An analytical model for predicting the machining deformation of a plate blank considers biaxial initial residual stresses



The initial residual stress in a blank is one of the main causes of machining deformation that has become a major concern in manufacturing aerospace monolithic structures. An analytical prediction model for machining deformation that considers biaxial residual stresses is proposed to investigate the quantitative relationship between deformation and initial residual stress. Finite element method (FEM) simulations and machining experiments are then conducted to validate the accuracy of the analytical model. Results calculated using the analytical model are consistent with the FEM and experiment results. Eventually, the quantitative relationships between deformation and initial residual stress under three typical machining strategies are determined. The effects of workpiece position in the blank on machining deformation are summarized based on these quantitative relationships.


Machining deformation Analytical model Biaxial initial residual stresses Plate blank 


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Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

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  1. 1.
    Masoudi S, Amini S, Saeidi E, Eslami-Chalander H (2014) Effect of machining-induced residual stress on the distortion of thin-walled parts. Int J Adv Manuf Technol 76:597–608. doi: 10.1007/s00170-014-6281-x CrossRefGoogle Scholar
  2. 2.
    Liu L, Sun J, Chen W, Zhang J (2016) Finite element analysis of machining processes of turbine disk of Inconel 718 high-temperature wrought alloy based on the theorem of minimum potential energy. Int J Adv Manuf Technol:1–13. doi: 10.1007/s00170-016-9026-1
  3. 3.
    Huang X, Sun J, Li J (2015) Finite element simulation and experimental investigation on the residual stress-related monolithic component deformation. Int J Adv Manuf Technol 77:1035–1041. doi: 10.1007/s00170-014-6533-9 CrossRefGoogle Scholar
  4. 4.
    Liao YG, Hu SJ (2001) An integrated model of a fixture–workpiece system for surface quality prediction. Mech Eng:810–818. doi: 10.1007/s001700170108
  5. 5.
    Satyanarayana S, Melkote SN (2004) Finite element modeling of fixture-workpiece contacts: single contact modeling and experimental verification. Int J Mach Tools Manuf 44:903–913. doi: 10.1016/j.ijmachtools.2004.02.010 CrossRefGoogle Scholar
  6. 6.
    Estrems M, Sánchez HT, Faura F (2003) Influence of fixtures on dimensional accuracy in machining processes. Int J Adv Manuf Technol 21:384–390. doi: 10.1007/s001700300044 CrossRefGoogle Scholar
  7. 7.
    Sánchez HT, Estrems M, Faura F (2006) Analysis and compensation of positional and deformation errors using integrated fixturing analysis in flexible machining parts. Int J Adv Manuf Technol 29:239–252. doi: 10.1007/s00170-005-2515-2 CrossRefGoogle Scholar
  8. 8.
    Siebenaler SP, Melkote SN (2006) Prediction of workpiece deformation in a fixture system using the finite element method. Int J Mach Tools Manuf 46:51–58. doi: 10.1016/j.ijmachtools.2005.04.007 CrossRefGoogle Scholar
  9. 9.
    Liu S, Zheng L, Zhang ZH, Wen DH (2006) Optimal fixture design in peripheral milling of thin-walled workpiece. Int J Adv Manuf Technol 28:653–658. doi: 10.1007/s00170-004-2425-8 CrossRefGoogle Scholar
  10. 10.
    Chen W, Ni L, Xue J (2008) Deformation control through fixture layout design and clamping force optimization. Int J Adv Manuf Technol 38:860–867. doi: 10.1007/s00170-007-1153-2 CrossRefGoogle Scholar
  11. 11.
    Lu C, Zhao HW (2015) Fixture layout optimization for deformable sheet metal workpiece. Int J Adv Manuf Technol 78:85–98. doi: 10.1007/s00170-014-6647-0 CrossRefGoogle Scholar
  12. 12.
    Article O (2013) Design and optimization of machining fixture layout using ANN and DOE. 1573–1586. doi: 10.1007/s00170-012-4281-2
  13. 13.
    Sundararaman K, Padmanaban K, Sabareeswaran M (2016) Optimization of machining fixture layout using integrated response surface methodology and evolutionary techniques. Proc Inst Mech Eng Part C J Mech Eng Sci 230:2245–2259. doi: 10.1177/0954406215592920 CrossRefGoogle Scholar
