figure 16: Time histories of forces observed in all suspension points The figures 17,18 and 19 illustrate the time history obtained for vertical displacement and vertical acceleration of the vehicle as well as the suspension displacement The evaluation of the load levels acting on the chassis enables to proceed the structural analysis, in order to identifl potentially critical regions In order to reduce the computational cost of the analysis and to minimize the input data, the structural analysis of the chassis can be accomplished in two steps Firstly, a global analysis of the whole chassis was made to verify its macroscopical behavior This global model uses simple finite elements as beams, allowing a very simple modeling job From the recovery of internal stresses, the regions with greater probability of fail can be found These regions are isolated and modeled by more sophisticated finite elements such shells of solids, representing faithfblly its geometry From this model, named local model, the nominal values of stress concentration factors can be obtained Relating the critical stresses with the excitation that comes fiom the terrain, a time history of nominal stresses in these point of interest can be obtained This procedure is necessary because the global model does not considers the real geometry of the part This methodology reduces abruptly the analysis time without significant looses on the results and is currently used for the analysis Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 of several complex structural components (Withcomb & Woo [1993]) Only the global model will be presented here THE GLOBAL MODEL - Figure 20 illustrates the chassis geometry, as well as the suspension fixation points These are the points where the loads that come fiom the simulation are applied the most significant stresses in a more complex traffic situation Figure 22: Front and back suspension systems and its reactions Figure 20: Basic geometry of chassis and suspension The figure 21 illustrates the finite element mesh used, as well as some critical regions that were isolated to be used as a reference during the construction of the local models The boundary conditions applied to the detailed model come fiom this local model, and were applied on the sectioned end point So, the local model is defined by cuts made near the connections considered critical in the global model, and applying proper boundary conditions on its extremities The same analysis were repeated for the back suspension system The reactions so obtained were the loading effectively applied to the finite element global model A summary of the obtained stresses is presented in the tables and For the analysis with the loading applied in fiont suspension, the connection that showed the most sigdcant forces is the union A and the wnnection that has the largest resultant moment is the point B When the loading is applied to the back suspension, the connection with greater shear and normal forces is again the connection A, while the largest resultant moment acts on the wnnection C These are the most solicited points of the structure, for the analyzed loading The tables and present also the resultant stresses (F,e M ) Ponto A Ponto B F, 35.351 1 M, -5289.9 F, F, 3918.6 1744.5 Mv -10630 I M7 788.23 F, 2024.9 M, 11899.6 Table 1: Internal forces at critical points with loading applied on the fiont suspension system F (N) e M (N.m) Figure 21: Finite elements mesh used for the global model and some isolated critical regions The static analysis of the structure by the finite elements method was made by the dynamic loads obtained during the t&c simulation of the vehicle From now, all analysis was performed using a reference vertical loading of lOOON applied on the suspension extremity This reference value allows the identification of the stress concentration factor that is used to relate the force applied on the wheel (fiom terrain excitation) and the critic stress To obtain the distribution of the loads on the chassis, an analysis of the reactions fiom suspension was made when a vertical force acts on the wheel This model is illustrated in figure 22 It is important to note that this analysis considerations not consider other traflic situations as curves or breaking, and thus not supply definitive values, but no doubt represent Ponto A Ponto C F, -3033.4 I M, 4810.3 I F, 33.965 F, 560.53 F, 3084.94 M, -239.70 -2409.0 5385.1 Table 2: Internal forces at critical points with loading applied on the back suspension system F (N) e M (N.m) RELIABILJTY ANALYSIS Once obtained the stress concentration factors fiom each critical point of the chassis, the reliabii analysis can be performed The time histories of the stresses are necessary in order to carry out this calculus, regarding the fail criteria used For instance, if the fitil criteria used is the Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 fragile rupture of the weld at the critical connections, the time histories of the equivalent stress on every critical point is necessary This can be accomplished in the following way: If K is the value of the stress concentration factor on such point, and the nominal values of the acting stresses (shear, compression, bending and torsion) can be composed in a consistent way, the equivalent nominal stress value a, can be evaluated as then the real equivalent stress is defined by: However, o, is obtained by the global model, being thus the response to the reference loading applied (1000 N), which correspond to one given instant of the time history of the forces acting on the suspension (known from the simulation in service) Then: a,,( t ) = K ~~ ( t ) where n is the safety factor n = pR/pS, similar to the popular safety coefficient, but now considering the statistical properties of the load and strength time histories In the eq.