Abstract
Dual-directional coupled aerodynamic bearing (DCAB) systems have received considerable attention over the past few years. These systems are primarily used to solve air lubrication problems in high-precision mechanisms and equipment that run at a high rotational speed and require high rigidity and precision. DCABs have the advantages of axial and radial thrust and provide high rigidity, dual-directional support, and high load-carrying capacity. In DCAB systems, the nonlinearity of the air film pressure and dynamic problems, such as critical speed, unbalanced air supply, or poor design, can cause the instability of the rotor-bearing system and phenomena such as nonperiodic or chaotic motion under certain parameters or conditions. Therefore, to investigate what conditions lead to nonperiodic phenomena and to avoid irregular vibration, the properties and performance of the DCAB system were explored in detail by using three numerical methods for verifying the accuracy of the numerical results. The rotor behavior was also studied by analyzing the spectral response, the bifurcation phenomenon, Poincaré maps, and the maximum Lyapunov exponent. The numerical results indicate that chaos occurs in the DCAB system for specific ranges of the rotor mass and bearing number. For example, when the rotor mass (mr) is 5.7 kg, chaotic regions where the maximum Lyapunov exponents are greater than 0 occur at bearing number ranges of 3.96–3.98 and 4.63–5.02. The coupling effect of the rotor mass and bearing number was also determined. This effect can provide an important guideline for avoiding an unstable state.
Highlights
Air lubrication theory was introduced in 1886 by Reynolds, who derived the well-known Reynolds equation that indicates the relationship among air pressure distribution, density, and velocity [1].In 1958, Whipple [2] analyzed the characteristics of herringbone-grooved air bearings
Rotor center the displacements bearings and the rotor mass were used as bifurcation parameters and a obtained with the perturbation method exhibited unstable numerical phenomena under specific bifurcation diagram was stability analysis
The finite-difference method (FDM), perturbation method, and hybrid method were used in the numerical analysis to determine the gas film pressure distribution and gas film thickness function of the Reynolds equation
Summary
Air lubrication theory was introduced in 1886 by Reynolds, who derived the well-known Reynolds equation that indicates the relationship among air pressure distribution, density, and velocity [1]. Wang et al [13,14,15] have analyzed the gas film pressure distribution in different air-bearing systems and have proposed effective solutions for investigating rotor dynamics. They proposed a numerical method with fast convergence for analyzing the Reynolds equation. The range of dynamic behaviors chaos must be avoided, in precision bearing systems In this regard, this study mainly exhibited by this system under different operating conditions was studied. The range of dynamic behaviors exhibited bifurcation properties of the nonlinear behavior produced by the system rotor were examined These by this system under different operating conditions was studied. Can be used to judge if the system displays chaos and predicts dynamic system trajectories accurately
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