Application of the Modern Taylor Series Method to a Multi-Torsion Chain

Stability, Convergence, Modern Taylor Series Method, Differential equations, Continuous system modelling

In this paper the adoption 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 behind it 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. The chosen experiment setup is a multitorsional oscillator chain which reproduces typical dynamic behavior of industrial mechanical engineering problems. It's rotatory dynamics are described by linear differential equations. For the test series the system is operated in a closed-loop configuration. An analytic 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 at the experiment. The performance of the Modern Taylor Series Method is demonstrated by comparing its results to simulation results from conventional mixed-step numerical integration methods from the software tool Matlab/Simulink. Furthermore, the improvement in numerical accuracy as well as stability is illustrated.