Skip to main content
SpringerLink
Log in

Low-stiffness spring element constraint boundary condition method for machining deformation simulation

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The 3-2-1 constraint principle has been widely applied as the boundary conditions for the finite element method (FEM) to simulate machining deformation of aerospace structure components. However, this principle is inconsistent with the actual contact surface between workpieces and worktables because it provides only three constraint points. These points have rarely been studied in terms of positions and distances. In addition, the applicability of the principle is limited for the workpiece with geometric centers difficult to find or centers without nodes. Therefore, this study proposed a new boundary condition method, low-stiffness spring element constraint method (SECM), drawing on FEM theories and related mechanic theories. With the method proposed this study established the FE model of machining deformation, and then compared the simulation results with both the analytical results and the experimental results of milling and deformation measurements. Good agreement is found between the three results. Finally, this study examined the effect of the three constraint points on simulation of the 3-2-1 principle in terms of point positions and distances. A comparison between SECM and the 3-2-1 principle revealed that SECM is closer to the actual working conditions and more reliable with wider application, which suggests that SECM can replace the 3-2-1 principle as the boundary conditions for the workpiece.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

B :

Geometric matrix

c :

Thickness of each layer

D :

Elastic matrix of the material

E :

Young’s modulus

F ix :

Nodal force

h :

Half width of the element

I :

Inertia moment

j :

Number of layers along the thickness direction

k :

Spring element stiffness

k rs :

Sub-block matrices (r, s = 1, 2, 3, 4)

K :

Total stiffness matrix

K e :

Stiffness matrix of the FE

I :

Half the length of the element

m :

Number of nodes in the X-direction for each row

M :

Equivalent moment per unit width

n :

Number of nodes in the Z-direction for each row

[P] :

Total node load vector

α :

Node displacement vector

[q] :

Total node displacement vector

R :

Radius of the arc ABM1

σ x0i :

Stress function matrix

t :

Thickness of the element

uj, ur :

Displacements of the target and reference position along the X-direction, respectively

wj, wr :

Displacements of the target and the reference position along the Z-direction, respectively

z :

Distance from the point to the neutral plane

z x0i :

Distance from the ith layer to the neutral plane after removing the material

α :

Equal to half of the arc angle corresponding to the arc ABM1

ε :

Strain of the element

μ :

Poisson’s ratio

σ :

Stress of the element

σ j :

Equivalent normal stress at any point on both end faces of the workpiece

σ x0j :

Average stress of each layer

ξ, η :

Dimensionless parameters

References

  1. X. D. Qi, W. Zhang, H. Tian, X. W. Zheng, K. Q. Yu and Y. F. Yang, Research on overall aluminum alloy flange machining deformation, Materials Science Forum, 836 (2016) 436–443.

    Article  Google Scholar 

  2. X. Cerutti and K. Mocellin, Parallel finite element tool to predict distortion induced by initial residual stresses during machining of aeronautical parts, International Journal of Material Forming, 8(1) (2015) 255–268.

    Article  Google Scholar 

  3. X. Cerutti and K. Mocellin, Influence of the machining sequence on the residual stress redistribution and machining quality: analysis and improvement using numerical simulations, The International Journal of Advanced Manufacturing Technology, 83(1–4) (2016) 1–15.

    Google Scholar 

  4. H. J. Gao, Y. D. Zhang, Q. Wu and J. Song, An analytical model for predicting the machining deformation of a plate blank considers biaxial initial residual stresses, The International Journal of Advanced Manufacturing Technology, 93(1–4) (2017) 1–14.

    Google Scholar 

  5. X. M. Huang, J. Sun and J. F. Li, Finite element simulation and experimental investigation on the residual stress-related monolithic component deformation, The International Journal of Advanced Manufacturing Technology, 77(5–8) (2015) 1035–1041.

    Article  Google Scholar 

  6. Y. Wei and X. W. Wang, Computer simulation and experimental study of machining deflection due to original residual stress of aerospace thin-walled parts, The International Journal of Advanced Manufacturing Technology, 33(3) (2007) 260–265.

    Article  MathSciNet  Google Scholar 

  7. Z. J. Wang, W. Y. Chen, Y. D. Zhang, Z. T. Chen and Q. Liu, Study on the machining distortion of thin-walled part caused by redistribution of residual stress, Chinese Journal of Aeronautics, 18(2) (2005) 175–179.

    Article  Google Scholar 

  8. H. Y. Dong and Y. L. Ke, Study on machining deformation of aircraft monolithic component by FEM and experiment, Chinese Journal of Aeronautics, 19(3) (2006) 247–254.

    Article  Google Scholar 

  9. M. Zhan, Q. T. Guo, L. Yue and B. Q. Zhang, Finite element model updating of jointed structure based on modal and strain frequency response function, Journal of Mechanical Science and Technology, 33(10) (2019) 4583–4593.

    Article  Google Scholar 

  10. A. Rasti, M. H. Sadeghi and S. S. Farshi, Finite element prediction of fatigue lifetime for different hole making strategies, Journal of Mechanical Science and Technology, 33(11) (2019) 5227–5233.

