modelacion de una suspension de autobus

7/23/2019 Modelacion de Una Suspension de Autobus

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EngOpt 20123rdInternational Conference on Engineering Optimization

Rio de Janeiro, Brazil, 01 - 05 July 2012.

Modeling of the suspension of a passenger bus by finite element software.

Carlos A. Reyes Ruiz, Edgar I. Ramrez Daz, Osvaldo Ruiz Cervantes, Rafael Schouwenaars, Armando Ortiz

Prado.

Departamento de manufactura y materiales de la Facultad de Ingeniera, Universidad Nacional Autnoma de Mxico,Circuito exterior, Ciudad Universitaria, Delegacin Coyoacn, C. P. 04510, D. F.

[email protected], [email protected],[email protected],[email protected],[email protected]

1. AbstractThe goal of this work is to calculate loads and moments at the fixing points of a commercial passenger bus suspension using finiteelement software, under different loading conditions. Structural analysis of the bus frame requires the determination of the loadstransmitted from suspension to frame under different operational conditions, to optimize the design and analysis the interactionbetween the suspension and the structural frame of the bus.Starting from dynamic automotive equations, loads associated to each of the three axles are calculated under maximum loadingconditions. The conditions evaluated to obtain axle forces are: suspended weight (static bus at maximum load); acceleration andbreaking, leading to load transference between front and rear axles; cornering, which represents load transfer from one side of the busto the other; cornering and breaking, which implies superposition of two conditions mentioned before.The geometry of the different components was obtained directly from the CAD files for each commercial suspension and axle. Thedegrees of freedom were also identified from the original drawing, either between movement between the components of thesuspension as between suspension and bus body elements. Using the loads obtained with analytical equations, the values to beapplied to each tire were determinated. Most components were modeled by wire elements, to which the mechanical properties ofsteel and different cross-sections were assigned. Additionally, connectors were used to model of dynamic components such as airsprings, shock absorbers and tires, whose behavior was described by characteristic curves.The most critical elements were found to be air springs, which according to dynamic analysis carries an elevated percentage of theload, while for curving conditions the torsion bars become critical components. The models provided the reactions at all fastenersbetween the suspension and the bus, which provides information for the design of the suspension brackets as well as a detailed inputfor the optimization of the structural frame of the bus.

2. Keywords: Suspension analysis, FEM, automotive dynamics.

3. Introduction

3.1 GeneralDue to the high costs associated to the development of new vehicle models, computer simulations of vehicle dynamics become moreand more important in the product development process. While large multinational companies employ integrated design teams andthe latest advances in computational technology and software using the economy of scale, many smaller companies are active in thedesign and construction of passenger buses according to local requirements and market specifications, principally in countries withemerging economies where usage conditions may significantly differ from the design specifications for Europe and the United States.To maintain a complete design team together with computational facilities and specialized software is often not feasible for suchcompanies.Specifically, vehicle dynamics, also called handling simulation, is only a small part of the design process, which means that it isuneconomic for most small companies to own the corresponding licenses for such specialized softwares since they only use them

temporarily. Software used in structural analysis is much more common in the industry today and simulating vehicle dynamics withthis kind of software could result in direct and indirect economic savings and new design possibilities. Due to the high license coststhe companies want to be able to do as many simulations as possible in one software. Abaqus seems to be a good alternative to theexisting specialized software because it is possible to perform the desired handling simulations in a straightforward and flexible way.If software has the possibility to perform a handling simulation, generally it can also perform simpler analyses, such as simulations ofa single front suspension [1].The suspension system of vehicles consists of a set of elements which absorb road surface irregularities while maintaining contactbetween tire and road all the time. Road irregularities are transferred directly to the wheels, which are in direct contact with thesuspension, which in turns connects the wheels to the chassis. Its function is to reduce the dynamic effects of irregularities in orderincrease passenger comfort and reduce dynamic loads on the structural frame of the vehicle. The suspension also increases thestability and control of the vehicle during handling, due to improved contact between the wheels and the surface and a redistributionof forces over all wheels, thereby optimizing the distribution of friction forces during breaking and turning. This enhances thestability and security of the vehicle. Suspension is also responsible for the comfort level and passenger security, decreasing suddenmovements and acceleration effects in a significant way.
mailto:[email protected],%[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected],%[email protected]


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A good suspension system must be elastic in order to absorb ground irregularities and avoiding strong hits. Small irregularities areabsorbed by tires while bigger irregularities are absorbed by the elastic elements of the system. It is important to avoid excessiveoscillations on the suspension, this is achieved by shock absorbers which restrict this oscillating movement generated by elasticelements, preferentially by critically damping the system.There are two fundamental components in the vehicle weight: the first one is suspended weight (the weight of the chassis and

everything loaded on the chassis), the second one is non-suspended weight (tires, brake system, etc.). The suspension system is thelink between both [2].

