GENERAL OSCILLATORY MODEL OF VEHICLES FOR PASSENGER TRANSPORT - Dragan Sekulić, Vlastimir Dedović, Dušan Mladenović

GENERAL OSCILLATORY MODEL OF VEHICLES FOR PASSENGER TRANSPORT - Dragan Sekulić, Vlastimir Dedović, Dušan Mladenović Dragan Sekulić 1, Vlastimir Dedović 2, Dušan Mladenović 3 1,2,3 University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia Abstract: This paper defines a generalized oscillatory model of land transport passenger vehicles. The model is built in the ADAMS/View software, and is intended for simulation studies of the oscillatory behavior of road and rail vehicles. By the use of this model it is possible to carry out analysis of the user s oscillatory comfort (driver and all/each passenger). Different oscillatory comfort zones on the platform of the vehicle can be mapped by considering the comfort parameters of each user. The model can be used also for the analysis of other problems of vertical vehicle dynamics (for example the evaluation of vehicle active safety). The paper presents some of the results of simulations made - the change of acceleration on the seats of three users and changes of the wheel vertical reactions of an intercity bus. Oscillatory excitation of the model is carried out using the recorded signal of roughness of an asphalt-concrete pavement in good condition. Keywords: general oscillatory model of vehicles, vertical vehicle dynamics, simulation, ADAMS/View 1. Introduction The rating of the oscillatory behavior of ground vehicles for passenger transport can be carried out by using experimental and simulation studies. Simulation studies are performed by using oscillatory models and appropriate software packages (Genta, 1997; Pečeliūnas, et al., 2005; Iwincki, 2006; Sekulić and Dedović, 2011). Models are specifically designed and often tied to the vehicle under consideration and have limited application. By generalizing such models a wider range of applications can be achieved. The purpose of this paper is to define and develop a more generalized model that could be used to analyze the oscillatory behavior of road and rail vehicles for transport of passengers. Ground transport means for passenger transport can be described for the purpose as a system of rigid bodies attached by elasto-damping joint elements. In order to achieve a practical solution by modeling, it is necessary to introduce various assumptions and simplifications so that a model could enable an analysis of such aspects of vehicle behavior, significant for the purpose of research. General oscillatory model should include elements (rigid bodies and joints) that have a major impact on the oscillatory behavior of the vehicle and users oscillatory comfort, for example, elastically supported vehicle mass (vehicle body), the seats of users, suspensions, axles and wheels. Some simplified models of road and rail vehicles for passenger transport, presented as a system of interconnected rigid bodies, are shown in Fig. 1 and Fig. 2. Fig. 1. Simplified model of road vehicle as a system of interconnected rigid bodies Fig. 2. Simplified model of rail vehicle as a system of interconnected rigid bodies 1 Corresponding author: d.sekulic@sf.bg.ac.rs 808

