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

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

Článek WoS

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.

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, Taylor series, Numerical integration, Torsion chain

Simulation, Taylor series, Numerical integration, Torsion chain

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

2014

03.04.2013

Elsevier Science

Simulation Modelling Practice and Theory

1569-190X

SIMULATION MODELLING PRACTICE AND THEORY

2013

33

Nizozemsko

89

101

13

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

http://hdl.handle.net/