A new multibody system approach for tire modeling using ANCF finite elements

Abstract

This paper introduces a new computational multibody system framework for developing accurate tire models using the finite element absolute nodal coordinate formulation (ANCF). Absolute nodal coordinate formulation finite elements are used to create the geometry and perform the finite element/multibody system analysis of the tires. The computational procedure used in this study allows for modeling composite tires and for using a continuum-based air pressure and contact tire force models. The absolute nodal coordinate formulation tire mesh, which allows for high spinning speed, has a constant inertia matrix and zero Coriolis and centrifugal forces. The concept of the absolute nodal coordinate formulation reference node, introduced recently, is used to develop linear connectivity conditions between the tire tread and rim, thereby allowing for imposing these linear conditions at a preprocessing stage. Using this approach, the dependent variables are eliminated at a preprocessing stage before the start of the simulation. The reference node, which is not associated with a particular finite element, is used to define the inertia of the rigid rims. The inertia coefficients associated with the rim reference nodes are first developed in terms of the absolute nodal coordinate formulation position and gradient coordinates. The rigidity of each rim is enforced during the dynamic analysis using six nonlinear algebraic constraint equations that are combined with the dynamic differential equations of motion using the technique of Lagrange multipliers. It is shown in this investigation that the concept of the absolute nodal coordinate formulation reference node can be used to develop a complete vehicle model using one absolute nodal coordinate formulation mesh in which the redundant variables are systematically eliminated at a preprocessing stage, and consequently, the number of differential and algebraic equations that need to be solved is significantly reduced. The use of the new approach proposed in this paper is demonstrated using a vehicle model described by one absolute nodal coordinate formulation mesh.

Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF

“…However, the ANCF beam elements may currently model only simple cross-sectional shapes [27]. Despite that, when practical applications are considered, such as [29], the computation cost of the method should be considered. One may try to parallelize the ANCF method by using existing approaches that are originally developed for multi-rigid-body dynamics [9,20].…”

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

“…This approach might be used to build a beam structures with more than two layers across the height or to create a model with layers in both transversal directions. In addition, the use of multi-layer structures further enables the modelling of complex systems like vehicle tires (Patel et al, 2016). As will be shown later in the paper, the multi-layer beam model may ensure a better convergence when the nearly incompressible materials are used.…”

“…As will be shown later in the paper, the multi-layer beam model may ensure a better convergence when the nearly incompressible materials are used. It is worth noting that the approach for modelling a multi-layer beam used by Patel et al (2016) and introduced in (Liu et al, 2011) is based on subdomains with different material properties created within a single element and cannot be easily adopted for hyperelastic and nonlinear material models.…”

System Identification Algorithm for Computing the Modal Parameters of Linear Mechanical Systems

“…The optimal control problem is particularly challenging in the case of rigid and flexible multibody systems, which represent mechanical systems formed by continuum bodies, kinematic joints, force fields and control actuators [45][46][47][48][49][50]. Another important application of the system identification scientific discipline is the refinement of a finite element model through dynamic testing for the design of vibration control systems based on open-loop and closed-loop control schemes [51][52][53][54]. The methodologies of time domain analysis employed in the general area of applied system identification are of interest for this investigation because the state-space models obtained through these numerical procedures can be readily used for developing effective control actions employing well-established and robust algorithms, such as, for example, the pole placement method, the linear-quadratic regulator technique and the H-infinity method, as well as more advanced nonlinear control approaches [55][56][57][58][59][60][61].…”