CC BY
1
№ 1(130)
январь, 2025 г.
TECHNOLOGY OF MATERIALS AND PRODUCTS OF THE TEXTILE
AND LIGHT INDUSTRY
DOI - 10.32743/UniTech.2025.130.1.19137
MATHEMATICAL MODEL OF HEAT TREATMENT OF A SEWING MACHINE RACK USING A LASER BEAM
Shavkat Aliev
Lecturer
"University of Business and Science", Republic of Uzbekistan, Namagan E-mail: [email protected]
Nazirjon Safarov
Doctor of Technical Sciences, Professor, Namangan Engineering and Technology Institute, Republic of Uzbekistan, Namagan E-mail: [email protected]
МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ТЕРМИЧЕСКОЙ ОБРАБОТКИ ЗУБЧАТОЙ РЕЙКИ ШВЕЙНОЙ МАШИНЫ С ПОМОЩЬЮ ЛАЗЕРНОГО ЛУЧА
Алиев Шавкат Бахтияр угли
преподаватель, University of Business and Science, Республика Узбекистан, г. Наманган
Сафаров Назиржон Мухаммаджанович
д-р техн. наук, профессор, Наманганский инженерно-технологический институт, Республика Узбекистан, г. Наманган
ABSTRACT
The article provides information on the theoretical foundations, technological processes and equipment for laser heat treatment of low-carbon steel, which has received the widest industrial application of all laser processing technologies. Physical phenomena of hardening, models for calculating the main technological parameters of the process are considered. Recommendations are given for choosing modes of processing steel materials using continuous and pulse-periodic radiation of industrial lasers.
АННОТАЦИЯ
В статье приводятся сведения по теоретическим основам, технологическим процессам и оборудованию для лазерная термическая обработка малоуглеродистой стали, которая из всех технологий лазерной обработки получила наиболее широкое промышленное применение. Рассмотрены физические явления закалки, модели для расчета основных технологических параметров процесса. Даны рекомендации по выбору режимов обработки стальных материалов с использованием непрерывного и импульсно-периодического излучения промышленных лазеров.
Keywords: laser heat treatment, steel, technology, continuous, industrial application, plasma, electron beam radiation, beam, luminous flux, material hardening, efficiency.
Ключевые слова: лазерная термообработка, сталь, технология, непрерывно, промышленное применение, плазменной, электронно-лучевой излучения, луч, световой поток, закаления материала, эффективность.
Introduction
The characteristics of physical phenomena on the front surface of a section are determined by the power density of the light flux. As the power density increases,
the surface temperature and the average velocity of its movement also rise. Compared to conventional heat sources used in oxygen, plasma, and electron beam processing, focused laser beams provide 1.5 times higher
Библиографическое описание: Aliev Sh.B., Safarov N.M. MATHEMATICAL MODEL OF HEAT TREATMENT OF A SEWING MACHINE RACK USING A LASER BEAM // Universum: технические науки : электрон. научн. журн. 2025. 1(130). URL: https://7universum. com/ru/tech/archive/item/19137
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energy density delivered to an anomalously small area of influence.
In just one second, such a light flux not only melts refractory materials but also partially vaporizes their surface. During the cutting process, the light flux incident on the material is partially absorbed by the material's surface, the molten film, and the cut's sidewalls, while some of it is reflected. At high energy densities, a portion of the radiation is absorbed by the decomposition products of the material, which reduces the efficiency of the cutting process.
The main physical processes in laser technologies are as follows [1]:
Vaporization (and ablation in the molten phase) -This is the most common process underlying many industrial technologies for materials used in microelectronics, micromechanics, and micro-optics. Issues of precision and quality remain relevant to this day.
Heating to softening (or melting) temperatures and deformation in the viscous-liquid phase, accompanied by mechanical effects such as stretching and rotation. This process is used in the production of near-field optical probes, medical optical devices, and more.
Directed local heating, which creates a controlled stress field leading to manageable deformation of sheet materials. This process is used not only for shaping but also for precise assembly and alignment of microme-chanical components (laser forming).
Localized heating, which generates excessive gas (or vapor) pressure between two material interfaces (e.g., a film and a substrate) to create directed micro-deformations and displacements.
Layer-by-layer synthesis of three-dimensional objects, including methods such as stereolithography, selective laser heating, and laminated object manufacturing.
Laser processes combined with other radiation or plasma to induce absorption for enhanced processing.
Manipulation of microparticles (molecular assembly) - This involves trapping particles in the center of laser radiation using light pressure and constructing microstructures from them.
