Theoretical Investigation on Performance Characteristics of Aerostatic Journal Bearings with Active Displacement Compensator

Vladimir Kodnyanko; Stanislav Shatokhin; Andrey Kurzakov; Yuri Pikalov; Maxim Brungardt; Lilia Strok; Iakov Pikalov

doi:10.3390/app11062623

Theoretical Investigation on Performance Characteristics of Aerostatic Journal Bearings with Active Displacement Compensator

Applied Sciences ◽

10.3390/app11062623 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2623

Author(s):

Vladimir Kodnyanko ◽

Stanislav Shatokhin ◽

Andrey Kurzakov ◽

Yuri Pikalov ◽

Maxim Brungardt ◽

...

Keyword(s):

Air Flow ◽

Stability Margin ◽

Quality Criteria ◽

Dynamic Compliance ◽

Theoretical Research ◽

Elastic Displacement ◽

Nonlinear Boundary Value Problems ◽

Elastic Suspension ◽

Aerostatic Bearings ◽

Dynamic Quality

Active aerostatic bearings are capable of providing negative compliance, which can be successfully used to automatically compensate for deformation of the machine tool system in order to reduce the time and improve the quality of metalworking. The article considers an aerostatic radial bearing with external combined throttling systems and an elastic displacement compensator, which is an alternative to aerostatic bearings with air flow rate compensators. The results of the mathematical modeling and theoretical research of stationary and nonstationary modes of operation of bearings with slotted and diaphragm throttling systems are presented. A counter-matrix sweep method has been developed for solving linear and nonlinear boundary value problems in partial derivatives with respect to the function of the square of the pressure in the bearing gap and inter-throttling bearing cavities for any values of the relative shaft eccentricity. A numerical method is proposed for calculating the dynamic quality criteria, and the transfer function of the dynamic compliance of a bearing with small displacements is considered as a linear automatic control system with distributed parameters. An experimental verification of the theoretical characteristics of the bearing was carried out, which showed a satisfactory correspondence among the compared data. It is shown that bearings with a throttle system have the best quantitative and qualitative load characteristics. The possibility of optimal determination of the values of a number of important parameters that provide the bearing with optimal performance and a high stability margin is established. It is shown that bearings with an elastic suspension of the movable sleeve allow one to compensate for significant movements, which can be larger than the size of the air gap by an order of magnitude or more. In these conditions, similar bearings with air flow compensators would be obviously inoperative.

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Dynamic Quality of an Aerostatic Thrust Bearing with a Microgroove and Support Center on Elastic Suspension

Mathematics ◽

10.3390/math9131492 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1492

Author(s):

Vladimir Kodnyanko ◽

Stanislav Shatokhin ◽

Andrey Kurzakov ◽

Lilia Strok ◽

Yuri Pikalov ◽

...

Keyword(s):

Dynamic Characteristics ◽

Negative Impact ◽

Aerostatic Bearing ◽

Elastic Suspension ◽

Variable Parameters ◽

Aerostatic Bearings ◽

Improved Design ◽

Dynamic Quality ◽

Bearing Layer

The disadvantage of aerostatic bearings is their low dynamic quality. The negative impact on the dynamic characteristics of the bearing is exerted by the volume of air contained in the bearing gap, pockets, and microgrooves located at the outlet of the feeding diaphragms. Reducing the volume of air in the flow path is a resource for increasing the dynamic quality of the aerostatic bearing. This article presents an improved design of an axial aerostatic bearing with simple diaphragms, an annular microgroove, and an elastic suspension of the movable center of the supporting disk. A mathematical model is presented and a methodology for calculating the static characteristics of a bearing and dynamic quality indicators is described. The calculations were carried out using dimensionless quantities, which made it possible to reduce the number of variable parameters. A new method for solving linearized and Laplace-transformed boundary value problems for transformants of air pressure dynamic functions in the bearing layer was applied, which made it possible to obtain a numerical solution of problems sufficient for practice accuracy. The optimization of the criteria for the dynamic quality of the bearing was carried out. It is shown that the use of an elastic suspension of the support center improves its dynamic characteristics by reducing the volume of compressed air in the bearing layer and choosing the optimal volume of the microgroove.

