Springback Analysis of the Stiffened Panel Milling from the Bent Plate

  • Chun-Guo LiuEmail author
  • Tao Yue
  • Xiao-Tong Yu
Regular Paper


An analytical method considering the redistribution of residual stress in the bent plate is proposed to predict the springback of the stiffened panel when milling the panel layer by layer. Two types of stiffened panel, namely, a panel with crosswise stiffeners and a panel with lengthwise stiffeners, were selected as examples and were analyzed during the removal of each layer. Moreover, a finite-element simulation of the milling process was conducted to make comparisons with the analytical results, which demonstrates similar stress distribution and springback values. The maximum stress variation and springback value appeared when the milling depth reached the initial neutral surface. When the plate thickness decreased, the errors between analytical results and FEM results increased, and the lengthwise-stiffened panel was less affected by errors than the crosswise-stiffened panel because of a larger moment of inertia. The effects of different milling thicknesses per layer, initial plate thickness, and bending radius were also analyzed. Moreover, the milling experiment was performed to make verification. The results suggest that the analytical method can predict the springback of the stiffened panel effectively. The proposed method can also be applied to other similar forming conditions.


Residual stress Springback Milling Bent plate FE simulation 

List of symbols


Half of the plate thickness

\(\Delta t\)

The thickness of removed layer

t1, t2

The thickness of the stiffer and the plate


The height of the stiffener


The centroid of the cross section


The elastic modulus


The stress in x-direction


The principal stress


The initial yield stress

\(\sigma_{\text{x}}^{\prime }\)

The residual stress in the lengthwise stiffeners


The strain


The strain caused by milling after springback


Hardening index


Hardening coefficient


Poisson ratio


The width of the plate


The curvature of the plate


The times of milling


Distance between initial yield surface and the neutral surface


The bending moment


The bending moment in the bending process


The bending moment when the surface of the plate starts to yield

\(\varPhi (\kappa )\)

The function of the bending moment and the curvature


The curvature after springback

\(\upalpha,\upalpha^{\prime }\)

The bending angle of the plate before and after springback,

\(y,y^{\prime }\)

The y coordinate before and after springback

\(\Delta L,\Delta L^{\prime }\)

The elongation of the y-th layer before and after springback

\(r,r^{\prime }\)

