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<p>This study develops a cutting force prediction model for variable-pitch ball-nose cutters used in multi-axis milling. It starts by defining the five-axis machining coordinate system and creating a geometric model of the cutter. Then, using micro-element cutting force theory, the study establishes a cutting force model specific to ball-nose milling.To simplify the complexity from dynamic tool orientations, the research proposes a practical method. It projects the engagement region onto a plane that is perpendicular to the tool axis. This approach accurately defines the boundary curve. After calculating the engagement region with a fixed tool axis, a rotation transformation matrix is applied. This helps determine the engagement domain in the tool coordinate system for any tool orientation.The study also finds the instantaneous entry and exit angles for each element. It does this by identifying intersection points between the infinitesimal projection circle and the engagement domain boundary, along with the lines connecting their centers.Lastly, the research introduces a method for identifying milling force coefficients based on the average milling force per tooth cycle. Through systematic milling experiments, these coefficients are calibrated. The results indicate that the predicted milling forces closely match the measured ones, with a maximum root mean square error of 6.74%. This validates the model’s effectiveness for variable-pitch ball-nose cutters.</p>

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Modeling and experimental study of cutting forces of a variable pitch ball-end cutter in five-axis milling

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年1月28日

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  • Weijun Tian,
  • Jinhua Zhou,
  • Junxue Ren,
  • Yizhuo Wang,
  • Zerui Bai

摘要

This study develops a cutting force prediction model for variable-pitch ball-nose cutters used in multi-axis milling. It starts by defining the five-axis machining coordinate system and creating a geometric model of the cutter. Then, using micro-element cutting force theory, the study establishes a cutting force model specific to ball-nose milling.To simplify the complexity from dynamic tool orientations, the research proposes a practical method. It projects the engagement region onto a plane that is perpendicular to the tool axis. This approach accurately defines the boundary curve. After calculating the engagement region with a fixed tool axis, a rotation transformation matrix is applied. This helps determine the engagement domain in the tool coordinate system for any tool orientation.The study also finds the instantaneous entry and exit angles for each element. It does this by identifying intersection points between the infinitesimal projection circle and the engagement domain boundary, along with the lines connecting their centers.Lastly, the research introduces a method for identifying milling force coefficients based on the average milling force per tooth cycle. Through systematic milling experiments, these coefficients are calibrated. The results indicate that the predicted milling forces closely match the measured ones, with a maximum root mean square error of 6.74%. This validates the model’s effectiveness for variable-pitch ball-nose cutters.