Abstract
The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear mathematical model solved by bond graph, the ranges of excitation frequency were determined, in which the movement of the couplings is chaotic. For three couplings, the 3D distributions of the largest Lyapunov exponent and correlation dimension diagram (CDD) were plotted. The proposed diagram (CDD) illustrates how the geometric structure of the attractor changes when the conditions of excitation change. The classic Poincare cross-section, completed by us with the density of points distribution, significantly enhances information about geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. The areas with the highest densification of the Poincaré cross section are most often located in places where the chaotic attractor is curved.
Highlights
The subject of the model research included in this paper is the tire flexible coupling
The adoption of such model assumptions was aimed at eliminating the influence of dynamic effects of the propulsion system, which are caused by the elastic deformations of the drive system components
Model tests were carried out for various values of the mathematical model parameters in order to demonstrate the complexity of the non-linear dynamics of the coupling
Summary
The subject of the model research included in this paper is the tire flexible coupling. From a theoretical point of view, the optimum mechanical properties of the flexible coupling to the dedicated drive system should be based on the transmitted torque (as in most cases) and mainly, based on the viscoelastic properties of the flexible connector present in the flexible coupling. These properties are identified based on static or dynamic characteristics recorded under experimental conditions [1,2,3,4,5]. Depending on the coupling connector material used, couplings with linear and non-linear mechanical characteristics are distinguished [8, 10, 11]
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