  14. 14.
    Ratchev S, Govender E, Nikov S, Phuah K, Tsiklos G (2003) Force and deflection modelling in milling of low-rigidity complex parts. J Mater Process Technol 143–144:796–801. doi: 10.1016/S0924-0136(03)00382-0 CrossRefGoogle Scholar
  15. 15.
    Ratchev S, Liu S, Huang W, Becker AA (2004) A flexible force model for end milling of low-rigidity parts. J Mater Process Technol 153–154:134–138. doi: 10.1016/j.jmatprotec.2004.04.300 CrossRefGoogle Scholar
  16. 16.
    Ratchev S, Nikov S, Moualek I (2004) Material removal simulation of peripheral milling of thin wall low-rigidity structures using FEA. Adv Eng Softw 35:481–491. doi: 10.1016/j.advengsoft. 2004.06.011 CrossRefGoogle Scholar
  17. 17.
    Ratchev S, Liu S, Huang W, Becker AA (2004) Milling error prediction and compensation in machining of low-rigidity parts. Int J Mach Tools Manuf 44:1629–1641. doi: 10.1016/j.ijmachtools.2004.06.001 CrossRefGoogle Scholar
  18. 18.
    Ratchev S, Huang W, Liu S, Becker AA (2004) Modelling and simulation environment for machining of low-rigidity components. J Mater Process Technol 153–154:67–73. doi: 10.1016/j.jmatprotec.2004.04.301 CrossRefGoogle Scholar
  19. 19.
    Ratchev S, Liu S, Becker AA (2005) Error compensation strategy in milling flexible thin-wall parts. J Mater Process Technol 162–163:673–681. doi: 10.1016/j.jmatprotec.2005.02.192 CrossRefGoogle Scholar
  20. 20.
    Ratchev S, Liu S, Huang W, Becker AA (2006) An advanced FEA based force induced error compensation strategy in milling. Int J Mach Tools Manuf 46:542–551. doi: 10.1016/j.ijmachtools.2005.06.003 CrossRefGoogle Scholar
  21. 21.
    Ning H, Zhigang W, Chengyu J, Bing Z (2003) Finite element method analysis and control stratagem for machining deformation of thin-walled components. J Mater Process Technol 139:332–336. doi: 10.1016/S0924-0136(03)00550-8 CrossRefGoogle Scholar
  22. 22.
    Benardos PG, Mosialos S, Vosniakos GC (2006) Prediction of workpiece elastic deflections under cutting forces in turning. Robot Comput Integr Manuf 22:505–514. doi: 10.1016/j.rcim.2005.12.009 CrossRefGoogle Scholar
  23. 23.
    Aijun T, Zhanqiang L (2008) Deformations of thin-walled plate due to static end milling force. J Mater Process Technol 206:345–351. doi: 10.1016/j.jmatprotec.2007.12.089 CrossRefGoogle Scholar
  24. 24.
    López de Lacalle LN, Lamikiz A, Sánchez JA, Salgado MA (2007) Toolpath selection based on the minimum deflection cutting forces in the programming of complex surfaces milling. Int J Mach Tools Manuf 47:388–400. doi: 10.1016/j.ijmachtools.2006.03.010 CrossRefGoogle Scholar
  25. 25.
    Desai KA, Rao PVM (2008) Effect of direction of parameterization on cutting forces and surface error in machining curved geometries. Int J Mach Tools Manuf 48:249–259. doi: 10.1016/j.ijmachtools.2007.08.007 CrossRefGoogle Scholar
  26. 26.
    Saffar RJ, Razfar MR (2010) Simulation of end milling operation for predicting cutting forces to minimize tool deflection by genetic algorithm. Mach Sci Technol 14:81–101. doi: 10.1080/10910340903586483 CrossRefGoogle Scholar
  27. 27.
    Rai JK, Xirouchakis P (2009) FEM-based prediction of workpiece transient temperature distribution and deformations during milling. Int J Adv Manuf Technol 42:429–449. doi: 10.1007/s00170-008-1610-6 CrossRefGoogle Scholar
  28. 28.
    Puls H, Klocke F, Döbbeler B, Peng B (2016) Multiscale modeling of thermoelastic workpiece deformation in dry cutting. Procedia CIRP 46:27–30. doi: 10.1016/j.procir.2016.03.195 CrossRefGoogle Scholar
  29. 29.
    Fu WE, Cohen PH, Ruud CO (2009) Experimental investigation of the machining induced residual stress tensor under mechanical loading. J Manuf Process 11:88–96. doi: 10.1016/j.jmapro.2009.11.001 CrossRefGoogle Scholar
  30. 30.
    Nasr MNA, Ng EG, Elbestawi MA (2008) A modified time-efficient FE approach for predicting machining-induced residual stresses. Finite Elem Anal Des 44:149–161. doi: 10.1016/j.finel.2007.11.005 CrossRefGoogle Scholar
  31. 31.
