Modeling of the suspension of a passenger bus by finite element software.Carlos A. Reyes Ruiz, Edgar I. Ramírez Díaz, Osvaldo Ruiz Cervantes, Rafael Schouwenaars, Armando OrtizPrado.Departamento de manufactura y materiales de la Facultad de Ingeniería, Universidad Nacional Autónoma de México,Circuito exterior, Ciudad Universitaria, Delegación Coyoacán, C. P. 04510, D. F.c.reyesruiz@gmail.com, edgarisaac10@yahoo.com.mx, orcervantes@hotmial.com, raf_schouwenaars@yahoo.com,armandoo@unam.mx1. 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. Introduction3.1 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 software’s since they only use themtemporarily. 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.

Page 2EngOpt 2012 – 3rd International Conference on Engineering OptimizationRio de Janeiro, Brazil, 01 - 05 July 2012.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 andeverything 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.WeightHorizontal forceat auxiliary axleFront axle weightMassDrive axle weight

VelocityAuxiliary axle weightCurve ratioEquivalent axleMoment at frontaxleSlope angleMoment atequivalent axleAccelerationElastic stiffness offront axleGravityElastic stiffness ofrear axleHorizontal force at frontaxleRoll center offront suspensionHorizontal force atdriving axleRoll center of rearsuspensionFigure 1. Free body diagram with variables and geometric parameters.

Page 3EngOpt 2012 – 3rd International Conference on Engineering OptimizationRio de Janeiro, Brazil, 01 - 05 July 2012.=− − −

(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:=21.38 +0.381.38 +0.38 +1.38

(5)=21.38 + +0.38

(6)=23.6 + +

(7)=1 2+ − 1

+2

(8)=1 2+ − 1

+2

(9)4. Methodology4.1 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.

Page 4EngOpt 2012 – 3rd International Conference on Engineering OptimizationRio de Janeiro, Brazil, 01 - 05 July 2012.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 valuesk [kN/m]860B [Ns/m]4000The 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 assignedcross-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.

Page 5EngOpt 2012 – 3rd International Conference on Engineering OptimizationRio de Janeiro, Brazil, 01 - 05 July 2012.Figure 5. Modeling process.Figure 6. Axle visualization with cross-section rendered. a) front, b) drive and, c) auxiliary axle respectively.

Page 6EngOpt 2012 – 3rd International Conference on Engineering OptimizationRio de Janeiro, Brazil, 01 - 05 July 2012.5. Results and discussionThe 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. HTRFcorresponds 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