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Gas journal bearings are widely employed in high-speed spindles for the micromachining industry. Compared to their oil and rolling counterparts, gas bearings have a longer life span, lower friction and a lower level of noise. In order to design accurate high-speed spindles supported by externally pressurized gas bearings, it is vital to analyze the characteristics of rotor bearing systems. In this paper, we present an analysis of the unbalance response of a high-speed spindle supported by gas journal bearings. A number of aspects to enhance the accuracy of the system are discussed. We performed the analysis by considering a nonlinear and a linearized numerical model validated through experimental measurements.

This paper takes the micro tilting-pad gas bearing as the research object. Based on the continuous model, first-order slip model, and Wu's new slip model, the static and dynamic Reynolds equations with the slip effect are established and solved by MATLAB software. First, a hybrid method integrating the Newton–Raphson iteration and finite difference methods was used to solve the static Reynolds equation. Then, the dynamic Reynolds equation was calculated by combining the partial derivative method with the equivalent coefficient method. So, the static and dynamic performance of the micro tilting-pad gas bearing can be obtained. The calculation results indicate that the bearing capacity and film pressure of the tilting-pad gas bearing are reduced, and the dynamic stiffness is reduced after considering the slip effect. In the calculation results, the value of the continuous model is the largest, followed by the first-order slip model, Wu's new slip model is minimum. It provides a reference for the design of the micro tilting-pad gas bearing.

Porous media gas bearings utilize gas as a lubricating medium to achieve non-contact support technology. Compared with traditional liquid-lubricated bearings or rolling bearings, they are more efficient and environmentally friendly. With the uniform gas film pressure of gas bearings, the rotating shaft can achieve mechanical motion with low friction, high rotational speed, and long service life. They have significant potential in improving energy efficiency and reducing carbon emissions, enabling oil-free lubrication. By eliminating the friction losses of traditional oil-lubricated bearings, porous media gas bearings can reduce the energy consumption of industrial rotating machinery by 15–25%, directly reducing fossil energy consumption, which is of great significance for promoting carbon neutrality goals. They have excellent prospects for future applications in the civil and military aviation fields. Based on the three-dimensional flow characteristics of the bearing’s fluid domain, this paper considers the influences of the transient flow field in the variable fluid domain of the gas film and the radial pressure gradient of the gas film, establishes a theoretical model and a three-dimensional simulation model for porous media gas bearings, and studies the static–dynamic pressure coupling mechanism of porous media gas bearings. Furthermore, through the trial production of bearings and performance tests, the static characteristics are verified, and the steady-state characteristics are studied through simulation, providing a basis for the application of gas bearings made from porous media materials in the civil and military aviation fields.

This study delves into the dynamic behavior of ultra-high-speed rotor systems underpinned by helium hydrostatic gas bearings, with a focus on the impact of rotational velocity on system performance. We have formulated an integrative dynamic model that harmonizes the rotor motion equation with the transient Reynolds equation. This model has been meticulously resolved via the Finite Difference Method (FDM) and the Wilson-Θ technique. Our findings unveil intricate nonlinear dynamics, including 2T-periodic and multi-periodic oscillations, and underscore the pivotal role of first-order temporal fluctuations, which account for over 20% of the transient pressure at rotational speeds exceeding 95.0 krpm. Further, we have executed empirical studies to evaluate the system’s performance in practical settings. It is observed that when the ratio of low-frequency to fundamental frequency approaches 0.3 and the amplitude ratio exceeds 3, the vigilant monitoring of system stability and reliability is imperative. Collective insights from both computational simulations and experimental studies have enriched our understanding of the dynamic attributes of ultra-high-speed rotor systems. These revelations are crucial for the advancement of more efficacious and resilient rotor systems designed for high-speed applications.

Porous gas bearings (PGBs) have a proactive application in aerospace and turbomachinery. This study investigates the gas lubrication performance of a PGB with the condition of velocity slip boundary (VSB) owing to the high Knudsen number in the gas film. The Darcy-Forchheimer laws and modified Navier-Stokes equations were adopted to describe the gas flow in the porous layer and gas film region, respectively. An improved bearing experimental platform was established to verify the accuracy of the derived theory and the reliability of the numerical analysis. The effects of various parameters on the pressure distribution, flow cycle, load capacity, mass flow rate, and velocity profile are demonstrated and discussed. The results show that the gas can flow in both directions, from the porous layer to the gas film region, or in reverse. The load capacity of the PGB increases with an increase in speed and inlet pressure and decreases with an increase in permeability. The mass flow rate increases as the inlet pressure and permeability increase. Furthermore, the simulation results using VSB are in agreement with the experimental results, with an average error of 3.4%, which indicates that the model using VSB achieves a high accuracy. The simulation results ignoring the VSB overrate the load capacity by 16.42% and undervalue the mass flow rate by 11.29%. This study may aid in understanding the gas lubrication mechanism in PGBs and the development of novel gas lubricants.

Gas bearings have been widely applied to high-speed rotating machines due to their low friction and high rotational speed advantages. Nevertheless, gas lubrication is low viscosity and compressible. It causes the gas bearing-rotor system easy to produce self-excited vibration, which leads to instability of the rotor system and hinders the increase of rotor system speed. It is necessary to study the nonlinear behaviors of the aerostatic bearing-rotor system and the nonlinear vibration of the gas bearing-rotor system, especially considering the distribution mass and flexible and gyroscopic effects of the real rotor. In this paper, the nonlinear behavior of the gas bearing-rotor system is investigated from the viewpoint of nonlinear dynamics. Firstly, the dynamics model of a gas bearing rotor is established by combining the transient Reynolds equation and rotor dynamic equation obtained by finite element method (FEM). The transient Reynolds equation is solved using a hybrid method combining the differential transform method (DTM) and finite difference method (FDM). Then the transient gas force is substituted into the FEM rotor dynamic equation. In the end, based on the bifurcation diagram, the orbit of the rotor center, the frequency spectrum diagram and Poincaré map, the rotor system’s nonlinear behaviors are studied using a solution for the rotor dynamic equation with the Newmark method. Results show that there exists a limited cycle motion in the autonomous rotor system and half-speed whirl in the nonautonomous rotor system.

