Model Order Reduction of a Car Body

The model order reduction (MOR) process in this work is based on a 2012 Toyota Camry model for crash simulation purposes. The model is available for the FE solverLS-Dyna, which is commonly used for transient crash simulations.

For editing and conversion of a LS-Dyna model to the FE solver ANSYS the preprocessor HyperMesh is used in this work. After the FE geometry of the vehicle body is transferred from the crash simulation model to a model suitable for structural flexibility investigation, the MOR process described in section 2.5 can be conducted and is shown in figure 4.13.

FE model

FE matrix Calculation

• Removal of all non-structural components

• RBE definition

• Linear-elastic material definition

• System export from HyperMesh to ANSYS

• Calculation of unbounded system

Boundary mode calc.

• Import to MATLAB

• Interface definition

• Calculation of boundary modes

Inner mode Calculation

• Export of bounded system to ANSYS

• Modal analysis of bounded system in ANSYS

• Import of bounded system to MATLAB

Reduced System

• Calculation of orthonormal, reduced system

• Evaluation of system integrals, sec. 2.3.4

• SID file export Generation

Figure 4.13: Process of SID data generation for a large vehicle model.

This process involves several consecutive steps that usually can be executed within a numerical environment likeMATLAB. The converted FE model consists

of 6.24 million DOF, due to the large-scale FE model the model reduction process is performed partially in MATLAB and ANSYS to allow the process to be executed on a desktop workstation.

Definition of the boundary modes and selection of the inner modes largely influ-ences the system behavior in flexible multibody simulations. The vehicle model requires interface nodes at all suspension attachment points and engine attach-ment points. However, using all interface nodes as boundary nodes would require a large number of elastic DOF and limit the number of inner DOF to be retained in the reduced system. Therefore, to circumvent an unnecessary large system, only the interface nodes for major force application points are used as bound-ary nodes in this process. The suspension domes support the car body weight and act as the force application points of the suspension springs. Hence the suspension domes are chosen as boundary nodes, the remaining interface nodes are not used for the bounded system. Overall the reduced model consists of 46 shape modes, 12 boundary modes and 34 inner modes. The 12 boundary modes consist of 3 translational DOF at each suspension dome. Six rigid body modes are removed after the MOR process and the final model consists of 40 elastic coordinates.

CHAPTER REAL-TIME VEHICLE DYNAMICS

SIMULATION WITH STRUCTURAL FLEXIBILITY

The methods and numerical solvers presented in chapter 2 are tested and vali-dated with several numerical examples. The vehicle model assembled based on the data available from [42] is transferred into a RT-capable vehicle dynamics simulation and validated with a standard driving maneuver using the commer-cial MBS software ADAMS. The procedure pursued to gain the vehicle model is shown in figure 5.1. Besides the extraction of the flexible body it is important to gain geometric and inertial data of all required rigid bodies as well.

Full Vehicle

Flexible Components

Rigid Components

Model Order Reduction

Flexible MBS

Tire/Road Model

Numerical Environment Figure 5.1: Toolchain for flexible vehicle dynamics simulation.

The numerical environment chosen for the model setup is MATLAB/Simulink [65], which provides a broad choice of built-in numerical integrators and the option to generate RT-capable C-code from the generated models. Several target platforms are supported to use the models in RT environments, which may be a field of use for future work.

In section 5.2 the commercial MBS software used for validation is ADAMS [36], a common choice for MBS simulations. The software formulates the EOM in cartesian coordinates and introduces constraints as algebraic equations. The resulting set of DAE can be integrated on index-3, index-2 and index-1 level with built-in integrators. The MF-tire model and several road models including the OpenCRG model are included in this software, which allows an easy comparison of simulation results.

Several models are tested and shown in this chapter. The methods on index-2 and index-1 formulation of constraint equations shown in chapter 2 is realized in two models that only vary in the constraint formulation. The linearly implicit Euler scheme is implemented for the index-2 model and shown in section 5.1.2.

The built-in ODE4 solver of Simulink is used for the index-1 model in sec-tion 5.1.3. To demonstrate the differences between rigid and flexible MBS the simulations are compared with identical simulation models without flexible bod-ies in section 5.3.

Generalized coordinates are suitable for heavily constrained systems and tree-like structures, but not usable for kinematic loops tree-like they occur in suspension setups. In contrast to the suspension kinematics that are usually connected with connection rods, wheel carrier and wheel are constrained by a rotational joint, removing five DOF from the system. By creating a generalized subsystem that combines wheel carrier and wheel to one subsystem with 7 DOF and a conventional DAE formulation for car body and suspension constraints, the sys-tem dimension can be reduced significantly by 24 coordinates and 20 constraint equations. Such a model is shown in section 5.1.4 and compared to the other models.

5.1 Simulation Setup

This section first describes the vehicle model used for numerical examples and model validation in this thesis, afterwards the setup of the numerical index-2 model is explained. The realization of an index-1 formulation is outlined as well and the vehicle model with generalized subsystems is shown.