Mutibody Vehicle Dynamics Analysis Using an Explicit-Implicit Integrator With Subsystem Synthesis Method

Author(s):  
Sung-Soo Kim ◽  
Wan Hee Jeong ◽  
Junyoun Jo ◽  
Ji-Hyeun Wang

This paper proposes an explicit-implicit numerical integration method in order to apply to multibody vehicle dynamics model based on a subsystem synthesis method. The subsystem synthesis method can provide effective means to independently analyze each subsystem with virtual reference body. In the proposed method, the explicit integration is used for solving the equations of motion for a base body, while the implicit integration is utilized for obtaining the solutions of the equations of motion for each subsystem. For the purpose of the application of the implicit formulas easily, a subsystem synthesis method with the Cartesian coordinates is developed. In order to show the application viability and effectiveness of the proposed method, an extensive comparative study has been performed through simulations. Then, the proposed method is compared to conventional implicit integration method applied to an overall system. When simulating the bump run of a multibody vehicle model with compliance effect such as bushing elements, the proposed method achieves about 2 times computational speed-up. Furthermore, the simulation study reveals that the larger the number of the attached subsystems is, the better the computational efficiency of the proposed method is than that of the conventional implicit integration method.

1988 ◽  
Vol 110 (4) ◽  
pp. 382-388
Author(s):  
Liang-Wey Chang ◽  
James F. Hamilton

This paper presents a method for simulating systems with two inertially coupled motions, i.e., a slow motion and a fast motion. The equations of motion are separated into two sets of coupled nonlinear ordinary differential equations. For each time step, the two sets of equations are integrated sequentially rather than simultaneously. Explicit integration methods are used for integrating the slow motion since the stability of the integration is not a problem and the explicit methods are very convenient for nonlinear equations. For the fast motion, the equations are linear and the implicit integrations can be used with guaranteed stability. The size of time step only needs to be chosen to provide accuracy of the solution for the modes that are excited. The interaction between the two types of motion must be treated such that secular terms do not appear due to the sequential integration method. A lumped model of a flexible pendulum will be presented in this paper to illustrate the application of the method. Numerical results for both simultaneous and sequential integration are presented for comparison.


Author(s):  
Sung-Soo Kim ◽  
Kyoungnam Ha ◽  
Dohyun Kim ◽  
Taeoh Tak ◽  
Seung-Eon Shin

Real-time multibody vehicle dynamics software has been developed for virtual handling tests. The software can be utilized for hardware in the loop simulations and consists of three modules such as a graphical vehicle modeling preprocessor, real time dynamics solver, and virtual reality graphic postprocessor for virtual handling tests. In the graphical vehicle modeling preprocessor, vehicle hard point data for a suspension model are automatically converted into multibody vehicle model. In the real time dynamics solver, efficient subsystem synthesis method is used to create multibody equations of motion a subsystem by a subsystem. In the virtual reality graphic postprocessor, virtual proving ground environment has been also developed by using OpenGL for virtual handling tests. This software is written C and can be converted to the S-function as a plant model in the RT-LAB real time environment for HILS application.


Author(s):  
Sung-Soo Kim ◽  
Young-Seok Oh

Abstract A real-time multibody vehicle dynamics model has been developed using a subsystem synthesis method in a PC-based workstation. The subsystem synthesis method produces 6 × 6 matrix form of equations of motion for the chassis and small size each of suspension subsystem equations of motion separately. Simulations such as, bump-run, stop-and-go, and brake-in-turn have been carried out. Solutions have been validated to compare with those from the model with the conventional recursive formulation. CPU times taken for simulations have been also measured to verify the real-time simulation capability of the proposed vehicle model.


2018 ◽  
Vol 11 (8) ◽  
pp. 3391-3407 ◽  
Author(s):  
Zacharias Marinou Nikolaou ◽  
Jyh-Yuan Chen ◽  
Yiannis Proestos ◽  
Jos Lelieveld ◽  
Rolf Sander

Abstract. Chemical mechanism reduction is common practice in combustion research for accelerating numerical simulations; however, there have been limited applications of this practice in atmospheric chemistry. In this study, we employ a powerful reduction method in order to produce a skeletal mechanism of an atmospheric chemistry code that is commonly used in air quality and climate modelling. The skeletal mechanism is developed using input data from a model scenario. Its performance is then evaluated both a priori against the model scenario results and a posteriori by implementing the skeletal mechanism in a chemistry transport model, namely the Weather Research and Forecasting code with Chemistry. Preliminary results, indicate a substantial increase in computational speed-up for both cases, with a minimal loss of accuracy with regards to the simulated spatio-temporal mixing ratio of the target species, which was selected to be ozone.


Author(s):  
Aaron F. Shinn ◽  
S. P. Vanka

A semi-implicit pressure based multigrid algorithm for solving the incompressible Navier-Stokes equations was implemented on a Graphics Processing Unit (GPU) using CUDA (Compute Unified Device Architecture). The multigrid method employed was the Full Approximation Scheme (FAS), which is used for solving nonlinear equations. This algorithm is applied to the 2D driven cavity problem and compared to the CPU version of the code (written in Fortran) to assess computational speed-up.


Author(s):  
J. H. Choi ◽  
A. A. Shabana ◽  
Roger A. Wehage

Abstract In this investigation, a procedure is presented for the numerical solution of tracked vehicle dynamics equations of motion. Tracked vehicles can be represented as two kinematically decoupled subsystems. The first is the chassis subsystem which consists of chassis, rollers, idlers, and sprockets. The second is the track subsystem which consists of track links interconnected by revolute joints. While there is dynamic force coupling between these two subsystems, there is no inertia coupling since the kinematic equations of the two subsystems are not coupled. The objective of the procedure developed in this investigation is to take advantage of the fact that in many applications, the shape of the track does not significantly change even though the track links undergo significant configurations changes. In such cases the nonlinearities propagate along the diagonals of a velocity influence coefficient matrix. This matrix is the only source of nonlinearities in the generalized inertia matrix. A permutation matrix is introduced to minimize the number of generalized inertia matrix LU factor evaluations for the track.


2020 ◽  
Vol 86 (2) ◽  
Author(s):  
Christopher G. Albert ◽  
Sergei V. Kasilov ◽  
Winfried Kernbichler

Accelerated statistical computation of collisionless fusion alpha particle losses in stellarator configurations is presented based on direct guiding-centre orbit tracing. The approach relies on the combination of recently developed symplectic integrators in canonicalized magnetic flux coordinates and early classification into regular and chaotic orbit types. Only chaotic orbits have to be traced up to the end, as their behaviour is unpredictable. An implementation of this technique is provided in the code SIMPLE (symplectic integration methods for particle loss estimation, Albert et al., 2020b, doi:10.5281/zenodo.3666820). Reliable results were obtained for an ensemble of 1000 orbits in a quasi-isodynamic, a quasi-helical and a quasi-axisymmetric configuration. Overall, a computational speed up of approximately one order of magnitude is achieved compared to direct integration via adaptive Runge–Kutta methods. This reduces run times to the range of typical magnetic equilibrium computations and makes direct alpha particle loss computation adequate for use within a stellarator optimization loop.


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