    Ulutan D, Erdem Alaca B, Lazoglu I (2007) Analytical modelling of residual stresses in machining. J Mater Process Technol 183:77–87. doi: 10.1016/j.jmatprotec.2006.09.032 CrossRefGoogle Scholar
  32. 32.
    Huang XM, Sun J, Li JF, Han X, Xiong QC (2013) An experimental investigation of residual stresses in high-speed end milling 7050-T7451 aluminum alloy. Adv Mech Eng. doi: 10.1155/2013/592659
  33. 33.
    Sharman ARC, Hughes JI, Ridgway K (2006) An analysis of the residual stresses generated in Inconel 718™ when turning. J Mater Process Technol 173:359–367. doi: 10.1016/j.jmatprotec.2005.12.007 CrossRefGoogle Scholar
  34. 34.
    Outeiro JC, Umbrello D, M’Saoubi R (2006) Experimental and numerical modelling of the residual stresses induced in orthogonal cutting of AISI 316L steel. Int J Mach Tools Manuf 46:1786–1794. doi: 10.1016/j.ijmachtools.2005.11.013 CrossRefGoogle Scholar
  35. 35.
    Jiang XH, Li BZ, Yang JG, Zuo XY, Li K (2013) An approach for analyzing and controlling residual stress generation during high-speed circular milling. Int J Adv Manuf Technol 66:1439–1448. doi: 10.1007/s00170-012-4421-8 CrossRefGoogle Scholar
  36. 36.
    Denkena B, Boehnke D, León L (2008) Machining induced residual stress in structural aluminum parts. Prod Eng 2:247–253. doi: 10.1007/s11740-008-0097-1 CrossRefGoogle Scholar
  37. 37.
    Özel T, Zeren E (2007) Finite element modeling the influence of edge roundness on the stress and temperature fields induced by high-speed machining. Int J Adv Manuf Technol 35:255–267. doi: 10.1007/s00170-006-0720-2 CrossRefGoogle Scholar
  38. 38.
    Zeng C, Tian W, Liao WH (2016) The effect of residual stress due to interference fit on the fatigue behavior of a fastener hole with edge cracks. Eng Fail Anal 66:72–87. doi: 10.1016/j.engfailanal.2016.04.012 CrossRefGoogle Scholar
  39. 39.
    Choi Y (2009) A study on the effects of machining-induced residual stress on rolling contact fatigue. Int J Fatigue 31:1517–1523. doi: 10.1016/j.ijfatigue.2009.05.001 CrossRefGoogle Scholar
  40. 40.
    Jiang Z, Liu Y, Li L, Shao W (2014) A novel prediction model for thin plate deflections considering milling residual stresses. Int J Adv Manuf Technol 74:37–45. doi: 10.1007/s00170-014-5952-y CrossRefGoogle Scholar
  41. 41.
    Izamshah R, Mo JPT, Ding S (2011) Hybrid deflection prediction on machining thin-wall monolithic aerospace components. Proc Inst Mech Eng Part B J Eng Manuf 226:592–605. doi: 10.1177/0954405411425443 CrossRefGoogle Scholar
  42. 42.
    Li B, Jiang X, Yang J, Liang SY (2015) Effects of depth of cut on the redistribution of residual stress and distortion during the milling of thin-walled part. J Mater Process Technol 216:223–233. doi: 10.1016/j.jmatprotec.2014.09.016 CrossRefGoogle Scholar
  43. 43.
    Huang X, Sun J, Li J (2015) Effect of initial residual stress and machining-induced residual stress on the deformation of aluminium alloy plate. Stroj Vestnik/Journal Mech Eng 61:131–137. doi: 10.5545/sv-jme.2014.1897 CrossRefGoogle Scholar
  44. 44.
    Wei Y, Wang XW (2007) Computer simulation and experimental study of machining deflection due to original residual stress of aerospace thin-walled parts. Int J Adv Manuf Technol 33:260–265. doi: 10.1007/s00170-006-0470-1 CrossRefGoogle Scholar
  45. 45.
    Wang ZJ, Chen WY, Zhang YD, Chen ZT, Liu Q (2005) Study on the machining distortion of thin-walled part caused by redistribution of residual stress. Chinese J Aeronaut 18:175–179. doi: 10.1016/S1000-9361(11)60325-7 CrossRefGoogle Scholar
  46. 46.
    Dong H, Ke Y (2006) Study on machining deformation of aircraft monolithic component by FEM and experiment. Chinese J Aeronaut 19:247–254. doi: 10.1016/S1000-9361(11)60352-X CrossRefGoogle Scholar
  47. 47.
    Liu L, Sun J, Chen W, Sun P (2015) Study on the machining distortion of aluminum alloy parts induced by forging residual stresses. Proc Inst Mech Eng Part B J Eng Manuf. doi: 10.1177/0954405415583805
  48. 48.
    Guo H, Zuo DW, Wu HB, Xu F, Tong GQ (2009) Prediction on milling distortion for aero-multi-frame parts. Mater Sci Eng A 499:230–233. doi: 10.1016/j.msea.2007.11.137 CrossRefGoogle Scholar
