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<p>Cycloid planetary gear reducers are widely used due to their high reduction ratio, large contact ratio, high load capacity, and compact size. However, at speed ratios of 10 to&#xa0;15, their transmission performance declines, particularly when using a&#xa0;tooth number difference (TND) of one. To address this, an optimized tooth profile modification method is proposed to enhance the transmission performance of cycloid planetary gear reducers with a&#xa0;TND of one. Unlike conventional approaches, this study introduces a&#xa0;novel modification approach based on a&#xa0;predetermined transmission error of the mechanism. This method employs a&#xa0;parameterized logarithmic function and incorporates additional tip/root relief. A&#xa0;loaded contact analysis model, considering bearing clearance, is used to evaluate the effects of modification parameters on contact characteristics. Two case studies are conducted: a&#xa0;comparative study assessing conventional and new modification methods, and a&#xa0;demonstration study analyzing the effects of bearing clearance and tip/root relief in an 11-tooth cycloid gear. The results highlight improvements in contact ratio, load distribution, and transmission errors under real working conditions. The analysis results demonstrate that using the proposed approach enhances cycloid gear reducers with 11&#xa0;teeth by increasing the contact ratio and reducing contact stresses, bearing loads, and transmission errors. The impact of bearing clearance remains minimal. It enables the development of cycloid gear reducers with fewer teeth, expanding their applicable speed ratios while maintaining improved transmission performance.</p>

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Design and analysis of cycloid planetary gears with transmission error-based flank modification for smaller gear ratios

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Shyi-Jeng Tsai,
  • Pei-Chen Cho,
  • Yi-Hwa Chen,
  • Ling-Chiao Chang,
  • Qi-You Zhuang

摘要

Cycloid planetary gear reducers are widely used due to their high reduction ratio, large contact ratio, high load capacity, and compact size. However, at speed ratios of 10 to 15, their transmission performance declines, particularly when using a tooth number difference (TND) of one. To address this, an optimized tooth profile modification method is proposed to enhance the transmission performance of cycloid planetary gear reducers with a TND of one. Unlike conventional approaches, this study introduces a novel modification approach based on a predetermined transmission error of the mechanism. This method employs a parameterized logarithmic function and incorporates additional tip/root relief. A loaded contact analysis model, considering bearing clearance, is used to evaluate the effects of modification parameters on contact characteristics. Two case studies are conducted: a comparative study assessing conventional and new modification methods, and a demonstration study analyzing the effects of bearing clearance and tip/root relief in an 11-tooth cycloid gear. The results highlight improvements in contact ratio, load distribution, and transmission errors under real working conditions. The analysis results demonstrate that using the proposed approach enhances cycloid gear reducers with 11 teeth by increasing the contact ratio and reducing contact stresses, bearing loads, and transmission errors. The impact of bearing clearance remains minimal. It enables the development of cycloid gear reducers with fewer teeth, expanding their applicable speed ratios while maintaining improved transmission performance.