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8Современные инновации, системы и технологии // Modern Innovations, Systems and Technologies
2022; 2(4) eISSN: 2782-2818 https://www.oajmist.com
УДК: 621.9.015 EDN: VMSHZA нщр
DOI: https://doi.org/10.47813/2782-2818-2022-2-4-0324-033Q IIB
Расчетные модели для оценки напряженно-деформированного состояния в поверхностном слое
деталей при поверхностном пластическом деформировании обкатыванием и выглаживанием
Бахтиёржон Касимов1, Мансурбек Муминов2, Акбар Аброров3, Хумоюн
Мирзакаримов1
1 Андижанский машиностроительный институт, Андижан, Узбекистан
2АО "Пахтасаноат илмий маркази", Ташкент, Узбекистан 3Бухарский инженерно-технологический институт, Бухара, Узбекистан
Аннотация. В работе выполнено обоснование выбора расчетной модели для оценки напряженного состояния при отделочно-упрочняющей обработке, в частности, при дробеударной обработке. Приведены аналитические зависимости для расчета компонентов и интенсивности напряжений в поверхностном слое полубесконечного тела под действием распределенной нагрузки по сферической поверхности.
Ключевые слова: поверхностно-пластическое деформирование, сосредоточенная и распределенная сила, нормальные и касательные напряжения, интенсивность напряжений, площадь контакта.
Для цитирования: Касимов, Б., Муминов, М., Аброров, А., & Мирзакаримов, Х. (2022). Расчетные модели для оценки напряженно-деформированного состояния в поверхностном слое деталей при поверхностном пластическом деформировании обкатыванием и выглаживанием. Современные инновации, системы и технологии - Modern Innovations, Systems and Technologies, 2(4), 0324-0330. https://doi.org/10.47813/2782-2818-2022-2-4-0324-0330
Calculation models for the assessment of deflected mode in the surface layer of parts during surface plastic deformation by
running and smoothing
Bakhtiyorjon Kasimov1, Mansurbek Muminov2, Akbar Abrorov3, Khumoyun
Mirzakarimov1
1 Andijan Machine-Building Institute, Andijan, Uzbekistan
© B. Kasimov, M. Muminov, A. Abrorov, K. Mirzakarimov, 2022
0324
2 JSC "Scientific Center of Cotton Industry ", Tashkent, Uzbekistan 3Bukhara Engineering-Technological Institute, Bukhara, Uzbekistan
Abstract. The choice of a calculation model for the assessment of the stress state during finishing-hardening processing, in particular, during shot-impact processing are substantiated in the work. Analytical dependencies for calculating the components and intensity of stresses in the surface layer of a semi-infinite body under the action of a distributed load over a spherical surface are presented.
Keywords: surface-plastic deformation, concentrated and distributed force, normal and shear stresses, stress intensity, contact area.
For citation: Kasimov B., Muminov M., Abrorov A., & Mirzakarimov K. (2022). Calculation models for the assessment of deflected mode in the surface layer of parts during surface plastic deformation by running and smoothing. Modern Innovations, Systems and Technologies, 2(4), 0324-0330. https://doi.org/10.47813/2782-2818-2022-2-4-0324-0330
INTRODUCTION
Majority of the important parts of machines and mechanisms (parts of the working bodies) are subject to high requirements for the quality of the treated surfaces, determined by a set of geometric, physical, and mechanical parameters: surface roughness, strength and hardness, residual stresses, dislocation density. The required quality of the surface layer of parts can be achieved by finishing-hardening processing, in particular, by surface-plastic deformation (SPD). This type of machining, being the simplest and most effective method of strain hardening, has now proven itself reliably and is therefore widely used in mechanical engineering.
It should be considered that the properties of the part begin to form already at the stage of obtaining the blank (casting, forging, welding, and cutting). The correct choice of material and the method of obtaining the blank greatly affect the dynamic strength of the material, increasing the durability of machine parts [1]. A further increase in the durability of parts in the manufacture is achieved by using various methods of thermal, chemical-thermal treatment, surface-plastic deformation (SPD).
Efficient working of new equipment, characterized by good design and quality of manufacturing, is possible only under optimal operating conditions. With unsatisfactory maintenance, there are sometimes cases of loss of performance even of new machines at the very beginning of operation. Therefore, operational methods are an integral part of a set of measures to increase the reliability and durability of machines [2, 3]. The technological process
of manufacturing, assembly and control of products should ensure the required level of quality of the products, including operability and reliability, with the least amount of time and money [4]. All components of the technological process - the processing method and the equipment used, the sequence of operations, tools and processing modes, control methods determine its output parameters and, first of all, the quality indicators of the product specified by the designer in the technical requirements, i.e., its accuracy, quality of the machined surface, mechanical properties and others.
