PSI - Issue 37

Rogério Lopes et al. / Procedia Structural Integrity 37 (2022) 81–88 R. F. Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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3. Numerical modelling A deformable structural model for a double-body articulated bus was considered for modal vibration study using FEM analysis. In addition, the suspension material is stiffer when compared with the tractor and trailer metallic framed body. Besides, it was assumed that the parking brake was fully blocking all wheels with regard to the condition of the vehicle. This means that the equivalent stiffness components responsible for tire modelling have their contact with the ground fully restrained. In the Fig. 2 is schematized the model and the definition of trailer and tractor. The FEM simulation was carried out with the commercial software ABAQUS © . The presented model is a simplification of a real vehicle, where the estimated properties of the mass and inertia matrix contribute to proceed with a reliable approach. The simulation relies on a multibody model with more than one module connected by a towing articulation. The main goal is to understand the dynamic behavior of the bus structure and the main consequences resulting from the loading condition. The suspension set is linked to the vehicle body via resilient press-fit bushings mounted in brackets. These hinges are supposed to have conditional free rotations according to their kinematics, will be described later. Owing to this notation, the tire behavior is equivalent to four spring models giving the elastic component of the tire (three linear and one rotational) and four damping elements (three linear and one rotational). In this sense, it was necessary to include a sub-system that enabled the simulation of the joint. This sub-system should be capable of vertical rotation allowed by a hinge similar to the one used in the suspension and transverse rotation. In order to model such a system, it is possible to adopt a kinematic connection type only allows the rotation about an axis with an associated damping coefficient. This type of bus is fitted with an articulation, which generates the connection hinge to rotate in the horizontal plane of approximately ±45° and a rotation range in the vertical plane of approximately ±10° . For the case of rotation in the horizontal plane, this motion has a viscous damping factor of 60000 ( / ) within (±4°) operating angle. The finite element (FE) mesh consists of 4-node reduced integration shell elements, having hourglass control (S4R). These elements are combined with standard 8-node hexahedral linear brick elements with reduced integration with hourglass control (C3D8R). The characteristics of the FE mesh are listed in Table 2Table 2. The present numerical analysis examines the deformation associated to the bus chassis. It must be noted that the chassis was approached by an evenly distributed plate with a uniformly distributed thickness. This is a simplified model to evaluate stress and strain in the chassis structure, where the whole mass is concentrated. The mechanical characteristics are used as defined in Table 1. The von-Mises stress is considered as a key factor in understanding how the chassis behaves when subjected to the passengers’ mass. Fig. 3 presents the von-Mises stress profile on the chassis structure. The rear module relative to the tractor reveals a larger stress, mainly in the area surrounding the wheel hub. The critical zone is identified at the joint which is marked in red, the stress accounted for the maximum value of 187.6 ( ) . Fig. 3. Illustration of the von Mises stresses on the chassis structure, the values are in [MPa]. 0.0 31.3 62.5 93.8 125.1 156.4 187.6 Table 2: FE mesh specifications. Tractor Trailer Suspension(6x) Articulation Type S4R S4R 9634 9867 C3D8R C3D8R Number of elements Number of nodes 14875 15200 1816 2572 962 1588