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Applied theory of contact interaction of elastic bodies and the creation on it is based on the processes of formation of supports of friction-rolling with rational geometry

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However, the current theory of elastic contact does not sufficiently search for a rational geometric shape of contacting surfaces in a fairly wide range of conditions of work of rolling friction. Experimental search in this area is limited by the complexity of the measuring equipment and experimental equipment used, as well as high labor intensity and durability ...

• Received conventions
• CHAPTER 1. Critical analysis of the status of the question, goals and objectives of the work
  • 1. 1. Systemic analysis of the current state and trends in the field of improving the elastic contact of the bodies of complex
    • 1. 1. 1. The current state of the theory of local elastic contact of the bodies of complex shape and optimization of geometric contact parameters
    • 1. 1. 2. The main directions of improving the technology of grinding the working surfaces of the rolling form
    • 1. 1. 3. Modern technology of forming wind superfining surfaces
  • 1. 2. Research tasks
• Chapter 2. Elastic contact mechanism
• Complex geometric shape
  • 2. 1. The mechanism of the deformed state of the elastic contact of the bodies of the complex
  • 2. 2. The mechanism of the intense state of the contact area of \u200b\u200bthe elastic bodies of complex shape
  • 2. 3. Analysis of the effect of the geometric shape of contacting bodies on the parameters of their elastic contact
• conclusions
• Chapter 3. Forming a rational geometric shape of parts on grinding operations
  • 3. 1. Forming the geometric shape of rotation parts by grinding by inclined to the axis parts around
  • 3. 2. Algorithm and program for calculating the geometric shape of parts on grinding operations by inclined circle and stress-deformation state of the region of its contact with elastic body in the form of a bowl
  • 3. 3. Analysis of the effect of grinding process parameters by inclined circle on the reference ability of the ground surface
  • 3. 4. Studies of technological capabilities of grinding process by inclined to the axis of the workpiece with grinding circle and the operational properties of bearings made with its use
• conclusions
• Chapter 4. Basics of the formation of parts profile on superfining operations
  • 4. 1. Mathematical model of the mechanism of the process of formation of parts during superfinishing
  • 4. 2. Algorithm and program for calculating the geometric parameters of the treated surface
  • 4. 3. Analysis of the influence of technological factors on the parameters of the process of formation of the surface during superfinishing
• conclusions
• Chapter 5. Results of studying the effectiveness of the process of forming superfine
  • 5. 1. Methods of experimental studies and processing experimental data
  • 5. 2. Regression analysis of the indicators of the process of forming superfinishing depending on the characteristics of the instrument
  • 5. 3. Regression analysis of the indicators of the process of forming superfinishing depending on the processing mode
  • 5. 4. General mathematical model of the process of forming superfine
  • 5. 5. Performance of roller bearings with a rational geometric shape of working surfaces
• conclusions
• Chapter 6. Practical application of research results
  • 6. 1. Improving constructs of supports of friction-rolling
  • 6. 2. Method of grinding rings bearings
  • 6. 3. Method for monitoring the profile track rolling rings of bearings
  • 6. 4. Methods of superfining parts of the type of rings of a complex profile
  • 6. 5. Method for picking bearings with rational geometric shape of working surfaces
• conclusions

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Applied theory of contact interaction of elastic bodies and the creation on its basis the processes of formation of friction-rolling support with rational geometry ( abstract, term, diploma, control)

It is known that the problem of the development of the economy in our country depends largely on the lifting industry based on the use of progressive technology. This provision primarily refers to bearing production, since the activity of other sectors of the national economy depends on the quality of bearings and the effectiveness of their production. Increasing the operational characteristics of rolling friction supports will increase the reliability and resource of machines and mechanisms, the competitiveness of equipment on the world market, which means it is a problem of paramount importance.

A very important direction in improving the quality of rolling friction supports is the technological ensuring the rational geometric shape of their working surfaces: bodies and rolling tracks. In the works of V. M. Alexandrova, O. Yu. Davidenko, A.B. Queen, A.I. Lurie, A.B. Orlova, I.Ya. Staple mana and others. It is convinmed that giving the working surfaces of elastically contacting parts of the mechanisms and machines of a rational geometric shape can significantly improve the parameters of elastic contact and significantly increase the operational properties of friction nodes.

However, the current theory of elastic contact does not sufficiently search for a rational geometric shape of contacting surfaces in a fairly wide range of conditions of work of rolling friction. The experimental search in this area is limited by the complexity of the measuring equipment and experimental equipment used, as well as the high difficulty and duration of research. Therefore, currently there is no universal technique for choosing a rational geometric shape of the contacting surfaces of machine parts and instruments.

A serious problem on the path of practical use of nodes of friction of rolling machines with rational geometry of contact is the lack of effective ways of their manufacture. Modern methods of grinding and adjusting the surfaces of machine parts are designed mainly on the manufacture of surfaces of parts relative to a simple geometric shape, the profiles of which are defined with circular or straight lines. Methods of forming superfining, developed by the Saratov Scientific School, are very effective, but their practical application is designed only for the treatment of external surfaces of the type of rolling track of the internal rollers of roller bearings, which limits their technological capabilities. All this does not allow, for example, to effectively manage the form of a form of contact voltages of a number of rolling friction structures, and therefore, significantly influence their operational properties.