Further in this paper, the similarities and differences between individual elements of road and rail passenger transport vehicles have been presented. Comparative analysis provides a basis for the design of the general oscillatory model which can be used for investigation of the oscillatory comfort of each user. Comprehension of user s comfort parameters allows mapping of the oscillatory comfort on the vehicle platform (Sekulić, 2013). General oscillatory model, presented in this paper, is built in the ADAMS/View modulus of the MSC.ADAMS software. 2. Comparative analysis of road and rail vehicle components 2.1. Elastically suspended mass of the vehicle Road and rail vehicles for passenger transport are characterized by having a suspended mass (vehicle body) within which there are seats for passengers, with or without suspension system. Fig. 3(a) and Fig. 3(b) show the elastically suspended vehicle mass with seats, for a bus and for a rail passenger vehicle. Vehicle body itself can be modeled as a rigid or as elastic (Sekulić, 2013; Tianfei, et al., 2010). In this paper, the assumption is made that the vehicle body is rigid. Fig. 4 shows an elastically supported rigid vehicle body with seats, modeled in the ADAMS/View software. Geometric parameters (e.g. length, width and height) and mass parameters (masses and moments of inertia) in the ADAMS/View software working environment can be easily changed and adapted to a particular type of vehicle by using the commands intended for their setting. Fig. 3. Vehicle body with seats a) bus and b) rail passenger vehicle Fig. 4. Elastically suspended mass of the vehicle as a rigid body, equipped with passenger seats 2.2. Passengers and drivers seats It is known that the vibrations of the vehicle are transmitted to user s body through the seat. The seats are usually rigidly mounted, usually to the floor of the vehicle, and the attenuation of vibrations is performed by their elastic cushions only. The driver s seat, unlike the passenger s one, has its own system of suspension that allows an improved comfort. In the ADAMS/View software, user s seats are modeled as rigid bodies connected to the floor of the vehicle body through translational joints. These joints allow a vertical motion only. In order to evaluate the effect of vibration on the comfort of users, the markers can be placed on seats with aim to collect the signals of translational acceleration in the x, y and z-axes direction. Fig. 5 and Fig. 6 show the driver s and the passenger seats of a bus and of a rail passenger vehicle. Fig. 7 shows the model of the seat formed in the ADAMS/View software. 809

Fig. 5. Fig. 6. The seats of a) bus driver and b) bus passengers The seats of a) rail vehicle driver and b) rail vehicle passengers Fig. 7. Model of the seat in the ADAMS/View software 2.3. Axles, wheels and suspension systems Regarding the road passenger transport vehicles, elastic suspension system may be designed with rigid axles or with independent wheels. Road surface roughness (oscillatory excitation) is transmitted to the axles through elastic wheels (tires). Fig. 8 shows an example of the front and rear rigid axle of a bus. Fig. 8. Bus rigid axles a) front and b) rear Tires have a significant impact on the oscillatory behavior of road vehicles. In this respect, their elastic properties in radial direction are particularly important. The railway passenger vehicles have rigid axles (Fig. 9(a)), connected to the bogie by the axle housing (Fig. 9(b)). One bogie usually have two rigid axles (Fig. 9), and a rail passenger vehicle generally has two of them (Fig. 10). Unlike road passenger vehicles, rail vehicles have solid wheels. Track irregularities (oscillatory excitation) are transferred to the axle through rigid wheels. Oscillatory excitation is transmitted from axles to the bogie through the elements of primary suspension. The bogie is connected to vehicle body by secondary suspension system with two air springs (Fig. 9). While designing a general oscillatory model, the essential difference between road and railway vehicles is in the transmission of oscillatory excitation (elastic and rigid wheels) and it has to be taken into account. 810

Fig. 9. Bogie of rail passenger vehicle (a) rigid axle with wheels and (b) the axle housing Fig. 10. The railway passenger vehicle with two bogies The axle housing contains the elements of the primary suspension system - steel springs and hydraulic shock absorbers (Fig. 9(b)). The springs and dampers are connected to the frame of the bogie. When defining a general vehicle oscillatory model, two (or more) axles of the bogie are replaced by a single equivalent axle. The equivalent axle means one axle with the same oscillatory characteristics as the set of axles replaced. Equivalent spring stiffness and equivalent shock absorbers damping can be, according to the scheme shown in Fig. 11, calculated by using expressions (Eq. (1) and Eq. (2)). Fig. 11. Schematic representation of a) elastic suspension of a rail vehicle and b) equivalent axle 811

