Size-dependent responses of micro-end mill based on strain gradient elasticity theory

  • Yicong Du
  • Qinghua SongEmail author
  • Zhanqiang Liu
  • Bing Wang
  • Yi Wan


A significant size effect will occur on the tool part of micro-end mill due to its small diameter, which means the internal structure of the tool part material will affect the mechanical properties of the tool part. In view of this, a comprehensive method considering size effect is proposed in this paper to predict both the static and dynamic behaviors of micro-end mill more accurately. Based on the strain gradient elasticity theory (SGET) and Hamilton’s principle, dynamic model of micro-end mill tool is presented, in which the Timoshenko beam model (TBM) considering the shear deformations and rotary inertia effects is employed. Based on the presented model, the static and dynamic behaviors of micro-end mill is obtained utilizing the finite element method (FEM). The influences of size effect on micro-end mill are investigated in detail by contrasting the static and dynamic behaviors of micro-end mill with different tool diameters and different length-to-diameter ratios, respectively. In order to verify the accuracy and efficiency of the presented method, an improved experiment is performed in this paper.


Micro-end mill Size effect Strain gradient elasticity theory Static deflection Dynamic response 


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Funding information

The authors are grateful to the financial supports of the National Natural Science Foundation of China (no. 51875320), Young Scholars Program of Shandong University (no. 2015WLJH31), the United Fund of Ministry of Education for Equipment Pre-research (no. 6141A02022116), and the Key Research and Development Plan of Shandong Province (no. 2018GGX103007).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

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

Authors and Affiliations

  • Yicong Du
    • 1
  • Qinghua Song
    • 1
    • 2
    Email author
  • Zhanqiang Liu
    • 1
    • 2
  • Bing Wang
    • 1
  • Yi Wan
    • 1
    • 2
  1. 1.Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical EngineeringShandong UniversityJinanPeople’s Republic of China
  2. 2.National Demonstration Center for Experimental Mechanical Engineering EducationShandong UniversityJinanPeople’s Republic of China

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