Description
A commercial vehicle is a type of motor vehicle that may be used for transporting goods or passengers. The European Union defines "commercial motor vehicle" as any motorised road vehicle, which by its type of construction and equipment is designed for, and capable of transporting, whether for payment or not: (1) more than nine persons, including the driver; (2) goods and "standard fuel tanks".
STATIC AND DYNAMIC ANALYSIS OF A COMMERCIAL VEHICLE WITH VAN BODY A Thesis
by
Kassahun Mekonnen
Submitted to the School of Graduate Studies of Addis Ababa University in partial fulfillment of the requirements for M.Sc. Degree in Mechanical Engineering
Advisor Dr. Alem Bazezew Department of Mechanical Engineering Faculty of Technology Addis Ababa University May 2008
ACKNOWLEDGEMENTS
First of all, I thank God for giving me the strength to accomplish this thesis. I would like to thank my advisor Dr. Alem Bazezew for his valuable guidance and support throughout the course of this thesis. I also like to extend my gratitude to the members of the Department of Mechanical Engineering, Addis Ababa University, for their concern and willingness to help me in every possible way. I would also like to thank Ato Thomas (Technometals Engineering P.L.C), Ato Asheber Techane, Ato Abaraham Assefa, and W/t Rahel Tadesse for providing me with the necessary data which are used in the development of the thesis. I am also grateful to other friends of mine who have been very cooperative. Finally, thanks are due to my mother and father, Almaz and Mekonnen, and my brother and sisters, Dawit, Imuye and Hanna for their encouragement.
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TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF FIGURES LIST OF TABLES LIST OF SYMBOLS ABSTRACT 1. INTRODUCTION 1.1. Background 1.2. Objectives of the study 1.3. Methodology 1.4. Organization of the thesis 1.5. Scope and limit of the thesis 1.6. Commercial vehicle with van body structure 2. LITERATURE REVIEW 3. PHYSICAL AND MATHEMATICAL MODELING 3.1. Coordinate systems 3.2. Motion and forces with reference to vehicle dynamics 3.3. Road roughness model 3.4. Tire model 3.5. Vehicle multibody model 3.6. Finite element model i iv vi vii x 1 1 3 3 4 5 5 8 16 17 18 20 29 29 42 ii
4. ANALYSIS AND RESULTS 4.1. Static Analysis 4.2. Modal Analysis 4.3. Random Vibration Analysis 5. CONCLUSIONS AND RECOMMENDATIONS 5.1. Conclusions 5.2. Recommendations REFERENCES BIBLIOGRAPHY
48 48 52 57 68 68 68
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List of figures
Fig 1.1 ISUZU NPR model commercial vehicle with van body structure Fig 3.1 SAE Vehicle Axis System Fig 3.2 Forces on a commercial vehicle Fig 3.3 Power Spectral Density as function of spatial frequency for various types of road and runway Fig 3.4 Classification of Road Surface Roughness by ISO. Fig 3.5 Profiles of Roads in Addis Ababa Fig 3.6 Spectral Density plotted as function of Spatial frequency for Class B road roughness Fig 3.7 Spectral Density plotted as function of Spatial frequency for Class H road roughness Fig 3.8 Profile for road with Class B roughness classification Fig 3.9 Profile for road with Class H roughness classification Fig 3.10 linear model of tire Fig 3.11 Multibody models of a vehicle Fig 3.12 Quarter car model of the vehicle Fig 3.13 PSD function of response of unsprung mass at the front wheels Fig 3.14 PSD function of response of unsprung mass at the rear wheels Fig 3.15 Solid model of the vehicle Fig 3.16 finite element model Fig 3.17 eight noded solid element Fig 3.18 four noded shell element Fig 3.19 Spring-Damper element Fig 4.1 Solution procedure diagram Fig 4.2 Vertical deflection due to static loads Fig 4.3 Von mises stresses due to static loads Fig 4.4 Z-component of stress due to static loads (bending stress in the chassis)
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Fig 4.5 First mode Fig 4.6 Second mode Fig 4.7 Third mode Fig 4.8 Fourth mode Fig 4.9 Response due to class B roughness at 80km/hr Fig 4.10 Response due to class H roughness at 30km/hr Fig 4.11 Response due to roll motion Fig 4.12 Locations of nodes for which PSD responses are determined Fig 4.13 PSD responses of selected nodes due to class B roughness at 80km/hr Fig 4.14 PSD responses of selected nodes due to class H roughness at 30km/hr Fig 4.15 Displacement-time histories of selected nodes at 80km/hr Fig 4.16 Displacement-time histories of selected nodes at 30km/hr
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List of Tables Table 3.1 Values of Csp and N for Power Spectral Density Functions for various Surfaces Table 3.2 Classification of Road Roughness by ISO. Table 3.3 IRI values of some of recently upgraded roads in Ethiopia Table 3.4 Stiffness and Damping Properties of tires
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List of Symbols
X - longitudinal axis of Earth fixed coordinate system Y- lateral axis of Earth fixed coordinate system Z - vertical axis of Earth fixed coordinate system x - longitudinal axis of vehicle fixed coordinate system y - lateral axis of vehicle fixed coordinate system z - vertical axis of vehicle fixed coordinate system p - roll motion of vehicle q - pitch motion of vehicle r - yaw motion of vehicle Txf - Traction force at the front wheel Txr - Traction force at the rear wheel Rxf - Rolling resistance at the front wheel Rxr - Rolling resistance at the rear wheel D - Aerodynamic Drag Wf - Axle load at the front wheel Wr - Axle load at the rear wheel Max -Inertial force due to acceleration/deceleration
-power spectral density of road roughness - spatial frequency
¡
tire mass
¡ – stiffness of tire
¡
tire dampingconstant sprung mass
¢
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£¤¢ ¢ ¥
¢§¦
?sprung mass spring stiffness shock absorber damping constant Base excitation Response of unsprung mass Response of sprung mass Transfer function matrix
amplitude of base excitation amplitude of response of unsprung mass amplitude of response of sprung mass
strain energy - external work - strain vector - displacement vector - the surface loads vector { }- the stress vector – displacement transformation matrix - nodal displacement vector - strain-displacement matrix - element stiffness matrix. global stiffness matrix - element mass matrix. - global mass matrix - force vector - nodal force vector
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- reaction force vector density amplitude vector
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ABSTRACT
A vehicle and its structural components are subjected to loads which cause stresses, strains, deflections, vibration and noise in the components. To achieve a quality vehicle, i.e. one having longer fatigue life, reduced weight, reduced cost, and so on, it becomes necessary to use materials of appropriate strength and stiffness property with the most appropriate geometry (form). One way to achieve this is evaluation and assessment of responses of the vehicle to different loads. This research addresses responses of a vehicle to static and dynamic loads. The entire analysis is done for an ISUZU NPR model commercial vehicle with van body. The method used is finite element modeling and analysis for which the inputs are obtained from quarter car model analysis. The responses to static loads and random excitation caused by road roughness are determined. Components and, particularly areas which are much affected by the different loads are indentified. Finally, conclusions based on the results and recommendations which can be extensions of this research are also presented.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER ONE INTRODUCTION
1.1 BACKGROUND During service, any vehicle is subjected to loads that cause stresses, vibrations and noise in the different components of its structure. This requires appropriate strength, stiffness and fatigue properties of the components to be able to stand these loads. On top of that, quality of a vehicle, as a system, which include efficient energy consumption, safety, and provision of comfort to the user are highly desired. All the above largely demand refined and complex design and manufacturing procedures involved during the production stage. This, in turn, requires good understanding of the internal systems of the vehicle and the characteristics of the different body structures in reaction to static and dynamic loads. Vehicle dynamics, a discipline of broader significance, is an area where the basics of analyses on vehicles are dealt with. Forces/loads acting on vehicles can be categorized as road, aerodynamic, and gravity loads. Of all these, forces and moments generated by tires at the ground are significant in controlling motion of the vehicle [1]. The response of the vehicle structures to these loads are dealt with in vehicle dynamics. The responses of a vehicle are defined in terms of deflections, stresses, strains, natural frequencies, random response functions, fatigue life and so on. Evaluation of the above is what puts the basis on which robustness of a vehicle system or design is ascertained in terms of its mechanical behavior. Simulation of vehicle responses largely concentrates on determination of the above.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Different researches have been carried out regarding the performance, the response of components to static and dynamic loads, crashworthiness, safety and others by different institutions and automotive companies. Particularly, with the growing simulation capability using computers, researches are facilitated that are aimed at achieving better quality products. The application of computer aided engineering (CAE) analysis to problems of this sort, in combination with prototype development and testing, enables to achieve structures having longer fatigue life, reduced cost, light weight and improved comfort. In light of this purpose, as stated earlier, advancements in the area are growing further. At nationwide and faculty level, only a few researches have been conducted in the area of vehicle dynamics. However, there are local companies engaged in the construction of truck, bus, and van body structures. Examples of these are companies which construct bus body structures on ISUZU NPR model commercial vehicle by removing the cab, and years back, there used to be companies building “wuyiyit”, a locally manufactured taxi body structure, on TOYOTA, NISSAN, and PEUGEOT model pick up vehicles. Building trailer chassis frames is also an experience in some companies. In addition, there are other companies which construct van body structures on ISUZU NPR and FSR, and MITSUBISHI model commercial vehicles. In these companies, the use of researches and computer aided engineering analysis is far below what it should be. Some of these companies make use of graphics softwares to prepare drawings. To my understanding, this indicates regarding the engineering aspect that includes design and analysis, little is done. However, as mentioned earlier, these are the bases for achieving structure having longer fatigue life, reduced cost and reduced weight. Thus, this prompts implementation of existing theoretical knowledge and facilities towards addressing the problem in the area.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
1.2 OBJECTIVES OF THE STUDY General Objective: The objective of the study is to produce results which may help to rectify problems associated with structures of a commercial vehicle and which also may be of significance during design of van body structure of the vehicle after carrying out static and dynamic analysis, combining existing theoretical knowledge and advanced analytical methods. Specific Objectives: i. To develop mathematical and finite element model of the major components of a commercial vehicle with van body structure which include chassis, cab, and van body structure and carry out static, dynamic analysis of the structures. ii. Based on the analysis, identify points and sections which are highly loaded (stressed) due to the loads by means of which the overall intensity of loading in the structures is assessed. iii. Arrive at conclusions and propose recommendations on the basis of (i) and (ii).
1.3 METHODOLOGY To fulfill the objectives of the study the following are used. i. Literature Review: Survey of books, journal articles, proceedings of international conferences, auto manufacturer catalogues, and other relevant literature is done. ii. Data Collection: data regarding the van body structure are collected from Technometals Engineering (Addis Ababa). The data include dimensions of the structure, material used to construct the structure, and construction methods. Road roughness data of some roads
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
is obtained from Civil Engineering Department, AAU. Data regarding ISUZU NPR model commercial vehicle are obtained from specifications prepared for the vehicle and official website of ISUZU company. Other data used in the thesis are obtained from books, and handbooks. iii. Modeling and Analysis: The finite element model development as well as the corresponding static and dynamic analysis is performed using ANSYS software. iv. Conclusions and Recommendations.
1.4 ORGANIZATION OF THE THESIS The body of this thesis is divided into five main chapters. The first chapter discusses background and objectives of the study. In addition, the details of the model vehicle used in the analysis are also discussed in the same chapter. The second chapter covers the review of some of the journal articles, proceedings and publications which were referred to during the course of the thesis. Also, in relation and comparison with previous works, what is done in this thesis will be stated. The mathematical and finite element modeling is discussed in the third chapter. Road roughness, tire modeling, and multibody models representing different motions of a vehicle presented. Also, covered in this chapter is discretization of the solid model of the commercial vehicle used for the analysis into finite elements and the mathematical formulation of these elements. The results obtained from the static and dynamic analysis of the vehicle and discussions based on these results are included in the fourth chapter. Finally, the fifth chapter covers conclusions drawn based on the results of the analysis, and recommendations for future work.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
1.5 SCOPE AND LIMIT OF THE THESIS As it can be seen, numerous types of simulations/analyses can be carried out regarding behavior of a vehicle. In this research, as stated earlier, static and dynamic analysis of a commercial vehicle structure are carried out. The dynamic analysis includes only modal and random response analysis of the structures. Nonlinear behavior which components could experience is not dealt with and, linear and isotropic material models are used for the entire analysis. In the dynamic analysis, damping properties of the structures is not considered. However, damping due to shock absorber of the vehicle is included in the analysis. The analysis is carried out for the main load bearing structure of the vehicle, i.e., chassis side frames and cross members, steel frames of the van body structure, and cab. Wind shields, door frames, and cover plates of the van body structure are not dealt with. The effect of the engine is taken into account by distributing its weight into the side frames of the chassis. 1.6 COMMERCIAL VEHICLE WITH VAN BODY Commercial vehicles with van body structure built on chassis frame find large application in different companies. There are also different companies engaged in construction of the body structures with variants for use in different environment. The specific model used in this analysis is ISUZU NPR model commercial vehicle (fig 1.1). This vehicle is chosen for it is one of the most commonly used both here in Ethiopia and abroad. *It is observed that the model chosen for this analysis is one of the most popular and highly sold around the world including the most developed nations.
*Official website of ISUZU Japan
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig.1.1 ISUZU NPR model commercial Vehicle with van body
Data for the vehicle are given below: Gross Vehicle Weight (GVW): 7500kg Gross Combined Weight (GVW + Payload): 11000kg Engine type: Diesel, inline 4 cylinder, overhead cam (OHC), direct injection. Maximum power: 76KW@3200rpm Maximum torque: 268Nm@1800rpm Overall length: 6610mm Wheelbase: 3815mm Wheel centre (front wheels): 1680mm Wheel centre (rear wheels: dual): 1650mm Height (excluding van body): 2250mm
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The van body structure frames are built with steel tubes that are welded to one another. The doors are hinged to the body structure. The outside of the structure is covered with steel plate that is joined with rivets, while the inside is covered with aluminum plate. The structure frames with the cover plates are welded to the checkered plate. The structure is connected to the chassis frame with bolt connections.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER TWO LITERATURE REVIEW
Vehicle Dynamics is an area on which different researches have been carried out. Different people at institutional and individual level involved in the area produced findings which are relevant in the automotive industry. In nearly all the literature reviewed it is observed that most of the researches constitute development of virtual or prototype models and all the analyses are performed on these models. Verification of the results is accomplished by comparison made with experimental results. Listed below are some of the literatures surveyed that are deemed to be significant to this research that is conducted on analysis of body structure of a vehicle.