Main part
Laser technologies rely not only on high power density but also on high photon density, which is critical for nonlinear processes (e.g., nonlinear absorption in weakly absorbing media) and selective technologies such as chemical and biomedical applications. Strong and ultra-strong electromagnetic fields can be utilized within the laser beam's focal area. Recently, technologies based on light pressure (e.g., microparticle manipulation and atom-molecular assembly via laser trapping) have emerged. The light pressure P^ = e(l + R) is determined by the radiation energy density e and the reflection coefficient R of the surface, assuming normal incidence of light [2].
Most laser technologies, however, are based on the thermal effects of radiation, which will be analyzed in detail.
январь, 2025 г.
When a laser beam strikes the material surface, part of the radiation is reflected, while another part penetrates and is absorbed by the material.
The propagation of radiation within the material is typically described by the Beer-Lambert law [3]:
q(x) = q0(1 — R) exp(-ax),
where q(x) is the radiation intensity at a depth x, q(x) is the incident radiation intensity, R is the reflection coefficient, and a is the material's absorption coefficient. Absorption of radiation leads to material heating. Depending on the strength of absorption, two heating modes are observed: strong (surface) absorption and weak (bulk) absorption.
Laser radiation with wavelengths corresponding to the strong absorption spectral region of the material is used in most technological processes, as it ensures localized effects and high energy efficiency. Strong absorption occurs in metals, semiconductors, and dielectrics when the radiation wavelength aligns with the primary absorption region of the material. In these cases, the penetration depth of radiation is typically much smaller than the characteristic heat diffusion length (1/a«Vax, where т is the radiation exposure time, and a is the thermal diffusivity of the material). Under such conditions, the heat source within the material is effectively localized near the surface. This is accounted for in solving the heat conduction equation using appropriate boundary conditions at the surface. The thickness of the heated layer is determined by the characteristic heat diffusion length Vot. Bulk absorption regimes, where 1/aWaT, are employed when creating volumetric heat sources within the material or directing radiation deep inside for localized processing [4].
Various mathematical methods are used to solve heat conduction equations, including integral transformations (e.g., Laplace transforms), Fourier methods (separation of variables), and source methods. It is important to note that during heating, the optical and ther-mophysical properties of the material, such as the reflection coefficient R, may change. Additionally, the temporal and spatial structure of the radiation significantly influences the heating process. These factors must sometimes be considered to accurately predict the temporal and spatial temperature distribution within the irradiated object.
When a material is heated by laser radiation, various processes are activated, including emission processes (electrons, ions, neutral molecules), surface and bulk chemical reactions, structural changes, thermal expansion, thermomechanical effects, melting, and vaporization. These processes may underpin specific technological applications, such as drilling and cutting (vaporization and melting), welding (melting), and thermal strengthening (structural changes).
In practice, determining the exact thermal parameters is often unnecessary. Instead, estimating the critical power density (qn), critical power (Pn), or critical energy ((Wn) is usually sufficient. The critical power density of radiation is the value at which defined changes
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occur in the irradiated material. Theoretically, qn is defined as the incident power density (q0) that raises the maximum material temperature T„to the threshold level for the process initiation (e.g., the boiling point for vaporization). At the end of the interaction, initial parameters of the heated area, typically a circular spot with ra-
dius r0, can be determined using expressions for the surface temperature at the center of the irradiated zone. In strong absorption regimes, these expressions are as follows:
2qo(1-R)VOi i 1
T----
uF ierfcih) + TN'
_ _ 2q0(1-R)r0 _ 1 - ь + lN,
(2.1) (2.2)
For radiation in the volumetric absorption mode:
T -
2q0(1-R)r pcS
{i-exp{-B-îEi(-B}+T"
(2.3)
Here, 5 represents the penetration depth of light into the material (for absorption described by the Bouguer law, 5 = 1/ a — the integral attenuation function); TN is the initial temperature.
Expression (2.3) has two specific cases [5]:
a) r0 » 4ar
b) r0 « Jar
T -
T- ^s +Tn
2q0(1 - R)r2 , I , ax
4kS
here, k represents the thermal conductivity of the material.