Gas bearings are widely used in micro- and small turbomachinery. Because of the pursuit of high efficiency, turbomachinery adopts small clearance of rotor and stator. The gas bearing rotor system easily suffers from rub impact due to the inherently low damping and load capacity of gas film. Axial rub impact may lead to catastrophic failure of gas bearing rotor system. Previous work put emphasis on radial rub, and only a few papers researched on the axial rub impact by simulation method. In this paper, dynamic responses of full annular axial rub are investigated numerically and experimentally. A single span flexible rotor test rig is established to support this research. Dynamic characteristics of full annular axial rub of this gas bearing rotor system are obtained with finite element language-APDL. Dynamic characteristics within full speed range are experimentally researched based on the test rig. The dynamic behaviors are analyzed by means of waterfall diagrams, frequency spectrums, orbit trails, and vibration amplitude waveforms. During speed up, half speed whirl and gas film oscillation occur in radial direction. During speed down, the full annular axial rub between rotor thrust disk and gas bearing occurs. When lightly axial rub impact happens, the vibration patterns in the radial direction change barely, and 0 Hz component appears in the axial direction. When serious full annular axial rub impact happens, 0 Hz component occurs in both radial and axial directions and rotor orbit shows transverse motion in radial direction. These forms of dynamic characteristics can be effectively used to diagnose the full annular axial rub impact.

Recently research into active gas bearings has had an increase in popularity. There are several factors that can make the use of gas bearings favourable. Firstly gas bearings have extremely low friction due to the usage of gas as the lubricant which reduce the needed maintenance. Secondly gas bearings is a clean technology which makes it possible to use for food processing, air condition and applications with similar requirements. Active gas bearings are therefore useful for applications where downtime is expensive and dirty lubricants such as oil are inapplicable. In order to keep as low downtime as possible it is important to be able to determine when a fault occurs. Fault diagnosis of active gas bearings is able to minimize the necessary downtime by making certain the system is only taken offline when a fault has occurred. Usually industry demands the removal of any sensor redundancy in systems. This makes it impossible to isolate faults using passive fault diagnosis. Active fault diagnosis methods have been shown able to isolate faults when there is no sensor redundancy. This makes active fault diagnosis methods relevant for industrial systems. It is in this paper shown possible to apply active fault diagnosis to diagnose parametric faults on a controllable gas bearing. The fault diagnosis is based on a statistical detector which is able to quantify the quality of the diagnosis scheme.

This paper presents the dynamic behavior of a rigid rotor supported by a pair of self-acting gas-lubricated bearings which is used in a turbo-expander, the key equipment in a large-scale cryogenic system. In order to restrict the vibration of the rotor relative to bearings, elastomers are mounted between bearings and shell. A finite difference method has been employed to solve the Reynolds equation in time-dependent states. The center orbits of the rotor are got by solving the motion equations. The system state trajectory, Poincare maps, logarithmic spectra maps and bifurcation diagrams are used to analyze the dynamic behavior of the system. The effect of the elastomer suspension to absorb the vibration is verified by comparison with the system with rigid suspension. A set of mass values, damping exponent values and stiffness of elastomer are calculated and compared in this paper. The results show that the rotor center loses its regular behavior gradually with the increase in the rotor mass. The square damping exponent model of the elastomer shows more stability than linear damping suspension model, and the quadratic damping exponent model has a similar motion behavior compared with a linear model. A suitable stiffness of the elastomer is important to the stability of the system. The elastomer with a low stiffness may cause the large amplitude of the vibration, and the system may lose its regular behavior when the stiffness is large enough.

In recent years, the opposed high-speed gas bearing system has been gradually valued and used in the field of precision machinery, especially for precision instruments and mechanisms requiring high speed, high precision, and high rigidity. Although the bearing capacity is not as good as the oil film bearings, it can provide a working environment where the rotor can generate high speed and low heat without deformation of the shaft, and the gas pressure distribution of clearance in bearing also has better stability. Due to the strong nonlinearity of the gas film pressure function of gas bearings and the fact that the actual shaft system possesses dynamic problems including critical speed, spindle imbalance or improper bearing design, it will cause the rotation process of the shaft to produce a nonperiodic motion and instability, and even chaotic motion under certain parameters. And these irregular movements can even cause machine damage or process delays when serious, so in order to understand the process of working under the conditions where the system will have a nonperiodic phenomenon and to avoid the occurrence of irregular vibration especially chaos. In this paper, the opposed high-speed gas bearing system feature will be discussed in detail with three different numerical analysis methods, i.e. the finite difference method, perturbation method, and mixing method. The relevant theories include dynamic trajectories, spectrum analysis, bifurcation diagram, Poincare map, and the maximum Lyapunov exponents. From the results of nonlinear dynamic behavior of the rotor center, periodic and nonperiodic motions occur at different rotor masses and bearing parameters, respectively. Especially, for the chaos of shaft exists at specific intervals and can be distinguished efficiently. Meanwhile, it is found to ensure that the bearing system can suppress the phenomena of chaos actively by adjusting the bearing parameters, and reduce the system loss caused by irregular vibration. It is expected to be an important basis for designing a precision shaft or mechanism and to enhance the stability and performance of bearing system.