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A prediction model of the cutting force–induced deformation while considering the removed material impact

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Abstract

Due to the unique low rigidity of thin-walled parts, significant machining deformation may occur in the milling process. A deformation prediction model is presented in this paper while considering the effect of the removed material on the global stiffness matrix. Aiming at reducing the scale of the global stiffness matrix, the super-element method is firstly used and the scale of the stiffness matrix is significantly reduced about 30%. And then, the stiffness matrix of the in-process workpiece (IPW) is directly obtained by eliminating the contribution of the removed nodes in the global stiffness matrix. This method can avoid re-building the geometric model or re-meshing the finite element (FE) model in the machining process. To improve the inverse calculation efficiency of the stiffness matrix, a novel nodes re-sorting method is proposed based on the calculation order of the matrix blocks in LU decomposition and inverse calculation. Furthermore, the optimal stiffness direction is discussed and applying the cutting force in this direction can minimize the machining deformation. The simulation results verified the existence of the optimal stiffness direction. Finally, the simulation and experiment are carried out to validate the accuracy of the proposed model.

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All data generated in this work are included in this paper.

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Funding

This work was supported by grants from the National Natural Science Foundation of China (52005030) and the Aeronautical Science Foundation of China (2019160M5002).

Author information

Authors and Affiliations

  1. School of Mechanical Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China

    Xiaolin Xi, Yonglin Cai, Haitong Wang & Defu Zhao

  2. Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology (Beijing Jiaotong University), Ministry of Education, Beijing, China

    Yonglin Cai & Haitong Wang

Authors
  1. Xiaolin Xi
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  2. Yonglin Cai
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  3. Haitong Wang
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  4. Defu Zhao
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Contributions

Xiaolin Xi proposed the method and conducted the numerical simulation. She also drafted the manuscript. Yonglin Cai and Haitong Wang discussed the prediction model and revised the manuscript. Defu Zhao conducted the experiment and processed data.

Corresponding author

Correspondence to Yonglin Cai.

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The authors declare no competing interests.

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Appendix

Appendix

APDL command adopted in this paper is listed as below.

  1. a

    For the generation and use pass of the super-element

ANTYPE, SUBSTR

! To choose a substructure generation

SEOPT, Filename

! To specify the name of the super-element matrix file

M, MAINDOF

! To define master DOF

D, MAINDOF

! To define constrain nodes

ET,1,MATRIX50

! To define MATRIX50 as the element type

MP

! To define material prosperity of the element

SE, Filename

! To read the super-element matrix

CPINTF

! To connect the pairs of nodes at the interface

  1. b

    For the extraction of the basic information of the elements and nodes

  1. 1.

    External nodes number of the FE model, ExtNd

    NSEL,S,EXT

  2. 2.

    The coordinate of nodes, NdGeom

    *GET,NdGeom,NODE,ND,LOC,X

  3. 3.

    Nodes number of each element, Ele_nodes

    *Do,I,1,num,1

    ! num, number of nodes contained in each element

    *GET,Ele_ndoes(eleth,I),ELEM,eleth,NODE,I

    *ENDDO

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Xi, X., Cai, Y., Wang, H. et al. A prediction model of the cutting force–induced deformation while considering the removed material impact. Int J Adv Manuf Technol 119, 1579–1594 (2022). https://doi.org/10.1007/s00170-021-08291-w

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  • DOI: https://doi.org/10.1007/s00170-021-08291-w

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