2 2 ( b ra ) ( b ra ) ce c2 c 2 2 2 b b 2 2 ( b ra ) ( b ra ) be b2 b 2 2 2 b b (1) Road passenger vehicles elastic tires characteristics (stiffness and damping in radial direction) as well as the characteristics of springs (stiffness) and hydraulic shock absorbers (damping) of the primary suspension system of rail passenger vehicle are modeled in the ADAMS/View software by SPRING-DAMPER elements (Fig. 12). (2) Fig. 12. SPRING-DAMPER elements used for modeling the characteristics of radial tires, elastic and damping elements of the vehicle suspension system For the purpose of this analysis, it can be assumed that the tire is characterized by linear radial stiffness (Miege, 2004). Damping force in the tire is small and often neglected. Within rail vehicle, the characteristics of elastic elements (steel springs) and hydraulic shock absorbers of the primary suspension systems are generally nonlinear (Iwincki, 2006). Characteristics of springs and shock absorbers, whether linear or nonlinear, can be defined by analytical expressions using ADAMS/View function Builder tools. SPLINE function enables introduction of springs and shock absorbers characteristics explored through laboratory testing, already written in some of the text files. In the case of springs and dampers linear characteristics, the force in the SPRING-DAMPER element is linearly dependent on the relative displacement and relative velocity of supports of this element (markers I and J, Fig. 13). Fig. 13. SPRING-DAMPER element with markers 812

The force generated by SPRING-DAMPER element is defined by Eq. (3) b( dz F Fp dt) c( z L p ) F p za za z Lp, z L, p (3) where in: z dz/dt b c L p F p - distance between the element supports; - relative velocity of element supports motion; - shock absorber damping coefficient; - spring stiffness; - preloaded length of springs (reference length of spring); - preloaded spring force (reference force in the spring); The dominant oscillatory motions of solid axle of the vehicle with elastic tires are vertical displacement and angular displacement around the longitudinal CG axis of the axle. The dominant oscillatory motions of the rail vehicle bogie are vertical displacement and angular displacements around bogie longitudinal and transverse CG axis. Reduction to the equivalent axle during the development of the general oscillatory model allows ignoring the angular displacement around the transverse bogie CG axis (Fig. 11). In the ADAMS/View software, axle of the road vehicle or rail vehicle bogie is represented as a rigid body with the appropriate mass and moments of inertia (see Fig. 12). Using two joints - Inline Primitive Joint and Parallel axes Primitive Joint, the motion of the axle rigid body within the general oscillatory model is limited to vertical motion and angular motion around its longitudinal CG axis (Fig. 14). Fig. 14. Joints introduced to restrict the motion of rigid bodies (vehicle body and axle/bogie) of the general oscillatory model Modern buses are equipped with an air suspension system. The elastic element of such a system is the air spring support. Fig. 8 shows a typical bus pneumatic suspension system. The body is suspended by the air springs and hydraulic telescopic shock absorbers at the front and rear axles of the bus. Front axle usually has two air springs and four telescopic shock absorbers and the rear axle has four air springs and four telescopic shock absorbers (Fig. 8(a) and Fig. 8(b)). The axles are also connected to the structure by corresponding connection rods to prevent unwanted motions. The body of the vehicle, when considered as a rigid, has six degrees of freedom (DOF). However, due to the type of joints, some motions of the body can be neglected (eg. angular motion around the vertical axis of the vehicle center of gravity (yaw)). The dominant oscillatory motions are the vertical displacement (up and down), the angular motion around the transverse CG axis (pitching) and angular motion around the longitudinal CG axis (rolling) (Dedović, 2004). In order to take into account dominant oscillatory motions already mentioned, the body of the general oscillatory model of vehicle is connected to the fixed part GROUND (road/track surface) through two joints - Inline Primitive Joint and Perpendicular Primitive Joint (Fig. 14). The combination of these two joints allows translation of the body in vertical direction and angular body motion around the longitudinal and transversal CG axis. 813