METHODS
The simplest to implement and effective in creating a high-quality surface layer of parts (favorable compressive residual stresses, low surface roughness, depth and degree of hardening) are such methods of finishing and hardening treatment as running and diamond burnishing. Despite the fact that running with slipping occurs when running with a ball in the contact zone, and with diamond burnishing, only sliding occurs, there are similarities between them regarding the nature of the deformation of the surface layer, the ratio of acting forces and friction coefficients, as well as in the patterns of formation of a microprofile of the machined surfaces.
The high quality of the surface layer, achieved by surface-plastic deformation, increases the fatigue strength, contact endurance, wear resistance of parts, and thereby increases the durability of machines and mechanisms [5].
Finishing-hardening processing of parts by rolling and smoothing is characterized by the locality of plastic deformation of the surface layer. Because of the force impact of the deforming body, a deformation zone is created on the contact surface, the initial shape of which corresponds to a dimple, which causes a certain deflected mode along the thickness of the surface layer. Subsequently, as the deforming tool is rolled or smoothed, the entire surface of the cylindrical part is covered with a deformation zone in the form of a continuous helix due to the longitudinal feed, the value of which determines the degree of overlap of the current deformation centers [6, 7].
Because of the local nature of the process of interaction of bodies during surface-plastic deformation, the deflected mode of the surface layer of the part turns out to be inhomogeneous in thickness, i.e. there is an uneven elastic-plastic deformation with its characteristic features: the formation of compressive residual stresses, distortion of the crystal lattice and an increase in the density of dislocations, and an increase in hardness.
RESULTS: CALCULATION MODEL
In order to assess the deflected mode in the surface layer of parts during rolling and smoothing, the following calculation models of loading can be used [8, 9], which differ in the type of load (concentrated or distributed force), the shape and law of load distribution on the boundary of a semi-infinite body:
1. a concentrated force P is applied on the boundary of a semi-infinite body;
2. a uniformly distributed load P is applied within the area of a circle on the boundary of a semi-infinite body;
3. distributed load P0 over the "hemisphere" (proportional to the ordinates of the spherical surface), applied over the area of the circle on the boundary of the semi-infinite body (Figure 1).
The last loading model most accurately reflects the mechanics of contact interaction when a ball is pressed into a semi-infinite body, since the result of this interaction is a plastically deformed zone in the form of a spherical surface. In the direction of penetration (along the z-axis), shear stresses on areas parallel to the coordinate planes are equal to zero (ixy= Tzx= Tyz=0). Therefore, the normal stresses will be principal.
h
/ ( f A / IITM /x .
/ \ 1 >
у/ г
Figure 1. Calculation scheme for the stress state created by a distributed load over the "hemisphere" at the boundary of the semi-infinite body.
The ordinates h of a hemisphere built on this site represent the load distribution P over the area of a circle with a radius:
Современные инновации, системы и технологии // Modern Innovations, Systems and Technologies
2022; 2(4) https://www.oajmist.com
p h h
— = -, p = p о — = po
a
a
a2 -(л2 + y2)
a
= p о
11
2 2 x2 + y 2
a
where, p0 is the pressure in the center of the circular platform F; p is pressure corresponding
to the h ordinate of the hemisphere The maximum load P will be:
P = J pdF = hdF ,
F
(1)
r 2 3
where I hdF = —n- a is volume bounded by a hemisphere of a radius. Consequently,
F 3
3 P
Po =~r--2 .
2 7 • a
Thus, when the load is distributed over the "hemisphere", the highest pressure is 1.5 times higher than its average value.
The stress components under a load distributed over a circular contact can be determined
from the dependencies:
1
az = - Po
1+
^2
v a
=°X ="Po[(1 + M) -
1 1 ч z an
---7 - (1 + ju) — arctg— ]
2 ГЛ a z
(2)
1 +
z v a y
where z is the distance to some considered point of the surface layer; ju is Poisson's coefficient.
Due to the axial symmetry of the stress state in the case of a circular contact area, we have Ox = Cy. The normal stresses Ox and Oy, in contrast to Oz, depend on the elastic properties of the material (Poisson's coefficient). If we take z = 0 in formulas (2), then
^z =- Po';°x
Po
1 + 2j 2
a
Y .