In a range of laser processing technologies, the surface being treated is scanned using laser beams. The results of thermal processing depend on the scanning speed (Vsk).
ln(i9A_) + TN
For a fast-moving source » l) the maximum
temperature on the strongly absorbing treated surface of the material is:
T _ 2 qo(1-R) 2ar0 ^
~ к J vsk n
For a slowly moving source:
T
qo(1-R)ro к
(Vsaro«i)
(1-Vskn)
V 4a J
+ T
(2.4)
(2.5)
(2.6)
Another important parameter in laser processing is the rate of the activated process in the irradiated material. For many thermally activated processes, such as evaporation, various thermochemical reactions, the
rate of the process V depends exponentially on the temperature T, and is most commonly described by the Frenkel equation [6]:
V(T)-c0eXp(-R%)
(2.7)
here, Lm is the activation energy of the process per unit mass (e.g., evaporation heat, etc.); c0 is the speed of sound in the solid; Rc is the universal gas constant; ^ is the molar (atomic) mass of the material being treated.
Specifically, the vaporization front — the boundary between the vaporized and condensed (melted) medium — penetrates deeper into the material at a certain
rate V(T), which is a function of the surface temperature T.
When the material evaporates, a mechanical impulse related to the reactive effect of the escaping vapor leads to a return force. The return pressure can be estimated as half of the saturated vapor pressure PT, with
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the return pressure Rqay and the vapor pressure on the material surface Rbomb being equal in magnitude.
PT — Rnnv + R
qay
xbomb,
(2.8)
In laser-induced evaporation, we assume R
bomb
0, and we obtain the equation P = 0,5 • R
qay
The saturated vapor pressure at a temperature T, which is equal to the evaporation surface temperature, is determined from the Clausius-Clapeyron equation:
rr—^Mmi-v
(2.9)
Here, L™ represents the latent heat of evaporation per unit mass of the material, and P0 is the saturated vapor pressure at temperature T0 (for example, at the boiling point T = Tq , the saturated vapor pressure at normal pressure is P0 = 105 [7]).
Determining the temperature of the material subjected to laser radiation and calculating the evaporation rate based on this allows for the acquisition of the integral characteristics of the processing process and the determination of the necessary parameters for the processing regime.
Figure 2.1. The relationship between the required energy consumption and the thickness of the metal for different
radiation power levels: 1 - W=2 kVt; 2 - W=3,5kVt
In some cases, the heat model of radiation effects is insufficient for a proper analysis of laser technology processes. For example, in deep hole drilling, the absorption of radiation in the vapor produced in the channel cannot be neglected, and so on [8,9].
Conclusion
Laser technologies based on rapid thermal expansion of materials exist when irradiated with laser radiation. The technology for cleaning the surface of a solid
body from contaminating particles using dry laser radiation involves rapidly heating the irradiated particles and/or the surface layer of the main material using a laser pulse and thermal expansion. After the pulse ends, inertia forces cause the particles to detach and be expelled from the surface.
References:
1. Анисимов С.И., Имас Я.А., Романов Г.С., Ходыко Ю.В. Действие излучения большой мощности на металлы. - М.: Наука, 1970.
2. Рэди Дж.Ф. Действие лазерного излучения. - М.: Мир, 1974.
3. Вейко В.П., Либенсон М.Н. Лазерная обработка. - Л.: Лениздат, 1973.
4. Григорьянц А.Г., Шиганов И.Н. Лазерная техника и технология. Лазерная сварка металлов, т. 5. - М.: Высшая школа, 1988.
5. Григорьянц А.Г., Сафонов А.Н. Лазерная техника и технология. Основы лазерного термоупрочнения сплавов, т. 6. - М.: Высшая школа, 1988.
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ТЕХНИЧЕСКИЕ НАУКИ_январь. 2025 г.
6. Аборкин А.В., Бабин Д.М., Бокарев Д.В., Елкин А.И. Влияние отжига на структуру и свойства алюмомат-ричных композитов, упрочненных WC1- x/УНТ структурами//Сборник трудов V Международной научно-технической конференции «Живучесть и конструкционное материаловедение (ЖивКоМ - 2020)». Москва, 27-29 октября 2020 г. С. 3-6.
7. Aborkin A., Khorkov K., Prusov E., Ob'edkov A., Kremlev K., Perezhogin I., Alymov M. Effect of Increasing the Strength of Aluminum Matrix Nanocomposites Reinforced with Microadditions of Multiwalled Carbon Nanotubes Coated with TiC Nanoparticle // Nanomaterials. 2019. Vol.9. Is.11. Article 1596. https://doi.org/ 10.3390/nano9111596.
8. Animesh B., Eisen W.B. Hot Consolidation of Powders & Particulates. Metal Powder Industries Federation, Princeton, USA, 2003. 254 p.
9. German R.M. (Ed.) Powder Metallurgy Science, 2nd ed.; Metal Powder Industries Federation: Princeton, NJ, USA, 1994. 472 p.
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