{'fraction_non_alphanumeric': 0.01569506726457399, 'fraction_numerical': 0.0, 'mean_word_length': 5.288732394366197, '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}}
Bearing contact of a helical gear pair with involute teeth pinion and modified circular-arc teeth gear

Abstract This paper investigates the contact ellipse of a helical gear set, composed of an involute pinion and a modified circular-arc gear based on curvature analysis. This gear drive exhibits point contact and parabolic transmission error due to the double crowning effect of the gear, i.e. crowning in both profile and longitudinal directions. The principal directions and curvatures of the generating tool surfaces were derived by means of differential geometry and Rodrigues’ equation. The principal directions and curvatures of the pinion and gear surfaces were obtained directly from the generating surfaces. Finally, the determination of the contact ellipses of the mating tooth surfaces was achieved. Numerical examples are also provided to demonstrate the computational results.