Y. Zhanwang, and C. Zongyu, [2] developed finite element model for Minicar Changan Star 6350 using SDRC/I-DEAS. The model was imported to MSC.Patran to generate the mesh and the dynamic analysis of the model was accomplished using MSC.Nastran. The analysis included modal analysis of the load bearing structures, the chassis and the body structure frame, in which the first 100 natural frequencies were determined in torsion and bending modes, and transient dynamic analysis of the structures due to road loads that were introduced in the form of acceleration excitations. They obtained results which happened to show good consistency with experimental results, and concluded that the Minicar is able to meet dynamic design requirements. H. S. Kim, Y. S. Hwang, and H. S. Yoon, [3] presented a method for prediction of dynamic stress time histories. The method, referred to as hybrid superposition method, employs hybrid sum of pseudostatic stresses and modal acceleration stresses. Static stress coefficients and modal
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
stress coefficients used in the determination of pseudostatic stresses are obtained using finite element codes such as MSC.Nastran, while the time histories of body and surface loads are obtained using flexible multibody dynamic analysis code, DADS. Through a governing equation, the above two are combined to generate the dynamic stress time histories which lead to prediction of fatigue life. A bus system in which dynamic stress time histories are determined for a critical pillar joint is presented as an example to prove validity of the method. M. Fermer, G. McInally, and G. Sandin [4] carried out fatigue analysis of Volvo S80 Bi-fuel. In a virtual environment, the fatigue life analysis of the fuel and gas tanks, crossmember for fuel tank, crossmember for gas tank and spot welds was undertaken before development of a prototype. The MBS-Code ADAMS was used to undertake the simulations with parallel and torsional excitation input loads. Of the different sizes of floor plate thickness used in the analysis, one that is able to withstand fatigue failure with the inclusion of stiffening swage was chosen based on which prototype was developed and tested. The shake rig test conducted on the prototype proved the robustness of the structural frames and concluded that the FE-Based analysis has been successfully used to speed up development of a new product. I. Johansson and M. Gustavsson [5] presented a paper that discusses implementation of FE methods for dynamic analysis of heavy trucks. The approach used involves development of FEmodel of the vehicle and its subsystems, i.e. frame, superstructure, engine, cab, axles and chassis suspensions, and steering system. Also included in the modeling are problem size reduction, global motion and centrifugal forces, lateral tyre model and gyroscopic moments. The analysis focused on analysis of road, wheel and brake, and driveline induced vibrations, static load cases and fatigue life prediction. An example was presented which shows the lateral and vertical acceleration of the cab structure due to periodic excitation of axle due to wheel run out. It was
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
concluded that, FE-based complete vehicle analysis has the advantage to cover broad range of analyses with one type of model. F. Oijer [6] developed force histories for different components of a heavy truck under different road load conditions. The environment in which the vehicle was driven was described by vertical road profile and curve radii. The road profile was applied to the tires and a driver model was used to produce the desired yaw. The complete vehicle model was produced using shells, bars, spring and damper elements. Tire slip, gyroscopic moments, and centrifugal forces were also considered. Further, for the analysis, tires of two types, one-point contact and flexible ring type, depending on the road surface, and nonlinear characteristics, among other things, were also used. Modal Transient Analysis (SOL 112), a feature in MSC.Nastran, is used for the response studies. Force histories were generated for rear and front axle suspensions with bad road models (low frequency), and the same histories were developed for the cab suspension with high frequency road having transient obstacles. All the results obtained were compared with measured values and the fictitious fatigue life ratio (calculated life/measured life) was found to be between 1.5 and 2. Further, comparison was made of force histories for cab suspension with flexible and rigid models of the cab. It was finally concluded that, MSC.Nastran is proved fast and accurate enough to give reasonable results. T. Parnell, C. White, and S. Day [7] conducted finite element simulation of 180o Rollover for Heavy Truck Vehicles. The simulation was carried out for evaluating structural integrity and occupant crash system design in heavy trucks. The finite element model for the cab structure was done using ANSYS. The rollover simulation consists of two phases; the initial phase is rollover event wherein rigid body kinematic analysis was performed using the computer code DADS. The deformation phase starts at the instant of cab-to-ground contact and for this phase, the quasiMay 2008 10
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
static finite element simulations were performed in another computer package LS-DYNA3D. Projection of the results obtained in the rigid body analysis to LS-DYNA3D model was accomplished with a MATLAB script file. Two cab structures were physically tested for which the Resultant Platen forces in the structures were recorded with time and comparison with simulation results proved good agreement between the two. In conclusion, it was stated that FE based techniques can fully be used to evaluate rollover phenomena in heavy trucks. S. Chiba, K. Aoyama, K. Yanabu, H. Tachibana, K. Matsuda, and M. Uchikura [8] presented a paper that discusses fatigue strength prediction of Truck Cab. The method discussed was developed as part of a program to change full model of a Mitsubishi light-duty truck. The method involves generation of stress time diagrams based on which fatigue life for the cab is predicted. Static and Eigen value analysis for the FE model were performed using MSC.Nastran and the simulation to generate the load history was done using ADAMS taking the Eigen value results as input. The load history along with the static analysis results were used to complete the fatigue life analysis using another package, FALANCS. All the results obtained were compared with experimental results and ended up with little discrepancies. D. C. Lee, H.S. Choi, and C. S. Han [9] presented a paper that focuses on multicriteria optimization of automotive body structure design. The optimization includes definition of objective and constraint functions that are defined as functions of design variables. The optimal solution (optimum values of the design variables) is defined using what is known as Paretooptimal solution. As an example, a dynamic analysis simulation of a vehicle was conducted which has the objective of minimizing intensity of vibration due to engine idle shake, wheel unbalance shake, and road shake. Initially, values were taken representing different dimensions of the different vehicle components (design variables) and these values were optimized using the
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
method. Based on these values a FE-model was developed and the corresponding excitations under the three cases were determined. In conclusion, it was underlined that such optimization approaches provide efficient design during early stages of development. Jin Yi-Min [10] implemented finite element methods to analyze and evaluate minivan body structure. The analysis included static, dynamic, fatigue, crashworthiness, optimization and design sensitivity analysis. The static analysis was conducted taking into account the bending and torsion loads. The dynamic analysis comprised two sources, tire unbalance and engine excitation and the corresponding NVH analyses was carried out. In the paper, presented are the strength analysis in both torsion and bending case and modal analysis results. The FE analysis was accomplished through the use of MSC.Nastran. The results obtained for the dynamic analysis were compared with experimental test results and found to be in good agreement. J. N. Lee and P.E. Nikravesh [11] presented a paper on steady state response of multibody systems where a vehicle system was discussed as an example. The equations of motion for a multibody system are described in terms of relative joint accelerations and, in steady state configuration, the relative joint accelerations between bodies become zero which lead to conversion of differential equations of motion to algebraic set of equations for the steady state response. Based on the method discussed, the vehicle was assumed to have a certain forward speed and steer angles for the front and rear wheels; the resulting steady state angular velocities and vertical displacement of the chassis along with the spinning speed of the wheel were determined. Comparison was made with results obtained from transient dynamic analysis. Asheber Techane in his M.Sc. thesis [12] conducted dynamic analysis of a locally manufactured bus body structure. The solid model of the structure was developed in AutoCAD classic
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
environment and the generation of the FE model and the dynamic analysis were performed using ANSYS. Modal analysis which reveals the natural behavior of the structure and PSD (power spectral density) analysis are included in the dynamic analysis of the structure and it was concluded that the roof of the bus structure is prone to higher deflection, and as a recommendation it was forwarded that there be carried out complete evaluation of the vehicle to prove robustness of the structure in terms of its mechanical properties. S. S. Kim, A. A. Shabana and E. J. Haug [13] presented a paper on nonlinear, and transient dynamic analysis of vehicles systems composed of interconnected rigid and flexible components. In the method used, for a system, equations of motion and constraints are formulated in terms of a minimal set of generalized coordinates. As an example, a cross country truck for which the corresponding vehicle and road surface model developed was considered. The resulting displacement and acceleration of centre of gravity of the chassis frame of the truck were determined for two cases. The first case being the truck traversing a road bump and the second taken as the truck traverses a random terrain. For the purpose of comparison, flexible and rigid body models of the frame were considered, and it was depicted that the peak acceleration of the centre of gravity in the former case was higher. F. Lan, J. Chen, and J. Lin [14] presented a paper that dealt with optimization of light weight bus side structures. The optimization targeted reduction in the number and weight of parts in the whole body structure. For this purpose, two structures, with and without supporting structures between longitudinal waist beams of the side frame were considered. The FE-model for the structure without the support was developed in the computer package UG and mesh generated in MSC.Patran. The FE Analysis was completed using ANSYS. The deflections and stresses under static loading case were determined and modal analyses were also performed. All the results
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
obtained were compared with experimental results obtained. In addition, sensitivity analysis, selecting different important component dimensions, and light weight optimization were also studied. In conclusion, it is stated that the structure with support is proved valuable enabling significant alleviation of body weight and satisfactory performance requirements of load carrying capacity. H. S. Kim, H. J. Yim, and C. B. Kim [15] presented a paper on computational durability prediction of body structures in prototype vehicles. The finite element analysis performed using MSC.Nastran gives static correction modes that are to be used in multibody dynamic analysis (Using DADS) and static stress coefficients which in superposition with the results of the multibody dynamic analysis are used to determine the dynamic stress histories. The dynamic stress histories, in turn, are used to predict the fatigue life, performed using another package P3/FATIGUE, of critically loaded members of the body structure. Based on the method, analysis of prototype bus body structure was performed taking into account two drive conditions, namely, city mode and Belgian mode. In conclusion, it was underlined that the methodology can be used as efficient and reliable means for the sign-off of durability of a prototype vehicle with actual service environments in the early development stage. Joao Goncalves and Jorge Ambrosio [16] presented a paper on optimization of vehicle suspension systems for improved comfort of Road vehicles. An algorithm is developed for comfort optimization in which the different characteristics of the vehicle components are the design variables on which appropriate constraints are imposed. The ride optimization is attained by finding the optimum values of the characteristic quantities in face of their importance for the comfort of the occupant. To exemplify the method employed, a vehicle is simulated over two
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
different road profiles at two different speeds. It was concluded that the methods applied lead to stable and efficient optimization procedures. As can be seen, all the research focus on static, dynamic, fatigue, crash and optimization analysis of vehicles and their different components. It is further indicated that different computer packages such as MSC.Patran/MSC.Nastran, ANSYS, ADAMS, DADS, and IDEAS are used to develop the virtual models (FE models) of vehicles and their different components and perform the required type of analysis. In addition, experimental tests are made use of to ensure acceptance of results obtained for the virtual models. In this research, the static and dynamic analysis of an ISUZU NPR model commercial vehicle is carried out such that the method used combines multibody and finite element models of the vehicle. The static and modal analyses are carried out using usual methods of analysis. The random response is done using finite element analysis such that results obtained from multibody (Quarter car model) analysis are used as input for the finite element model. Modeling, finite element discretization and all the analyses are carried out using ANSYS, and the same solid and finite element model is used for all types of analysis.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER THREE PHYSICAL AND MATHEMATICAL MODELING
Vehicle motion which includes acceleration, braking, ride and turning is response of the system to loads imposed on the vehicle from the tires, gravity, and aerodynamic loads. In addition, stresses, deflections, vibration (ride and noise) induced in the components of the vehicle are also responses of the vehicle. Ride and noise are associated with dynamic response of the body structure and other parts to excitations produced by different sources. The main sources of these excitations include road roughness, wheel run out, engine and driveline vibrations and aerodynamic loads. Of these, road roughness causes significant amount of the body structure vibration [1]. Determination of static and dynamic responses of the vehicle necessitates development of models representing the vehicle system. Appropriate physical and mathematical models are necessary to arrive at reasonable results. Equations of motions, the solution of which gives the response of the system, and which govern the system at hand are formulated based on the mathematical model. Closed form solutions are attainable for models of less complication which happen to approximate the problem reality to a lesser extent. The better the reality is modeled the complicated the model becomes and this calls for advanced solution methods the implementation of which is possible using highly capable computers and computer softwares. In this respect, finite element modeling and analysis is worth mentioning. Multibody models of vehicles are also used for simulation purpose. They involve modeling of a system such that it is reduced to system of interconnected rigid bodies. Such models, as is usually the case, are used to deal with bounce (translation motion in the vertical direction) and
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
pitch, and bounce, pitch and roll motions of the vehicle. Also, more advanced analysis of vehicles is also carried out using such models. In this chapter, the definition of some of the quantities used to define motion and loads, the physical and mathematical modeling of the problem are presented. 3.1 COORDINATE SYSTEMS. Vehicle motion and the response of the vehicle to excitations are described using quantities which do represent some reality with respect to the motion and/or response of the vehicle. To define the different motion quantities and loads (forces and moments) associated with vehicle motion and simulations regarding the motion, different axes systems are in use. Worth mentioning here are, systems defined by Society of Automotive Engineers, SAE [1] and International Standards Organization, ISO. [17] Throughout this report, all the quantities discussed are defined with regard to the SAE convention discussed below. Two coordinate systems in the SAE convention are of importance in vehicle simulations. These are the Vehicle fixed coordinate system (Fig 3.1) and the Earth fixed coordinate system. The vehicle coordinate system has its origin at the center of gravity of the vehicle and travels with the vehicle. The longitudinal(x) axis lies along the vertical plane of symmetry of the vehicle and the lateral
axis is taken positive to the right. The vertical (z) axis is chosen such that the system is right handed, i.e. positive downward.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.1 SAE Vehicle Axis System
The Earth fixed coordinate system(X-Y-Z) is selected to coincide with the vehicle coordinate system at the start of maneuver which from then on remains fixed on the earth. The absolute motion quantities are defined with respect to this coordinate system and the components of these quantities are defined along the axes of the vehicle fixed coordinate system. 3.2 MOTION AND FORCES WITH REFERENCE TO VEHICLE DYNAMICS The motion of a vehicle is defined by different translational and rotational (angular) components. Using the vehicle fixed coordinate system introduced in the previous article the linear velocity and acceleration of the vehicle are decomposed along the three axes producing the longitudinal, lateral and vertical components. Roll, pitch, and yaw correspond to the rotational motion about the x-, y- and z- axes of the vehicle fixed coordinate system. Forces and moments are the causes for state and trajectory that a vehicle attains during the course of motion. The loads include aerodynamic, gravity and loads generated at the tire ground contact. The primary forces with which the motion of the vehicle is controlled are developed at the tire ground contact. Fig 3.2a and b show the most significant forces on the vehicle in the x-z plane. The effect due to payload is not considered.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.2 Forces on a Commercial Vehicle
The forces in the longitudinal direction include traction force at the front and rear wheel Txf and Txr, rolling resistance at the front and rear wheels Rxf and Rxr, aerodynamic resistance D. The front and rear axle loads are represented by Wf and Wr. Max stands for the inertial force that prevails during acceleration and deceleration. In fig 3.2a), the forces on the van body and the remaining part are considered separately. The sub index v indicates a load on the van body while wv indicates a load on the remaining part of the body.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.3 ROAD ROUGHNESS MODEL Road roughness, as outlined in the introduction, is the major source of excitation. It stands for the irregularities in the road profile. Sine waves, step functions, and triangular waves can serve as models to represent road roughness. Nonetheless, random function modeling more realistically defines road profiles. Random processes are defined using power spectral density (PSD) functions. Mathematically, PSD function of a random variable/process represents the Fourier transform of the autocorrelation function of the random process. Autocorrelation or correlation of a function with itself indicates how the value of a random variable a time is related to the value at time
The autocorrelation function is dependent on the period and not on the specific time, In addition, other parameters like expected (mean) value, root mean squared value, variance, and standard deviation are used to describe random variables and processes. Based on this, a random function representing a random variable is said to be stationary, if the expected value of the function at time is the same as the expected value at time A random road profile is In this
stationary as long as a contour representing portion of the road repeats itself after time, study, stationary conditions are considered.
PSD measure of road roughness is one of the internationally recognized methods to describe road roughness. The road elevation profile is decomposed into series of trigonometric waves varying in their amplitude and frequency. The plot of density of the mean square values of amplitudes versus the spatial frequency gives the PSD function corresponding to the signal. Spatial frequency represents the number of cycles corresponding to specific amplitude per unit length
and it is the inverse of wave length.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Different road roughness ranging from that of smooth runway to off-road ground could be modeled as random signals which are defined with PSD functions. Fig 3.3 shows PSD representation of typical road profiles published in SAE Transaction. Accordingly, the relationship between power spectral density
¨
and the spatial frequency
can be
approximated by:
¨
(3.1) is the power spectral density of the road roughness elevation profile, and
¨
In the equation,
and N are constants whose values for the different road profiles are given in Table 3.1. The values of the constants differ depending on different conditions. The area under the
¨
curve
shows the variance of the function. The higher the area is the higher the level of roughness.