Thus, ensuring a systematic approach to improving the geometric shape of the working surfaces of rolling friction assemblies and its technological support should be considered as one of the most important directions for further improvement of the operational properties of mechanisms and machines. On the one hand, the study of the effect of the geometric shape of the contacting elastic bodies of the complex form on the parameters of their elastic contact allows you to create a universal methodology for improving the design of rolling friction supports. On the other hand, the development of the basics of technological support of the specified form of details ensures effective production of supports of rolling friction mechanism and machines with increased operational properties.

Therefore, the development of the theoretical and technological foundations of improving the parameters of the elastic contact of the details of the rolling friction supports and the creation on this basis of highly efficient technologies and equipment for the production of rolling bearings is a scientific problem that is important for the development of domestic engineering.

The aim of the work is to develop an applied theory of local contact interaction of elastic bodies and the creation of the processes of forming friction-rolling supports with rational geometry, aimed at improving the performance of bearing nodes of various mechanisms and machines.

Methods of research. The work was made on the basis of the fundamental provisions of the theory of elasticity, modern methods of mathematical modeling of the deformed and intense state of locally contacting elastic bodies, modern provisions of mechanical engineering technology, the theory of abrasive processing, theory of probabilities, mathematical statistics, mathematical methods of integral and differential calculation, numerical calculation methods.

Experimental studies were carried out using modern techniques and equipment using experimental planning methods, experimental data processing, and regression analysis, as well as using modern computer software packages.

Accuracy. Theoretical provisions of work are confirmed by the results of experimental studies made in both laboratory and production conditions. The reliability of theoretical provisions and experimental data is confirmed by the introduction of the results of work in production.

Scientific novelty. The paper developed an applied theory of local contact interaction of elastic bodies and created on its basis the processes of formation of friction-rolling supports with rational geometry, opening the possibility of a significant increase in the operational properties of bearing supports and other mechanisms and machines.

The main provisions of the dissertation endowed with the defense:

1. Applied theory of local contact of the elastic bodies of the complex geometric shape, which takes into account the impermanence of the eccentricity of the contact ellipse and the various forms of the initial gap profiles in the main sections described by power dependencies with arbitrary indicators.

2. The results of studies of the intense state in the field of elastic local contact and an analysis of the influence of a complex geometric shape of elastic bodies on the parameters of their local contact.

3. The mechanism of formation of rolling friction supports with a rational geometric shape on the surface grinding operations by inclined to the axis of the workpiece with grinding circle, the results of the analysis of the effect of grinding parameters by the inclined circle on the supporting ability of the grinding surface, the results of the study of the technological capabilities of the grinding process by inclined to the axis of the workpiece grinding circle and operational properties of bearings made with its use.

4. The mechanism of the process of formation of parts during superfining, taking into account the complex kinematics of the process, uneven degree of insolence of the tool, its wear and formation during the processing process, the results of the analysis of the effect of various factors on the process of removal of metal at various points of the profile of the workpiece and forming its surface

5. Regression multifactoric analysis of the technological capabilities of the process of forming superfining parts of bearings on the superfine machines of the latest modifications and operational properties of bearings made using this process.

6. Methods of targeted design of the rational design of the working surfaces of parts of the complex geometric shape of the type of rolling bearings parts, a comprehensive method of manufacturing rolling support parts, which includes preliminary, final processing and control of geometric parameters of work surfaces, the design of new technological equipment created on the basis of new technologies and intended for Production of rolling support parts with rational geometric shape of working surfaces.

The basis for this work includes materials of numerous studies of domestic and foreign authors. Experience and support for a number of specialists of the Saratov Bearing Plant, the Saratov Research and Production Enterprise of non-standard products of Mechanical Engineering, Saratov State technical University and other organizations, kindly agreed to take part in the discussion of this work.

The author considers his duty to express special thanks to valuable advice and multilateral assistance provided in the fulfillment of this work, a deserved figure of science of the Russian Federation, Dr. Technical Sciences, Professor, Academician of Raen Yu. V. Chebotarev and Dr. Technical Sciences, Professor A.M. Cleaner.

The limited amount of work did not allow to give exhaustive answers to a number of affected issues. Some of these issues are more fully reviewed in the published works of the author, as well as in joint work with graduate students and applicants ("https: // Site", 11).

334 Conclusions:

1. The method of targeted design of the rational design of the working surfaces of parts of a complex geometric shape of the type of rolling bearings and as an example, a new design of the ball bearing with a rational geometric shape of rolling tracks was proposed.

2. A comprehensive technology for the manufacture of rolling support parts, which includes the preliminary, final processing, control of the geometric parameters of working surfaces and picking bearings.

3. The designs of the new technological equipment created on the basis of new technologies and intended for the manufacture of parts of rolling supports with a rational geometric shape of work surfaces are proposed.