To introduce the oscillatory excitation in the general oscillatory model (recorded or modeled longitudinal roughness of road or track), four rigid bodies are defined as so-called false masses, connected to the road/track surface (part GROUND) by translatory joints (Fig. 15). The oscillatory excitation can be introduced to translatory joints by using the function CUBSPL (Renguang, 1997). It should be noted that the defined rigid bodies of the oscillatory model, i.e. false masses, in case of a rail vehicle, represent the left and right solid wheels of the equivalent front and rear rigid axle. Fig. 15. False masses and translational joints 3. General oscillatory model Comparative analysis shows that among the elements that influence the oscillatory behavior of road and rail vehicles, in terms of vehicle dynamics, there is a great similarity, which allows defining and building a single general oscillatory model. Fig. 16 shows such a vehicle model built in ADAMS/View software. The values of the vehicle geometric parameters (wheelbase, height, width and length of the body, the users seat position), the vehicle oscillatory parameters (stiffness and damping characteristics of each individual suspension), as well as the values of parameters of masses (seats, body, axles, moments of inertia of the body and axles, etc.) can be easily changed in the software. Fig. 16. General oscillatory model for the analysis of vehicle oscillatory behavior Based on the general oscillatory model, using the appropriate commands for tuning different parameters of the vehicle, it is possible to form oscillatory models for specific buses. An example is a double-decker tourist bus, Fig. 17. Fig. 18 shows the oscillatory model of this bus, allowing the analysis of oscillatory comfort on the passenger seats installed on both vehicle decks. 814

Fig. 17. Fig. 18. Double-decker bus Oscillatory model of double-decker bus With minor modifications, the general model can be improved in order to approach the real vehicle. Paper (Sekulić, 2013) presents the built of an original spatial oscillatory model of intercity bus IK 301 with 65 DOF, with a system of elastic suspension modeled more precisely. This original model has been used as a specific groundwork for determination of the approximately equal oscillatory comfort zones defined and more closely explored in this work. 3.1. Application of the general oscillatory model with the IK 301 bus Fig. 19(a) shows the seat layout in the intercity bus IK 301. The bus is equipped with driver and co-driver seats, as well as 53 passenger seats. Fig. 19(b) shows the general oscillatory model with seat layout that corresponds to the one on the IK 301 bus. All the parameters of the model (geometry, oscillatory and mass parameters) are adjusted according to the relevant parameters of the actual bus IK 301. The values of the parameters are derived from the available literature (Mladenović, 1997; Nijemčević, et al., 2001; Simić, et al., 1979). Fig. 19. Seat layout of a) intercity bus IK 301 and b) IK 301 oscillatory model Elements of the IK 301 oscillatory model (total number of rigid bodies, joints introduced and forces) are listed in table 1. Table 2 lists an overview of the joints introduced between the rigid bodies of the bus IK 301 oscillatory model and DOFs excluded by these joints. 815

3 Translational DOF removed 2 1 0 International Conference on Traffic and Transport Engineering - Belgrade, November 27-28, 2014 Table 1 Elements of the bus IK 301 oscillatory model Overview of the bus oscillatory model Values Rigid bodies 62 Joints between rigid bodies: Inline joint 3 Parallel axis joint 2 Perpendicular joint 1 Translational joint 59 Total number of joints 65 Force elements in model: SPRING-DAMPER elements 63 Motions introduced - CUBSPL function 4 Table 2 Summary of joints of the oscillatory model bus IK 301 and the degrees of freedom which the introduced joints exclude Rotational DOF removed 0 1 2 3 Perpendicular Primitive Joint Paralel Axes Primitive Joint Inline Primitive Joint Translational Joint The expression (4) represents Gruebler s equation used to determine the number of degrees of freedom (DOF) of a mechanical systems composed of multiple interconnected rigid bodies (Mechanical Dynamics, Incorporated, 2001). DOF (number of movable parts*6) According Gruebler s equation, the number of degrees of freedom of the particular IK 301 bus oscillatory model is equal to the: DOF ( 62*6) (3* In_ J *2 2* PA _ J *2 1* Pe _ J *1 59* Tr _ J *5) 4* Tr _ M 62 where in: (joint i constraints i) i j motion j (4) In_J PA_J Pe_J Tr_J Tr_M - Inline Joint; - Parallel Axes Joint; - Perpendicular Joint; - Translational Joint; - Translational Motion; 3.2. The oscillatory excitation of the bus IK 301 model Fig. 20 shows an actually recorded signal of the roughness of a asphalt-concrete pavement in good condition as a function of time. Roughness is registered on the road section of 161 m and at the speed of the of 80 km/h (RoadRuf Software, 1997). Measuring vehicle has recorded roughness on two tracks. 816