Fig 3.3 Power spectral density as function of spatial frequency for various types of road and runway [18]
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Description Smooth runway Rough runway Smooth highway Highway with gravel
N 3.8 2.1 2.1 2.1
Csp 4.3 x 10-11 8.1 x 10-6 4.8 x 10-7 4.4 x 10-6
Table 3.1 Values of Csp and N for Power Spectral Density Functions for various Surfaces [18]
On the other hand, the International organization for Standardization (ISO) classifies road surface roughness into eight classes (classes A-H) based on power spectral density [18]. Accordingly, the relationship between the power spectral density and the spatial frequency for different classes of road profile may be approximated by two straight lines with different slopes (Fig 3.4). The corresponding relationships are: For
¨ ¨
; and
(3.2a)
for
¨ ¨
(3.2b)
¨
In the above equations,
and
, as discussed earlier, represent the power spectral density
and the spatial frequency.
corresponds to the value of the spatial frequency which is equal to The values of N1 and N2, respectively, are 2 and 1.5. for each class of road roughness.
cycles/m or wavelength equal to
Table 3.2 gives the range of spectral density at
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.4 Classification of Road Surface Roughness by ISO [18]
Road Class A(Very Good) B(Good) C(Average) D(Poor) E(Very Poor) F G H
Degree of Roughness, ¨ ( *10-6 m2/cycles/m) Range <8 8-32 32-128 128-512 512-2048 2048-8192 8192-32768 >32768
Table 3.2 Classification of Road Roughness by ISO [18].
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The Ethiopian Roads Authority (ERA) uses the International Roughness Index (IRI) to evaluate road roughness of roads in service and under construction. IRI stands for total accumulated vertical movement of a vehicle divided by the distance traveled by the vehicle during motion. It is given in meters per kilometer. There exists relationship between PSD values or, particularly, the area under
¨
curve and the IRI, i.e. as the roughness increases, both the area and IRI
increase. The data shown in Table 3.3 indicates the IRI value for recently upgraded interstate asphalt roads in Ethiopia. Similar data for gravel roads is not made available for these roads show much roughness not expressed with IRI. Fig 3.5 shows roads with different profile in Addis Ababa.
Actual Result (%) Surface IRI, m/km Road Name Addis-Wolliso Addis-Commando Commando-Gohatsion Addis - Modjo Modjo-Nazareth Melkasa-Sodere Modjo-Ziway Ziway-Shashemene Shashemene-Awassa Road Length(km) 112 109 76 55 17 7 87 90 26 Good<4.5 100 100 100 100 100 53 99 100 100 Fair 4.5-6 0 0 0 0 0 33 0 0 0 Poor 6-9 0 0 0 0 0 14 1 0 0
*Table 3.3 IRI values of some of recently upgraded roads in Ethiopia
*Obtained from data prepared by Ethiopian Roads Authority
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.5 Profiles of Roads in Addis Ababa a) Addis Ababa ring road: near megenagna b) alley in Addis Ababa: near Inqulal Fabrica
In this research, for the purpose of dynamic analysis, roads of two different roughness classes are taken into account. In the first case, the condition in which the vehicle traverses over roads like the ring road is dealt with, while motion over rough pavement is the second case considered. The input PSD function corresponding to each case is determined as follows. In an experiment conducted on road roughness [19], it was proved that for a road with IRI of 3.4 (classified “good” by ERA) the value of lies between ?? indicating that it belongs to
class B of roads as per the ISO classification. As for the other case, assuming worst road roughness condition, class H road is considered. The corresponding PSD functions for both functions which are taken as an input for the quarter car model (section 3.4) are defined below.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Class B: For
©
cycles/m ;and cycles/m
¨
(3.3a)
for
(3.3b)
Fig 3.6 Spectral Density plotted as function of Spatial frequency for Class B road roughness (log-log Scale)
Class H: For
©
cycles/m ; and (3.4a)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
for
¨
cycles/m (3.4b)
Fig 3.7 Spectral Density plotted as function of spatial frequency for Class H road roughness (log-log Scale)
For a vehicle moving with velocity, V, the power spectral density in terms of circular frequency, (number of cycles per second,)
¨
can be determined as: (3.5)
©
The Spectral density shown above can be used to generate the road elevation profile such that , function representing the road contour as function of displacement, ? is considered as Gaussian random process with mean zero, and spectral density function,
¨
The equation
shown below is used to generate function
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, [19].
27
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
???
(3.6)
where, ,
?
, square root of the area under
¨
curve. ; and
¨
are random variables with spectral density,
is the number of sample points of Possible elevation profiles for the two types of roads considered in this analysis over a distance of 50m are shown below. The wavelength range chosen for the determination of the road profile is between 0.1 and 100metres [19]. Fig 3.8 is taken at 80km/hr speed while Fig 3.9 is obtained at 30km/hr.
Fig 3.8 Profile for road with Class B roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.9 Profile for road with Class H roughness classification
3.4 TIRE MODEL Tires are components of a vehicle which provide the necessary traction for the vehicle to advance over pavements. Tires are characterized by their stiffness and damping properties. The stiffness properties fall into three categories which are static, nonrolling dynamic and rolling dynamic stiffness. The stiffness characteristics depend much on the inflation pressure. For passenger car tires the rolling dynamic stiffness is approximated 10-15% less than the static stiffness, and 5% and 26% in truck and tractor tires respectively. In addition, velocity of the vehicle affects the *rolling dynamic stiffness such that the value is higher at low velocities [18]. In vehicle simulations, the rolling dynamic stiffness is preferred to the other types. Some of the important properties of tires are given in table 3.4. *Rolling represents rotational motion of the tire
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Tire 11-36(4 ply)
Inflation pressure(kPa) 82.7
110.3
7.5-16(6 ply)
138
193
Load(kN) 6.67 8 9.34 6.67 8 9.34 3.56 4.45 4.89 3.56 4.45 4.89
Static stiffness(kN/m) 357.5 357.5 379.4 386.7 394 175.1 175.1 182.4 218.9 226.2 255.4
Average nonrolling dynamic stiffness(kN/m) 379.4 394 423.2 394 437.8 423.2 218.9 233.5 248.1 233.5 262.7 277.3
Damping coefficient(N/m/s) 2.4 2.6 3.4 2.1 2.5 2.5 0.58 0.66 0.88 0.36 0.66 0.73
Table 3.4 Stiffness and Damping Properties of tires [18]
In studies regarding dynamic response of tires, a linear single degree of freedom model consisting of a spring and damper element is used (Fig 3.10). In this research, the stiffness properties of 7.5-16(6 ply) tire are used in the analysis.
Fig 3.10 linear model of tire
,
, and
stand for mass, stiffness, and damping of the tire.
3.5 VEHICLE MULTIBODY MODEL Multibody models are used to determine responses of vehicles. In such models, stiffness, mass and damping properties of the different components are considered such that the appropriate combination of these gives the mathematical model based on which equations governing the
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
model/system are formulated. The model can vary from the simple and most common two degree of freedom model to a model having higher degree of freedom. Vehicle motion, as discussed in the previous section, is characterized by translations in the longitudinal, lateral, and vertical directions and roll, pitch and yaw motions. The corresponding multibody models for bounce and pitch, and bounce, pitch and roll are shown in fig 3.11a&b.
(a)
(b)
Fig3. 11 Multibody models of a vehicle a) bounce and pitch model b) bounce, pitch and roll model
The four degree of freedom model (fig 3.11a) consists of sprung and unsprung masses of the vehicle. The sprung mass comprises part of the vehicle supported by the suspension and includes the chassis and components supported by it. The unsprung mass, on the other hand, consists of the axle, tire and other components not supported by the suspension. In most vehicles, the ratio of the sprung to unsprung mass is 10:1[1]. The model shown in fig 3.11b is a seven degree of freedom system in which the roll motion is included. The roll motion results from difference in excitation between the left and right wheels. The equations of motion for the four degree of freedom bounce and pitch model are given as:
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
and
stand, respectively, for the sprung and unsprung masses of the vehicle. The stiffness
and damping of the suspension, i.e. stiffness of the spring and shock absorber damping are represented as masses and and and . and correspond to the vertical displacements of the unsprung
are the vertical and angular displacement of the sprung mass.
is mass
moment of inertia for the sprung mass. =0 =0 (3.7a) (3.7b)
=0
(3.7c)
=0
(3.7d)
In this research, the dynamic analysis is carried out for both cases, i.e., bounce and pitch and bounce, pitch and roll cases. In the former case, the same PSD input is applied at two points (nodes) in the finite element model which correspond to the left and right wheels. And, inputs of the same PSD function are applied at points corresponding to the rear left and right wheels. The analysis for the bounce, pitch and roll case is carried out by applying four different PSD inputs at points (nodes) corresponding to the four wheels.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The PSD input to be applied at the points corresponding to the wheels are not exactly equal to the excitation at the tire ground contact point. Since damping occurs due to tire and shock absorber, the excitation at the points will be different. To determine the excitations at these points, quarter car model of the vehicle, discussed in the next section is used. QUARTER CAR MODEL Different types of model are used in vehicle simulations. The models are developed in such a way that the properties of important components of the vehicle are represented so as to make the results of any analysis realistic. One such model used frequently to study the behavior of vehicles under different road roughness conditions, to measure road roughness characteristics and to deal with any vehicle road interaction analysis is the quarter car model (Fig 3.12). The model represents the motion and/or response characteristics at one of wheels of a two-axle vehicle system. The basic model is a two degree of freedom system consisting of the sprung and unsprung masses of the vehicle. In addition, stiffness of the suspension spring, damping of shock absorber, and stiffness of the tire are also included in the model.
Fig 3.12 Quarter car model of the vehicle.
and
correspond to the vertical displacements of the unsprung and sprung mass respectively .
while the vertical displacement of the tire-ground contact point is represented by
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
In the discretization of the multibody model (fig 3.11b), the chassis and the superstructure of a vehicle are modeled as lumped masses at the front, and rear wheels and a coupling mass at the centroid. The sprung and unsprung masses in the quarter car model represent half the lamped mass and axle mass at the wheels. In passenger cars, the coupling mass has less magnitude in comparison with the other two. However, the coupling mass has comparable magnitude in the case of trucks. Thus, the model is more feasible for simulations with regard to passenger cars. Nonetheless, the model still finds significance in simulations associated with trucks [20]. In this research, the quarter car model is used to determine the response of the unsprung mass which is the input for the dynamic analysis part of the finite element analysis. The PSD response is going to be introduced to the FEM model through an element incorporated in the model having stiffness and damping properties which are the same as those of the suspension. In road modeling section, for the two classes of roads used in this analysis, it was indicated that the road roughness which in turn is the vertical displacement, of the tire ground contact point
is defined by the PSD function which is shown below (eqns3.3a-3.4b). Class B For cycles/m ; and
©
for
cycles/m
¨
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Class H For cycles/m ; and
©
for
cycles/m
¨
The power spectral densities of
and
of the unsprung and sprung masses, in each case, are the determination of
determined through the introduction of the transfer function matrix, which is detailed below.
The equations of motion are given as: (3.8) (3.9)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Rewriting (3.10) (3.11) In matrix form,
(3.12)
The term, excitation, zo such that:
refers to the force transmitted to the unsprung mass due to the displacement To determine the transfer function matrix, a harmonic input is assumed for
(3.13) – amplitude of the input excitation The assumed harmonic output will be of the form
(3.14)
,
- amplitudes of the responses of the unsprung and sprung mass.
Substituting these equations in the equation of motion:
(3.15)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The transfer function matrix relates the output to the input such that:
This gives,
(3.16)
=
=
Where,
In multidegree of freedom system, the spectral density function of the response is given by [21] (3.17) Where, is the Spectral density function matrix of a load or excitation, is the Spectral density function matrix of the responses. And, is the complex conjugate of the transfer function. , by
¨
Denoting the spectral density function of the load for the quarter car model becomes:
, the spectral density function matrix of
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
¨
(3.18)
Thus,
¨
(3.19)
Where,
¨
¨
¨
¨
and,
Similarly, in terms of the spatial frequency term, (3.20) In the above equations, the diagonals of the spectral density functions matrix of the responses, and function,
May 2008
represent the power spectral density functions of , is used as input for the FE analysis, while
and
respectively. The PSD would be the response of
38
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
the superstructure mainly the chassis frame, the cab and the van body structure under the condition that these structures are modeled by an equivalent mass having equivalent inertia properties. Thus, using the above equations, the PSD functions of responses the unsprung masses under the two types of road conditions used in this analysis are shown in figs 3.13 & 3.14. The inputs for the finite element analysis are taken as combination of data from the figures.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.13 PSD function of response of unsprung mass at the front wheels a) road with class B roughness classification b) road with class H roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.14 PSD function of response of unsprung mass at the rear wheels a) road with class B roughness classification b) road with class H roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.6 FINITE ELEMENT MODELING Finite element method is used to analyze the response of the vehicle to the static and dynamic loads. Simplified models such as the ones discussed in the previous section could have been used for the analysis purpose. However, models which describe the vehicle more realistically are required. This calls for implementation of more advanced approach and this is the ground for carrying out the analysis based on the finite element model of the vehicle. The development of the finite element model and formulation increases degrees of freedom for the model. The determination of unknown degrees of freedom for the model, in turn, leads to larger number of equations and generation of higher size matrices. The solution to these equations is performed using multiphysics or structural analysis software such as ANSYS which is the one used in this analysis. In this research, the solid model of the vehicle (Fig 3.15), in addition to the analysis, is developed using ANSYS.
Fig 3.15 Solid model of the vehicle May 2008 42
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.5.1 Finite Element Formulation The solid model of the vehicle is discretized into finite elements. The cab structure of the vehicle is discretized using shell (SHELL63) elements. Solid three dimensional (SOLID185) elements are used to discretize the chassis and van body structure. The suspension is modeled using spring-damper (COMBIN14) elements. The finite element model (fig 3.16) consists of 83546 eight noded solid elements, 10209 four noded shell elements and 4 spring damper elements.
Fig 3.16 finite element model
In the theory of finite element structural analysis, Hamilton’s principle is used in the dynamic analysis equation formulation. In this case, the Lagrangian, is defined as: (3.21) Where, is kinetic energy, and is the potential energy.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Hamilton’s principle is concerned with minimization of the Lagrangian, such that (3.22) The potential energy of a linear elastic body is given by (3.23) Where, is the strain energy; and is the work potential of surface, body and external loads. For a linear element, the potential energy can be written as { } where, strain vector for the element is displacement vector for the element is the body force vector, and is the surface loads vector { }is the stress vector The strain vector is related to the stress vector by the equation: (3.25) is constitutive matrix, (3.24)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Thus, (3.26) Displacement vector, ? can be expresses in terms on the nodal displacement vector as: = – displacement transformation matrix; and - nodal displacement vector The strain and displacement vectors are related by the matrix, = is strain-displacement matrix The first term in equation (3.24) represents the strain energy and using equations (3.25) and (3.28), it can be re-written as = = where, is element stiffness matrix. (3.29) such that (3.28) (3.27)
The first term on the right side expression is the kinetic energy term, , i.e. (3.30) Using equation (3.27)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
= = where, is element mass matrix. (3.31)
The governing equations, as stated earlier, are determined by minimization of the functional, i.e. potential energy and the Lagrangian. (3.32) Equation (3.32) is the governing equation for an element. Substituting the appropriate displacement transformation matrices, strain displacement matrices, and constitutive matrices, the stiffness and mass matrices can be determined. i) Eight noded isoparametric solid element
In this analysis, eight noded three dimensional isoparametric element (fig 3.17) is used in the discretization of the chassis, and van body structure. The element has eight nodes with each having three translational degrees of freedom.
Fig 3.17 eight noded solid element
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
ii)
Four noded shell element
Four noded shell elements (fig 3.18) are used to model the cab structure of the vehicle. The element has four nodes with each having six degrees of freedom.
Fig 3.18 Four noded shell element
iii)
Spring-Damper Element
Spring-Damper elements are used to model the suspension of the vehicle. The longitudinal spring-damper is a two noded tension-compression element with up to three translational degrees of freedom at each node.
Fig 3.19 Spring-Damper Element
The elements used, particularly the first two elements, differ in nodal degrees of freedom. However, this is taken care of in ANSYS by taking zero values for degrees of freedom not in use.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER FOUR ANALYSIS AND RESULTS
The analysis carried out using the finite element model consists of static analysis, modal analysis, and response determination under random excitation. The same finite element model is used for all the analyses. The difference among the cases considered lies in the application of loads and boundary conditions. The solution procedure followed for the analysis is shown in the diagram below.
