Abstract
Aiming at the particularity of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine, the model of gear transmission system in radial braiding machine was simplified. The non-linear dynamic equations of a n-elements closed-loop gear transmission system with symmetrical structure including static transmission error, the random disturbance of meshing damping and backlash were considered. For convenience of calculation n = 3, the equations were solved numerically by using Runge-Kutta. The dynamic transmission error(DTE) with different backlash, dynamic meshing forces with and without the random disturbance of meshing damping, the amplitude of dynamic transmission error at n = 1000 r/min and b = 2.65 × 10−5 m, root mean square(RMS) of DTE and the mean value of DTE of the first pair of gears were analyzed. The simulation results show that different backlash and the random disturbance of meshing damping have a great influence on the dynamic displacement error and meshing force of the gear pair, and RMS and the mean value of DTE changes at different rotational speeds. The results will provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine and have great practical significance for improving the braiding quality.
Highlights
Braiding plays an important role in textile industry
The performance analysis of composite materials, parameters, braiding process, and structure have been studied by scholars.Some works concerning the problem of corrosion in metallic materials treated with Swarm Optimization techniques and the work in which the problem of corrosion in composite materials is treated by means of acoustic techniques [1,2,3]
This paper proposes Runge-Kutta method for solving the dynamic equations of the multiple-stage closed-loop gear transmission system with symmetrical structure for 3D circular braiding machine to help engineers effectively understand the dynamic displacement error and dynamic meshing force under different backlash and the random disturbance of meshing damping, which can provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine, and have great practical significance for improving the braiding quality
Summary
Braiding plays an important role in textile industry. It’s very interesting for scholars to study braiding with the emergence of new materials and different types of braiding machines. Studies on non-linear dynamic feature of a multiple-stage closed-loop gear transmission system for 3D circular braiding machine are scarce. Singh [16] established a non-linear dynamic model of single-stage gear system considering error and backlash in 1990. To the authors’ knowledge, there is no research on non-linear dynamic characteristics of closed-loop gear transmission system for 3D circular braiding machine. This paper proposes Runge-Kutta method for solving the dynamic equations of the multiple-stage closed-loop gear transmission system with symmetrical structure for 3D circular braiding machine to help engineers effectively understand the dynamic displacement error and dynamic meshing force under different backlash and the random disturbance of meshing damping, which can provide a reference for realizing the smoothness of the closed-loop gear transmission system with symmetrical structure for 3D braiding machine, and have great practical significance for improving the braiding quality.
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