«Актуальные вопросы в сфере социально-экономических, технических и естественных наук и информационных технологий» (3-4 апреля 2014г.)

Gybin O. I., Zhutska A. O., Rusakova A. V.

Oles Honchar Dnipropetrovsk National University

MATHEMATICAL MODELING OF THERMAL PROCESSES IN LASER PROCESSING OF COATINGS BASED ON PHASE TRANSITIONS

One of the trends, that is developing rapidly nowadays and is surely important for engineering and laser treatment, is coating that is applied to any surface by the hot-gas products or other methods. The laser treatment goal is to improve the performance properties of coatings. Extra coating of surfaces is required because that the cover on its finalproduction stage is presented as a semi-finished product and its final properties are determined mainly by the subsequent processing. The use of laser radiation for the surfacetreatment can lead to corrosion and wear resistant layers on a substrate surface porosity reduction in melting of coating surface. Thermal processes that occur in the presence of phase transitions have significant impact on final performance properties of coatings by laser treatment because their mathematical modeling is real scientific and technical challenge [1].

The mathematical model of thermal processes in the processing of coatings by laser radiation was made, taking into account the surface evaporation through non-classical boundary conditions and thermal boundary resistance at its base and surface. At the stage of system warming up to the beginning of phase transformations, temperature fields and basic covering can be calculated by the quasilinear heat equation:

(1)

(2)

the initial conditions are   the boundary conditions on the outer surfaces are:

, (3)

and conditions of the fourth type, next to the contact are:

(4)

In the warming-up phase, a base-coating with foundering and surface evaporation heat equation is as the following:

(5)

where flow heat equation for the liquid and solid phases covering, as well as Stefan’s condition at the front point. The initial conditions   can be obtainedfrom the first warming-up stage and   is taken from the equation   On the treated outer coating surface, the boundary condition is given:   The velocity of the evaporation front is taken from the equation:   which still requires to add the initial condition  Here   - is a specific heat vaporization of coating material;   - a specific heat melting;   - its melting temperature;   - a coordinate evaporation front;   - the Dirac delta function. Thermal properties of the coating are given as follows:

, (6)

where the subscript p – referes to the liquid phase, and the index  т  – to hard one. To solve this problem the method of finite differences with previous smoothing coefficients of equation (5) is used [2].

A mathematical model and a difference scheme make it possible to carry out numerical study of thermal processes in the processing of laser radiation coating as well as tochoose treatment regime parameters under which the system base coverage temperature fields will be formed to provide the improvement of the coating performance properties.

The list of references:

1. Губін О. І. Математичне моделювання теплових процесів при обробці покриттів лазерним випромінюванням / О. І. Губін // Системні технології. Регіональний міжвуз. зб. наук. праць. – Дніпропетровськ, 2010. – Вип. 2 (67). – С. 17–27.

2. Самарский А. А. Вычислительная теплопередача / А. А. Самарский, П. Н. Вабищевич. – М.: Эдиториал, 2003. – 784 с.