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

Abstract

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.

Theoretical Study of the Static and Dynamic Characteristics of a Slotted Adaptive Hydrostatic Thrust Bearing with a Regulator of the Lubricant Output Flow

“…The characteristic polynomial of the TF (48) can be reduced to the form of the polynomial (47) by multiplying the first by the constant b 0 . Studies of adaptive slip bearings show that the sign of static compliance is determined by the coefficient b 0 [18,19]. In this case, the coefficients of the denominator polynomial for stable systems always remain positive, which indicates the stability of such dynamical systems.…”

“…Studies have shown that the inflow of additional energy contributes to a significant deterioration in the dynamic quality of the structure up to the loss of stability [15,16]. It is possible to improve the dynamics of the bearings due to the complication of the design through the use of an external combined throttling system (ECTS) whereby an additional hydraulic resistance is installed between the bearing gap and the regulator, which makes it possible to put in place an inter-throttle chamber, the volume of lubrication of which acts as a viscous damper for energy dissipation [17,18].…”

A Three-Dimensional Slip Velocity Model for Water-Lubricated Hydrodynamic Journal Bearings

“…With regard to fluid lubrication, numerical methods such as the finite difference method are frequently adopted to solve the simplified Reynolds lubrication equation [29][30][31][32]. The above method is easy to apply to bearings with simple shapes, as inertial and radial flow are ignored.…”