3.2 Automotive dynamicsStarting from a free body diagram and considering the variables that appear in figure 1, load equations for each axle were obtainedfor different conditions.

Table 1. Nomenclature.

Weight Horizontal forceat auxiliary axle

Front axle weight Mass Drive axle weight Velocity Auxiliary axle weight Curve ratio

Equivalent axle Moment at frontaxle Slope angle Moment at

equivalent axle Acceleration Elastic stiffness of

front axle Gravity Elastic stiffness of

rear axle Horizontal force at front

axle Roll center of

front suspension

Horizontal force atdriving axle

Roll center of rearsuspension

Figure 1. Free body diagram with variables and geometric parameters.


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=

(1)

= + +

(2)

Where

= 0.7223 (3) = 0.2777 (4)In a similar way, equations for horizontal and vertical forces due to the cornering condition can be obtained:

= 2

1.38+0.38

1.38+0.38+1.38 (5)

= 2

1.38++0.38 (6)

= 2

3.6++ (7)

=12

+1+

2 (8)

= 12

+1 +

2 (9)

4. Methodology

4.1 Applied loadsFrom equations presented in 3.2, loads associated to each of the three bus axles are determined for the assumption of a bus atmaximal load.The conditions evaluated are: suspended weight (SW), which is a static bus at maximum load (209 kN); acceleration (AC) andbraking (BR), which determine the load transfer between front and rear axles; cornering, which represents the load transfer from oneside of the bus to the other; cornering and braking, this implies superposition of two conditions mentioned before.For acceleration and braking the values considered involve the slope of the road surface that produces a critical load at the front orrear axles (2), negative slope for front axle (FA) and positive slope for drive (DA) and auxiliary (AA) axles, depending on the case.In the combination of two conditions, curving and braking, the vertical (right (VR) and left (VL)) and horizontal (HORIZ) forces toapply at each side of the three axles are shown in figure 2.

Figure 2. Loads distribution by axle for different conditions evaluated. a) Static weight (SW), acceleration (AC) and, braking (BR);b) cornering and braking.

4.2 ModelingThe geometry of the different part was obtained directly from the CAE files for each commercial suspension axle shown in figure 3,the cross-section of each part and freedom degrees were identified either for part-part movement or part-bus body elements.


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Figure 3. Solid drawing with fastener names for a) front axle (FA), b) drive axle (DA) and, c) auxiliary axle (AA).

Modeling of the parts was done considering wire elements, to which mechanical properties of steel and corresponding cross-sectionswere assigned. Additionally, connectors were used for the modeling of the dynamic components such as air springs, shock absorbersand tires, from loads obtained to each axle characteristic curves behavior were assigned. Figure 4 shows the characteristic curves forfront and rear axles and shock absorbers respectively. Table 2 shows the elastic stiffness constant (k) and damping coefficient (B)

assigned to each tire.

Figure 4. Characteristic curves assigned to a) frontal and rear air spring and, b) shock absorber [3].

Table 2. Elastic stiffness (k) and damping coefficient assigned to tires [4].

Tire values

k [kN/m] 860

B [Ns/m] 4000

The general idea of the process is shown in figure 5, where, from the initial solid assembly of suspension systems, geometry andspace points of interest for all different components in the draft. This information allows drawing and assembly in the software andfinally to obtain a model for each suspension.Despite model simplifications associated to the use of wire elements, the graphic representation allows visualization of the assigned

cross-section to each element for a better understanding. A model of each axle is presented in figure 6.With the model of each axle and all the fasteners developed, the loads were applied to the corresponding tire. Reaction forces andmoments were obtained at all fasteners, air springs (AS); shock absorbers (SA); as well as all superior (SF) and inferior (IF) fastenerelements. For the first set of loading conditions, due to symmetry there is no difference between right and left side, but for curvingthere are important differences and then it is necessary to differentiate between right and left reactions. The code used to identify thefasteners of each axle are shown in figure 3.


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Figure 5. Modeling process.

Figure 6. Axle visualization with cross-section rendered. a) front, b) drive and, c) auxiliary axle respectively.


