Prediction of cutting force of ball-end mill for pencil-cut machining

  • Z. C. WeiEmail author
  • M. L. Guo
  • M. J. Wang
  • S. Q. Li
  • S. X. Liu


There are a number of concave circular blending surfaces with minor curvature radius in the corner of curved surface part, like complex mold cavity. Pencil-cut machining has shorter path and completer material remove than other strategies of clean-up machining which make it high efficiency, high precision, and high utilization rate of equipment. In this paper, contact between cutter and concave crescent cylinder (CCC) including cutter workpiece engagement (CWE) and in-cut cutter edge (ICCE) is studied based on an analytic method, and a prediction model of the cutting force for pencil-cut machining with the ball-end mill is established. The cutter, the CCC, and the feed direction for pencil-cut machining are parametrically defined. In cutter contact normal coordinate system, the analytic expressions of tool geometry, CCC, and the cutter sweep surface of the cutter are derived, and then the CWE is obtained by the intersection of the space surfaces, which the CWE in the tool coordinate is realized by the three-dimensional rotation transformation. The cutter edge curve is discreted into a series of infinitesimal element, based on the criteria of the cutter edge element in the CWE, an analytic algorithm to calculate the ICCE is proposed, and the precision of the boundary points can be further improved by the dichotomy. Combining ICCE with instantaneous chip thickness considering cutter run-out and micro-element milling force theories of ball-end mill, the prediction model of cutting force for pencil-cut machining of CCC with ball-end mill is established. A series of pencil-cut machining experiments and simulations were arranged. The performance of pulling milling is better than that of pushing milling. The CWE and ICCE obtained by the analytical method agree well with that of experiment and solid modeling simulation. The cutting force experiments verify the correctness of the milling force predictive model.


Pencil-cut machining Cutting force prediction Cutter workpiece engagement (CWE) In-cut cutter edge (ICCE) Ball-end mill Cutter run-out 


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Funding information

This research is supported by the Natural Science Foundation of Liaoning No. 201602174 and the Fundamental Research Funds for the Central Universities No. DUT17GF213.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Z. C. Wei
    • 1
    Email author
  • M. L. Guo
    • 1
  • M. J. Wang
    • 1
  • S. Q. Li
    • 1
  • S. X. Liu
    • 1
  1. 1.Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of EducationDalian University of TechnologyDalianPeople’s Republic of China

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