The radius of the neutral surface before and after springback


The moment of inertia

I1, I2

The moment of inertia of the stiffer and the plates


The moment of inertia of the plate after milling


The springback ratio


The ratio of ys and t


The residual stress after springback


The stress after the first layer is milled


The stress after the n-th layer is milled


The residual stress in the plate of the stiffened panels after springback


The stress released after milling


The bending moment released after millng

Fmn, Mmn

The stress and the bending moment caused by the removal of the n-th layer

Ffin, Mfin

The total stress and bending moment caused by milling process

k1, k2

The coefficients of the stress increment increment for the upper and lower sides

k1n, k2n

The coefficients of linear stress increments after the n-th layer is milled



  1. 1.
    Yan, Y. (2009). Forming modeling and path optimization technology forpress bending of aluminum alloy high-stiffener integral panel (pp. 60–66). Beijing: School of Mechanical Engineering and Automation, Beihang University.Google Scholar
  2. 2.
    Yan, Y., Wang, H. B., & Wan, M. (2011). Prediction of stiffener buckling in press bend forming of integral panels. Journal of Plasticity Engineering, 21(11), 2459–2465.Google Scholar
  3. 3.
    Li, B. Y. (2015). Research on machining deformation technologies for wallboard on cutting force and residual stress (pp. 15–16). Harbin: Harbin Institute of Technology.Google Scholar
  4. 4.
    Dong, Y. N. (2016). Prediction and control of fracture in multi-point press forming of aluminum alloy integral panel (pp. 8–9). Jilin: Jilin University.Google Scholar
  5. 5.
    Meng, L. H., Atli, M., & He, N. (2017). Measurement of equivalent residual stresses generated by milling and corresponding deformation prediction. Precision Engineering, 50, 160–170.CrossRefGoogle Scholar
  6. 6.
    Krottenthaler, M., Schmid, C., & Schaufler, J. (2013). A simple method for residual stress measurements in thin films by means of focused ion beam milling and digital image correlation. Surface & Coatings Technology, 215, 247–252.CrossRefGoogle Scholar
  7. 7.
    Sebastiani, M., Eberl, C., & Bemporad, E. (2014). Focused ion beam four-slot milling for Poisson’s ratio and residual stress evaluation at the micron scale. Surface & Coatings Technology, 251, 51–61.CrossRefGoogle Scholar
  8. 8.
    Vilčeka, I., Řehořa, J., & Caroua, D. (2017). Residual stresses evaluation in precision milling of hardened steel based on the deflection-electrochemical etching technique. Robotics and Computer-Integrated Manufacturing, 47, 112–116.CrossRefGoogle Scholar
  9. 9.
    Wang, G. Q., Lei, M. K., & Guo, D. M. (2016). Interactions between surface integrity parameters on AISI 304 austenitic stainless steel components by ultrasonic impact treatment. Procedia CIRP, 45, 323–326.CrossRefGoogle Scholar
  10. 10.
    Lundberg, M., Saarimäki, J., & Moverare, J. (2017). Surface integrity and fatigue behaviour of electric discharged machined and milled austenitic stainless steel. Materials Characterization, 124, 215–222.CrossRefGoogle Scholar
  11. 11.
    Zhou, N., Peng, R. L., & Pettersson, R. (2016). Surface integrity of 2304 duplex stainless steel after different grindingoperations. Journal of Materials Processing Technology, 229, 294–304.CrossRefGoogle Scholar
  12. 12.
    Sun, J., & Guo, Y. B. (2009). A comprehensive experimental study on surface integrity by end milling Ti–6Al–4 V. Journal of Materials Processing Technology, 209(8), 4036–4042.CrossRefGoogle Scholar
  13. 13.
    Arunachalam, R. M., Mannan, M. A., & Spowage, A. C. (2004). Residual stress and surface roughness when facing age hardened Inconel 718 with CBN and ceramic cutting tools. International Journal of Machine Tools and Manufacture, 44(9), 879–887.CrossRefGoogle Scholar
  14. 14.
    Li, B. Z., Jiang, X. H., & Yang, J. G. (2015). Effects of depth of cut on the redistribution of residual stress and distortion during the milling of thin-walled part. Journal of Materials Processing Technology, 216, 223–233.CrossRefGoogle Scholar
  15. 15.
    Ma, Y., Feng, P. F., & Zhang, J. F. (2016). Prediction of surface residual stress after end milling based on cutting force and temperature. Journal of Materials Processing Technology, 235, 41–48.CrossRefGoogle Scholar
  16. 16.
    Liang, S. Y., & Su, J. C. (2007). Residual stress modelling in orthogonal machining. CIRP Annals-Manufacturing Technology, 56(1), 65–68.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Huang, K., & Yang, W. Y. (2016). Analytical modeling of residual stress formation in workpiece material due to cutting. International Journal of Mechanical Sciences, 114, 21–34.CrossRefGoogle Scholar
  18. 18.
    Salahshoor, M., & Guo, Y. B. (2014). Finite element simulation and experimental validation of residual stresses in high speed dry milling of biodegradable Mg–Ca Alloys. Procedia CIRP, 80, 153–159.Google Scholar
  19. 19.
    Yang, D., Liu, Z. Q., & Ren, X. P. (2016). Hybrid modeling with finite element and statistical methods for residual stress prediction in peripheral milling of titanium alloy Ti–6Al–4V. International Journal of Mechanical Sciences, 108–109, 29–38.CrossRefGoogle Scholar
  20. 20.
    Jiang, H., Umbrello, D., & Shivpuri, R. (2006). Investigation of cutting conditions and cutting edge preparations for enhanced compressive subsurface residual stress in the hard turning of bearing steel. Journal of Materials Processing Technology, 171(2), 180–187.CrossRefGoogle Scholar
  21. 21.
    Yu, T. X., & Zhang, L. C. (1992). Plastic bending theory and its application (chapter 2) (1st ed.). Beijing: Science Press.Google Scholar

Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Roll Forging Research InstituteJilin University (Nanling Campus)ChangchunPeople’s Republic of China
  2. 2.College of Materials Science and EngineeringJilin University (Nanling Campus)ChangchunPeople’s Republic of China

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