    Article  Google Scholar 

  11. Y. M. Pyo, D. S. Kim, S. K. Kim and D. J. Cha, Numerical investigation on combustion instability modeling in a lean pre-mixed gas turbine combustor combining finite element analysis with local flame transfer function, Journal of Mechanical Science and Technology, 33(11) (2019) 5547–5559.

    Article  Google Scholar 

  12. H. J. Gao, Y. D. Zhang, Q. Wu and B. H. Li, Investigation on influences of initial residual stress on thin-walled part machining deformation based on a semi-analytical model, Journal of Materials Processing Technology, 262 (2018) 437–448.

    Article  Google Scholar 

  13. L. B. Liu, J. F. Sun, W. Y. Chen and P. F. Sun, Study on the machining distortion of aluminum alloy parts induced by forging residual stresses, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 231(4) (2015) 618–627.

    Article  Google Scholar 

  14. Z. T. Tang, T. Yu, L. Q. Xu and Z. Q. Liu, Machining deformation prediction for frame components considering multifactor coupling effects, The International Journal of Advanced Manufacturing Technology, 68(1–4) (2013) 187–196.

    Article  Google Scholar 

  15. Y. B. Bi, Q. L. Cheng, H. Y. Dong and Y. L. Ke, Machining distortion prediction of aerospace monolithic components, Journal of Zhejiang University-Science A, 10(5) (2009) 661–668.

    Article  Google Scholar 

  16. Y. Yang, M. Li and K. R. Li, Comparison and analysis of main effect elements of machining distortion for aluminum alloy and titanium alloy aircraft monolithic component, The International Journal of Advanced Manufacturing Technology, 70(9) (2014) 1803–1811.

    Article  Google Scholar 

  17. Q. Wu, D. P. Li and Y. D. Zhang, Detecting milling deformation in 7075 aluminum alloy aeronautical monolithic components using the quasi-symmetric machining method, Metals, 6(4) (2016) 80.

    Article  Google Scholar 

  18. Y. D. Zhang and H. W. Zhang, Finite element simulation of machining deformation for aeronautical monolithic component, Journal of Beijing University of Aeronautics and Astronautics, 35(2) (2009) 188–192 (in Chinese).

    Google Scholar 

  19. Z. Zhang, L. Li, Y. F. Yang, N. He and W. Zhao, Machining distortion minimization for the manufacturing of aeronautical structure, The International Journal of Advanced Manufacturing Technology, 73(9) (2014) 1765–1773.

    Article  Google Scholar 

  20. P. Zeng, Fundamentals of Finite Element Analysis, 1st Ed., Tsinghua University, Beijing, China (2008) (in Chinese).

    Google Scholar 

  21. C. Zienkiewicz, R. L. Taylor and D. Fox, The Finite Element Method for Solid and Structural Mechanics, 7th Ed., Butterworth Heinemann, Oxford, UK (2013).

    MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the referees of this paper for their valuable and very helpful comments.

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: this work was partially supported by Civil Aerospace Technology Pre-research Project, China (B0109), Defense Industrial Technology Development Program, China (JCKY2018601 C002), State Key Laboratory of Virtual Reality Technology Independent Subject, China (BUAA-VR-16ZZ-07), National Science and Technology Major Project, China (2014ZX040 01011), and Beijing Natural Science Foundation, China (3172021).

Author information

Authors and Affiliations

  1. State Key Laboratory of Virtual Reality Technology and Systems, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    He-chuan Song, Yi-du Zhang, Qiong Wu & Han-jun Gao

  2. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    He-chuan Song, Yi-du Zhang, Qiong Wu & Han-jun Gao

Authors
  1. He-chuan Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi-du Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiong Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Han-jun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiong Wu.

Additional information

He-chuan Song is a Ph.D. of the School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, China. His research interests include process simulation of aerospace components, simulation and control of machining deformation of thin-walled components, and simulation research on radial-axial large ring rolling technology and residual stress relief.

Yi-du Zhang is a Professor of the School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, China. He received his Ph.D. in Mechanical Engineering from Beijing University of Aeronautics and Astronautics. His research interests include prediction and control of machining deformation, and dynamics of mechanical system.

Qiong Wu is an Associate Professor of the School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, China. He received his Ph.D. in Mechanical Engineering from Beijing University of Aeronautics and Astronautics. His research interests include material machining deformation, and the manufacturing and analysis of metal matrix composites.

Han-jun Gao is an Assistant Professor of the School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing, China. He received his Ph.D. in Mechanical Engineering from Beijing University of Aeronautics and Astronautics. His research interests include prediction and control of machining deformation, and performance simulation of aerospace complex mechanical products.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, Hc., Zhang, Yd., Wu, Q. et al. Low-stiffness spring element constraint boundary condition method for machining deformation simulation. J Mech Sci Technol 34, 4117–4128 (2020). https://doi.org/10.1007/s12206-020-0905-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0905-x

Keywords

Search

Navigation