Fig 4.1 Solution procedure diagram
4.1 STATIC ANALYSIS The static analysis is concerned with determination of response of the model/vehicle to steady loads whose value remains unchanged with time. The response of the vehicle is expressed in terms of stresses, strains and displacements. The basic equation governing static equilibrium condition of the system is given in equation 4.1.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
(4.1) Where, LV JOREDO VWLIIQHVV PDWUL[ {? is the nodal displacement vector is the load vector The global stiffness matrix is taken as the summation of element matrices, i.e. (4.2) The load vector, in turn, is taken as the sum of nodal applied load vector and reaction load vector. (4.3) The solution to the equation (4.1) gives nodal translational and rotational displacements. The corresponding stresses and strains are obtained using strain-displacement and strain-stress (constitutive) relations. The deflections between two nodes are determined using assumed shape functions. Loads and Results In the analysis, the situation considered is the standstill condition of the vehicle on a level road loaded to the maximum payload. The other loads considered include weight of the engine, weight of two persons in the cabin, and weight of the vehicle itself. The nodes corresponding to the four wheels (axle-suspension connection), i.e. one of the nodes of the spring damper elements in the finite element are constrained in translation. Figs 4.2 through fig 4.4 show the
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
stresses and deflections in the vehicle due to static loads. The units of quantities in the figures and of different quantities in other sections are in SI.
Fig 4.2 Vertical deflection due to static loads
Fig 4.3 Von mises stress due to static loads
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 4.4 *Z-component of stress due to static loads (bending stress in the chassis)
The vertical deflection shown in fig 4.2 includes deflection of the spring and static deflection of the vehicle structures. The vertical deflection is observed to be maximum at the rear of the van body and the chassis. Fig 4.3 and 4.4 show that, of the other components, the chassis gets highly stressed. This is attributed to the fact that all the static loads including the weight of the van body and the cabin, and the engine are taken by the chassis frames and this causes bending loads in the frames which cause higher bending stresses. The bending stresses are particularly of maximum intensity where there is change in the cross section of the chassis near the engine. Nonetheless, the stress level in the frames is far below the yield or ultimate strength of the chassis material. Under static conditions, the safety factor is around eight.
*Z taken along the longitudinal(X) direction of SAE vehicle coordinate system. May 2008 51
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
4.2 MODAL ANALYSIS Modal analysis provides results which indicate the natural vibration characteristics of a component or structure. It involves determination of the natural frequencies and modes of vibration. In addition to studying vibration characteristics, the results obtained from modal analysis can be used in other dynamic analyses such as spectrum analysis. The equation of motion for an undamped system is: (4.4) For a linear system, the responses (displacements) will be of harmonic form. Thus, ?? Where, is amplitude of mode shape of natural frequency, (4.5)
Substituting in equation (4.4),
This gives, =0 (4.6)
The solution to equation (4.6) gives Eigen values, the square roots of which are the natural frequencies and Eigen vectors, vectors of amplitudes corresponding to the natural frequencies. Loads and Results The only types of loads considered in the modal analysis of the vehicle are nodal displacement constraints. Thus, four nodes corresponding to the joint of the suspension and axle (wheel) are
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
constrained in translation. The first four mode shapes and the associated displacements are depicted in figs 4.5 through 4.8.
a)
b)
Fig 4.5 First mode a) mode shape b) longitudinal displacement
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 4.6 Second mode a) mode shape b) lateral displacement
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 4.7 Third mode a) mode shape (yaw) b) x- displacement
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 4.8 Fourth mode a) mode shape (roll) b) y- displacement
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
4.3 RANDOM VIBRATION ANALYSIS Random vibration analysis deals with response of a structure to random dynamic loads. The responses are defined using power spectral density functions. In addition, 1 displacement and stresses also characterize the responses. The implication of 1 displacement and stresses is that, say, for a component, if the 1 stress is specified to have value , then during motion of the vehicle, , and of the time, the stress level is at or below , of the time, between and . of the time between and
Loads and Results Three different cases are considered for the purpose of analysis. In the first case, the vehicle moves with speed of ?? on class B road, and in the second case, motion of the vehicle on ??. The third case is used to simulate roll motion. Roll motion,
class H road with speed of
as defined earlier, results due to difference in excitation between the left and right wheels. Thus, to study this condition, motion of the vehicle with wheels on one side on asphalt pavement and wheels on the other side on rough pavement is considered. This case somehow simulates the situation on narrow roads with rough pedestrian pavements in Addis Ababa though not a very common situation. In fig 3.13 and 3.14 are given, the responses of the unsprung mass determined using the quarter car model. The results of modal analysis and data from these tables are used as input for the analysis. Discrete values of frequencies and PSD values taken from these graphs are used to define base excitations at the nodes of the spring-damper (COMBIN14) elements in the finite element model. Fig 4.9 through 4.11 show the 1 y- component displacements and von mises stresses obtained for the three conditions. The PSD responses of three points, locations of which
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
shown in Fig 4.12, and having higher 1 displacement on the cabin, chassis, and van body the locations of which are shown in fig 12 are shown in fig 4.13 and fig 4.14. The band width taken is between 1.3754 and 3.9222cycles/sec which correspond to the fourth and six mode natural frequencies.
a)
b)
Fig 4.9 Response due to class B roughness at 80km/hr a) 1 y-component displacement b) 1 von mises stress May 2008 58
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 4.10 Response due to class H roughness at 30km/hr a) 1 y-component displacement b) 1 von mises stress
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 4.11 Response due to roll motion a) 1 y-component displacement b) 1 von mises stress
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 4.12 Locations of nodes for which PSD responses are determined
a)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
b)
c)
Fig 4.13PSD responses of selected nodes due to class B roughnesss at 80km/hr a) cabin b) chassis c) van body
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
c)
Fig 4.14 PSD responses of selected nodes due to class H roughnesss at 30km/hr a) cabin b) chassis c) van body
Using equation (3.6), the PSD responses shown in the above figures are transformed to displacement versus time plots shown in the figures below. However, in this case, the band width taken is between 1.3754 and 3.9222cycles/sec.
a)
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b)
64
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
c)
Fig 4.15 Displacement-time histories of selected nodes at 80km/hr a) cab b) chassis c) van body
c)
Fig 4.16 Displacement-time histories of selected nodes at 30km/hr a) cab b) chassis c) van body May 2008 65
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The 1 stress and displacement responses indicate that, on a pavement with class B roughness, hardly any stresses and displacements will be experienced by the vehicle structures. However, in the case of motion on a rough pavement such as on road with class H roughness, the stress and displacement responses are higher. Further, it is noted that, the cabin structure experiences the maximum stress and displacement. In the case of static analysis, it was observed that, in the part of the chassis frames where there is change in cross section, there occur higher stresses and the same part is seen to be affected by dynamic loads (fig 4.10). The spectral density responses are shown for two cases i.e. motion on road with class B roughness and motion on road with class H roughness. The responses are plotted as function of spatial frequency such that PSD values corresponding to the natural frequencies of different mode shapes are used in the analysis. The implication of the PSD function response plots can be expressed as follows. In the previous chapter, it was discussed that the area under PSD curve stands for the variance of the PSD function and the higher the area means the higher the level of roughness. The plots generated in the case of motion on rough pavement (class H) show that the areas under the PSD curves in this case are higher than those generated in the case of pavement with B pavement roughness. This means, the response in the former case is rougher. In addition, it can also be seen that, the response for the node (point) taken on the cabin structure is rougher than the responses of nodes taken on the van body and chassis. The displacement time histories shown in fig 4.16 are presented to show some of the possible displacement variations with time. Consistent with the PSD responses discussed earlier, the displacement in the case of motion on rough pavement (class H), the displacement variation with
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time is rougher than that of pavement with class B roughness. The magnitudes of displacements in fig 4.16 are lower than that expected taking into account the 1 displacement response
(fig4.10). This is because, the band width selected is between is 1.3754, and 3.9222. The wider the bandwidth, the more consistent the two are going to be. Nonetheless, the responses depicted show magnitudes of the expected order and close to the 1 displacement response.
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CHAPTER FIVE CONCLUSION AND RECOMMENDATIONS
5.1 CONCLUSION In this study, the responses of a commercial vehicle with van body are determined under static and dynamic loads, the results of which are believed to be significant. The analysis includes stress and displacement/deflection responses of the vehicle to the loads. The dynamic analysis is carried out taking into account different road roughness conditions. From the results obtained in the analysis, the following can be concluded: • The chassis, particularly, part of the chassis where there is change in cross-section is affected the most by static loads. • The cabin structure experiences the highest deflections and stresses due to random excitations caused by road roughness. • Part of the chassis which is affected the most by static loads is also affected by dynamic loads, comparable to highly loaded points on the cabin structure. • The van body structure, in any of the cases considered, has comparable displacement/deflection with the chassis. However, the level of stress, in any of the cases, is very low and incomparable to highly stressed points in the cab and chassis. 5.2 RECOMMENDATIONS The analysis performed in this research is based on some assumptions and restrictions. However, complete structural analysis and, thus, understanding of behavior of the vehicle is attained taking
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every possible detail into account. Therefore, the following are recommended for future work as extensions and elaborations of this research. • Fatigue life determination based on dynamic stress histories of critically loaded points or sections of the vehicle structure. • • Further investigation of the cabin structure due to dynamic loads. The effects of wind shield, and door structures on the overall stiffness characteristics of the vehicle structure. • Inclusion of nonlinear and damping characteristics of structures in the dynamic analysis of the vehicle structure.
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REFERENCES
[1]. Gillespie, T. D., “Fundamentals of Vehicle Dynamics”, Society of Automotive Engineers Inc., USA, 1992 [2]. Zhanwang, Y., and Zongyu, C., “Dynamic Response Analysis of Minicar Changan Star 6350”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 http://www.mscsoftware.com/support/library/conf/auto00/p02200.pdf [3]. Kim, H. S., Hwang, Y. S., Yoon, H. S., Dynamic Stress Analysis of a Bus Systems”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000. http://www.mscsoftware.com/support/library/conf/auto00/p03200.pdf [4]. Fermer, M., McInally, G., Sandin, G., “Fatigue Life Analysis of Volvo S80 Bi-fuel”, Proceedings of 1st MSC worldwide automotive conference, MSC, 1999 http://www.mscsoftware.com/support/library/conf/auto99/p00499.pdf [5]. Johansson, I., and Gustavsson, M., “FE-based Vehicle Analysis of Heavy Trucks Part I” Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 www.mscsoftware.com/support/library/conf/auto00/p01200.pdf [6]. Oijer, F., “FE-based Vehicle Analysis of Heavy Trucks Part II”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 www.mscsoftware.com/support/library/conf/auto00/p01100.pdf [7]. Parnell, T., White, C., and Day, S., “Finite Element Simulation of 180o Rollover for Heavy Truck Vehicles”, ASCE Engineering mechanics conference, Baltimore, 1999. http://citeseer.ist.psu.edu/407030.html
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[8]. Chiba, S., Aoyama K., Yanabu, K., Tachibana, H., Matsuda, K., Uchikura, M., “ Fatigue Strength Prediction of Truck Cab by CAE” , Journal of Mitsubishi Motors Technical Review, Vol.15, 2003, pp. 54-60. http://sciencelinks.jp/j-east/article/200310/000020031003A0250701.php [9]. Lee, D. C., Choi, H. S., Han, C. S., “ Design of Automotive Body Structure Using Multicriteria Optimization” , Journal of Structural and Multidisciplinary Optimization, Vol. 32, 2006, pp. 161-167. http://www.springerlink.com/content/y70812k267632r47/ [10]. Jin-yi-min, “ Analysis and Evaluation of Minivan Body Structure” , Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000. http://www.mscsoftware.com/support/library/conf/auto00/p00500.pdf [11]. Lee, J. N., Nikravesh, P. E., “ Steady State Analysis of Multibody Systems with Reference to Vehicle Dynamics” , Journal of Nonlinear Dynamics, Vol. 5, 1994, pp. 181-192. http://www.springerlink.com/content/jwu5842568731t84/ [12]. Asheber Techane, “ Dynamics and Vibration Analysis of Bus Body Structures” , M. Sc. Thesis, Addis Ababa University, Addis Ababa, 2007 [13]. Kim, S. S., Shabana, A. A., and. Haug, E. J., “ Vehicle Dynamic Analysis with Flexible Components” , Iowa State University, 1984. http://www.stormingmedia.us/93/9392/P939200.html
[14]. Lan, F., Chen, J., Lin, J., “ Comparative analysis of bus side structures and light weight optimization” , Journal of Automobile Engineering, Vol. 218, 2004, pp.1067-1075. http://www.ingentaconnect.com/content/pep/jae/2004/00000218/00000010/art00001
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[15]. Kim, H. S., Yim, H. J., Kim, C. B., “ Computational Durability Prediction of Body Structures in Prototype Vehicles” , International Journal of Automotive Technology, Vol. 3, 2002, pp.129-135. http://society.kisti.re.kr/~Eksae/_notes/data/pdf/v3n4_1.pdf [16]. Goncalves, J., Ambrosio, J., “ Optimization of Vehicle Suspension Systems for Improved Comfort of Road Vehicles Using Flexible Multibody Dynamics” , Journal of Nonlinear Dynamics, Vol. 34, 2003, pp.113-131. http://www.springerlink.com/content/w7878702v784r26g/ [17]. Sayers, M. “ Standard Terminology for Vehicle Simulations” , University of Michigan Transport Research Institute” , USA, 1996 [18]. Wong, J. Y., “ Theory of Ground Vehicles” , John Wiley and sons, Inc., New York, 1993 [19]. Awasthi, E., Singh T., Das, A., “ On Pavement Roughness Indices” , Journal of Institution of Engineers (India), Vol. 84, 2004, [20]. Rill, G., “ Vehicle Dynamics” , Fachhochschule Regensburg, Germany, 2007 [21]. Wirsching, P. H, Paez, T. L., Ortiz, K.,“ Random Vibrations” , John Wiley and sons, Inc., New York, 1995
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BIBLIOGRAPHY
[1]. Gibbs, H. G., “ Stress, Vibration and Noise Analysis in Vehicles” , Applied Science Publishers Ltd, London, 1975 [2]. Beermann, H. J., Tidbury, G.,” The Analysis of Commercial Vehicle Structures” , Mechanical Engineering Publications Ltd, London, 1989 [3]. Reimpell, J., Stoll, H., Betzler, W., “ The Automotive Chassis: Engineering Principles” , Reed Elsevier and Professional Publishing Ltd, USA, 2001 [4]. Deshmukh, P. S., “ Rollover and Roof Crush Analysis of Low Floor Mass Transit Bus” , M.Sc. Thesis, Wichita State University, USA, 2006 [5].” ANSYS Reference Guide” , CADD Centre Training Services Private Limited” , India, 2004 [6]. Desai, C. S., Abel, J., F., “ Introduction to the Finite Element Method” , Van Nostrand Reinhold Company, New York, 1972 [7]. Huebner, K. H., Thornton, E., A., Byrom, T., G., “ The Finite Element Method for Engineers” , John Wiley and sons, Inc., USA, 1993 [8]. Krishnamoorthy, C. S.,” Finite Element Analysis Theory and Programming” , Tata McGrawHill Publishing Company Limited, New Delhi [9]. Ambrosio, J., “ Crash Analysis and Dynamical Behavior of Light Road and Rail Vehicles” , Journal of Vehicle System Dynamics, Vol.43, pp.385 - 411
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doc_132980799.pdf
A commercial vehicle is a type of motor vehicle that may be used for transporting goods or passengers. The European Union defines "commercial motor vehicle" as any motorised road vehicle, which by its type of construction and equipment is designed for, and capable of transporting, whether for payment or not: (1) more than nine persons, including the driver; (2) goods and "standard fuel tanks".
