{'fraction_non_alphanumeric': 0.023837902264600714, 'fraction_numerical': 0.0, 'mean_word_length': 5.288389513108614, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A dynamic modeling approach for the winding spindle during start-up with a coupled flexible support system

A polyester filament winding spindle is the most complex winding rotor system, due to its high speed, heavy load, and frequency-dependent parameters; furthermore, the spindle's rotating speed constantly changes and it is continually crossing the critical speed points. This paper presents an approach to establish the finite element model of the winding spindle to predict its dynamic behavior characteristics during start-up. Firstly, three finite element models of the discrete single component were developed based on the Timoshenko beam theory. The bending, transverse shear effect, and gyroscopic moment were considered in these models. The flexible supporting system, which consists of a deep groove ball bearing and several rubber O-rings, is simplified by a nonlinear spring and damper. Its frequency-dependent dynamic supporting parameters are identified by experiment. Secondly, a fully dynamic model of the polyester winding spindle system, which consists of the cantilever supporting arm, shaft, and sleeve, as well as the flexible and rigid coupling elements, was established. Thirdly, the Newmark method was used to develop a program for solving the dynamic equations of the spindle system in MATLAB®. Based on the model of the spindle system and the computation program, the effects of the supporting stiffness, damping, and start-up time on the spindle's unbalanced response were investigated. The results indicate that the model of the spindle system presented in this paper is suitable for the prediction of the dynamic performance during its start-up.