Siberian State Industrial University (Novokuznetsk, Russia):

V. I. Bazaikin, Dr. Eng., Prof., Chair of Applied Mathematics and Informatics, e-mail: bazaikin.vi@yandex.ru
O. L. Bazaikina, Cand. Eng., Associate Prof., Chair of Applied Mathematics and Informatics
M. V. Temlyantsev, Dr. Eng., Prof., Vice-Rector on Science and Innovations
O. S. Babushkina, Student

A model of the temperature field in a cylindrical sample arising under the action of a short-term energy pulse on the cylinder end has been proposed. The temperature field for solving the task for a homogeneous heat equation and the temperature field for a particular solution of a inhomogeneous equation with a triangular pulse shape of a heat load have a common zero initial condition, which is a real description of the onset and propagation of a pulse. The method of solving a model task uses both the solution expansion in terms of the basis of the task eigenfunctions, and the Laplace transform of the task in the time coordinate. By changing the parameters of the thermal sources distribution density, it is possible to vary the resulting temperature field. The set of temperature versus time curves in different cross sections of the cylinder with two maxima simulates a spectrum of different heat treatments of the sample, some of which are hardening. A numerical example of loading a cylindrical tablet with a radius of 12 mm and a height of 10 mm from steel 40KhN with a triangular-shaped temperature pulse of 163 ms with a height having a maximum equal to the melting temperature of steel 40KhN is given. At selected values of the pulse parameters, the sample sections located at a distance from 0.5 mm to 1 mm from the loaded plane of the tablet fall into the temperature zone of the austenite-pearlitic transition between Ar3 = 700 °C and Ar1 = 660 °C. Changes in the pulse temperature in the cross section at a distance of 6 mm from the loaded plane correspond to heat treatment, which consists of quenching with a high cooling rate and subsequent high tempering. Heat treatment creates a martensitic structure (effect of long-range action hardening).

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