STATIC AND DYNAMIC ANALYSIS OF A COMMERCIAL VEHICLE WITH VAN BODY A Thesis
by
Kassahun Mekonnen
Submitted to the School of Graduate Studies of Addis Ababa University in partial fulfillment of the requirements for M.Sc. Degree in Mechanical Engineering
Advisor Dr. Alem Bazezew Department of Mechanical Engineering Faculty of Technology Addis Ababa University May 2008
ACKNOWLEDGEMENTS
First of all, I thank God for giving me the strength to accomplish this thesis. I would like to thank my advisor Dr. Alem Bazezew for his valuable guidance and support throughout the course of this thesis. I also like to extend my gratitude to the members of the Department of Mechanical Engineering, Addis Ababa University, for their concern and willingness to help me in every possible way. I would also like to thank Ato Thomas (Technometals Engineering P.L.C), Ato Asheber Techane, Ato Abaraham Assefa, and W/t Rahel Tadesse for providing me with the necessary data which are used in the development of the thesis. I am also grateful to other friends of mine who have been very cooperative. Finally, thanks are due to my mother and father, Almaz and Mekonnen, and my brother and sisters, Dawit, Imuye and Hanna for their encouragement.
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TABLE OF CONTENTS ACKNOWLEDGEMENTS LIST OF FIGURES LIST OF TABLES LIST OF SYMBOLS ABSTRACT 1. INTRODUCTION 1.1. Background 1.2. Objectives of the study 1.3. Methodology 1.4. Organization of the thesis 1.5. Scope and limit of the thesis 1.6. Commercial vehicle with van body structure 2. LITERATURE REVIEW 3. PHYSICAL AND MATHEMATICAL MODELING 3.1. Coordinate systems 3.2. Motion and forces with reference to vehicle dynamics 3.3. Road roughness model 3.4. Tire model 3.5. Vehicle multibody model 3.6. Finite element model i iv vi vii x 1 1 3 3 4 5 5 8 16 17 18 20 29 29 42 ii
4. ANALYSIS AND RESULTS 4.1. Static Analysis 4.2. Modal Analysis 4.3. Random Vibration Analysis 5. CONCLUSIONS AND RECOMMENDATIONS 5.1. Conclusions 5.2. Recommendations REFERENCES BIBLIOGRAPHY
48 48 52 57 68 68 68
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List of figures
Fig 1.1 ISUZU NPR model commercial vehicle with van body structure Fig 3.1 SAE Vehicle Axis System Fig 3.2 Forces on a commercial vehicle Fig 3.3 Power Spectral Density as function of spatial frequency for various types of road and runway Fig 3.4 Classification of Road Surface Roughness by ISO. Fig 3.5 Profiles of Roads in Addis Ababa Fig 3.6 Spectral Density plotted as function of Spatial frequency for Class B road roughness Fig 3.7 Spectral Density plotted as function of Spatial frequency for Class H road roughness Fig 3.8 Profile for road with Class B roughness classification Fig 3.9 Profile for road with Class H roughness classification Fig 3.10 linear model of tire Fig 3.11 Multibody models of a vehicle Fig 3.12 Quarter car model of the vehicle Fig 3.13 PSD function of response of unsprung mass at the front wheels Fig 3.14 PSD function of response of unsprung mass at the rear wheels Fig 3.15 Solid model of the vehicle Fig 3.16 finite element model Fig 3.17 eight noded solid element Fig 3.18 four noded shell element Fig 3.19 Spring-Damper element Fig 4.1 Solution procedure diagram Fig 4.2 Vertical deflection due to static loads Fig 4.3 Von mises stresses due to static loads Fig 4.4 Z-component of stress due to static loads (bending stress in the chassis)
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Fig 4.5 First mode Fig 4.6 Second mode Fig 4.7 Third mode Fig 4.8 Fourth mode Fig 4.9 Response due to class B roughness at 80km/hr Fig 4.10 Response due to class H roughness at 30km/hr Fig 4.11 Response due to roll motion Fig 4.12 Locations of nodes for which PSD responses are determined Fig 4.13 PSD responses of selected nodes due to class B roughness at 80km/hr Fig 4.14 PSD responses of selected nodes due to class H roughness at 30km/hr Fig 4.15 Displacement-time histories of selected nodes at 80km/hr Fig 4.16 Displacement-time histories of selected nodes at 30km/hr
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List of Tables Table 3.1 Values of Csp and N for Power Spectral Density Functions for various Surfaces Table 3.2 Classification of Road Roughness by ISO. Table 3.3 IRI values of some of recently upgraded roads in Ethiopia Table 3.4 Stiffness and Damping Properties of tires
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List of Symbols
X - longitudinal axis of Earth fixed coordinate system Y- lateral axis of Earth fixed coordinate system Z - vertical axis of Earth fixed coordinate system x - longitudinal axis of vehicle fixed coordinate system y - lateral axis of vehicle fixed coordinate system z - vertical axis of vehicle fixed coordinate system p - roll motion of vehicle q - pitch motion of vehicle r - yaw motion of vehicle Txf - Traction force at the front wheel Txr - Traction force at the rear wheel Rxf - Rolling resistance at the front wheel Rxr - Rolling resistance at the rear wheel D - Aerodynamic Drag Wf - Axle load at the front wheel Wr - Axle load at the rear wheel Max -Inertial force due to acceleration/deceleration
-power spectral density of road roughness - spatial frequency
¡
tire mass
¡ – stiffness of tire
¡
tire dampingconstant sprung mass
¢
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£¤¢ ¢ ¥
¢§¦
?sprung mass spring stiffness shock absorber damping constant Base excitation Response of unsprung mass Response of sprung mass Transfer function matrix
amplitude of base excitation amplitude of response of unsprung mass amplitude of response of sprung mass
strain energy - external work - strain vector - displacement vector - the surface loads vector { }- the stress vector – displacement transformation matrix - nodal displacement vector - strain-displacement matrix - element stiffness matrix. global stiffness matrix - element mass matrix. - global mass matrix - force vector - nodal force vector
viii
- reaction force vector density amplitude vector
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ABSTRACT
A vehicle and its structural components are subjected to loads which cause stresses, strains, deflections, vibration and noise in the components. To achieve a quality vehicle, i.e. one having longer fatigue life, reduced weight, reduced cost, and so on, it becomes necessary to use materials of appropriate strength and stiffness property with the most appropriate geometry (form). One way to achieve this is evaluation and assessment of responses of the vehicle to different loads. This research addresses responses of a vehicle to static and dynamic loads. The entire analysis is done for an ISUZU NPR model commercial vehicle with van body. The method used is finite element modeling and analysis for which the inputs are obtained from quarter car model analysis. The responses to static loads and random excitation caused by road roughness are determined. Components and, particularly areas which are much affected by the different loads are indentified. Finally, conclusions based on the results and recommendations which can be extensions of this research are also presented.
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CHAPTER ONE INTRODUCTION
1.1 BACKGROUND During service, any vehicle is subjected to loads that cause stresses, vibrations and noise in the different components of its structure. This requires appropriate strength, stiffness and fatigue properties of the components to be able to stand these loads. On top of that, quality of a vehicle, as a system, which include efficient energy consumption, safety, and provision of comfort to the user are highly desired. All the above largely demand refined and complex design and manufacturing procedures involved during the production stage. This, in turn, requires good understanding of the internal systems of the vehicle and the characteristics of the different body structures in reaction to static and dynamic loads. Vehicle dynamics, a discipline of broader significance, is an area where the basics of analyses on vehicles are dealt with. Forces/loads acting on vehicles can be categorized as road, aerodynamic, and gravity loads. Of all these, forces and moments generated by tires at the ground are significant in controlling motion of the vehicle [1]. The response of the vehicle structures to these loads are dealt with in vehicle dynamics. The responses of a vehicle are defined in terms of deflections, stresses, strains, natural frequencies, random response functions, fatigue life and so on. Evaluation of the above is what puts the basis on which robustness of a vehicle system or design is ascertained in terms of its mechanical behavior. Simulation of vehicle responses largely concentrates on determination of the above.
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Different researches have been carried out regarding the performance, the response of components to static and dynamic loads, crashworthiness, safety and others by different institutions and automotive companies. Particularly, with the growing simulation capability using computers, researches are facilitated that are aimed at achieving better quality products. The application of computer aided engineering (CAE) analysis to problems of this sort, in combination with prototype development and testing, enables to achieve structures having longer fatigue life, reduced cost, light weight and improved comfort. In light of this purpose, as stated earlier, advancements in the area are growing further. At nationwide and faculty level, only a few researches have been conducted in the area of vehicle dynamics. However, there are local companies engaged in the construction of truck, bus, and van body structures. Examples of these are companies which construct bus body structures on ISUZU NPR model commercial vehicle by removing the cab, and years back, there used to be companies building “wuyiyit”, a locally manufactured taxi body structure, on TOYOTA, NISSAN, and PEUGEOT model pick up vehicles. Building trailer chassis frames is also an experience in some companies. In addition, there are other companies which construct van body structures on ISUZU NPR and FSR, and MITSUBISHI model commercial vehicles. In these companies, the use of researches and computer aided engineering analysis is far below what it should be. Some of these companies make use of graphics softwares to prepare drawings. To my understanding, this indicates regarding the engineering aspect that includes design and analysis, little is done. However, as mentioned earlier, these are the bases for achieving structure having longer fatigue life, reduced cost and reduced weight. Thus, this prompts implementation of existing theoretical knowledge and facilities towards addressing the problem in the area.
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1.2 OBJECTIVES OF THE STUDY General Objective: The objective of the study is to produce results which may help to rectify problems associated with structures of a commercial vehicle and which also may be of significance during design of van body structure of the vehicle after carrying out static and dynamic analysis, combining existing theoretical knowledge and advanced analytical methods. Specific Objectives: i. To develop mathematical and finite element model of the major components of a commercial vehicle with van body structure which include chassis, cab, and van body structure and carry out static, dynamic analysis of the structures. ii. Based on the analysis, identify points and sections which are highly loaded (stressed) due to the loads by means of which the overall intensity of loading in the structures is assessed. iii. Arrive at conclusions and propose recommendations on the basis of (i) and (ii).
1.3 METHODOLOGY To fulfill the objectives of the study the following are used. i. Literature Review: Survey of books, journal articles, proceedings of international conferences, auto manufacturer catalogues, and other relevant literature is done. ii. Data Collection: data regarding the van body structure are collected from Technometals Engineering (Addis Ababa). The data include dimensions of the structure, material used to construct the structure, and construction methods. Road roughness data of some roads
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is obtained from Civil Engineering Department, AAU. Data regarding ISUZU NPR model commercial vehicle are obtained from specifications prepared for the vehicle and official website of ISUZU company. Other data used in the thesis are obtained from books, and handbooks. iii. Modeling and Analysis: The finite element model development as well as the corresponding static and dynamic analysis is performed using ANSYS software. iv. Conclusions and Recommendations.
1.4 ORGANIZATION OF THE THESIS The body of this thesis is divided into five main chapters. The first chapter discusses background and objectives of the study. In addition, the details of the model vehicle used in the analysis are also discussed in the same chapter. The second chapter covers the review of some of the journal articles, proceedings and publications which were referred to during the course of the thesis. Also, in relation and comparison with previous works, what is done in this thesis will be stated. The mathematical and finite element modeling is discussed in the third chapter. Road roughness, tire modeling, and multibody models representing different motions of a vehicle presented. Also, covered in this chapter is discretization of the solid model of the commercial vehicle used for the analysis into finite elements and the mathematical formulation of these elements. The results obtained from the static and dynamic analysis of the vehicle and discussions based on these results are included in the fourth chapter. Finally, the fifth chapter covers conclusions drawn based on the results of the analysis, and recommendations for future work.
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1.5 SCOPE AND LIMIT OF THE THESIS As it can be seen, numerous types of simulations/analyses can be carried out regarding behavior of a vehicle. In this research, as stated earlier, static and dynamic analysis of a commercial vehicle structure are carried out. The dynamic analysis includes only modal and random response analysis of the structures. Nonlinear behavior which components could experience is not dealt with and, linear and isotropic material models are used for the entire analysis. In the dynamic analysis, damping properties of the structures is not considered. However, damping due to shock absorber of the vehicle is included in the analysis. The analysis is carried out for the main load bearing structure of the vehicle, i.e., chassis side frames and cross members, steel frames of the van body structure, and cab. Wind shields, door frames, and cover plates of the van body structure are not dealt with. The effect of the engine is taken into account by distributing its weight into the side frames of the chassis. 1.6 COMMERCIAL VEHICLE WITH VAN BODY Commercial vehicles with van body structure built on chassis frame find large application in different companies. There are also different companies engaged in construction of the body structures with variants for use in different environment. The specific model used in this analysis is ISUZU NPR model commercial vehicle (fig 1.1). This vehicle is chosen for it is one of the most commonly used both here in Ethiopia and abroad. *It is observed that the model chosen for this analysis is one of the most popular and highly sold around the world including the most developed nations.
*Official website of ISUZU Japan
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Fig.1.1 ISUZU NPR model commercial Vehicle with van body
Data for the vehicle are given below: Gross Vehicle Weight (GVW): 7500kg Gross Combined Weight (GVW + Payload): 11000kg Engine type: Diesel, inline 4 cylinder, overhead cam (OHC), direct injection. Maximum power: 76KW@3200rpm Maximum torque: 268Nm@1800rpm Overall length: 6610mm Wheelbase: 3815mm Wheel centre (front wheels): 1680mm Wheel centre (rear wheels: dual): 1650mm Height (excluding van body): 2250mm
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The van body structure frames are built with steel tubes that are welded to one another. The doors are hinged to the body structure. The outside of the structure is covered with steel plate that is joined with rivets, while the inside is covered with aluminum plate. The structure frames with the cover plates are welded to the checkered plate. The structure is connected to the chassis frame with bolt connections.
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CHAPTER TWO LITERATURE REVIEW
Vehicle Dynamics is an area on which different researches have been carried out. Different people at institutional and individual level involved in the area produced findings which are relevant in the automotive industry. In nearly all the literature reviewed it is observed that most of the researches constitute development of virtual or prototype models and all the analyses are performed on these models. Verification of the results is accomplished by comparison made with experimental results. Listed below are some of the literatures surveyed that are deemed to be significant to this research that is conducted on analysis of body structure of a vehicle.
