Force modeling of five-axis microball-end milling

Chi Xu, James Zhu, Shiv G. Kapoor

Research output: Contribution to journalArticlepeer-review


This paper presents a five-axis ball-end milling force model that is specifically tailored to microscale machining. A composite cutting force is generated by combining two force contributions from a shearing/ploughing slip-line (SL) field model and a quasi-static indentation (ID) model. To fully capture the features of microscale five-axis machining, a unique chip thickness algorithm based on the velocity kinematics of a ball-end mill is proposed. This formulation captures intricate tool trajectories as well as readily allows the integration of runout and elastic recovery effects. A workpiece updating algorithm has also been developed to identify tool-workpiece engagement. As a dual purpose, historical elastic recovery is stored locally on the meshed workpiece surface in vector form so that the directionality of elastic recovery is preserved for future time increments. The model has been validated through a comparison with five-axis end mill force data. Simulation results show reasonably accurate replication of end milling cutting forces with minimal experimental data fitting.

Original languageEnglish (US)
Article number031007
JournalJournal of Micro and Nano-Manufacturing
Issue number3
StatePublished - 2015


  • Five-axis
  • Force modeling
  • Indentation
  • Microball-end milling
  • Micromachining
  • Slip-line field model

ASJC Scopus subject areas

  • Mechanics of Materials
  • Process Chemistry and Technology
  • Industrial and Manufacturing Engineering


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