(13), V R and V s are the dispersion coefficients of the strength and load, respectively The damage fault is characterized by a gradative loose of the material properties In general, it is possible to say that the material, as the time increase, suffers some damage in a cumulative way The damage grows up with time up to a critical value that leads to the collapse of component The characterization of the statistic distribution for the damage life either analytically or experimentally is possible to calculate the reliability for damage fail as (Rosa 119911): obtained from the hypothesis of gaussian loading with narrow band In eq.(14), m and C ,are constants of the Woehler curve for the used material : (9) So, the equivalent stress time history can be obtained for each critical point Now a general reliability model can be used in order to determinate the safety levels in such points Following the methodology proposed by Rosa (Rosa [1991]), the reliability for two different situations can be checked: overloading and cumulative damage In a more rational study of the problem, probabilistic concepts should be applied, what means that there is always a possibility of failure The reliability for overloading is evaluated by (Rosa [I 99 11) : and r is the Gamma function The safe condition is achieved by holding the condition D < 1, because is the limit value that the part can resist without failure Alternatively, on can estimate the life time for the component given a desired reliability Another possibility is, given the desired reliability and the necessary life time, to estimate n for the point of interest CONCLUSION where C(t) is the desired reliability to a desired life time t and h(t) the average fail rate h is given by the probability of interference A , between the strength and the load distributions, and by if peak frequency Considering both, the strength and the load distributions as gaussian distributions, we can use the peak distribution for the load Moreover, if the load distribution has a narrow band, then the peak distribution follows a Rayleigh distribution, which has as parameters of definition the standard deviation of the normal distribution So, the interference probability can be calculated by: where Vs is the load dispersion coefficient and E is given by: The present paper developed an analysis based on the dynamic simulation of a small size vehicle with tubular structure over an unpaved terrain Using a RBSM several traffic situations were simulated using numerical integration softwares to solve the differential equations of the problem The terrain was numerically simulated from its PSD, as proposed by Dodds e Robson [1973] To consider the situations in which the vehicle does not touch the ground, the equations of transversal displacement were modified to represent the ballistic character of these situations This effect is rarely considered in simulations of this kind This analysis allowed the survey of the loads acting on the link points of the suspension on chassis As the main interest was the chassis, this results were used only in a static analysis by finite elements of the chassis This procedure indicated the critical points positions The present work also introduced a methodology possible to be used for the evaluation of critical stresses in points of interest These results can be used to evaluate the time histories for the relevant stresses, necessary for further reliability analysis In addition, an extremely simple and effective formulation for overload and damage reliability evaluation is suggested REFERENCES Gillespe, Thomas D.; Fundamentals of Vehicle Dynamics, Society of Automotive Engineering, 1992 Downloaded from SAE International by Univ of California Berkeley, Friday, July 29, 2016 Dodds,C J e Robson, J D.; The Description of Road Surface Roughness, Journal of Sound and Vibration 31, pp 175-183, 1973 17 Tutsim 6.55 Automatizering, 1989 Rosa, E.; A p l i c q h de Confiabilidade no Projeto de Componentes Automotivos, Anais VI SIMEA, vol 1, pp 673-689, Slo Paulo, 1991 Rosa, E., Marczak, R.J e Luersen, M.A.; Mitodo para Anlilise de ResistGncia de Pe~as Submetidas a SolicitqGes Aleatbrias, Anais VII SIMEA, pp 333342, SBo Paulo, 1993 Whitcomb, J.D., Woo, K.; Aplication of Iterative GlobaL/Zocal Finit Element Analisys Part I: Linear Analisys, Comm Num Meth Eng., vol 9, pp 745-756, 1993 Whitcomb, J.D., Woo, K.; Aplication of Iterative GIobaVZocal Finit Element Analisys Part 2: Geometrically Non-Linear Analisys, Comm Num Meth Eng., vol 9, pp 757-766, 1993 Pereira, S.C., Marczak, R.J.; Shaskwat 150-FE: Simula#o em Servi~o/ Suspensh, Relatorio Interno, UFSC, 1989 Pereira, S.C., Marczak, R.J.; Shaskwat 150-FE: Andise de Resist2ncia / Suspensh, Relatorio Intemo, UFSC, 1989 Craig, R.R.; Structural Dynamics, mcGraw-Hill, 1982 10 Wang, T L.; Shahawy, M & Huang, D Z.; Dynamic Response of Highway Trucks Due to Road Surface Roughness , Computers & Structures, 6, pp 1055-1067, 1993 11.Pati1,M.K e Palanicharny, M S.; A Mathematical Model of Tractor-Occupant System With a New Seat Suspension for Minimization of Vibration Response, Appl Mathematical Modelling,l2, pp 63-71, 1988 12 Wyatt, T A e May, H I.; The Generation of Stochastic Load Functions to Simulate Wind Loading on Structures, Earthquake Eng Struct Dynamics, 1, pp 217224, 1973 13 El Madany, M M e Abduljabbar, Z.; Design Evaluation of Advanced Suspension Systems for Truck Ride Confort, omputers and Structures, 36, pp 321-33 1, 1990 14 Karamihas, S M e Gillespie, T.; Methodology For CaractmenzingThe Road Damaging Dynamics of Truck Tamdem Suspensions, SAE BRASIL 93, paper 93 1693-E, Slo Paulo, 1993 15 Bourassa, P e Massoud, M.; Terrain Profile and OffRoad Vehicle Behavior Simulatratron, Anais V COBEM, Campinas, pp C- 127-C 136, 1979 16 ANSYS 5.0 Systems, 1991 - User's Guide, Swanson Analysis - User's Manual, Meerman