Y. Zhanwang, and C. Zongyu, [2] developed finite element model for Minicar Changan Star 6350 using SDRC/I-DEAS. The model was imported to MSC.Patran to generate the mesh and the dynamic analysis of the model was accomplished using MSC.Nastran. The analysis included modal analysis of the load bearing structures, the chassis and the body structure frame, in which the first 100 natural frequencies were determined in torsion and bending modes, and transient dynamic analysis of the structures due to road loads that were introduced in the form of acceleration excitations. They obtained results which happened to show good consistency with experimental results, and concluded that the Minicar is able to meet dynamic design requirements. H. S. Kim, Y. S. Hwang, and H. S. Yoon, [3] presented a method for prediction of dynamic stress time histories. The method, referred to as hybrid superposition method, employs hybrid sum of pseudostatic stresses and modal acceleration stresses. Static stress coefficients and modal
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stress coefficients used in the determination of pseudostatic stresses are obtained using finite element codes such as MSC.Nastran, while the time histories of body and surface loads are obtained using flexible multibody dynamic analysis code, DADS. Through a governing equation, the above two are combined to generate the dynamic stress time histories which lead to prediction of fatigue life. A bus system in which dynamic stress time histories are determined for a critical pillar joint is presented as an example to prove validity of the method. M. Fermer, G. McInally, and G. Sandin [4] carried out fatigue analysis of Volvo S80 Bi-fuel. In a virtual environment, the fatigue life analysis of the fuel and gas tanks, crossmember for fuel tank, crossmember for gas tank and spot welds was undertaken before development of a prototype. The MBS-Code ADAMS was used to undertake the simulations with parallel and torsional excitation input loads. Of the different sizes of floor plate thickness used in the analysis, one that is able to withstand fatigue failure with the inclusion of stiffening swage was chosen based on which prototype was developed and tested. The shake rig test conducted on the prototype proved the robustness of the structural frames and concluded that the FE-Based analysis has been successfully used to speed up development of a new product. I. Johansson and M. Gustavsson [5] presented a paper that discusses implementation of FE methods for dynamic analysis of heavy trucks. The approach used involves development of FEmodel of the vehicle and its subsystems, i.e. frame, superstructure, engine, cab, axles and chassis suspensions, and steering system. Also included in the modeling are problem size reduction, global motion and centrifugal forces, lateral tyre model and gyroscopic moments. The analysis focused on analysis of road, wheel and brake, and driveline induced vibrations, static load cases and fatigue life prediction. An example was presented which shows the lateral and vertical acceleration of the cab structure due to periodic excitation of axle due to wheel run out. It was
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concluded that, FE-based complete vehicle analysis has the advantage to cover broad range of analyses with one type of model. F. Oijer [6] developed force histories for different components of a heavy truck under different road load conditions. The environment in which the vehicle was driven was described by vertical road profile and curve radii. The road profile was applied to the tires and a driver model was used to produce the desired yaw. The complete vehicle model was produced using shells, bars, spring and damper elements. Tire slip, gyroscopic moments, and centrifugal forces were also considered. Further, for the analysis, tires of two types, one-point contact and flexible ring type, depending on the road surface, and nonlinear characteristics, among other things, were also used. Modal Transient Analysis (SOL 112), a feature in MSC.Nastran, is used for the response studies. Force histories were generated for rear and front axle suspensions with bad road models (low frequency), and the same histories were developed for the cab suspension with high frequency road having transient obstacles. All the results obtained were compared with measured values and the fictitious fatigue life ratio (calculated life/measured life) was found to be between 1.5 and 2. Further, comparison was made of force histories for cab suspension with flexible and rigid models of the cab. It was finally concluded that, MSC.Nastran is proved fast and accurate enough to give reasonable results. T. Parnell, C. White, and S. Day [7] conducted finite element simulation of 180o Rollover for Heavy Truck Vehicles. The simulation was carried out for evaluating structural integrity and occupant crash system design in heavy trucks. The finite element model for the cab structure was done using ANSYS. The rollover simulation consists of two phases; the initial phase is rollover event wherein rigid body kinematic analysis was performed using the computer code DADS. The deformation phase starts at the instant of cab-to-ground contact and for this phase, the quasiMay 2008 10
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static finite element simulations were performed in another computer package LS-DYNA3D. Projection of the results obtained in the rigid body analysis to LS-DYNA3D model was accomplished with a MATLAB script file. Two cab structures were physically tested for which the Resultant Platen forces in the structures were recorded with time and comparison with simulation results proved good agreement between the two. In conclusion, it was stated that FE based techniques can fully be used to evaluate rollover phenomena in heavy trucks. S. Chiba, K. Aoyama, K. Yanabu, H. Tachibana, K. Matsuda, and M. Uchikura [8] presented a paper that discusses fatigue strength prediction of Truck Cab. The method discussed was developed as part of a program to change full model of a Mitsubishi light-duty truck. The method involves generation of stress time diagrams based on which fatigue life for the cab is predicted. Static and Eigen value analysis for the FE model were performed using MSC.Nastran and the simulation to generate the load history was done using ADAMS taking the Eigen value results as input. The load history along with the static analysis results were used to complete the fatigue life analysis using another package, FALANCS. All the results obtained were compared with experimental results and ended up with little discrepancies. D. C. Lee, H.S. Choi, and C. S. Han [9] presented a paper that focuses on multicriteria optimization of automotive body structure design. The optimization includes definition of objective and constraint functions that are defined as functions of design variables. The optimal solution (optimum values of the design variables) is defined using what is known as Paretooptimal solution. As an example, a dynamic analysis simulation of a vehicle was conducted which has the objective of minimizing intensity of vibration due to engine idle shake, wheel unbalance shake, and road shake. Initially, values were taken representing different dimensions of the different vehicle components (design variables) and these values were optimized using the
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method. Based on these values a FE-model was developed and the corresponding excitations under the three cases were determined. In conclusion, it was underlined that such optimization approaches provide efficient design during early stages of development. Jin Yi-Min [10] implemented finite element methods to analyze and evaluate minivan body structure. The analysis included static, dynamic, fatigue, crashworthiness, optimization and design sensitivity analysis. The static analysis was conducted taking into account the bending and torsion loads. The dynamic analysis comprised two sources, tire unbalance and engine excitation and the corresponding NVH analyses was carried out. In the paper, presented are the strength analysis in both torsion and bending case and modal analysis results. The FE analysis was accomplished through the use of MSC.Nastran. The results obtained for the dynamic analysis were compared with experimental test results and found to be in good agreement. J. N. Lee and P.E. Nikravesh [11] presented a paper on steady state response of multibody systems where a vehicle system was discussed as an example. The equations of motion for a multibody system are described in terms of relative joint accelerations and, in steady state configuration, the relative joint accelerations between bodies become zero which lead to conversion of differential equations of motion to algebraic set of equations for the steady state response. Based on the method discussed, the vehicle was assumed to have a certain forward speed and steer angles for the front and rear wheels; the resulting steady state angular velocities and vertical displacement of the chassis along with the spinning speed of the wheel were determined. Comparison was made with results obtained from transient dynamic analysis. Asheber Techane in his M.Sc. thesis [12] conducted dynamic analysis of a locally manufactured bus body structure. The solid model of the structure was developed in AutoCAD classic
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
environment and the generation of the FE model and the dynamic analysis were performed using ANSYS. Modal analysis which reveals the natural behavior of the structure and PSD (power spectral density) analysis are included in the dynamic analysis of the structure and it was concluded that the roof of the bus structure is prone to higher deflection, and as a recommendation it was forwarded that there be carried out complete evaluation of the vehicle to prove robustness of the structure in terms of its mechanical properties. S. S. Kim, A. A. Shabana and E. J. Haug [13] presented a paper on nonlinear, and transient dynamic analysis of vehicles systems composed of interconnected rigid and flexible components. In the method used, for a system, equations of motion and constraints are formulated in terms of a minimal set of generalized coordinates. As an example, a cross country truck for which the corresponding vehicle and road surface model developed was considered. The resulting displacement and acceleration of centre of gravity of the chassis frame of the truck were determined for two cases. The first case being the truck traversing a road bump and the second taken as the truck traverses a random terrain. For the purpose of comparison, flexible and rigid body models of the frame were considered, and it was depicted that the peak acceleration of the centre of gravity in the former case was higher. F. Lan, J. Chen, and J. Lin [14] presented a paper that dealt with optimization of light weight bus side structures. The optimization targeted reduction in the number and weight of parts in the whole body structure. For this purpose, two structures, with and without supporting structures between longitudinal waist beams of the side frame were considered. The FE-model for the structure without the support was developed in the computer package UG and mesh generated in MSC.Patran. The FE Analysis was completed using ANSYS. The deflections and stresses under static loading case were determined and modal analyses were also performed. All the results
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
obtained were compared with experimental results obtained. In addition, sensitivity analysis, selecting different important component dimensions, and light weight optimization were also studied. In conclusion, it is stated that the structure with support is proved valuable enabling significant alleviation of body weight and satisfactory performance requirements of load carrying capacity. H. S. Kim, H. J. Yim, and C. B. Kim [15] presented a paper on computational durability prediction of body structures in prototype vehicles. The finite element analysis performed using MSC.Nastran gives static correction modes that are to be used in multibody dynamic analysis (Using DADS) and static stress coefficients which in superposition with the results of the multibody dynamic analysis are used to determine the dynamic stress histories. The dynamic stress histories, in turn, are used to predict the fatigue life, performed using another package P3/FATIGUE, of critically loaded members of the body structure. Based on the method, analysis of prototype bus body structure was performed taking into account two drive conditions, namely, city mode and Belgian mode. In conclusion, it was underlined that the methodology can be used as efficient and reliable means for the sign-off of durability of a prototype vehicle with actual service environments in the early development stage. Joao Goncalves and Jorge Ambrosio [16] presented a paper on optimization of vehicle suspension systems for improved comfort of Road vehicles. An algorithm is developed for comfort optimization in which the different characteristics of the vehicle components are the design variables on which appropriate constraints are imposed. The ride optimization is attained by finding the optimum values of the characteristic quantities in face of their importance for the comfort of the occupant. To exemplify the method employed, a vehicle is simulated over two
May 2008
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
different road profiles at two different speeds. It was concluded that the methods applied lead to stable and efficient optimization procedures. As can be seen, all the research focus on static, dynamic, fatigue, crash and optimization analysis of vehicles and their different components. It is further indicated that different computer packages such as MSC.Patran/MSC.Nastran, ANSYS, ADAMS, DADS, and IDEAS are used to develop the virtual models (FE models) of vehicles and their different components and perform the required type of analysis. In addition, experimental tests are made use of to ensure acceptance of results obtained for the virtual models. In this research, the static and dynamic analysis of an ISUZU NPR model commercial vehicle is carried out such that the method used combines multibody and finite element models of the vehicle. The static and modal analyses are carried out using usual methods of analysis. The random response is done using finite element analysis such that results obtained from multibody (Quarter car model) analysis are used as input for the finite element model. Modeling, finite element discretization and all the analyses are carried out using ANSYS, and the same solid and finite element model is used for all types of analysis.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER THREE PHYSICAL AND MATHEMATICAL MODELING
Vehicle motion which includes acceleration, braking, ride and turning is response of the system to loads imposed on the vehicle from the tires, gravity, and aerodynamic loads. In addition, stresses, deflections, vibration (ride and noise) induced in the components of the vehicle are also responses of the vehicle. Ride and noise are associated with dynamic response of the body structure and other parts to excitations produced by different sources. The main sources of these excitations include road roughness, wheel run out, engine and driveline vibrations and aerodynamic loads. Of these, road roughness causes significant amount of the body structure vibration [1]. Determination of static and dynamic responses of the vehicle necessitates development of models representing the vehicle system. Appropriate physical and mathematical models are necessary to arrive at reasonable results. Equations of motions, the solution of which gives the response of the system, and which govern the system at hand are formulated based on the mathematical model. Closed form solutions are attainable for models of less complication which happen to approximate the problem reality to a lesser extent. The better the reality is modeled the complicated the model becomes and this calls for advanced solution methods the implementation of which is possible using highly capable computers and computer softwares. In this respect, finite element modeling and analysis is worth mentioning. Multibody models of vehicles are also used for simulation purpose. They involve modeling of a system such that it is reduced to system of interconnected rigid bodies. Such models, as is usually the case, are used to deal with bounce (translation motion in the vertical direction) and
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
pitch, and bounce, pitch and roll motions of the vehicle. Also, more advanced analysis of vehicles is also carried out using such models. In this chapter, the definition of some of the quantities used to define motion and loads, the physical and mathematical modeling of the problem are presented. 3.1 COORDINATE SYSTEMS. Vehicle motion and the response of the vehicle to excitations are described using quantities which do represent some reality with respect to the motion and/or response of the vehicle. To define the different motion quantities and loads (forces and moments) associated with vehicle motion and simulations regarding the motion, different axes systems are in use. Worth mentioning here are, systems defined by Society of Automotive Engineers, SAE [1] and International Standards Organization, ISO. [17] Throughout this report, all the quantities discussed are defined with regard to the SAE convention discussed below. Two coordinate systems in the SAE convention are of importance in vehicle simulations. These are the Vehicle fixed coordinate system (Fig 3.1) and the Earth fixed coordinate system. The vehicle coordinate system has its origin at the center of gravity of the vehicle and travels with the vehicle. The longitudinal(x) axis lies along the vertical plane of symmetry of the vehicle and the lateral
axis is taken positive to the right. The vertical (z) axis is chosen such that the system is right handed, i.e. positive downward.May 2008
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.1 SAE Vehicle Axis System
The Earth fixed coordinate system(X-Y-Z) is selected to coincide with the vehicle coordinate system at the start of maneuver which from then on remains fixed on the earth. The absolute motion quantities are defined with respect to this coordinate system and the components of these quantities are defined along the axes of the vehicle fixed coordinate system. 3.2 MOTION AND FORCES WITH REFERENCE TO VEHICLE DYNAMICS The motion of a vehicle is defined by different translational and rotational (angular) components. Using the vehicle fixed coordinate system introduced in the previous article the linear velocity and acceleration of the vehicle are decomposed along the three axes producing the longitudinal, lateral and vertical components. Roll, pitch, and yaw correspond to the rotational motion about the x-, y- and z- axes of the vehicle fixed coordinate system. Forces and moments are the causes for state and trajectory that a vehicle attains during the course of motion. The loads include aerodynamic, gravity and loads generated at the tire ground contact. The primary forces with which the motion of the vehicle is controlled are developed at the tire ground contact. Fig 3.2a and b show the most significant forces on the vehicle in the x-z plane. The effect due to payload is not considered.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.2 Forces on a Commercial Vehicle
The forces in the longitudinal direction include traction force at the front and rear wheel Txf and Txr, rolling resistance at the front and rear wheels Rxf and Rxr, aerodynamic resistance D. The front and rear axle loads are represented by Wf and Wr. Max stands for the inertial force that prevails during acceleration and deceleration. In fig 3.2a), the forces on the van body and the remaining part are considered separately. The sub index v indicates a load on the van body while wv indicates a load on the remaining part of the body.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.3 ROAD ROUGHNESS MODEL Road roughness, as outlined in the introduction, is the major source of excitation. It stands for the irregularities in the road profile. Sine waves, step functions, and triangular waves can serve as models to represent road roughness. Nonetheless, random function modeling more realistically defines road profiles. Random processes are defined using power spectral density (PSD) functions. Mathematically, PSD function of a random variable/process represents the Fourier transform of the autocorrelation function of the random process. Autocorrelation or correlation of a function with itself indicates how the value of a random variable a time is related to the value at time
The autocorrelation function is dependent on the period and not on the specific time, In addition, other parameters like expected (mean) value, root mean squared value, variance, and standard deviation are used to describe random variables and processes. Based on this, a random function representing a random variable is said to be stationary, if the expected value of the function at time is the same as the expected value at time A random road profile is In this
stationary as long as a contour representing portion of the road repeats itself after time, study, stationary conditions are considered.
PSD measure of road roughness is one of the internationally recognized methods to describe road roughness. The road elevation profile is decomposed into series of trigonometric waves varying in their amplitude and frequency. The plot of density of the mean square values of amplitudes versus the spatial frequency gives the PSD function corresponding to the signal. Spatial frequency represents the number of cycles corresponding to specific amplitude per unit length
and it is the inverse of wave length.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Different road roughness ranging from that of smooth runway to off-road ground could be modeled as random signals which are defined with PSD functions. Fig 3.3 shows PSD representation of typical road profiles published in SAE Transaction. Accordingly, the relationship between power spectral density
¨
and the spatial frequency
can be
approximated by:
¨
(3.1) is the power spectral density of the road roughness elevation profile, and
¨
In the equation,
and N are constants whose values for the different road profiles are given in Table 3.1. The values of the constants differ depending on different conditions. The area under the
¨
curve
shows the variance of the function. The higher the area is the higher the level of roughness.
