Journal of South China University of Technology(Natural Science Edition) ›› 2026, Vol. 54 ›› Issue (1): 134-141.doi: 10.12141/j.issn.1000-565X.250053

• Mechanical Engineering • Previous Articles     Next Articles

Modeling of Milling Force for Ball End Milling Cutter Based on Oblique Cutting

JIN Qichao1  LI Jun1  YE Ziyin1  YU Hongyu1  GUO Lei3   

  1. 1. Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an 710064, Shaanxi, China；

    2. AECC Xi’an Aero-engine Ltd., Xi’an Shaanxi 710021, Shaanxi, China；

    3. National Key Laboratory of Precision Micro/Nano Manufacturing Technology, Xi’an Jiaotong University, Xi’an Shaanxi 710054, Shaanxi, China

  • Online:2026-01-25 Published:2025-06-17

Abstract: In order to address the challenges of complex three-dimensional force distributions under varying cutting edge angles and significant dynamic variations in undeformed chip thickness in ball-end milling, this study proposed a milling force prediction model integrating oblique cutting theory and dynamic kinematic simulation for high-precision cutting force analysis in multi-axis machining. First, an oblique cutting mechanical framework was established based on the equivalent plane method. The three-dimensional cutting problem was transformed into a two-dimensional plane through coordinate transformation, and a composite mechanical model incorporating shear and ploughing effects was derived, specifically characterizing the regulatory mechanisms of cutting edge angles on material flow direction and stress distribution. Subsequently, the geometric features of the ball-end cutter’s cutting edges were precisely reconstructed. A coupled tool-workpiece kinematic model was developed to solve the differential equations governing tooth motion trajectories, and dynamic machining surface morphology simulation was implemented via an improved Z-MAP algorithm to extract time-varying undeformed chip thickness distributions. Furthermore, a multi-scale mechanical mapping strategy was proposed, where the tool was discretized into micro-element cutting edges. The tangential, radial, and axial force components of each element were iteratively integrated based on the oblique cutting analytical model, ultimately synthesizing three-dimensional milling force time-domain signals. Experimental results demonstrated that the maximum prediction errors for axial , feed-direction , and cutting-width-direction  milling forces were 18.3%, 10.8%, and 22.4%, respectively, validating the model’s applicability in force analysis for complex geometric tools. By integrating kinematic simulation and microscopic mechanical analysis, this study provided theoretical support for optimizing process parameters and enhancing machining stability in ball-end milling operations.

Key words: oblique cutting, ball-end Mill, TANH constitutive model, tool-workpiece contact area, milling force model