Conclusion

1. As a result of the research, a system for finding a rational geometric shape of locally contacting elastic bodies and technological bases of their formation, which opens up the prospects for improving the working capacity of a wide class of other mechanisms and machines.

2. A mathematical model has been developed that reveals the mechanism of local contact of the elastic bodies of the complex geometric shape and takes into account the impermanence of the eccentricity of the contact ellipse and various forms of the initial gap profiles in the main sections described by power dependencies with arbitrary indicators. The proposed model summarizes the previously obtained solutions and significantly expands the scope of the practical application of the exact solution of contact tasks.

3. A mathematical model of the intense state of the region of the elastic local contact of the complex form of the complex form, showing that the proposed solution of the contact problem gives a fundamentally new result, which opens up a new direction to optimize the contact parameters of the elastic bodies, the nature of the distribution of contact voltages and providing effective increase The performance of the friction of mechanisms and machines.

4. A numerical solution of the local contact of the bodies of the complex form, the algorithm and the program for calculating the deformed and intense state of the contact area, allowing to purposefully design the rational structures of the working surfaces of parts.

5. An analysis of the effect of the geometric form of elastic bodies was performed on the parameters of their local contact, showing that due to changes in the form of bodies, it is possible to simultaneously control the form of the contact stresses, their magnitude and size of the contact site, which allows to provide a high supporting ability of contacting surfaces, and consequently, To a large extent, increase the performance properties of contact surfaces.

6. The technological basis for the manufacture of rolling friction supports with a rational geometric shape on technological operations of grinding and forming superfinishing is developed. These are the most frequently used technological operations in the exact machine-making machine, which ensures the wide practical implementation of the proposed technologies.

7. Developed technology grinding ball supports oblique to the axis of the workpiece with a grinding circle and a mathematical model of shaping of a grinded surface. It is shown that the formed form of the ground surface, in contrast to the traditional form, the arc of the circle has four geometric parameters, which significantly expands the ability to control the reference capacity of the surface being processed.

8. A complex of programs is proposed that ensure the calculation of the geometric parameters of the surfaces of parts obtained by grinding the inclined circle, intense and deformation state of the elastic body in rolling supports with different grinding parameters. An analysis of the effect of grinding parameters by the inclined circle on the supporting ability of the grinded surface is carried out. It is shown that changing the geometric parameters of the grinding process by the inclined circle, especially the angle of inclination, one can significantly redistribute contact voltages and at the same time vary the dimensions of the contact site, which significantly increases the carrying capacity of the contact surface and helps reduce friction on contact. Checking the adequacy of the proposed mathematical model gave positive results.

9. Studies of technological capabilities of grinding process by inclined to the axis of the workpiece with grinding circle and the operational properties of bearings made with its use are carried out. It is shown that the grinding process by the inclined circle contributes to an increase in processing performance compared to conventional grinding, as well as improved the quality of the treated surface. Compared to standard bearings, the durability of bearings made by grinding the inclined circle increases by 2-2.5 times, the waviness decreases by 11 dB, the friction torque decreases by 36%, and the speed spell increases more than twice.

10. A mathematical model of the mechanism of the process of forming parts during superfinishing is developed. In contrast to previous studies in this area, the proposed model provides the ability to determine the removal of the metal at any point of the profile, reflects the process of forming a tool profile during the processing process, a complex mechanism for its insolence and wear.

11. A set of programs that ensure the calculation of the geometric parameters treated with superfinishing of the surface, depending on the main technological factors. An analysis of the influence of various factors on the process of removal of metal at various points of the billet profile and the formation of its surface is performed. As a result of the analysis, it was established that the declaration of the working surface of the tool is determined by the decisive effect on the formation of the billet profile in the superfining process. The adequacy of the proposed model has been performed, which gave positive results.

12. A regression multifactoric analysis of the technological capabilities of the process of forming superfining bearing parts on the superfine machines of the latest modifications and operational properties of bearings made using this process are performed. A mathematical model of the superfining process is constructed, which determines the connection of the main performance indicators and the quality of the processing process from technological factors and which can be used to optimize the process.

13. A method of targeted designing a rational design of working surfaces of parts of a complex geometric shape of the type of rolling bearings and as an example, a new design of the ball bearing with a rational geometric shape of rolling tracks was proposed. A comprehensive technology for the manufacture of rolling support parts, which includes the preliminary, final processing, control of the geometric parameters of the working surfaces and the acquisition of bearings is developed.

14. Designs of new technological equipment created on the basis of new technologies and intended for the manufacture of rolling support parts with a rational geometric shape of working surfaces.