Fig 3.3 Power spectral density as function of spatial frequency for various types of road and runway [18]
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Description Smooth runway Rough runway Smooth highway Highway with gravel
N 3.8 2.1 2.1 2.1
Csp 4.3 x 10-11 8.1 x 10-6 4.8 x 10-7 4.4 x 10-6
Table 3.1 Values of Csp and N for Power Spectral Density Functions for various Surfaces [18]
On the other hand, the International organization for Standardization (ISO) classifies road surface roughness into eight classes (classes A-H) based on power spectral density [18]. Accordingly, the relationship between the power spectral density and the spatial frequency for different classes of road profile may be approximated by two straight lines with different slopes (Fig 3.4). The corresponding relationships are: For
¨ ¨
; and
(3.2a)
for
¨ ¨
(3.2b)
¨
In the above equations,
and
, as discussed earlier, represent the power spectral density
and the spatial frequency.
corresponds to the value of the spatial frequency which is equal to The values of N1 and N2, respectively, are 2 and 1.5. for each class of road roughness.
cycles/m or wavelength equal to
Table 3.2 gives the range of spectral density at
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.4 Classification of Road Surface Roughness by ISO [18]
Road Class A(Very Good) B(Good) C(Average) D(Poor) E(Very Poor) F G H
Degree of Roughness, ¨ ( *10-6 m2/cycles/m) Range <8 8-32 32-128 128-512 512-2048 2048-8192 8192-32768 >32768
Table 3.2 Classification of Road Roughness by ISO [18].
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The Ethiopian Roads Authority (ERA) uses the International Roughness Index (IRI) to evaluate road roughness of roads in service and under construction. IRI stands for total accumulated vertical movement of a vehicle divided by the distance traveled by the vehicle during motion. It is given in meters per kilometer. There exists relationship between PSD values or, particularly, the area under
¨
curve and the IRI, i.e. as the roughness increases, both the area and IRI
increase. The data shown in Table 3.3 indicates the IRI value for recently upgraded interstate asphalt roads in Ethiopia. Similar data for gravel roads is not made available for these roads show much roughness not expressed with IRI. Fig 3.5 shows roads with different profile in Addis Ababa.
Actual Result (%) Surface IRI, m/km Road Name Addis-Wolliso Addis-Commando Commando-Gohatsion Addis - Modjo Modjo-Nazareth Melkasa-Sodere Modjo-Ziway Ziway-Shashemene Shashemene-Awassa Road Length(km) 112 109 76 55 17 7 87 90 26 Good<4.5 100 100 100 100 100 53 99 100 100 Fair 4.5-6 0 0 0 0 0 33 0 0 0 Poor 6-9 0 0 0 0 0 14 1 0 0
*Table 3.3 IRI values of some of recently upgraded roads in Ethiopia
*Obtained from data prepared by Ethiopian Roads Authority
May 2008
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.5 Profiles of Roads in Addis Ababa a) Addis Ababa ring road: near megenagna b) alley in Addis Ababa: near Inqulal Fabrica
In this research, for the purpose of dynamic analysis, roads of two different roughness classes are taken into account. In the first case, the condition in which the vehicle traverses over roads like the ring road is dealt with, while motion over rough pavement is the second case considered. The input PSD function corresponding to each case is determined as follows. In an experiment conducted on road roughness [19], it was proved that for a road with IRI of 3.4 (classified “good” by ERA) the value of lies between ?? indicating that it belongs to
class B of roads as per the ISO classification. As for the other case, assuming worst road roughness condition, class H road is considered. The corresponding PSD functions for both functions which are taken as an input for the quarter car model (section 3.4) are defined below.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Class B: For
©
cycles/m ;and cycles/m
¨
(3.3a)
for
(3.3b)
Fig 3.6 Spectral Density plotted as function of Spatial frequency for Class B road roughness (log-log Scale)
Class H: For
©
cycles/m ; and (3.4a)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
for
¨
cycles/m (3.4b)
Fig 3.7 Spectral Density plotted as function of spatial frequency for Class H road roughness (log-log Scale)
For a vehicle moving with velocity, V, the power spectral density in terms of circular frequency, (number of cycles per second,)
¨
can be determined as: (3.5)
©
The Spectral density shown above can be used to generate the road elevation profile such that , function representing the road contour as function of displacement, ? is considered as Gaussian random process with mean zero, and spectral density function,
¨
The equation
shown below is used to generate function
May 2008
, [19].
27
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
???
(3.6)
where, ,
?
, square root of the area under
¨
curve. ; and
¨
are random variables with spectral density,
is the number of sample points of Possible elevation profiles for the two types of roads considered in this analysis over a distance of 50m are shown below. The wavelength range chosen for the determination of the road profile is between 0.1 and 100metres [19]. Fig 3.8 is taken at 80km/hr speed while Fig 3.9 is obtained at 30km/hr.
Fig 3.8 Profile for road with Class B roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Fig 3.9 Profile for road with Class H roughness classification
3.4 TIRE MODEL Tires are components of a vehicle which provide the necessary traction for the vehicle to advance over pavements. Tires are characterized by their stiffness and damping properties. The stiffness properties fall into three categories which are static, nonrolling dynamic and rolling dynamic stiffness. The stiffness characteristics depend much on the inflation pressure. For passenger car tires the rolling dynamic stiffness is approximated 10-15% less than the static stiffness, and 5% and 26% in truck and tractor tires respectively. In addition, velocity of the vehicle affects the *rolling dynamic stiffness such that the value is higher at low velocities [18]. In vehicle simulations, the rolling dynamic stiffness is preferred to the other types. Some of the important properties of tires are given in table 3.4. *Rolling represents rotational motion of the tire
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Tire 11-36(4 ply)
Inflation pressure(kPa) 82.7
110.3
7.5-16(6 ply)
138
193
Load(kN) 6.67 8 9.34 6.67 8 9.34 3.56 4.45 4.89 3.56 4.45 4.89
Static stiffness(kN/m) 357.5 357.5 379.4 386.7 394 175.1 175.1 182.4 218.9 226.2 255.4
Average nonrolling dynamic stiffness(kN/m) 379.4 394 423.2 394 437.8 423.2 218.9 233.5 248.1 233.5 262.7 277.3
Damping coefficient(N/m/s) 2.4 2.6 3.4 2.1 2.5 2.5 0.58 0.66 0.88 0.36 0.66 0.73
Table 3.4 Stiffness and Damping Properties of tires [18]
In studies regarding dynamic response of tires, a linear single degree of freedom model consisting of a spring and damper element is used (Fig 3.10). In this research, the stiffness properties of 7.5-16(6 ply) tire are used in the analysis.
Fig 3.10 linear model of tire
,
, and
stand for mass, stiffness, and damping of the tire.
3.5 VEHICLE MULTIBODY MODEL Multibody models are used to determine responses of vehicles. In such models, stiffness, mass and damping properties of the different components are considered such that the appropriate combination of these gives the mathematical model based on which equations governing the
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
model/system are formulated. The model can vary from the simple and most common two degree of freedom model to a model having higher degree of freedom. Vehicle motion, as discussed in the previous section, is characterized by translations in the longitudinal, lateral, and vertical directions and roll, pitch and yaw motions. The corresponding multibody models for bounce and pitch, and bounce, pitch and roll are shown in fig 3.11a&b.
(a)
(b)
Fig3. 11 Multibody models of a vehicle a) bounce and pitch model b) bounce, pitch and roll model
The four degree of freedom model (fig 3.11a) consists of sprung and unsprung masses of the vehicle. The sprung mass comprises part of the vehicle supported by the suspension and includes the chassis and components supported by it. The unsprung mass, on the other hand, consists of the axle, tire and other components not supported by the suspension. In most vehicles, the ratio of the sprung to unsprung mass is 10:1[1]. The model shown in fig 3.11b is a seven degree of freedom system in which the roll motion is included. The roll motion results from difference in excitation between the left and right wheels. The equations of motion for the four degree of freedom bounce and pitch model are given as:
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
and
stand, respectively, for the sprung and unsprung masses of the vehicle. The stiffness
and damping of the suspension, i.e. stiffness of the spring and shock absorber damping are represented as masses and and and . and correspond to the vertical displacements of the unsprung
are the vertical and angular displacement of the sprung mass.
is mass
moment of inertia for the sprung mass. =0 =0 (3.7a) (3.7b)
=0
(3.7c)
=0
(3.7d)
In this research, the dynamic analysis is carried out for both cases, i.e., bounce and pitch and bounce, pitch and roll cases. In the former case, the same PSD input is applied at two points (nodes) in the finite element model which correspond to the left and right wheels. And, inputs of the same PSD function are applied at points corresponding to the rear left and right wheels. The analysis for the bounce, pitch and roll case is carried out by applying four different PSD inputs at points (nodes) corresponding to the four wheels.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The PSD input to be applied at the points corresponding to the wheels are not exactly equal to the excitation at the tire ground contact point. Since damping occurs due to tire and shock absorber, the excitation at the points will be different. To determine the excitations at these points, quarter car model of the vehicle, discussed in the next section is used. QUARTER CAR MODEL Different types of model are used in vehicle simulations. The models are developed in such a way that the properties of important components of the vehicle are represented so as to make the results of any analysis realistic. One such model used frequently to study the behavior of vehicles under different road roughness conditions, to measure road roughness characteristics and to deal with any vehicle road interaction analysis is the quarter car model (Fig 3.12). The model represents the motion and/or response characteristics at one of wheels of a two-axle vehicle system. The basic model is a two degree of freedom system consisting of the sprung and unsprung masses of the vehicle. In addition, stiffness of the suspension spring, damping of shock absorber, and stiffness of the tire are also included in the model.
Fig 3.12 Quarter car model of the vehicle.
and
correspond to the vertical displacements of the unsprung and sprung mass respectively .
while the vertical displacement of the tire-ground contact point is represented by
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
In the discretization of the multibody model (fig 3.11b), the chassis and the superstructure of a vehicle are modeled as lumped masses at the front, and rear wheels and a coupling mass at the centroid. The sprung and unsprung masses in the quarter car model represent half the lamped mass and axle mass at the wheels. In passenger cars, the coupling mass has less magnitude in comparison with the other two. However, the coupling mass has comparable magnitude in the case of trucks. Thus, the model is more feasible for simulations with regard to passenger cars. Nonetheless, the model still finds significance in simulations associated with trucks [20]. In this research, the quarter car model is used to determine the response of the unsprung mass which is the input for the dynamic analysis part of the finite element analysis. The PSD response is going to be introduced to the FEM model through an element incorporated in the model having stiffness and damping properties which are the same as those of the suspension. In road modeling section, for the two classes of roads used in this analysis, it was indicated that the road roughness which in turn is the vertical displacement, of the tire ground contact point
is defined by the PSD function which is shown below (eqns3.3a-3.4b). Class B For cycles/m ; and
©
for
cycles/m
¨
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Class H For cycles/m ; and
©
for
cycles/m
¨
The power spectral densities of
and
of the unsprung and sprung masses, in each case, are the determination of
determined through the introduction of the transfer function matrix, which is detailed below.
The equations of motion are given as: (3.8) (3.9)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Rewriting (3.10) (3.11) In matrix form,
(3.12)
The term, excitation, zo such that:
refers to the force transmitted to the unsprung mass due to the displacement To determine the transfer function matrix, a harmonic input is assumed for
(3.13) – amplitude of the input excitation The assumed harmonic output will be of the form
(3.14)
,
- amplitudes of the responses of the unsprung and sprung mass.
Substituting these equations in the equation of motion:
(3.15)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
The transfer function matrix relates the output to the input such that:
This gives,
(3.16)
=
=
Where,
In multidegree of freedom system, the spectral density function of the response is given by [21] (3.17) Where, is the Spectral density function matrix of a load or excitation, is the Spectral density function matrix of the responses. And, is the complex conjugate of the transfer function. , by
¨
Denoting the spectral density function of the load for the quarter car model becomes:
, the spectral density function matrix of
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
¨
(3.18)
Thus,
¨
(3.19)
Where,
¨
¨
¨
¨
and,
Similarly, in terms of the spatial frequency term, (3.20) In the above equations, the diagonals of the spectral density functions matrix of the responses, and function,
May 2008
represent the power spectral density functions of , is used as input for the FE analysis, while
and
respectively. The PSD would be the response of
38
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
the superstructure mainly the chassis frame, the cab and the van body structure under the condition that these structures are modeled by an equivalent mass having equivalent inertia properties. Thus, using the above equations, the PSD functions of responses the unsprung masses under the two types of road conditions used in this analysis are shown in figs 3.13 & 3.14. The inputs for the finite element analysis are taken as combination of data from the figures.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.13 PSD function of response of unsprung mass at the front wheels a) road with class B roughness classification b) road with class H roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
a)
b)
Fig 3.14 PSD function of response of unsprung mass at the rear wheels a) road with class B roughness classification b) road with class H roughness classification
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.6 FINITE ELEMENT MODELING Finite element method is used to analyze the response of the vehicle to the static and dynamic loads. Simplified models such as the ones discussed in the previous section could have been used for the analysis purpose. However, models which describe the vehicle more realistically are required. This calls for implementation of more advanced approach and this is the ground for carrying out the analysis based on the finite element model of the vehicle. The development of the finite element model and formulation increases degrees of freedom for the model. The determination of unknown degrees of freedom for the model, in turn, leads to larger number of equations and generation of higher size matrices. The solution to these equations is performed using multiphysics or structural analysis software such as ANSYS which is the one used in this analysis. In this research, the solid model of the vehicle (Fig 3.15), in addition to the analysis, is developed using ANSYS.
Fig 3.15 Solid model of the vehicle May 2008 42
Static and Dynamic Analysis of a Commercial Vehicle with Van Body
3.5.1 Finite Element Formulation The solid model of the vehicle is discretized into finite elements. The cab structure of the vehicle is discretized using shell (SHELL63) elements. Solid three dimensional (SOLID185) elements are used to discretize the chassis and van body structure. The suspension is modeled using spring-damper (COMBIN14) elements. The finite element model (fig 3.16) consists of 83546 eight noded solid elements, 10209 four noded shell elements and 4 spring damper elements.
Fig 3.16 finite element model
In the theory of finite element structural analysis, Hamilton’s principle is used in the dynamic analysis equation formulation. In this case, the Lagrangian, is defined as: (3.21) Where, is kinetic energy, and is the potential energy.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Hamilton’s principle is concerned with minimization of the Lagrangian, such that (3.22) The potential energy of a linear elastic body is given by (3.23) Where, is the strain energy; and is the work potential of surface, body and external loads. For a linear element, the potential energy can be written as { } where, strain vector for the element is displacement vector for the element is the body force vector, and is the surface loads vector { }is the stress vector The strain vector is related to the stress vector by the equation: (3.25) is constitutive matrix, (3.24)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
Thus, (3.26) Displacement vector, ? can be expresses in terms on the nodal displacement vector as: = – displacement transformation matrix; and - nodal displacement vector The strain and displacement vectors are related by the matrix, = is strain-displacement matrix The first term in equation (3.24) represents the strain energy and using equations (3.25) and (3.28), it can be re-written as = = where, is element stiffness matrix. (3.29) such that (3.28) (3.27)
The first term on the right side expression is the kinetic energy term, , i.e. (3.30) Using equation (3.27)
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
= = where, is element mass matrix. (3.31)
The governing equations, as stated earlier, are determined by minimization of the functional, i.e. potential energy and the Lagrangian. (3.32) Equation (3.32) is the governing equation for an element. Substituting the appropriate displacement transformation matrices, strain displacement matrices, and constitutive matrices, the stiffness and mass matrices can be determined. i) Eight noded isoparametric solid element
In this analysis, eight noded three dimensional isoparametric element (fig 3.17) is used in the discretization of the chassis, and van body structure. The element has eight nodes with each having three translational degrees of freedom.
Fig 3.17 eight noded solid element
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
ii)
Four noded shell element
Four noded shell elements (fig 3.18) are used to model the cab structure of the vehicle. The element has four nodes with each having six degrees of freedom.
Fig 3.18 Four noded shell element
iii)
Spring-Damper Element
Spring-Damper elements are used to model the suspension of the vehicle. The longitudinal spring-damper is a two noded tension-compression element with up to three translational degrees of freedom at each node.
Fig 3.19 Spring-Damper Element
The elements used, particularly the first two elements, differ in nodal degrees of freedom. However, this is taken care of in ANSYS by taking zero values for degrees of freedom not in use.