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Non-Iterative Finite Element Scheme for Combined Annular-Thrust Porous Aerostatic Bearings Analysis

ASME/STLE 2012 International Joint Tribology Conference ◽

10.1115/ijtc2012-61088 ◽

2012 ◽

Cited By ~ 1

Author(s):

Polina V. Khan ◽

Pyung Hwang

Keyword(s):

Finite Element ◽

Air Flow ◽

Three Dimensional ◽

Finite Element Scheme ◽

Element Scheme ◽

Numerical Example ◽

Key Points ◽

Aerostatic Bearings

The key points of method derivation and a numerical example for bearing with three dimensional air flow are presented.

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Translational vibrations of flat plate with elastic suspension in air flow

10.22616/erdev.2021.20.tf033 ◽

2020 ◽

Author(s):

Marina Cerpinska ◽

Grigory Panovko ◽

Shravan Koundinya Vutukuru ◽

Janis Viba ◽

Martins Irbe

Keyword(s):

Flat Plate ◽

Air Flow ◽

Elastic Suspension

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Theoretical Efficiency Study of Output Lubricant Flow Rate Regulating Principle on the Example of a Two-Row Aerostatic Journal Bearing with Longitudinal Microgrooves and a System of External Combined Throttling

Mathematics ◽

10.3390/math9141698 ◽

2021 ◽

Vol 9 (14) ◽

pp. 1698

Author(s):

Vladimir Kodnyanko ◽

Stanislav Shatokhin ◽

Andrey Kurzakov ◽

Yuri Pikalov ◽

Lilia Strok ◽

...

Keyword(s):

Flow Rate ◽

Dynamic Characteristics ◽

Machine Tools ◽

Theoretical Study ◽

Load Capacity ◽

Finite Difference Methods ◽

Output Flow ◽

Aerostatic Bearings ◽

Dynamic Quality ◽

Active Flow

Due to their vanishingly low air friction, high wear resistance, and environmental friendliness, aerostatic bearings are used in machines, machine tools, and devices that require high accuracy of micro-movement and positioning. The characteristic disadvantages of aerostatic bearings are low load capacity, high compliance and an increased tendency for instability. In radial bearings, it is possible to use longitudinal microgrooves, which practically exclude circumferential air leakage, and contributes to a significant increase in load-bearing capacity. To reduce compliance to zero and negative values, inlet diaphragm and elastic airflow regulators are used. Active flow compensation is inextricably linked to the problem of ensuring the stability of bearings due to the presence of relatively large volumes of gas in the regulator, which have a destabilizing effect. This problem was solved by using an external combined throttling system. Bearings with input flow regulators have a number of disadvantages-they are very energy-intensive and have an insufficiently stable load capacity. A more promising way to reduce compliance is the use of displacement compensators for the movable element. Such bearings also allow for a decrease in compliance to zero and negative values, which makes it possible to use them not only as supports, but also as active deformation compensators of the technological system of machine tools in order to reduce the time and increase the accuracy of metalworking. The new idea of using active flow compensators is to regulate the flow rate not at the inlet, but at the outlet of the air flow. This design has the energy efficiency that is inherent to a conventional bearing, but the regulation of the lubricant output flow allows the compliance to be reduced to zero and negative values. This article discusses the results of a theoretical study of the static and dynamic characteristics of a two-row radial aerostatic bearing with longitudinal microgrooves and an output flow regulator. Mathematical modeling and theoretical study of stationary modes have been carried out. Formulas for determining static compliance and load capacity are obtained. Iterative finite-difference methods for determining the dynamic characteristics of a structure are proposed. The calculation of dynamic quality criteria was carried out on the basis of the method of rational interpolation of the bearing transfer function, as a system with distributed parameters, developed by the authors. It was found that the volumes of the microgrooves do not have a noticeable effect on the bearing dynamics. It is shown that, in this design, the external combined throttling system is an effective means of maintaining stability and high dynamic quality of the design operating in the modes of low, zero and negative compliance.