Fig. 20. Bus oscillatory excitation - good asphalt-concrete, speed of 80 km/h The signal of road roughness is introduced as the oscillatory excitation to translatory joints of the oscillatory model by using CUBSPL functions (Fig. 15). 3.3. Simulation and some results For the purpose of numerical integration the Gear Stiff (GSTIFF) integrator is selected, with a formulation I3. GSTIFF integrator uses a backwards differentiation formula and Newton-Raphson algorithm for the numerical integration of the differential equation (Mechanical Dynamics, Incorporated, 2000). Simulation time was set to 7 seconds. Acceleration signals were selected every 0.001 second. The simulation is carried out so the bus oscillatory model has been set in equilibrium position by using the command "Find static equilibrium", and then dynamic simulation was performed. In Fig. 21 the accelerations obtained by the simulation for three different locations of the bus occupants have been shown - on the driver seat and on two passenger seats (passenger22 and passenger53), in directions of x, y and z-axis. Occupants suffer dominant acceleration along the z-axis. Four seconds after the beginning of simulation, vertical accelerations have the highest intensity for the entire simulation process. The reason for this is the left and right wheels of the bus pass over the bump whose height is approximately 4 cm (Fig. 20). Passenger in the back of the bus (seat 53) has the highest peak value of the vertical acceleration and it is approximately -6.0 m/s 2. Fig. 21. Changing the acceleration of a) driver b) passenger22 and c) passenger53 817

Fig. 22 shows the change of vertical reactions between road and bus wheels. All wheels during the simulation remain in contact with the ground. Fig. 22. Vertical reactions between road and bus wheels 4. Conclusion On the base of a comparative analysis the paper shows that, in context of vertical dynamics, there is a considerable similarity between road and rail passenger vehicles, with all their main elements: vehicle body, user seats, axles and suspension system. These elements have a dominant influence to the oscillatory behavior of the vehicle. Therefore, it is possible to define a general oscillatory model for simulation study of the oscillatory behavior of the vehicle, as well as its passive and active safety. The authors have designed such a general oscillatory model in ADAMS/View module of the MSC.ADAMS software. The values of vehicle masses parameters, as well as geometric and oscillatory parameters, can be changed by using the corresponding commands in the ADAMS/View software. This enables the adjustment of oscillatory model for the various kinds and types of vehicles. A general oscillatory model has been used in this paper to simulate the dynamic behavior of the vehicle and the parameters that characterize a modern intercity bus were applied. It has been shown that the actually recorded signal of road roughness can be used for the oscillatory excitation of the model, which is significant for more accurate simulation results. The model oscillatory excitation was the record of the actual roughness of a good asphalt-concrete pavement at a speed of 80 km/h. It has been proven that the general model presented allows studying the oscillatory comfort of each user of the vehicle (driver and each passenger). In this paper, as examples, the vertical and horizontal accelerations for three vehicle users were presented (driver, one passenger in the middle and one in the back of the bus), as well as vertical reactions between road and bus wheels. The information on accelerations that the vehicle users were exposed to, obtained by simulation, is an important prerequisite for mapping the comfort of the vehicle platform. Using the data resulting from simulations, the approximately equal oscillatory comfort zones has been defined. By using the presented model and the same methodology, besides accelerations and vertical reactions, one can analyze other relevant oscillatory parameters related to displacements, velocities, accelerations and forces in the system (e.g. deformation of elastic elements of the suspension system, radial deformation of the tire, vertical displacement and acceleration of axles, forces in elastic and damping elements, etc.). Acknowledgements Support for this research was provided by the Ministry of Education, Science and Technological Development of the Republic of Serbia under Grant No. TR36027. This support is gratefully acknowledged. 818

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