Analysis of Thermal Stresses and Strains Developing during the Heat Treatment of Windmill Shaft

Open access


In the paper the results of evaluation of the temperature and stress fields during four cycles of the heat treatment process of the windmill shaft has been presented. The temperature field has been calculated from the solution to the heat conduction equation over the whole heat treatment cycles of the windmill shaft. To calculate the stress field an incremental method has been used. The relations between stresses and strains have been described by Prandtl-Reuss equation for the elastic-plastic body. In order to determine the changes in the temperature and stress fields during heat treatment of the windmill shaft self-developed software utilizing the Finite Element Method has been used. This software can also be used to calculate temperature changes and stress field in ingots and other axially symmetric products. In the mathematical model of heating and cooling of the shaft maximum values of the strains have been determined, which allowed to avoid the crack formation. The critical values of strains have been determined by using modified Rice and Tracy criterion.

[1] I. Olejarczyk, A. Adrian, H. Adrian, B. Mrzygłód, Algorithm for controlling of quench hardening process of constructional steels, Achieves of Metallurgy and Materials 55, (1), 171-179 (2010).

[2] R.L.S. Otero, W.R. Otero, G.E. Otten, L.C.F. Canale, Quench factor characterization of steel hardening: A review, International Journal of Mechanical Engineering and Auromation 1, (3), 119-128 (2014).

[3] T. Domański, A. Bokota, The numerical model to prediction of phase components and stresses distribution in hardened tool steel for cold work, International Journal of Mechanical Sciences 96-97, 47-57 (2015).

[4] A. Gołdasz, Z. Malinowski, T. Telejko, A. Buczek, A. Szajding, J. Nowak, G. Styczeń, Opracowanie krzywych nagrzewania w piecu pokrocznym z wykorzystaniem systemu Datapaq Slab Reheat System, Hutnik Wiadomości Hutnicze 4, 262-266 (2013).

[5] P.D. Hodgson, K.M. Browne, D.C. Collinson, T.T. Pham, R.K. Gibs, A Mathematical model to simulate the thermomechanical processing of steel, 3rd International Seminar of the International Federation for Heat Treatment and Surface Engineering, Melbourne 139-159 (1991).

[6] A. Buczek, T. Telejko, Investigation of heat transfer coefficient during quenching in various cooling agents, International Journal of Heat and Fluid Flow 44, 358-364 (2013).

[7] B. Hadała, Implementation of the heat balance in the finite element solution to the temperature field of the plastically deformed material, International Journal of Thermal Sciences 71, 123-181 (2013).

[8] O. C. Zienkiewicz, Metoda elementów skończonych, 1972 Arkady, Warszawa.

[9] Z. Malinowski, Numeryczne modele w przeróbce plastycznej w wymianie ciepła, 2005 Uczelniane Wydawnictwa Naukowo-Dydaktyczne, Kraków.

[10] W.M. Garrison, N.R. Moody, Ductile fracture, J. Phys. Chem. Solids. 48, 1035-1074 (1987).

Archives of Metallurgy and Materials

The Journal of Institute of Metallurgy and Materials Science and Commitee on Metallurgy of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.571
5-year IMPACT FACTOR: 0.776

CiteScore 2016: 0.85

SCImago Journal Rank (SJR) 2016: 0.347
Source Normalized Impact per Paper (SNIP) 2016: 0.740

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 239 213 9
PDF Downloads 88 82 4