(3)
Because az =a =ar =a2 =a3 and ai = a -a2|, then the stress intensity is
equal to
1
о
= Po[-
3
^2
2 • (1 + - )
- (1 + m) • (1 - - • arctg —)] a z
(4)
V d j
Given calculation model of loading is applicable for the analytical description of the contact interaction in the shot-impact processing of machine parts for strain hardening. The stress intensity oi calculated by formula (4) allows further determining the level of specific stored energy Us, which is an energy criterion for the quality of the surface layer of parts after final machining and is responsible for the residual stress state. Estimation of the stored strain energy in the surface layer of parts after machining is based on several reasonable approaches that consider the fundamentals of the theory of dislocations, the thermodynamics of irreversible processes, and the energy analysis of the deformation diagram of materials.
CONCLUSION
The reviewed justification for the choice of a calculation model for assessing the stress state during finishing and hardening processing, in particular, during shot-impact, is the most effective processing, since finishing work and hardening properties are considered difficult in practice. The given analytical dependences for calculating the components and intensity of stresses in the surface layer of a semi-infinite body under the action of a distributed load over a spherical surface are calculated to the slightest accuracy, which corresponds to the relevance of this research.
REFERENCES
[1] Kasimov B. Experimental Determination of the Depth and Degree of Riveting of the Surface Layer of Batan Teeth. Middle European Scientific Bulletin. 2021; 18: 169-171.
[2] Kasimov B., Muminov M. and Shin I. Combined Strengthening of Batan Teeth of the Stb Loom. International Journal on Orange Technologies. 2021; 3.4: 223-225.
[3] Abrorov A., Kuvoncheva M., Muhammadov M. Ion-plasma nitriding of disk saws of a ginning machine. Modern Innovations, Systems and Technologies. 2021; 1(3): 30-35.
[4] Nazarov S. R., Kasimov B. M., Shin I. G. Algorithmization for calculating the intensity of residual stresses during shot-impact hardening of parts of technological machine. Progressive technologies and equipment: textiles, clothing, footwear. 2020; 81-84.
[5] Mukhammadiev D. M., Akhmedov Kh. A. and Ibragimov F. Kh. Research of a new
design of a steel grate of a saw gin. Problems of Mechanics. 2013; 3-4: 131-35.
[6] Abrorov A., Salimov Sh., Ibodullo S., Matluba K. Vacuum Installation of Technology of Deep Ion-Plasmic Nitriding Disc Saw of Fiber Separating Machines. International Journal of Advanced Research in Science, Engineering and Technology. 2020; 7(1): 12406-12409.
[7] Shin I. G. Technological methods for ensuring the quality and predicting the durability of machine parts for the primary processing of cotton: Dissertation of doctor of technical sciences. Tashkent: Tashkent Institute of Light and Textile Industry. 2014. 264 p.
[8] Shin I.G. Intensity of residual stresses during surface plastic deformation of machine parts. Hardening technologies and coatings. Moscow. 2010; 2: 10-13.
[9] Shin I.G. Influence of technological residual stresses on the fatigue strength of machine parts. Problems of textiles. 2004; 1: 63-68.
ИНФОРМАЦИЯ ОБ АВТОРАХ / INFORMATION ABOUT THE AUTHORS
Касимов Бахтиёржон Мурат угли, PhD, доцент, Андижанский машиностроительный институт, Андижан, Узбекистан
Муминов Мансурбек Рахимович, PhD, специалист, АО "Пахтасаноат илмий маркази" Ташкент, Узбекистан
Аброров Акбар Саидович, PhD, доцент, Бухарский инженерно-технологический институт, Бухара, Узбекистан E-mail: [email protected]
Мирзакаримов Хумоюн Равшанбек угли,
магистр, Андижанский машиностроительный институт, Андижан, Узбекистан
Bakhtiyorjon Kasimov, PhD, associate professor, Andijan Machine-Building Institute, Andijan, Uzbekistan
Mansurbek Muminov, PhD, specialist, JSC "Scientific Center of Cotton Industry" Tashkent, Uzbekistan
Akbar Abrorov, PhD, associate professor Bukhara Engineering-Technological Institute, Bukhara, Uzbekistan E-mail: [email protected]
Khumoyun Mirzakarimov, master degree student, Andijan Machine-Building Institute, Andijan, Uzbekistan
Статья поступила в редакцию 02.11.2022; одобрена после рецензирования 17.11.2022; принята
к публикации 18.11.2022.
The article was submitted 02.11.2022; approved after reviewing 17.11.2022; accepted for publication
18.11.2022.