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1. Modern problems of contact mechanics

Interaction

1.1. Classic hypothesis used when solving contact problems for smooth bodies

1.2. The influence of solid creep on their forming in the area of \u200b\u200bcontact

1.3. Evaluation of ragged rough surfaces

1.4. Analysis of contact interaction of multilayer structures

1.5. Relationship of mechanics and friction and wear problems

1.6. Features of the application of modeling in tribology 31 conclusions on the first chapter

2. Contact interaction of smooth cylindrical bodies

2.1. Solution of the contact problem for smooth isotropic disks and plates with cylindrical cavity

2.1.1. General formulas

2.1.2. Conclusion of the regional condition for movements in the area of \u200b\u200bcontact

2.1.3. The integral equation and its decision 42 2.1.3.1. Study of the obtained equation

2.1.3.1.1. Bringing a singular integrational equation to an integral equation with a kernel with a logarithmic feature

2.1.3.1.2. Rate of the norm of the linear operator

2.1.3.2. Approximate solution of the equation

2.2. Calculation of a fixed connection of smooth cylindrical bodies

2.3. Determination of movement in the movable connection of cylindrical bodies

2.3.1. Solving auxiliary problem for an elastic plane

2.3.2. Solving auxiliary task for an elastic disk

2.3.3. Determination of the maximum normal radial movement

2.4. Comparison of theoretical and experimental data of the study of contact stresses with internal tapping cylinders of close radii

2.5. Simulation of the spatial contact interaction of the system of coaxial cylinders of final sizes

2.5.1. Formulation of the problem

2.5.2. Solution of auxiliary two-dimensional tasks

2.5.3. Solution of the original problem 75 Conclusions and basic results of the second chapter

3. Contact tasks for rough bodies and their solution by adjusting the curvature of the deformed surface

3.1. Spatial nonlocal theory. Geometrical assumptions

3.2. Relative rapprochement of two parallel circles determined by the deformation of roughness

3.3. Method of analytical assessment of roughness deformation

3.4. Determination of movements in the contact area

3.5. Determination of auxiliary coefficients

3.6. Determination of the size of the elliptic area of \u200b\u200bcontact

3.7. Equations for determining the contact area close to circular

3.8. Equations for determining the contact area close to line

3.9. Approximate definition of coefficient A in the case of a contact area in the form of a circle or strip

3.10. Features of the averaging of pressures and deformations when solving a two-dimensional problem of internal contact of rough cylinders of close radii

3.10.1. The output of the integro-differential equation and its solution in the case of internal contact of the rough cylinders

3.10.2. Determination of reprimising coefficients ^ ^

3.10.3. Stressed landing of rough cylinders ^ ^ Conclusions and main results of the third chapter

4. Solution of contact tasks of viscoelasticity for smooth bodies

4.1. Basic provisions

4.2. Analysis of the principles of conformity

4.2.1. Principle of Volterra

4.2.2. Permanent transverse expansion coefficient during creep deformation

4.3. Approximate solution of a two-dimensional contact problem of linear creep for smooth cylindrical tel ^^

4.3.1. Common case of viscoelastic operators

4.3.2. Solution for the monotonous increasing area of \u200b\u200bcontact

4.3.3. Fixed connection solution

4.3.4. Simulation of contact interaction in the case of a uniformly aging isotropic plate

Conclusions and main results of the fourth chapter

5. Creeping surface

5.1. Features of contact interaction bodies with low yield strength

5.2. Construction of a model of deformation of the surface, taking into account the creep in the case of the elliptic area of \u200b\u200bthe contact

5.2.1. Geometrical assumptions

5.2.2. Surveys model model

5.2.3. Determination of medium deformations of the rough layer and medium pressures

5.2.4. Determination of auxiliary coefficients

5.2.5. Determination of the size of the elliptic area of \u200b\u200bcontact

5.2.6. Determination of the size of the circular area of \u200b\u200bcontact

5.2.7. Determination of the width of the contact area in the form of a strip

5.3. The solution of a two-dimensional contact task for the internal touch of rough cylinders, taking into account the creep surface

5.3.1. Setting the problem for cylindrical bodies. INTEGRO-DIFFERENTIAL EQUATION

5.3.2. Determination of reprimising coefficients 160 Conclusions and main results of the fifth chapter

6. Mechanics of the interaction of cylindrical bodies, taking into account the presence of coatings

6.1. Calculation of efficient modules in the theory of composites

6.2. Construction of a self-consistent method for calculating the effective coefficients of inhomogeneous media, taking into account the scatter of physicomechanical properties

6.3. Solution of the contact task for disk and plane with elastic composite coating on the hole circuit

6.3.1. Statement of the task and basic formulas

6.3.2. Conclusion of the regional condition for movements in the area of \u200b\u200bcontact

6.3.3. Integral equation and its decision

6.4. Solution of the problem in the case of orthotropic elastic coating with cylindrical anisotropy

6.5. Determination of the influence of viscoelastic aging coating on changing contact parameters

6.6. Analysis of the features of contact interaction of multicomponent coating and disk roughness

6.7. Modeling contact interaction with taking into account thin metal coatings

6.7.1. Contact ball with plastic coating and rough half-space

6.7.1.1. The main hypotheses and the model of interaction of solid bodies

6.7.1.2. Approximate solution of the task

6.7.1.3. Determination of the maximum contact convergence

6.7.2. Solution of the contact problem for a rough cylinder and a thin metal coating on the opening circuit

6.7.3. Determination of contact hardness with internal contact of cylinders

Conclusions and main results of the sixth chapter

7. Solution of mixed boundary value problems taking into account the wear of surfaces

Interacting tel

7.1. Features of the solution of the contact problem, taking into account the wear of the surfaces

7.2. Setting and solving the problem in the case of elastic deformation of roughness

7.3. Method of theoretical wear assessment, taking into account the creep surface

7.4. Method of wear evaluation, taking into account the effects of coverage

7.5. Final comments on the formulation of flat tasks taking into account the wear

Conclusions and main results of the seventh chapter

Recommended list of dissertations

• On the contact interaction between thin-walled elements and viscoelastic bodies when cutting and axisymmetric deformation, taking into account the aging factor 1984, Candidate of Physical and Mathematical Sciences Davtyan, Zavena Azibekovich

