An analytical model for cutter-workpiece engagement calculation in ball-end finish milling of doubly curved surfaces

  • Mohammad Ghorbani
  • Mohammad R. MovahhedyEmail author


This paper presents a new analytical model for calculating the cutter-workpiece engagement (CWE) boundaries in the ball-end finish milling process of curved surfaces. To this end, first, a quadratic mathematical representation considering the principal curvatures of the surface is employed to locally describe the workpiece surface around the instantaneous cutting region. This description, then, is utilized to find the intersection curves of the tool rotary and workpiece surfaces in three ball-end milling modes including slotting, first cutting, and following cutting. Through comparison studies, the model predictions are verified by the corresponding results obtained via solid modeling in computer-aided design (CAD) environment. The agreement between the results indicates that the model can accurately calculate the CWE boundaries in the ball-end milling of all inclined, convex, concave, and saddle surfaces. Good performance of the model is also demonstrated by comparing the computation time of the model with that of the z-map method. Finally, parametric studies are performed to reveal the effects of surface curvatures and cutting depth on the CWE region. The results show that the CWE is more affected by the surface curvatures as the cutting depth decreases, especially at the concave and saddle regions of the workpiece surface. The proposed analytical model is capable of calculating the CWE boundaries in both three-axis and five-axis milling processes, and there is no need to neither use any numerical solutions nor update the in-process workpiece geometry during the simulation of the CWE boundaries.


Ball-end finish milling Cutter-workpiece engagement Doubly curved surface Analytical model Principal curvatures 


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Precision Manufacturing Laboratory (PML), Department of Mechanical EngineeringSharif University of TechnologyTehranIran

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