As aerostatic bearings are used in high-speed metal-cutting machines to increase machining accuracy, there is the need to improve their characteristics, including compliance, which is usually high. In practical applications, a significant reduction of bearing compliance is often necessary, sometimes down to zero and even negative values, to ensure automatic compensation of the elastic deformation in the machine technological system. A decrease in compliance leads to deterioration in the dynamic performance of the bearing, so it is necessary to develop new designs that meet the above requirements. This article considers an aerostatic bearing, in which decrease in compliance is ensured by the use of air throttling with elastic orifices. To ensure its stability, the principle of combined external throttling was applied, which can substantially improve the dynamics of conventional aerostatic bearings. A mathematical model of the elastic orifice deformation was developed, together with the flow rate performance calculation method. The method ensured full qualitative and satisfactory quantitative agreement with the experimental data. The model was used in the mathematical modeling of the aerostatic bearing movement. The article also proposes a method to calculate the static load capacity and compliance of a bearing, as well as a numerical method for fast computation of its dynamic performance, which allows for real-time multi-parameter optimization by the bearing dynamic performance criteria. The study showed that there is an optimal set of design parameters for which low, zero, and negative static compliance of the bearing is ensured, with the necessary stability margin, high speed, and the non-oscillatory nature of the transient processes.

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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.

Stepped hydrostatic thrust bearings used in metal-cutting machines are characterized by high load capacity and damping, which ensure the stable operation of structures. However, in comparison with throttle thrust bearings, they have a high compliance. It is preferable that, in addition to the main bearing function, a modern hydrostatic bearing has the ability to provide low (including negative) compliance for the implementation of an adaptive function in order to actively compensate for the deformation of the machine resilient system, thereby increasing the accuracy of metalworking. This paper considers the design of a stepped hydrostatic thrust bearing, which, in order to reduce the compliance to negative values, features a technical improvement consisting of the use of an active displacement compensator on an elastic suspension. In this paper, the results of mathematical modeling and theoretical research of stationary and non-stationary modes of operation of the adaptive thrust bearing are presented. The possibility of a significant reduction in the static compliance of the structure, including the negative compliance values, is shown. It was found that negative compliance is provided in a wide range of loads, which can be up to 80% of the range of permissible bearing loads. The study of the dynamic characteristics showed that with a targeted selection of parameters that ensure optimal performance, the adaptive thrust bearing is able to operate stably in the entire range of permissible loads. It has been established that an adaptive stepped hydrostatic thrust bearing with a displacement compensator has a high stability margin, sufficient to ensure its operability when implementing the adaptive function.

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.