• Static and dynamic contact interaction of plates and cylindrical shells with rigid bodies 1983, Candidate of Physical and Mathematical Sciences Kuznetsov, Sergey Arkadyevich

• Technological support for the durability of machines based on hardening processing with simultaneous application of antifriction coatings 2007, Doctor of Technical Sciences Bersudsky, Anatoly Leonidovich

• Thermoplastic contact tasks for coatings 2007, Candidate of Physical and Mathematical Sciences of Gubareva, Elena Aleksandrovna

• Methods of solving contact problems for arbitrary bodies, taking into account the surface roughness by the end element method 2003, Candidate of Technical Sciences Olshevsky, Alexander Alekseevich

The dissertation (part of the author's abstract) on the topic "The theory of contact interaction of deformable solids with circular boundaries, taking into account the mechanical and microgeometric characteristics of surfaces"

The development of technology puts new challenges in the field of the study of the operability of cars and their elements. The increase in their reliability and durability is the most important factor determining the increase in competitiveness. In addition, the elongation of the service life of machinery and equipment, even to a small extent with a large saturation of technology, is equivalent to entering significant new production facilities.

The current state of the work processes of machines in combination with extensive experimental technique to determine the workloads and a high level of development of the applied theory of elasticity, with the existing knowledge of the physicomechanical properties of materials, allow the overall strength of the parts of the machines and devices with a sufficiently large warranty from breakdowns in normal conditions Services. At the same time, the tendency to reduce the largerness of the latter simultaneously with the simultaneous increase in their energy saturation is forced to revise well-known approaches and assumptions when determining the intense state of details and require the development of new settlement models, as well as the improvement of experimental research methods. Analysis and classification of the failures of mechanical engineering products showed that the main reason for the failure under operating conditions is not a breakdown, but wear and damage to their working surfaces.

Increased wear of parts in articulations in some cases violates the tightness of the working space of the machine, in others - the normal lubrication mode, in the third, leads to the loss of kinematic accuracy of the mechanism. Wear and damage to the surfaces reduce the fatigue strength of the parts and can cause their destruction after a certain service life with minor structural and technological concentrators and low rated voltages. Thus, elevated wear violate the normal interaction of parts in nodes, can cause significant additional loads and cause accidental destruction.

All this attracted to the problem of increasing the durability and reliability of cars a wide range of scientists of various specialties, designers and technologists, which allowed not only to develop a number of activities to improve the service life of the machine and create rational methods of care for them, but also on the basis of physics, chemistry, and Metal science to lay the foundations of teaching on friction, wear and lubrication in conjugation.

Currently, the significant efforts of engineers in our country and abroad are aimed at finding ways to solve the problem of determining the contact stresses of interacting parts, because To move on the calculation of the wear of materials to the tasks of structural wear resistance, the contact tasks of the mechanics of the deformable solid body have a decisive role. Significant importance for engineering practice are the solutions of contact problems of the theory of elasticity for bodies with circular boundaries. They constitute the theoretical basis for calculating such elements of machines as bearings, hinged connections, some types of gears, connections with tension.

The widest studies are made using analytical methods. It is the presence of fundamental bonds of modern integrated analysis and the theory of potential with such a dynamic region, as a mechanic, determined their rapid development and use in applied studies. The use of numerical methods is significantly expanding the ability to analyze the stress state in the contact area. At the same time, the bulky of the mathematical apparatus, the need to use powerful computing means significantly restrains the use of existing theoretical developments in solving applied tasks. Thus, one of the actual directions of development of mechanics is to obtain explicit approximate solutions of the tasks of the tasks that provide simplicity of their numerical implementation and with sufficient to practice the accuracy of the described phenomenon. However, despite the progress achieved, while it is difficult to obtain satisfactory results, taking into account local design features and microgeometry of interacting bodies.

It should be noted that the properties of contact have a significant impact on the wear processes, since due to the discreteness of contact with the touch of micronether, only on the individual sites forming the actual area. In addition, the protrusions formed during technological processing are diverse in shape and have different allocation of heights. Therefore, when modeling the topography of surfaces, it is necessary to introduce parameters characterizing the real surface into the statistical laws of distribution.

All this requires the development of a single approach to solving contact problems, taking into account the wear, the most fully taking into account both the geometry of interacting parts, microgeometric and rheological characteristics of surfaces, characteristics of their wear resistance and the possibility of obtaining an approximate solution with the least amount of independent parameters.

