Abstract
In this study, we attempt to analyze the influence of different excitation factors on the dynamic behavior of a gear transmission system in a braiding machine. In order to observe nonlinear characteristics, a mathematical model is established with a six-degrees-of-freedom gear system for consideration of multiple excitation factors. Iterative results are used to study the nonlinear characteristics of the gear system with respect to contact temperature, varying levels of friction, and disturbance of yarn tension using bifurcation diagrams, maximum Lyapunov exponents, phase diagrams, Poincare maps, and the power spectrum. The numerical results show that excitation factors such as temperature and surface friction, among others, have considerable influence on the nonlinear characteristics of the gear system in a braiding machine, and the model is evaluated to show the key regions of sensitivity. The analysis of associated parameters can be helpful in the design and control of braiding machines.
Highlights
Braiding is a traditional technique used in textile production
Ma et al [1] proposed a mathematical model of tension versus yarn displacement, and Guyader et al [2] analyzed the relationships between the process parameters and the geometry of the braid
Hajrasouliha et al [3] presented a theoretical model for the prediction of braid angle at any point of a mandrel with constant arbitrary cross section by considering the kinematic parameters of a circular braiding machine
Summary
Braiding is a traditional technique used in textile production. In recent years, the emergence of new materials and different types of braiding machines has led to an upsurge in research on braiding. Xiang-Feng [25] established a single-degree-of-freedom torsion-vibration model considering the temperature of the tooth surface, and Zhang [26] investigated the influence of multiple excitation factors operating on the dynamic characteristics of a gear system, including time-varying friction, transmission error, and backlash. Zhang et al [7] researched nonlinear dynamic characteristics of gear transmission systems in braiding machines and considered disturbance of yarn tension and transmission error, but not contact temperature or timevarying friction. We analyze nonlinear dynamic characteristics of a gear transmission system in a braiding machine and consider disturbance of yarn tension, transmission error, time-varying friction, and contact temperature; all of these factors are of potential importance in the development of models to improve braiding quality, and the associated parameters will be helpful in the design and control of braiding machines. Mp and mg are the masses of the gears; me is the effective mass; cpx, cpy, cgx, and cgy are the equivalent dampings of bearing; δpx is the random disturbance of cpx; δpy is the random disturbance of cpy; δgx is the random disturbance of cgx; δgy is the random disturbance of cgy; kpx, kpy, kgx, and kgy are the equivalent stiffnesses of bearings; fpx, fpy, fgx, fgy, and fhare the displacement functions of the bearing; Λ is the sign function; F(t) represents friction at the tooth surface; Fpx, Fpy, Fgx, and Fgy are the forces transmitted from the bearing; Fe1 and Fe2 are the eccentric forces; φp and φgare the angular displacements of the gear; φp(τ) and φg(τ) are the phase angles of eccentric force; ch is the damping coefficient of gear meshing; δch is the random yx oz Fij ωy
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