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Parameter Sensitivity Analysis on Dynamic Coefficients of Partial Arc Annular-Thrust Aerostatic Porous Journal Bearings

Applied Sciences ◽

10.3390/app112210791 ◽

2021 ◽

Vol 11 (22) ◽

pp. 10791

Author(s):

Pyung Hwang ◽

Polina Khan ◽

Seok-Won Kang

Keyword(s):

Degrees Of Freedom ◽

Low Cost ◽

Air Flow ◽

Nonlinear Behavior ◽

Journal Bearings ◽

Dynamic Coefficients ◽

Spindle Shaft ◽

Relative Eccentricity ◽

Aerostatic Bearings ◽

Stiffness And Damping

Aerostatic bearings are widely used in high-precision devices. Partial arc annular-thrust aerostatic porous journal bearings are a prominent type of aerostatic bearings, which carry both radial and axial loads and provide high load-carrying capacity, low air consumption, and relatively low cost. Spindle shaft tilting is a resource-demanding challenge in numerical modeling because it involves a 3D air flow. In this study, the air flow problem was solved using a COMSOL software, and the dynamic coefficients for tilting degrees of freedom were obtained using finite differences. The obtained results exhibit significant coupling between the tilting motion in the x-and y-directions: cross-coupled coefficients can achieve 20% of the direct coefficient for stiffness and 50% for damping. In addition, a nonlinear behavior can be expected, because the tilting motion within 3°, tilting velocities within 0.0012°/s, and relative eccentricity of 0.2 have effects as large as 20% for direct stiffness and 100% for cross-coupled stiffness and damping. All dynamic coefficients were fitted with a polynomial of eccentricity, tilting, and tilting velocities in two directions, with a total of six parameters. The resulting fitting coefficient tables can be employed for the fast dynamic simulation of the rotor shaft carried on the proposed bearing type.

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INTEGRATED STUDY OF THE EFFICIENCY OF GRINDING MATERIAL IN AN IMPACT-CENTRIFUGAL MILL

NEWS of National Academy of Sciences of the Republic of Kazakhstan ◽

10.32014/2021.2518-170x.74 ◽

2021 ◽

Vol 447 (3) ◽

pp. 129-136

Author(s):

D. Chyrkun ◽

A. Levdanskiy ◽

S. Yarmolik ◽

V. Golubev ◽

D. Zhumadullayev

Keyword(s):

Differential Equations ◽

Air Flow ◽

Separation Process ◽

Theoretical Research ◽

Design Parameters ◽

Separation Mechanism ◽

Technological Parameters ◽

Bulk Materials ◽

Working Volume ◽

Wide Range

The analysis of existing methods of air classification of crushed bulk materials is carried out, priority directions of their development and improvement are identified, the hardware design of these methods and the main approaches to the calculation of air classifiers are studied. The conclusion is made about a rather isolated motion of particles in the working volume of the classifier at optimal performance. The prospects of dry separation methods and the progressiveness of creating multistage gravitational classifiers have been established. Theoretical studies of the separation process in a gravity classifier with overflow shelves have been carried out. The regularities of the process of separation of bulk materials in air classifiers have been established, reliable methods have been developed for calculating their technological and design parameters in order to create highly efficient and productive industrial plants. Theoretical dependencies and differential equations are obtained, which characterize the influence on the separation mechanism of technological and design parameters of the classifier. The results of solving the equations of motion made it possible to determine the main design parameters of the apparatus based on the technological requirements for productivity and the dispersed composition of the final products. On the basis of theoretical research, analytical relationships and differential equations have been developed that describe the separation process in a gravity classifier with overflow shelves. The use of these equations made it possible to simulate the air flow in the classifier, to obtain a field of air flow velocities for any design and technological parameters. This, in turn, shows the direction of movement of particles of different sizes or densities and makes it possible to estimate the boundary size of separation, and also allows you to study the interaction of the air flow with the material being separated in a wide range of technological and design parameters of the classifier, and, ultimately, to determine the boundary size separation and particle size range of the resulting fractions of the finished product. The relationship between technological and design parameters of the apparatus is theoretically determined.

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