Communication of work with major scientific programs, themes. Studies were carried out in accordance with the following themes: "Develop a method for calculating contact stresses with an elastic contact interaction of cylindrical bodies, not described by the theory of Hertz" (Ministry of Education of the Republic of Belarus, 1997, No. 19981103); "The influence of micronics of contacting surfaces on the distribution of contact stresses in the interaction of cylindrical bodies having close in the magnitude of the radii" (Belarusian Republican Foundation Fund, 1996, No. GR 19981496); "Develop a method for predicting the wear of the suspension supports, taking into account the topographic and rheological characteristics of surfaces of interacting parts, as well as the presence of antifriction coatings" (Ministry of Education of the Republic of Belarus, 1998, No. 2009929); "Modeling the contact interaction of machine parts taking into account the randomness of the rheological and geometric properties of the surface layer" (Ministry of Education of the Republic of Belarus, 1999 No. 20001251)

The purpose and objectives of the study. Development of a single method of theoretical prediction of the effect of geometric, rheological characteristics of the roughness of the solid surfaces and the presence of coatings on the stress state in the contact area, as well as the establishment on this basis the patterns of changing the contact rigidity and wear resistance of conjugations on the example of the interaction of bodies with circular boundaries.

To achieve the goal required to solve the following problems:

Develop a method of approximate solution of problems of the theory of elasticity and viscoelasticity on the contact interaction of the cylinder and the cylindrical cavity in the plate using the minimum number of independent parameters.

Develop a nonlocal model of contact interaction of bodies, taking into account the microgeometric, rheological characteristics of surfaces, as well as the presence of plastic coatings.

Enough an approach that allows you to adjust the curvature of interacting surfaces by deformation of roughness.

Develop a method of approximate solution of contact problems for a disk and isotropic, orthotropic with cylindrical anisotropy and viscoelastic aging coatings on the hole in the plate, taking into account their transverse deformability.

Build a model and determine the effect of microgeometric features of the solid surface on the contact interaction with plastic coating on the counter.

Develop a method for solving problems taking into account the wear of cylindrical bodies, the quality of their surfaces, as well as the presence of antifriction coatings.

The object and subject of the study are non-classical mixed objectives of the theory of elasticity and viscoelasticity for bodies with circular boundaries, taking into account the nonlocality of the topographic and rheological characteristics of their surfaces and coatings, on the example of which in this paper developed a comprehensive method for analyzing the intense state in the area of \u200b\u200bcontact depending on the quality indicators their surfaces.

Hypothesis. When solving the boundary challenges, taking into account the quality of the surface of the bodies, a phenomenological approach is used, according to which the roughness deformation is considered as deformation of the intermediate layer.

Tasks with time-changing regional conditions are treated as quasistatic.

Methodology and methods of research conducted. When conducting research, the main equations of the mechanics of the deformable solid body, tribology, functional analysis were used. The method has been developed and substantiated to correct the curvature of loaded surfaces due to the deformations of micronovalities, which significantly simplifies the conducted analytical transformations and allows you to obtain analytical dependencies for the size of the contact area and contact voltages, taking into account the specified parameters without using the assumption about the smallness of the basic measurement of the roughness of the roughness of the roughness Contact area.

When developing a method of theoretical prediction of surface wear, observed macroscopic phenomena were considered as a result of the manifestation of statistically averaged relations.

The accuracy of the results obtained in the work is confirmed by comparisons of the resulting theoretical solutions and the results of experimental studies, as well as comparison with the results of some solutions found by other methods.

Scientific novelty and significance of the results obtained. For the first time, the example of the contact interaction of bodies with circular boundaries was summarizing, and a single method of comprehensive theoretical prediction of the influence of nonlocal geometric, rheological characteristics of rough surfaces of interacting bodies and the presence of coatings on the stress state, contact rigidity and wear resistance of conjugations were developed.

A comprehensive research complex allowed the theoretically substantiated method of solving the problems of solid mechanics, based on a consistent consideration of macroscopically observed phenomena, as the result of the manifestation of microscopic links statistically averaged at a significant portion of the contact surface.

As part of solving the problem:

A spatial nonlocal model of contact interaction of solid bodies with an isotropic surface roughness is proposed.

A method has been developed for determining the effect of the characteristics of the surface of solid bodies on the distribution of stresses.

An integro-differential equation obtained in contact problems for cylindrical bodies was investigated, which made it possible to determine the conditions for the existence and uniqueness of its solution, as well as the accuracy of the constructed approximations.

Practical (economic, social) significance of the results obtained. The results of theoretical studies are brought to acceptable techniques for practical use and can be directly applied during engineering calculations of bearings, sliding supports, gears. The use of the proposed solutions will reduce the time of creating new machine-building structures, as well as with great accuracy to predict their official characteristics.

Some results of the research performed were introduced on the NLP "Cycloprod", Altech NGOs.

The main provisions of the dissertation endowed with the defense:

Approximate solution of the problem of the mechanics of the deformed solid body on the contact interaction of the smooth cylinder and the cylindrical cavity in the plate, with sufficient accuracy of the described phenomenon when using the minimum number of independent parameters.

