Abstract
In recent years, spiral-grooved air bearing systems have attracted much attention and are especially useful in precision instruments and machines with spindles that rotate at high speed. Load support can be multidirectional and this type of bearing can also be very rigid. Studies show that some of the design problems encountered are dynamic and include critical speed, nonlinearity, gas film pressure, unbalanced rotors, and even poor design, all of which can result in the generation of chaotic aperiodic motion and instability under certain conditions. Such irregular motion on a large scale can cause severe damage to a machine or instrument. Therefore, understanding the conditions under which aperiodic behaviour and vibration arise is crucial for prevention. In this study, numerical analysis, including the Finite Difference and Differential Transformation Methods, is used to study these effects in detail in a front opposed-hemispherical spiral-grooved air bearing system. It was found that different rotor masses and bearing number could cause undesirable behaviour including periodic, subperiodic, quasi-periodic, and chaotic motion. The results obtained in this study can be used as a basis for future bearing system design and the prevention of instability.
Highlights
Graduate Institute of Precision Manufacturing, National Chin-Yi University of Technology, No 57, Sec. 2, Zhongshan Rd., Taiping Dist., Taichung 41170, Taiwan
From 2007 to 2011, Wang [16,17,18] used the Finite Difference Method to investigate gas film pressure in a herringbone air bearing system, and he used orbit graphs, spectrograms, and bifurcation diagrams to analyze the dynamic behaviour of the centres of the rotor and the journal
The results obtained by the hybrid method that combines both the Differential Transformation Method (DTM) and the Finite Difference Method (FDM) agree with the results of the traditional Finite Difference Method and Perturbation Method
Summary
The mathematical theory of gas lubrication was first introduced by Reynolds [1] in 1886 and he derived a partial differential equation related to pressure, density, relative motion, and speed, the well-known Reynolds equation. From 2007 to 2011, Wang [16,17,18] used the Finite Difference Method to investigate gas film pressure in a herringbone air bearing system, and he used orbit graphs, spectrograms, and bifurcation diagrams to analyze the dynamic behaviour of the centres of the rotor and the journal. He learned that, under different operational conditions, the centres of the rotor and the journal demonstrated periodic, quasi-periodic, and subharmonic motion, and he discovered that the system could generate nonlinear chaotic motion. Based on such analysis and study, determinations on whether the chaotic phenomena occur in the system and accurate prediction on the dynamic orbits of the system can be achieved
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