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<p>Accurate modeling of milling forces is essential for optimizing process parameters and implementing&#xa0;real-time force compensation strategies. However, in robotic milling, significant force-induced deformation is produced due to the low structural stiffness of industrial robots, leading to inaccuracies in milling force modeling. To address this issue, a novel milling force model incorporating the compliance of the industrial robot is proposed. Firstly, the joint stiffness model and Cartesian stiffness model of the industrial robot are derived to analyze the end-effector deformation under external loading. Then, a micro-element cutting model is established according to the geometric relationship of the end mill, the instantaneous undeformed chip thickness (IUCT) at the micro-element cutting edge of the end mill is derived and the instantaneous milling forces are obtained through integration. Considering the force-induced deformation of the industrial robot cannot be neglected&#xa0;during&#xa0;IUCT calculation, the deformation obtained by the stiffness model is incorporated into the original milling force model, new formulations&#xa0;for IUCT and milling forces are then constructed. The joint stiffness of the robot was experimentally identified, and milling experiments&#xa0;were conducted&#xa0;under multiple parameter sets&#xa0;to validate&#xa0;the proposed model.&#xa0;Experimental results demonstrate close agreement&#xa0;between predicted and measured milling forces,&#xa0;with a minimum mean force error of 10.17% across three orthogonal directions, which verifies&#xa0;the accuracy and feasibility of the proposed model.</p>

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Modeling of milling forces in end mill considering the force-induced deformation of industrial robot

  • 期刊论文

  • 发表日期：

    2025年10月2日

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  • Hang Li,
  • Xuejian Zhang,
  • Hongqi Fan,
  • Xiaobing Hu,
  • Zheyuan Zhang

摘要

Accurate modeling of milling forces is essential for optimizing process parameters and implementing real-time force compensation strategies. However, in robotic milling, significant force-induced deformation is produced due to the low structural stiffness of industrial robots, leading to inaccuracies in milling force modeling. To address this issue, a novel milling force model incorporating the compliance of the industrial robot is proposed. Firstly, the joint stiffness model and Cartesian stiffness model of the industrial robot are derived to analyze the end-effector deformation under external loading. Then, a micro-element cutting model is established according to the geometric relationship of the end mill, the instantaneous undeformed chip thickness (IUCT) at the micro-element cutting edge of the end mill is derived and the instantaneous milling forces are obtained through integration. Considering the force-induced deformation of the industrial robot cannot be neglected during IUCT calculation, the deformation obtained by the stiffness model is incorporated into the original milling force model, new formulations for IUCT and milling forces are then constructed. The joint stiffness of the robot was experimentally identified, and milling experiments were conducted under multiple parameter sets to validate the proposed model. Experimental results demonstrate close agreement between predicted and measured milling forces, with a minimum mean force error of 10.17% across three orthogonal directions, which verifies the accuracy and feasibility of the proposed model.