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Research Papers

# Iterative Refinement of Accelerations in Real-Time Vehicle Dynamics

[+] Author and Article Information
Yongjun Pan

School of Automotive Engineering,
Chongqing University,
Chongqing 400044, China
e-mail: yongjun.pan@cqu.edu.cn

Javier García de Jalón

Computational Mechanics Group,
INSIA-UPM,
e-mail: jgjalon@etsii.upm.es

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 12, 2017; final manuscript received July 7, 2017; published online October 9, 2017. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 13(1), 011009 (Oct 09, 2017) (7 pages) Paper No: CND-17-1113; doi: 10.1115/1.4037417 History: Received March 12, 2017; Revised July 07, 2017

## Abstract

A number of strategies can be followed for the real-time simulation of multibody systems. The main contributing factor to computational efficiency is usually the algorithm itself (the number of equations and their structure, the number of coordinates, the time integration scheme, etc.). Additional (but equally important) aspects have to do with implementation (linear solvers, sparse matrices, parallel computing, etc.). In this paper, an iterative refinement technique is introduced into a semirecursive multibody formulation. First, the formulation is summarized and its basic features are highlighted. Then, the basic goal is to iteratively solve the fundamental system of equations to obtain the accelerations. The iterative process is applied to compute corrections of the solution in an economic way, terminating as soon as a given precision is reached. We show that, upon implementation of this method, the computation time can be reduced at a very low implementation and accuracy costs. Two vehicles are simulated to prove the numerical benefits, namely a 16-degrees-of-freedom (DOF) sedan vehicle and a 40-degrees-of-freedom semitrailer truck. In short, a simple method to iteratively solve for the accelerations of vehicle systems in an efficient way is presented.

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## Figures

Fig. 1

Geometric description of the RK4 integrator Fig. 2

RK4 procedure with iterative refinement technique Fig. 3

Iterative refinement procedure Fig. 4

Sedan vehicle: multibody model Fig. 5

Semitrailer truck: multibody model Fig. 6

Sedan vehicle: X-, Y-, and Z-translations of the chassis Fig. 7

Semitrailer truck: X-, Y-, and Z-translations of the chassis Fig. 8

Number of iterations during a 1 s simulation ## Errata

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