PSI - Issue 37

Rogério Lopes et al. / Procedia Structural Integrity 37 (2022) 73–80 R. F. Lopes et al./ Structural Integrity Procedia 00 (2019) 000 – 000 3 as a result of longitudinal axis ( , for example), lateral (side “ drift ”) over , and vertical (up-down) over ; three axes rotations; “ Roll ” (over ), due to curve lateral forces, “dive/rise” (over ), due to road irregularities, and “ yaw ” (over ) due to steering maneuvers, with oscillation eventually aggravated by running with underinflated tires. The on-run vehicle/road interaction is performed by the vehicle suspension, a system consisting of an assembled set of control arms, trailing bars, springs and dampers. Regarding the vehicle body, this is a highly complex structure. In this study, the 3D stiffness parameters of the entire vehicle body are globalized which focusing only its effect on the mechanical links with the road, that are the axes and tires at the road contact points. To evaluate the stiffness matrix factors, a procedure related with the prescription of unitary displacements at the su spension system DOF’s level is described next with complement of details depicted in Fig. 3. In order to achieve the stiffness factor for the global body structure of the vehicle, it is required to evaluate forces at supports - wheel hubs (reactions to body via suspension arms and axes) and to obtain displacements at vehicle mid length and relative rotations between axes. Regarding the equivalent vehicle mass and dynamical inertia parameters, these factors are assessed considering the vehicle body as a solid owning an equivalent density calculated by the global mass/volume (as a solid) ratio. Further calculations of low order natural frequencies can be done through these simplifications with the uniform distributed load (passengers and structural members). Nevertheless, the considered mathematical developments are extensively described in (Lopes et al. 2021). = ℎ ℎ = 384 5 4 (1) Considering a set of three axes involving the tire geometry as shown in Fig. 2.a), there are three leading forces at the tire/ground contact surface: Radial stiffness ( − ) : = ̅̅̅̅̅ × (2) Longitudinal stiffness ( − ) = lateral or shear stiffness ( − ): = 0.5 ̅ ̅̅ ̅ × (3) a) In-plane oscillation In the Yaw rotation, an important detail must be taken into account when vehicle is parked, where the handbrake can be applied or not. If the first option holds, then due to constraints at each wheel, there are three equivalent { , , }8 spring stiffness. Otherwise, if the wheels keep released (handbrake not applied), Yaw rotation only depends of the tire shear (or lateral) stiffness. The motion and the frequency value of the vibration modes are presented in Fig. 2.b) and Eq. (4), respectively. 4 = 0.984 (4)

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a)

b)

Fig. 2. a) Simplified model of the wheel and its acting forces and b) an example of yaw motion.