Publication Details

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

FUCHS Georg, ŠÁTEK Václav, VOPĚNKA Václav, KUNOVSKÝ Jiří and KOZEK Martin. Application of the Modern Taylor Series Method to a multi-torsion chain. Simulation Modelling Practice and Theory, vol. 2013, no. 33, pp. 89-101. ISSN 1569-190X. Available from:
Czech title
Aplkace Moderni metody Taylorovy řady na multi-torsion chain
journal article
Fuchs Georg (TU-Wien)
Šátek Václav, Ing., Ph.D. (DITS FIT BUT)
Vopěnka Václav, Ing. (DITS FIT BUT)
Kunovský Jiří, doc. Ing., CSc. (DITS FIT BUT)
Kozek Martin, prof. (TU-Wien)

Simulation, Taylor series, Numerical integration, Torsion chain


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.

Simulation Modelling Practice and Theory, vol. 2013, no. 33, ISSN 1569-190X
Simulation Modelling Practice and Theory
Elsevier Science
   author = "Georg Fuchs and V\'{a}clav \v{S}\'{a}tek and V\'{a}clav Vop\v{e}nka and Ji\v{r}\'{i} Kunovsk\'{y} and Martin Kozek",
   title = "Application of the Modern Taylor Series Method to a multi-torsion chain",
   pages = "89--101",
   booktitle = "Simulation Modelling Practice and Theory",
   journal = "Simulation Modelling Practice and Theory",
   volume = 2013,
   number = 33,
   year = 2013,
   publisher = "Elsevier Science",
   ISSN = "1569-190X",
   doi = "10.1016/j.simpat.2012.10.002",
   language = "english",
   url = ""
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