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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,
Madrid 28031, Spain
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

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

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Fig. 1

Geometric description of the RK4 integrator

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Fig. 2

RK4 procedure with iterative refinement technique

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Fig. 3

Iterative refinement procedure

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Fig. 4

Sedan vehicle: multibody model

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Fig. 5

Semitrailer truck: multibody model

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Fig. 6

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

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Fig. 7

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

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Fig. 8

Number of iterations during a 1 s simulation

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