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5. Results and discussion

The graphics presented in figure 7 show critical cases to each axle. For the front axle this is the braking with a negative slopecondition, which increases loads at this axle; for drive and auxiliary axles loads obtained under an acceleration condition with apositive slope are reported.Graphics a), b) and c) in figure 7 show the reaction force components for the front, drive and auxiliary axles respectively. HTRF

corresponds to horizontal reaction force on a transversal bus direction, that is, from one side to the other; HLRF corresponds tohorizontal reaction force on a longitudinal bus direction, this is, from the front of the bus, to rear, and; VRF corresponds to reactionforce in vertical direction. Given that critical loads are in vertical direction, located at air spring fasteners, the size of these reactionforces is presented in figure 7 d). The largest reaction forces are located at frontal axle for the air springs and equals 35 kNapproximately, related to the fact that this axle has only two elements to support loads, while the rear axles have six air springs todistribute loads. Likewise, for this condition, transverse reaction forces occur of approximately 21-23 kN. Reaction forces in the rearaxles still mainly occur at the fasteners for the air spring, leaving other fasteners with loads which are an order of magnitude smaller.For cornering and braking, reaction forces are not symmetrical and therefore it is required to specify side, either right of left(RAS,LAS, RIF, LIF), where the reaction force appears. As in figure 7 d), magnitude of reaction forces are shown in figure 8. Forthe front axle the largest reaction force still appears at one air spring while superior and inferior fasteners shown a similar response tothose found for previous conditions, where superior fasteners are exposed to larger loads than inferior ones.Drive and auxiliary axles show a similar distribution of reaction forces at the air springs as in the case of the front axle, however forboth rear axles, a considerable increase in reaction force is observed in two of the four fasteners. For the drive axle, the mostimportant increase of reaction forces was at superior fasteners, despite the asymmetry due to curving, the magnitude of the reactionforces is quite similar but, from figure 9 b) it can be observed that direction of both is different. For the auxiliary axle the reactionforce increase is manifested in a similar way, with symmetrical magnitude and different direction, as can be seen in figure 9 c), but inthis case at inferior fasteners. For all three axles, the reaction forces obtained at the shock absorber fasteners remain negligible,however those values cannot be considered small all the time because they are elements whose reaction depends on velocity and willincrease under dynamic conditions.

Figure 7. Reaction forces for a) front axle under conditions of braking with negative slope; b) drive axle under acceleration andpositive slope and; c) auxiliary axle under acceleration condition with positive slope; d) Magnitude of the reaction forces for braking

with negative slope (FA) and acceleration with positive slope (DA and AA).


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Figure 8. Reaction force magnitude by side (R or L) at fasteners under cornering and braking condition.

The reaction forces obtained for the three axles under different conditions evaluated can be seen as shown in figure 9 a), b) and c).Here, the magnitude is represented by an arrow whose color corresponds to the value indicated in the legend. This kind ofinformation is mainly graphic, which is useful in order to generate an idea about how and where the mobile mechanism is working.For the three axles in figure 9, reaction forces are obtained for a cornering and braking condition.Additional information can be obtained from this model, by creating a general idea of the geometric assembly of the elements ofthese suspensions, the colors do not match with the legend scale, as they indicate the maximum level of stress in each of the parts in aseparate color legend which is not shown. Nonetheless, they indicate the critical parts in the assembly which allows to single out thecomponents which require a more refined analysis.

Figure 9. Reaction forces and graphic visualization of additional information (stress distribution) for a) front axle, b) drive axle and,

c) auxiliary axle.


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6. Conclusions

The work shows that a conventional multi-purpose finite element package provides a convenient way to analyze the dynamicbehavior of a vehicle under conditions of normal handling. The integration of CAD packages in the software, together with flexiblemethods to convert parts from engineering drawings into finite element meshes of different degrees of complexity is a clear

advantage and helps to facilitate the analysis. When reductions to fairly simple meshes, such as wireframes, are made, care should behad in the definition of the interactions between the elements, as inadequate descriptions of the degrees of freedom may induce smalldeviations of the true behavior.In the present work, fairly smooth operation conditions such as cornering and braking were analyzed. This resulted in theconclusion that the air springs are the main load carrying component of the suspension. Faster variations, due to irregularities of theroad surface, can be introduced with similar ease and combined with the loading conditions presented here, to analyze the operationconditions of the shock absorbers which are critical under such conditions. The corresponding models are being analyzed at the timeof writing. In the same sense, once the critical loading conditions are determined, transition from a wireframe model toward a full 3-D mesh of the critical components of the suspension can be performed without significant error, to provide detailed designinformation for these parts. Also this aspect of the design process is currently under investigation and will be reported in futurework.As a summary, it was found that the use of a single finite-element package for the multiple tasks of vehicle suspension design greatlysimplifies the complexity of the task and removes limitations which may be imposed when a collection of separate software packagesare used for the different tasks in the design process.

7. Acknowledgments.

The authors wish to thank G. lvarez Lozano, Roberto Cisneros Hernndez, E. Ramos Trejo, I. Cueva Guitrn, R. Cedeo Madera, I.Ayala Vargas, D. Garca Etchegaray and E. Alameda de la Mora for their technical assistance during the execution of this study.Financial support by CONACyT under grant CONACYT-SEP 168041 and by DGAPA under grant PAPIME PE103312 and PAPIITIN116612 is greatly acknowledged.

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