Dynamic Study of Pocket-Orifice Compensated Air Bearing System

腔孔節流氣壓軸承系統之動態分析研究

汪正祺(Cheng-Chi Wang) ； 張致文(Chih-Wen Chang) ； 李素娥(Tsui-Er Lee)

《中國機械工程學刊》 41卷5期 (2020/10) Pp. 575-584

摘要

Pocket-orifice compensated air bearing (PCAB) systems have been potential for use in high-rotational speed, and high-precision machine tool extensively and applied for a variety of mechanical engineering application. However, under certain operating conditions, PCAB systems exhibit non-periodic or chaotic motion as the result of a nonlinear pressure distribution within the gas film, gas supplied imbalances, an inappropriate design, and so forth. So, in order to understand and suppress as the bearing system occurs non-periodic motions and under what kind of operating conditions, the dynamic response of the PCAB system has been analyzed by using two different methods, namely a perturbation method and a hybrid numerical scheme combining the finite difference method and the differential transformation method. The key performances and solutions under different physical models obtained by these two methods are compared and verified. The dynamic behavior of rotor center has been examined under different operating conditions by bifurcation diagram, Poincaré maps, power spectra and Lyapunov exponents etc. The results reveals that the bearing number affects the orbits of the rotor which show chaotic behaviour in the interval of 16.41≦Λ＜18.2. The results obtained in this study can be used as a basis for future PCAB system design and the prevention of instability.

關鍵字

Pocket-Orifice Compensated ； Air bearing system ； Chaotic motion

並列摘要

本文旨在探討腔孔節流氣壓軸承系統針對高轉速、高剛性、高精度支承需求之精密儀器與機構的氣膜潤滑問題。此軸承由於具有外部供氣及腔孔節流兩種特性與優點，因此可提供較其他氣膜軸承系統具有更優異的穩定性。研究此軸承系統時，由於氣膜壓力函數具有強烈的非線性，且實際軸承系統所具有的動態問題包含臨界速度、供氣失衡或軸承設計不當等，都將導致轉子軸承系統在某些參數條件下，其旋轉過程中產生非週期或混沌運動及不穩定的現象。而這些不規則運動嚴重時甚至造成機件損傷或破壞，因此為能瞭解系統在工作的過程中何種狀況下會產生非週期的現象，以避免產生不規則的振動效應，本文以微擾法及混合法等數值分析的方式將軸承的相關特性做一詳盡的探討，並以相關理論包括分岔圖、龐卡萊映射、頻譜響應及李奧維指數針對轉子之非線性行為進行研究分析。結果顯示，以軸承數Λ為例，軸承數會影響轉子的軌跡與軸承系統性能，尤其轉子的動態軌跡在16.41≤Λ＜18.2的區間內會產生非線性混沌行為，此種非週期性行為會造成軸系損害。本研究所獲得的結果可以用作將來腔孔節流氣壓軸承系統的穩定性設計和防止轉子產生動態不穩定的設計基礎及重要依據。