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<p>Spiral bevel gear milling is characterized by significant fluctuations in cutting forces, which adversely affect surface integrity and tool longevity. Current cutting force models, primarily developed for mechanical cradle-style machine tools, are not applicable to modern fully numerical control (CNC) systems due to inherent kinematic differences. This paper introduces a novel theoretical cutting force model specifically tailored for the form milling of spiral bevel gears on fully CNC platforms. The model establishes an accurate kinematic mapping from conventional mechanical machines to CNC systems and utilizes an energy-based approach to derive analytical force expressions for micro-segment cutting edges, applicable to both inner and outer blades. Systematic finite element simulations validate the model’s predictive capabilities, demonstrating average errors of 23.3% for single-blade and 20.9% for double-blade resultant forces across various cutting conditions. Moreover, the correlation between simulated stress fields and experimental results elucidates the underlying mechanisms of tool wear and gear flank scratching, indicating that stress concentration is a key factor governing abrasive wear and chipping at low speeds. This research provides a validated theoretical foundation for optimizing spiral bevel gear milling processes in full CNC environments, thereby enhancing machining efficiency and tool longevity.</p>

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‌Mathematical modeling and finite element analysis of milling force for spiral bevel gear

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Jiaxue Ji,
  • Rui Xue,
  • Peng Wang,
  • Kan Xing,
  • Jiahao Wu

摘要

Spiral bevel gear milling is characterized by significant fluctuations in cutting forces, which adversely affect surface integrity and tool longevity. Current cutting force models, primarily developed for mechanical cradle-style machine tools, are not applicable to modern fully numerical control (CNC) systems due to inherent kinematic differences. This paper introduces a novel theoretical cutting force model specifically tailored for the form milling of spiral bevel gears on fully CNC platforms. The model establishes an accurate kinematic mapping from conventional mechanical machines to CNC systems and utilizes an energy-based approach to derive analytical force expressions for micro-segment cutting edges, applicable to both inner and outer blades. Systematic finite element simulations validate the model’s predictive capabilities, demonstrating average errors of 23.3% for single-blade and 20.9% for double-blade resultant forces across various cutting conditions. Moreover, the correlation between simulated stress fields and experimental results elucidates the underlying mechanisms of tool wear and gear flank scratching, indicating that stress concentration is a key factor governing abrasive wear and chipping at low speeds. This research provides a validated theoretical foundation for optimizing spiral bevel gear milling processes in full CNC environments, thereby enhancing machining efficiency and tool longevity.