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Static and Dynamic Analysis of a Commercial Vehicle with Van Body
CHAPTER FOUR ANALYSIS AND RESULTS
The analysis carried out using the finite element model consists of static analysis, modal analysis, and response determination under random excitation. The same finite element model is used for all the analyses. The difference among the cases considered lies in the application of loads and boundary conditions. The solution procedure followed for the analysis is shown in the diagram below.
Fig 4.1 Solution procedure diagram
4.1 STATIC ANALYSIS The static analysis is concerned with determination of response of the model/vehicle to steady loads whose value remains unchanged with time. The response of the vehicle is expressed in terms of stresses, strains and displacements. The basic equation governing static equilibrium condition of the system is given in equation 4.1.
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(4.1) Where, LV JOREDO VWLIIQHVV PDWUL[ {? is the nodal displacement vector is the load vector The global stiffness matrix is taken as the summation of element matrices, i.e. (4.2) The load vector, in turn, is taken as the sum of nodal applied load vector and reaction load vector. (4.3) The solution to the equation (4.1) gives nodal translational and rotational displacements. The corresponding stresses and strains are obtained using strain-displacement and strain-stress (constitutive) relations. The deflections between two nodes are determined using assumed shape functions. Loads and Results In the analysis, the situation considered is the standstill condition of the vehicle on a level road loaded to the maximum payload. The other loads considered include weight of the engine, weight of two persons in the cabin, and weight of the vehicle itself. The nodes corresponding to the four wheels (axle-suspension connection), i.e. one of the nodes of the spring damper elements in the finite element are constrained in translation. Figs 4.2 through fig 4.4 show the
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stresses and deflections in the vehicle due to static loads. The units of quantities in the figures and of different quantities in other sections are in SI.
Fig 4.2 Vertical deflection due to static loads
Fig 4.3 Von mises stress due to static loads
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Fig 4.4 *Z-component of stress due to static loads (bending stress in the chassis)
The vertical deflection shown in fig 4.2 includes deflection of the spring and static deflection of the vehicle structures. The vertical deflection is observed to be maximum at the rear of the van body and the chassis. Fig 4.3 and 4.4 show that, of the other components, the chassis gets highly stressed. This is attributed to the fact that all the static loads including the weight of the van body and the cabin, and the engine are taken by the chassis frames and this causes bending loads in the frames which cause higher bending stresses. The bending stresses are particularly of maximum intensity where there is change in the cross section of the chassis near the engine. Nonetheless, the stress level in the frames is far below the yield or ultimate strength of the chassis material. Under static conditions, the safety factor is around eight.
*Z taken along the longitudinal(X) direction of SAE vehicle coordinate system. May 2008 51
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4.2 MODAL ANALYSIS Modal analysis provides results which indicate the natural vibration characteristics of a component or structure. It involves determination of the natural frequencies and modes of vibration. In addition to studying vibration characteristics, the results obtained from modal analysis can be used in other dynamic analyses such as spectrum analysis. The equation of motion for an undamped system is: (4.4) For a linear system, the responses (displacements) will be of harmonic form. Thus, ?? Where, is amplitude of mode shape of natural frequency, (4.5)
Substituting in equation (4.4),
This gives, =0 (4.6)
The solution to equation (4.6) gives Eigen values, the square roots of which are the natural frequencies and Eigen vectors, vectors of amplitudes corresponding to the natural frequencies. Loads and Results The only types of loads considered in the modal analysis of the vehicle are nodal displacement constraints. Thus, four nodes corresponding to the joint of the suspension and axle (wheel) are
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constrained in translation. The first four mode shapes and the associated displacements are depicted in figs 4.5 through 4.8.
a)
b)
Fig 4.5 First mode a) mode shape b) longitudinal displacement
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a)
b)
Fig 4.6 Second mode a) mode shape b) lateral displacement
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a)
b)
Fig 4.7 Third mode a) mode shape (yaw) b) x- displacement
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a)
b)
Fig 4.8 Fourth mode a) mode shape (roll) b) y- displacement
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4.3 RANDOM VIBRATION ANALYSIS Random vibration analysis deals with response of a structure to random dynamic loads. The responses are defined using power spectral density functions. In addition, 1 displacement and stresses also characterize the responses. The implication of 1 displacement and stresses is that, say, for a component, if the 1 stress is specified to have value , then during motion of the vehicle, , and of the time, the stress level is at or below , of the time, between and . of the time between and
Loads and Results Three different cases are considered for the purpose of analysis. In the first case, the vehicle moves with speed of ?? on class B road, and in the second case, motion of the vehicle on ??. The third case is used to simulate roll motion. Roll motion,
class H road with speed of
as defined earlier, results due to difference in excitation between the left and right wheels. Thus, to study this condition, motion of the vehicle with wheels on one side on asphalt pavement and wheels on the other side on rough pavement is considered. This case somehow simulates the situation on narrow roads with rough pedestrian pavements in Addis Ababa though not a very common situation. In fig 3.13 and 3.14 are given, the responses of the unsprung mass determined using the quarter car model. The results of modal analysis and data from these tables are used as input for the analysis. Discrete values of frequencies and PSD values taken from these graphs are used to define base excitations at the nodes of the spring-damper (COMBIN14) elements in the finite element model. Fig 4.9 through 4.11 show the 1 y- component displacements and von mises stresses obtained for the three conditions. The PSD responses of three points, locations of which
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shown in Fig 4.12, and having higher 1 displacement on the cabin, chassis, and van body the locations of which are shown in fig 12 are shown in fig 4.13 and fig 4.14. The band width taken is between 1.3754 and 3.9222cycles/sec which correspond to the fourth and six mode natural frequencies.
a)
b)
Fig 4.9 Response due to class B roughness at 80km/hr a) 1 y-component displacement b) 1 von mises stress May 2008 58
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a)
b)
Fig 4.10 Response due to class H roughness at 30km/hr a) 1 y-component displacement b) 1 von mises stress
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a)
b)
Fig 4.11 Response due to roll motion a) 1 y-component displacement b) 1 von mises stress
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Fig 4.12 Locations of nodes for which PSD responses are determined
a)
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b)
c)
Fig 4.13PSD responses of selected nodes due to class B roughnesss at 80km/hr a) cabin b) chassis c) van body
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a)
b)
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c)
Fig 4.14 PSD responses of selected nodes due to class H roughnesss at 30km/hr a) cabin b) chassis c) van body
Using equation (3.6), the PSD responses shown in the above figures are transformed to displacement versus time plots shown in the figures below. However, in this case, the band width taken is between 1.3754 and 3.9222cycles/sec.
a)
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c)
Fig 4.15 Displacement-time histories of selected nodes at 80km/hr a) cab b) chassis c) van body
c)
Fig 4.16 Displacement-time histories of selected nodes at 30km/hr a) cab b) chassis c) van body May 2008 65
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The 1 stress and displacement responses indicate that, on a pavement with class B roughness, hardly any stresses and displacements will be experienced by the vehicle structures. However, in the case of motion on a rough pavement such as on road with class H roughness, the stress and displacement responses are higher. Further, it is noted that, the cabin structure experiences the maximum stress and displacement. In the case of static analysis, it was observed that, in the part of the chassis frames where there is change in cross section, there occur higher stresses and the same part is seen to be affected by dynamic loads (fig 4.10). The spectral density responses are shown for two cases i.e. motion on road with class B roughness and motion on road with class H roughness. The responses are plotted as function of spatial frequency such that PSD values corresponding to the natural frequencies of different mode shapes are used in the analysis. The implication of the PSD function response plots can be expressed as follows. In the previous chapter, it was discussed that the area under PSD curve stands for the variance of the PSD function and the higher the area means the higher the level of roughness. The plots generated in the case of motion on rough pavement (class H) show that the areas under the PSD curves in this case are higher than those generated in the case of pavement with B pavement roughness. This means, the response in the former case is rougher. In addition, it can also be seen that, the response for the node (point) taken on the cabin structure is rougher than the responses of nodes taken on the van body and chassis. The displacement time histories shown in fig 4.16 are presented to show some of the possible displacement variations with time. Consistent with the PSD responses discussed earlier, the displacement in the case of motion on rough pavement (class H), the displacement variation with
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time is rougher than that of pavement with class B roughness. The magnitudes of displacements in fig 4.16 are lower than that expected taking into account the 1 displacement response
(fig4.10). This is because, the band width selected is between is 1.3754, and 3.9222. The wider the bandwidth, the more consistent the two are going to be. Nonetheless, the responses depicted show magnitudes of the expected order and close to the 1 displacement response.
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CHAPTER FIVE CONCLUSION AND RECOMMENDATIONS
5.1 CONCLUSION In this study, the responses of a commercial vehicle with van body are determined under static and dynamic loads, the results of which are believed to be significant. The analysis includes stress and displacement/deflection responses of the vehicle to the loads. The dynamic analysis is carried out taking into account different road roughness conditions. From the results obtained in the analysis, the following can be concluded: • The chassis, particularly, part of the chassis where there is change in cross-section is affected the most by static loads. • The cabin structure experiences the highest deflections and stresses due to random excitations caused by road roughness. • Part of the chassis which is affected the most by static loads is also affected by dynamic loads, comparable to highly loaded points on the cabin structure. • The van body structure, in any of the cases considered, has comparable displacement/deflection with the chassis. However, the level of stress, in any of the cases, is very low and incomparable to highly stressed points in the cab and chassis. 5.2 RECOMMENDATIONS The analysis performed in this research is based on some assumptions and restrictions. However, complete structural analysis and, thus, understanding of behavior of the vehicle is attained taking
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every possible detail into account. Therefore, the following are recommended for future work as extensions and elaborations of this research. • Fatigue life determination based on dynamic stress histories of critically loaded points or sections of the vehicle structure. • • Further investigation of the cabin structure due to dynamic loads. The effects of wind shield, and door structures on the overall stiffness characteristics of the vehicle structure. • Inclusion of nonlinear and damping characteristics of structures in the dynamic analysis of the vehicle structure.
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REFERENCES
[1]. Gillespie, T. D., “Fundamentals of Vehicle Dynamics”, Society of Automotive Engineers Inc., USA, 1992 [2]. Zhanwang, Y., and Zongyu, C., “Dynamic Response Analysis of Minicar Changan Star 6350”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 http://www.mscsoftware.com/support/library/conf/auto00/p02200.pdf [3]. Kim, H. S., Hwang, Y. S., Yoon, H. S., Dynamic Stress Analysis of a Bus Systems”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000. http://www.mscsoftware.com/support/library/conf/auto00/p03200.pdf [4]. Fermer, M., McInally, G., Sandin, G., “Fatigue Life Analysis of Volvo S80 Bi-fuel”, Proceedings of 1st MSC worldwide automotive conference, MSC, 1999 http://www.mscsoftware.com/support/library/conf/auto99/p00499.pdf [5]. Johansson, I., and Gustavsson, M., “FE-based Vehicle Analysis of Heavy Trucks Part I” Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 www.mscsoftware.com/support/library/conf/auto00/p01200.pdf [6]. Oijer, F., “FE-based Vehicle Analysis of Heavy Trucks Part II”, Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000 www.mscsoftware.com/support/library/conf/auto00/p01100.pdf [7]. Parnell, T., White, C., and Day, S., “Finite Element Simulation of 180o Rollover for Heavy Truck Vehicles”, ASCE Engineering mechanics conference, Baltimore, 1999. http://citeseer.ist.psu.edu/407030.html
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[8]. Chiba, S., Aoyama K., Yanabu, K., Tachibana, H., Matsuda, K., Uchikura, M., “ Fatigue Strength Prediction of Truck Cab by CAE” , Journal of Mitsubishi Motors Technical Review, Vol.15, 2003, pp. 54-60. http://sciencelinks.jp/j-east/article/200310/000020031003A0250701.php [9]. Lee, D. C., Choi, H. S., Han, C. S., “ Design of Automotive Body Structure Using Multicriteria Optimization” , Journal of Structural and Multidisciplinary Optimization, Vol. 32, 2006, pp. 161-167. http://www.springerlink.com/content/y70812k267632r47/ [10]. Jin-yi-min, “ Analysis and Evaluation of Minivan Body Structure” , Proceedings of 2nd MSC worldwide automotive conference, MSC, 2000. http://www.mscsoftware.com/support/library/conf/auto00/p00500.pdf [11]. Lee, J. N., Nikravesh, P. E., “ Steady State Analysis of Multibody Systems with Reference to Vehicle Dynamics” , Journal of Nonlinear Dynamics, Vol. 5, 1994, pp. 181-192. http://www.springerlink.com/content/jwu5842568731t84/ [12]. Asheber Techane, “ Dynamics and Vibration Analysis of Bus Body Structures” , M. Sc. Thesis, Addis Ababa University, Addis Ababa, 2007 [13]. Kim, S. S., Shabana, A. A., and. Haug, E. J., “ Vehicle Dynamic Analysis with Flexible Components” , Iowa State University, 1984. http://www.stormingmedia.us/93/9392/P939200.html
[14]. Lan, F., Chen, J., Lin, J., “ Comparative analysis of bus side structures and light weight optimization” , Journal of Automobile Engineering, Vol. 218, 2004, pp.1067-1075. http://www.ingentaconnect.com/content/pep/jae/2004/00000218/00000010/art00001
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[15]. Kim, H. S., Yim, H. J., Kim, C. B., “ Computational Durability Prediction of Body Structures in Prototype Vehicles” , International Journal of Automotive Technology, Vol. 3, 2002, pp.129-135. http://society.kisti.re.kr/~Eksae/_notes/data/pdf/v3n4_1.pdf [16]. Goncalves, J., Ambrosio, J., “ Optimization of Vehicle Suspension Systems for Improved Comfort of Road Vehicles Using Flexible Multibody Dynamics” , Journal of Nonlinear Dynamics, Vol. 34, 2003, pp.113-131. http://www.springerlink.com/content/w7878702v784r26g/ [17]. Sayers, M. “ Standard Terminology for Vehicle Simulations” , University of Michigan Transport Research Institute” , USA, 1996 [18]. Wong, J. Y., “ Theory of Ground Vehicles” , John Wiley and sons, Inc., New York, 1993 [19]. Awasthi, E., Singh T., Das, A., “ On Pavement Roughness Indices” , Journal of Institution of Engineers (India), Vol. 84, 2004, [20]. Rill, G., “ Vehicle Dynamics” , Fachhochschule Regensburg, Germany, 2007 [21]. Wirsching, P. H, Paez, T. L., Ortiz, K.,“ Random Vibrations” , John Wiley and sons, Inc., New York, 1995
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BIBLIOGRAPHY
[1]. Gibbs, H. G., “ Stress, Vibration and Noise Analysis in Vehicles” , Applied Science Publishers Ltd, London, 1975 [2]. Beermann, H. J., Tidbury, G.,” The Analysis of Commercial Vehicle Structures” , Mechanical Engineering Publications Ltd, London, 1989 [3]. Reimpell, J., Stoll, H., Betzler, W., “ The Automotive Chassis: Engineering Principles” , Reed Elsevier and Professional Publishing Ltd, USA, 2001 [4]. Deshmukh, P. S., “ Rollover and Roof Crush Analysis of Low Floor Mass Transit Bus” , M.Sc. Thesis, Wichita State University, USA, 2006 [5].” ANSYS Reference Guide” , CADD Centre Training Services Private Limited” , India, 2004 [6]. Desai, C. S., Abel, J., F., “ Introduction to the Finite Element Method” , Van Nostrand Reinhold Company, New York, 1972 [7]. Huebner, K. H., Thornton, E., A., Byrom, T., G., “ The Finite Element Method for Engineers” , John Wiley and sons, Inc., USA, 1993 [8]. Krishnamoorthy, C. S.,” Finite Element Analysis Theory and Programming” , Tata McGrawHill Publishing Company Limited, New Delhi [9]. Ambrosio, J., “ Crash Analysis and Dynamical Behavior of Light Road and Rail Vehicles” , Journal of Vehicle System Dynamics, Vol.43, pp.385 - 411
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