Publication detail

Application of the Modern Taylor Series Method to a multi-torsion chain

FUCHS, G. ŠÁTEK, V. VOPĚNKA, V. KUNOVSKÝ, J. KOZEK, M.

Original Title

Application of the Modern Taylor Series Method to a multi-torsion chain

Type

journal article in Web of Science

Language

English

Original Abstract

In this paper the application of a novel high accuracy numerical integration method is presented for a practical mechanical engineering application. It is based on the direct use of the Taylor series. The main idea is a dynamic automatic order setting, i.e. using as many Taylor series terms for computing as needed to achieve the required accuracy. Previous results have already proved that this numerical solver is both very accurate and fast. In this paper the performance is validated for a real engineering assembly and compared to a Jacobian power series method. The chosen experiment setup is a multi-torsional oscillator chain which reproduces typical dynamic behavior of industrial mechanical engineering problems. Its rotatory dynamics are described by linear differential equations. For the test series the system is operated in a closed-loop configuration. A reference solution of the linear differential equations of the closed-loop system for the output variable is obtained with the mathematical software tool Maple and validated by comparison to measurements from the experiment. The performance of the Modern Taylor Series Method is demonstrated by comparison to standard fixed-step numerical integration methods from the software tool Matlab/Simulink and to the Jacobian power series approximation. Furthermore, the improvement in numerical accuracy as well as stability is illustrated and CPU-times for the different methods are given.

Keywords

Simulation, Taylor series, Numerical integration, Torsion chain

Authors

FUCHS, G.; ŠÁTEK, V.; VOPĚNKA, V.; KUNOVSKÝ, J.; KOZEK, M.

RIV year

2013

Released

3. 4. 2013

Publisher

Elsevier Science

ISBN

1569-190X

Periodical

SIMULATION MODELLING PRACTICE AND THEORY

Year of study

2013

Number

33

State

Kingdom of the Netherlands

Pages from

89

Pages to

101

Pages count

13

URL

http://www.sciencedirect.com/science/article/pii/S1569190X12001359

BibTex

@article{BUT103482,
  author="Georg {Fuchs} and Václav {Šátek} and Václav {Vopěnka} and Jiří {Kunovský} and Martin {Kozek}",
  title="Application of the Modern Taylor Series Method to a multi-torsion chain",
  journal="SIMULATION MODELLING PRACTICE AND THEORY",
  year="2013",
  volume="2013",
  number="33",
  pages="89--101",
  doi="10.1016/j.simpat.2012.10.002",
  issn="1569-190X",
  url="http://www.sciencedirect.com/science/article/pii/S1569190X12001359"
}