This work presents the development and computational implementation, on a multibody dynamics environment of a constitutive relation to model bushing elements associated with different mechanical joints used in the models of road and rail vehicles. This kind of elements can be found in a wide number of mechanisms, besides the suspension cars, where they play important roles in absorption of vibrations, for instance due to road irregularities, to prevent misalignment of axes and noise reduction from the transmission and to decrease wear of the mechanical joints. In vehicle dynamics, in particular, the ride and handling of a vehicle are conditioned by the existence of these bushing elements. Therefore, suitable bushing models for vehicle multibody models must be accurate and at the same time computationally efficient so that they can be included in the vehicle models for a more reliable dynamic response obtained from the multibody simulations. Bushings are made of a special rubber, used generally in absorption of energy, which present a nonlinear and viscoelastic relationship between the forces and moments and their corresponding displacements and rotations. In the methodology proposed here a finite element model of the bushing is developed in the framework of the FE code ABAQUS to obtain the curves of displacement and rotation versus force and moment for different loading cases. Then the characteristics obtained from the nonlinear finite element analysis are interpolated through carpet plots in order to have a continuous description of the constitutive relations for each bushing. The bushing is modeled in a multibody code as an arrangement of springs that restrain the motion between the bodies connected. The basic ingredients of the multibody model are the same vectors and points relations used to define kinematic constraints in any multibody formulation. In the process, four types of bushing joints are implemented: spherical, revolution, cylindrical and translational. Finally, the methodology is demonstrated through the simulation of two multibody models of a road vehicle, one with perfect kinematic joints, for the suspension subsystems, and the other with bushing joints. The tests conducted to measure and compare the handling and ride of the two MB models are a ride over a road bump and obstacle avoidance maneuver at different speeds.
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- Improved Bushing Models for Vehicle Dynamics
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