{'fraction_non_alphanumeric': 0.025220680958385876, 'fraction_numerical': 0.0025220680958385876, 'mean_word_length': 4.881481481481481, '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}}
Theoretical Approach to Wind Elbow Structure

A mathematical solution for the problem of winding one of the most commonly produced structures in piping, that is elbow fitting, is presented in this article. Fiber stable path is generated over the elbow geometry using either a geodesic or a nongeodesic path. The feed-eye movement of the filament-winding machine is calculated. A numerical example is given for geodesic and nongeodesic windings to clarify the solution. Two criteria are applied: (1) fixed plane for the feed-eye motion, and (2) constant fiber length from the feed-eye to the mandrel surface. In nonaxisymetric structure, there is no one general solution to the problem. Each nonaxisymetric structure has to be studied separately using the same approach presented in this study.