Detail publikace

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

Originální název

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

Anglický název

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

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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",
  annote="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.",
  address="Elsevier Science",
  booktitle="Simulation Modelling Practice and Theory",
  chapter="103482",
  doi="10.1016/j.simpat.2012.10.002",
  edition="NEUVEDEN",
  howpublished="print",
  institution="Elsevier Science",
  number="33",
  volume="2013",
  year="2013",
  month="april",
  pages="89--101",
  publisher="Elsevier Science",
  type="journal article in Web of Science"
}