Abstract
Residual stresses introduced into components in the course of manufacturing processes may considerably impair fatigue life and therefore the operational reliability and safety of the final product. Particularly in critical applications in the aerospace industry, where peripheral milling is a common surface finishing operation for components made from the titanium alloy Ti–6Al–4V, it is desirable to control the introduced residual stresses in the process while accounting for disturbance quantities such as tool wear. To this end, we propose a numerical scheme for the prediction of milling induced residual stresses that provides sufficient efficiency for real-time application. The scheme is based on a two-dimensional model where semi-analytical approaches from contact theory and thermoelasticity are combined with an approximate elasto-plastic solution technique based on an algorithm established in rolling contact mechanics to achieve the required performance in the plastic domain. Following the derivation of the numerical solution strategy, we turn our attention to the peripheral milling process under consideration and present predictions for the induced residual stresses along with a discussion of the general modeling approach, the major influencing factors on the predictions as well as efficiency aspects.
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References
Abboud, E., Shi, B., Attia, H., Thomson, V., Mebrahtu, Y.: Finite element-based modeling of machining-induced residual stresses in Ti–6Al–4V under finish turning conditions. Procedia Cirp 8, 63–68 (2013). https://doi.org/10.1016/j.procir.2013.06.066
Altintas, Y., Ber, A.: Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Appl. Mech. Rev. 54(5), B84–B84 (2001)
Barber, J.: Thermoelastic displacements and stresses due to a heat source moving over the surface of a half plane. J. Appl. Mech. 51, 637 (1984)
Boley, B.A., Weiner, J.H.: Theory of Thermal Stresses. Courier Corporation, North Chelmsford (2012)
Boussinesq, J.: Application Des Potentiels À L’étude de L’équilibre Et Du Mouvement Des Solides Élastiques, Principalement Au Calcul Des Deformations Et Des Pressions Que Produisent, Dans Ces Solides, Des Efforts Quelconques Exercés Sur und Petite Partie de Leur Surface Ou de Leur Intérieur; memoire Suivi de Notes Étendues Sur Divers Points de Physique Mathématique Et D’analyse; Par MJ Boussinesq. Paris, Gauthier-Villars (1885)
Bryant, M.: Thermoelastic solutions for thermal distributions moving over half space surfaces and application to the moving heat source. J. Appl. Mech. 55, 87 (1988). https://doi.org/10.1115/1.3173665
Calamaz, M., Coupard, D., Girot, F.: A new material model for 2d numerical simulation of serrated chip formation when machining titanium alloy Ti–6Al–4V. Int. J. Mach. Tools Manuf. 48(3–4), 275–288 (2008). https://doi.org/10.1016/j.ijmachtools.2007.10.014
Carslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids, 2nd edn. Clarendon Press, Oxford (1959)
Cerruti, V.: Ricerche intorno all’equilibrio de’corpi elastici isotropi: memoria. Coi tipi del Salviucci (1882)
Denkena, B., Nespor, D., Böß, V., Köhler, J.: Residual stresses formation after re-contouring of welded Ti–6Al–4V parts by means of 5-axis ball nose end milling. CIRP J. Manuf. Sci. Technol. 7(4), 347–360 (2014). https://doi.org/10.1016/j.cirpj.2014.07.001
Grove, T., Köhler, J., Denkena, B.: Residual stresses in milled \(\beta \)-annealed Ti–6Al–4V. Procedia CIRP 13, 320–326 (2014). https://doi.org/10.1016/j.procir.2014.04.054. 2nd CIRP Conference on Surface Integrity (CSI)
Huang, X., Zhang, X., Ding, H.: An analytical model of residual stress for flank milling of Ti–6Al–4V. Procedia Cirp 31, 287–292 (2015)
Jiang, Y., Sehitoglu, H.: An analytical approach to elastic–plastic stress analysis of rolling contact. ASME J. Tribol. 116, 577–587 (1994). https://doi.org/10.1115/1.2928885
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)
Ju, Y., Farris, T.: FFT thermoelastic solutions for moving heat sources. ASME J. Tribol. 119, 156–162 (1997). https://doi.org/10.1115/1.2832452
Köhler, J., Grove, T., Maiß, O., Denkena, B.: Residual stresses in milled titanium parts. Procedia CIRP 2, 79–82 (2012). https://doi.org/10.1016/j.procir.2012.05.044
Komanduri, R., Hou, Z.B.: Thermal modeling of the metal cutting process: part I-temperature rise distribution due to shear plane heat source. Int. J. Mech. Sci. 42(9), 1715–1752 (2000). https://doi.org/10.1016/S0020-7403(99)00070-3