The solution of nonlocal boundary value problems of the mechanics of the deformable solid, taking into account the geometric and rheological characteristics of their surfaces based on the method, allowing you to correct the curvature of interacting surfaces by deformation of roughness. The absence of assumptions about the smallness of the geometric sizes of the basic lengths of roughness measurement compared with the size of the contact area makes it possible to move to the development of multi-level models for deformation of the surface of solids.

The construction and substantiation of the method for calculating the movements of the boundaries of cylindrical bodies caused by the deformation of the surface layers. The results obtained allow you to develop a theoretical approach that determines the contact stiffness of the conjugation, taking into account the joint influence of all the features of the state of the surfaces of real tel.

Modeling the viscoelastic disk interaction and cavity in a plate of aging material, simplicity of the implementation of the results of which allows them to use them for a wide range of applied tasks.

Approximate solution of contact problems for disk and isotropic, orthotropic with cylindrical anisotropy, as well as viscoelastic aging coatings on the hole in the plate, taking into account their transverse deformability. This makes it possible to assess the effect of composite coatings with a low modulus of elasticity on the loading of conjugates.

Construction of a nonlocal model and determination of the effect of the characteristics of the roughness of the solid surface on the contact interaction with plastic coating on the counter.

Development of the method of solving boundary value problems, taking into account the wear of cylindrical bodies, the quality of their surfaces, as well as the presence of antifriction coatings. On this basis, a methodology that focuses mathematical and physical methods is proposed in the study of wear resistance, which makes it possible instead of research of real friction units to make the main emphasis on the study of the phenomena occurring in the area of \u200b\u200bcontact.

Personal contribution of the applicant. All results endowed with protection are obtained by the author personally.

Approbation of the dissertation results. The results of the research given in the thesis were presented at 22 international conferences and congresses, as well as conferences of the CIS countries and the Republican, among them: "Pontryaginian readings - 5" (Voronezh, 1994, Russia), "Mathematical models of physical processes and their properties" ( Taganrog, 1997, Russia), NordTrib "98 (EBELTOFT, 1998, Denmark), Numerical Mathematics and Computational Mechanics -" NMCM "98" (Miskolc, 1998, Hungary), "Modelling" 98 "(Praha, 1998, Czech Republic), 6th International Symposium on Creep and Coupled Processes (Bialowieza, 1998, Poland), "Computational Methods and Production: Reality, Problems, Perspectives" (Gomel, 1998, Belarus), "Polymer Composites 98" (Gomel, 1998, Belarus), " Mechanika "99" (Kaunas, 1999, Lithuania), II Belarusian Congress on theoretical and applied mechanics

Minsk, 1999, Belarus), INTERNAT. Conf. On Engineering Rheology, Icer "99 (Zielona Gora, 1999, Poland)," TRANSPORT STRENGROUT TRANSPORT TRANSFERS "(St. Petersburg, 1999, Russia), International Conference on MultiField Problems (Stuttgart, 1999, Germany).

Published results. According to the dissertation materials published 40 printed works, among them: 1 monograph, 19 articles in magazines and collections, including 15 articles under personal authorship. The total number of pages of published materials is 370.

Structure and scope of the dissertation. The thesis consists of introduction, seven chapters, conclusions, the list of used sources and applications. A full amount of the thesis is 275 pages, including the volume occupied by illustrations - 14 pages, tables - 1 page. The number of sources used includes 310 items.

Similar dissertation work in the specialty "Mechanics of the deformable solid body", 01.02.04 CIFRA VAC

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Conclusion of dissertation on the topic "Mechanics of the deformable solid body", Kravchuk, Alexander Stepanovich

Conclusion

In the course of the studies, a number of static and quasistatic problems of the mechanics of the deformable solid were also resolved. This allows you to formulate the following conclusions and indicate the results:

1. Contact voltages and surface quality are one of the main factors determining the durability of machine-building structures, which, in combination with a tendency to reduce the mass-darkened machines, the use of new technological and structural solutions leads to the need to revise and clarify the approaches and assumptions used in determining the stress state. , movements and wear in pairing. On the other hand, the bulky of the mathematical apparatus, the need to use powerful computing means is significantly contained by the use of existing theoretical developments in solving applied tasks and determine as one of the main directions of development of mechanics to obtain explicit approximate solutions of the tasks delivered, providing simplicity of their numerical implementation.

2. The approximate solution of the problem of the mechanics of the deformable solid body on the contact interaction of the cylinder and the cylindrical cavity in the plate with a minimum number of independent parameters is constructed, with sufficient accuracy describing the studied phenomenon.

3. For the first time, nonlocal boundary value problems of the theory of elasticity were solved, taking into account the geometric and rheological characteristics of roughness based on a method, allowing to correct the curvature of interacting surfaces. The absence of assumptions about the smallness of the geometric sizes of the basic measurement lengths of roughness compared with the size of the contact area makes it possible to correctly supply and solve the problem of the interaction of solid tel, taking into account the microgeometry of their surfaces with relatively small contact sizes, as well as go to the creation of multi-level roughness deformation models.