  49. 49.
    Cerutti X, Mocellin K (2015) Parallel finite element tool to predict distortion induced by initial residual stresses during machining of aeronautical parts. Int J Mater Form 8:255–268. doi: 10.1007/s12289-014-1164-0 CrossRefGoogle Scholar
  50. 50.
    Richter-Trummer V, Koch D, Witte A, dos Santos JF, de Castro PMST (2013) Methodology for prediction of distortion of workpieces manufactured by high speed machining based on an accurate through-the-thickness residual stress determination. Int J Adv Manuf Technol 68:2271–2281. doi: 10.1007/s00170-013-4828-x CrossRefGoogle Scholar
  51. 51.
    Husson R, Baudouin C, Bigot R, Sura E (2014) Consideration of residual stress and geometry during heat treatment to decrease shaft bending. Int J Adv Manuf Technol 72:1455–1463. doi: 10.1007/s00170-014-5688-8 CrossRefGoogle Scholar
  52. 52.
    Yang Y, Li M, Li KR (2014) Comparison and analysis of main effect elements of machining distortion for aluminum alloy and titanium alloy aircraft monolithic component. Int J Adv Manuf Technol 70:1803–1811. doi: 10.1007/s00170-013-5431-x CrossRefGoogle Scholar
  53. 53.
    Zhang Z, Li L, Yang YF, He N, Zhao W (2014) Machining distortion minimization for the manufacturing of aeronautical structure. Int J Adv Manuf Technol 73:1765–1773. doi: 10.1007/s00170-014-5994-1 CrossRefGoogle Scholar
  54. 54.
    Wu Q, Li D-P, Zhang Y-D (2016) Detecting milling deformation in 7075 aluminum alloy aeronautical monolithic components using the quasi-symmetric machining method. Metals (Basel) 6:80. doi: 10.3390/met6040080 CrossRefGoogle Scholar
  55. 55.
    Tang ZT, Yu T, Xu LQ, Liu ZQ (2013) Machining deformation prediction for frame components considering multifactor coupling effects. Int J Adv Manuf Technol 68:187–196. doi: 10.1007/s00170-012-4718-7 CrossRefGoogle Scholar
  56. 56.
    Rai JK, Xirouchakis P (2008) Finite element method based machining simulation environment for analyzing part errors induced during milling of thin-walled components. Int J Mach Tools Manuf 48:629–643. doi: 10.1016/j.ijmachtools.2007.11.004 CrossRefGoogle Scholar
  57. 57.
    Franchim AS, de Campos VS, Travessa DN, de Moura Neto C (2009) Analytical modelling for residual stresses produced by shot peening. Mater Des 30:1556–1560. doi: 10.1016/j.matdes.2008.07.040 CrossRefGoogle Scholar
  58. 58.
    Reihanian M, Naseri M (2016) An analytical approach for necking and fracture of hard layer during accumulative roll bonding (ARB) of metallic multilayer. Mater Des 89:1213–1222. doi: 10.1016/j.matdes.2015.10.088 CrossRefGoogle Scholar
  59. 59.
    Shin SHS (1995) Prediction of the dimensional instability resulting from machining of residually stressed components. Ph.D. dissertation, Texas Tech University: 13–14.Google Scholar
  60. 60.
    Timoshenko S, Woinosky-Krieger S (1959) Theory of plates and shells. Classic, Second edn. McGraw-Hill, New YorkGoogle Scholar
  61. 61.
    Rossini NS, Dassisti M, Benyounis KY, Olabi AG (2012) Methods of measuring residual stresses in components. Mater Des 35:572–588. doi: 10.1016/j.matdes.2011.08.022 CrossRefGoogle Scholar
  62. 62.
    Jiang X, Li B, Yang J, Zuo XY (2013) Effects of tool diameters on the residual stress and distortion induced by milling of thin-walled part. Int J Adv Manuf Technol 68:175–186. doi: 10.1007/s00170-012-4717-8 CrossRefGoogle Scholar
  63. 63.
    Yang D, Liu Z, Ren X, Zhuang P (2016) Hybrid modeling with finite element and statistical methods for residual stress prediction in peripheral milling of titanium alloy Ti-6Al-4V. Int J Mech Sci 108–109:29–38. doi: 10.1016/j.ijmecsci.2016.01.027 CrossRefGoogle Scholar

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© Springer-Verlag London 2017

Authors and Affiliations

  1. 1.State Key Laboratory of Virtual Reality Technology and Systems, School of Mechanical Engineering and AutomationNew Main Building Room B313 Beijing University of Aeronautics and AstronauticsBeijingPeople’s Republic of China

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