Krystof, J.: Berichte über Betriebswissenschaftliche Arbeiten, vol. 12. VDI Verlag, Tech. rep. (1939)
Lee, W.S., Lin, C.F.: Plastic deformation and fracture behaviour of Ti–6Al–4V alloy loaded with high strain rate under various temperatures. Mater. Sci. Eng. A 241(1–2), 48–59 (1998). https://doi.org/10.1016/S0921-5093(97)00471-1
Ma, Y., Feng, P., Zhang, J., Wu, Z., Yu, D.: Prediction of surface residual stress after end milling based on cutting force and temperature. J. Mater. Process. Technol. 235, 41–48 (2016). https://doi.org/10.1016/j.jmatprotec.2016.04.002
McDowell, D.: An approximate algorithm for elastic–plastic two-dimensional rolling/sliding contact. Wear 211(2), 237–246 (1997). https://doi.org/10.1016/S0043-1648(97)00117-8
McDowell, D., Moyar, G.: Effects of non-linear kinematic hardening on plastic deformation and residual stresses in rolling line contact. Wear 144(1), 19–37 (1991). https://doi.org/10.1016/0043-1648(91)90004-E
Merwin, J., Johnson, K.: An analysis of plastic deformation in rolling contact. Proc. Inst. Mech. Eng. Appl. Mech. Group 177(1), 676–690 (1963). https://doi.org/10.1243/PIME_PROC_1963_177_052_02
Muskhelishvili, N.I.: Some Basic Problems of The Mathematical Theory of Elasticity. Springer, Berlin (2013)
Nespor, D.: Randzonenbeeinflussung durch die rekonturierung komplexer investitionsgüter aus Ti–6Al–4V. PhD thesis, Gottfried Wilhelm Leibniz Universität Hannover (2015)
Sima, M., Özel, T.: Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti–6Al–4V. Int. J. Mach. Tools Manuf. 50(11), 943–960 (2010). https://doi.org/10.1016/j.ijmachtools.2010.08.004
Su, J.C., Young, K.A., Ma, K., Srivatsa, S., Morehouse, J.B., Liang, S.Y.: Modeling of residual stresses in milling. Int. J. Adv. Manuf. Technol. 65(5–8), 717–733 (2013). https://doi.org/10.1007/s00170-012-4211-3
Sun, J., Guo, Y.: A comprehensive experimental study on surface integrity by end milling Ti–6Al–4V. J. Mater. Process. Technol. 209(8), 4036–4042 (2009). https://doi.org/10.1016/j.jmatprotec.2008.09.022
Timošenko, S.P.: Theory of Elasticity. McGraw-Hill, New York (1970)
Ulutan, D., Özel, T.: Machining induced surface integrity in titanium and nickel alloys: a review. Int. J. Mach. Tools Manuf. 51(3), 250–280 (2011). https://doi.org/10.1016/j.ijmachtools.2010.11.003
Ulutan, D., Alaca, B.E., Lazoglu, I.: Analytical modelling of residual stresses in machining. J. Mater. Process. Technol. 183(1), 77–87 (2007). https://doi.org/10.1016/j.jmatprotec.2006.09.032
Ulutan, D., Arisoy, Y., Özel, T., Mears, L.: Empirical modeling of residual stress profile in machining nickel-based superalloys using the sinusoidal decay function. Procedia CIRP 13, 365–370 (2014). https://doi.org/10.1016/j.procir.2014.04.062
Umbrello, D.: Finite element simulation of conventional and high speed machining of Ti6Al4V alloy. J. Mater. Process. Technol. 196(1–3), 79–87 (2008). https://doi.org/10.1016/j.jmatprotec.2007.05.007
Wyen, C.F., Jaeger, D., Wegener, K.: Influence of cutting edge radius on surface integrity and burr formation in milling titanium. Int. J. Adv. Manuf. Technol. 67(1–4), 589–599 (2013). https://doi.org/10.1007/s00170-012-4507-3
Yang, D., Liu, Z., Ren, X., Zhuang, P.: 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, 29–38 (2016). https://doi.org/10.1016/j.ijmecsci.2016.01.027
Yang, D., Xiao, X., Liu, Y., Sun, J.: Peripheral milling-induced residual stress and its effect on tensile–tensile fatigue life of aeronautic titanium alloy Ti–6Al–4V. Aeronaut. J. 123(1260), 212–229 (2019). https://doi.org/10.1017/aer.2018.151
Zhou, R., Yang, W.: Analytical modeling of residual stress in helical end milling of nickel–aluminum bronze. Int. J. Adv. Manuf. Technol. 89(1–4), 987–996 (2017). https://doi.org/10.1007/s00170-016-9145-8
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The scientific work has been supported by the DFG within the research priority program SPP 2086. The authors thank the DFG for this funding and intensive technical support.
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Wölfle, C.H., Wimmer, M., Shahul Hameed, M.Z. et al. Towards real-time prediction of residual stresses induced by peripheral milling of Ti–6Al–4V. Continuum Mech. Thermodyn. 33, 1023–1039 (2021). https://doi.org/10.1007/s00161-020-00938-5
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DOI: https://doi.org/10.1007/s00161-020-00938-5