4. A method for calculating the highest contact displacements in the interaction of cylindrical tel is proposed. The results obtained allowed us to construct a theoretical approach that determines the contact rigidity of the conjugation taking into account the microgeometric and mechanical features of the surfaces of real tel.

5. Modeling the viscoelastic disk interaction and cavity in the plate made of aging material, the simplicity of the implementation of the results of which allows them to use them for a wide range of applied tasks.

6. Contact problems for the disk and isotropic, orthotropic, with cylindrical anisotropy and viscoelastic aging coatings on the hole in the plate, taking into account their transverse deformability, are solved. This makes it possible to estimate the effect of composite antifriction coatings with a low modulus of elasticity.

7. The model was constructed and the effect of the surface microgeometry of one of the interacting bodies and the presence of plastic coatings on the surface of the counter. This makes it possible to emphasize the leading effect of the characteristics of the surface of real composite bodies in the formation of the area of \u200b\u200bcontact and contact stresses.

8. A general method of solving cylindrical bodies, the quality of their antifriction coatings has been developed. boundary value problems with the wear of surfaces, as well as availability

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1. {!LANG-2772cd036515182057c72c51848bceef!} 17

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2. {!LANG-0c818a92dd94add5fff3f4868c63f033!} 37

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4. {!LANG-91a1dee388a00be3761a2cc4e3ed2b41!}

4.1. Basic provisions

4.2. Analysis of the principles of conformity

4.2.1. Principle of Volterra

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4.3.1. Common case of viscoelastic operators

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6. {!LANG-7f0cc63ed528f01aff3e8c180d794bd8!} 168

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7. {!LANG-b487013954a2a8abcc55264cc89993ab!} 218

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To achieve the goal required to solve the following problems:

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Develop a method for solving problems taking into account the wear of cylindrical bodies, the quality of their surfaces, as well as the presence of antifriction coatings.

The object and subject of the study are non-classical mixed objectives of the theory of elasticity and viscoelasticity for bodies with circular boundaries, taking into account the nonlocality of the topographic and rheological characteristics of their surfaces and coatings, on the example of which in this paper developed a comprehensive method for analyzing the intense state in the area of \u200b\u200bcontact depending on the quality indicators their surfaces.

Hypothesis. When solving the boundary challenges, taking into account the quality of the surface of the bodies, a phenomenological approach is used, according to which the roughness deformation is considered as deformation of the intermediate layer.

Tasks with time-changing regional conditions are treated as quasistatic.

Methodology and methods of research conducted. When conducting research, the main equations of the mechanics of the deformable solid body, tribology, functional analysis were used. The method has been developed and substantiated to correct the curvature of loaded surfaces due to the deformations of micronovalities, which significantly simplifies the conducted analytical transformations and allows you to obtain analytical dependencies for the size of the contact area and contact voltages, taking into account the specified parameters without using the assumption about the smallness of the basic measurement of the roughness of the roughness of the roughness Contact area.

When developing a method of theoretical prediction of surface wear, observed macroscopic phenomena were considered as a result of the manifestation of statistically averaged relations.

The accuracy of the results obtained in the work is confirmed by comparisons of the resulting theoretical solutions and the results of experimental studies, as well as comparison with the results of some solutions found by other methods.

Scientific novelty and significance of the results obtained. For the first time, the example of the contact interaction of bodies with circular boundaries was summarizing, and a single method of comprehensive theoretical prediction of the influence of nonlocal geometric, rheological characteristics of rough surfaces of interacting bodies and the presence of coatings on the stress state, contact rigidity and wear resistance of conjugations were developed.

A comprehensive research complex allowed the theoretically substantiated method of solving the problems of solid mechanics, based on a consistent consideration of macroscopically observed phenomena, as the result of the manifestation of microscopic links statistically averaged at a significant portion of the contact surface.

As part of solving the problem:

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A method has been developed for determining the effect of the characteristics of the surface of solid bodies on the distribution of stresses.

An integro-differential equation obtained in contact problems for cylindrical bodies was investigated, which made it possible to determine the conditions for the existence and uniqueness of its solution, as well as the accuracy of the constructed approximations.

Practical (economic, social) significance of the results obtained. The results of theoretical studies are brought to acceptable techniques for practical use and can be directly applied during engineering calculations of bearings, sliding supports, gears. The use of the proposed solutions will reduce the time of creating new machine-building structures, as well as with great accuracy to predict their official characteristics.

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The main provisions of the dissertation endowed with the defense:

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The solution of nonlocal boundary value problems of the mechanics of the deformable solid, taking into account the geometric and rheological characteristics of their surfaces based on the method, allowing you to correct the curvature of interacting surfaces by deformation of roughness. The absence of assumptions about the smallness of the geometric sizes of the basic lengths of roughness measurement compared with the size of the contact area makes it possible to move to the development of multi-level models for deformation of the surface of solids.

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Construction of a nonlocal model and determination of the effect of the characteristics of the roughness of the solid surface on the contact interaction with plastic coating on the counter.

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