- 學位論文
數值方法應用於深溝滾珠軸承變形及薄膜式節流器流量分析探討
Analysis and Investigation for Deflection of Deep Groove Bearing and Flow Rate of Membrane-Type Restrictor by Using Numerical Methods
摘要
滾珠軸承會隨著徑向負荷產生接觸變形，因此會造成軸頸的偏心，此將影響工具機之加工精度。對於靜壓軸承使用節流器會產生節流阻力決定軸頸偏移位置，而節流阻力須由節流器流量計算出來，因此本文研究了滾珠軸承受徑向力所產生接觸變形及靜壓軸承中薄膜式節流器流量的計算，作為結構彈性軸承設計的依據。 對於滾珠軸承變形計算，傳統上採用John-Harris方法(JHM)，其係基於Hertz接觸理論採半無限空間假設下推導出來，然而滾珠軸承幾何形狀複雜，因此JHM無法正確的計算出軸承接觸變形。對於薄膜式節流器傳統的流量計算公式，是先使用彈性公式計算出薄膜變形，然後帶入基於流體層流理論所導出之流量公式，然而傳統公式忽略薄膜與油膜耦合的效應，無法計算出正確的薄膜變形，此對流量計算影響非常大。 因此，本文利用有限元素法(FEM)基於懲罰函數法及耦合分析方法，分別計算軸承變形及節流器流量的計算，並藉由實驗結果分別確認有限元素計算結果之正確性。然而，使用有限元素法解滾珠軸承接觸問題及節流器薄膜-油膜耦合問題時，因需作迭代運算需較傳統方法花費較長之電腦計算時間。因此，本文使用有限元素方法計算結果及曲線配適(curve fitting)來改善Hertz接觸公式中負荷-接觸變形關係及彈性公式中薄膜變形-壓力關係，使得修正後之傳統公式之計算結果與FEM結果接近。
並列摘要
The ball bearing may generate deformation due to radial load, which causes shaft eccentricity. This will affect the precision of tool machine. For the hydrostatic bearing, the restrictor may generate the restriction resistance to decide the location of journal, in which the restriction resistance may be determined by calculating the flow rate of restrictor. Therefore this study studies the bearing deflection and restrictor flow rate determination for the design of bearing. The traditional bearing deflection determinations adopt John-Harris method (JHM) which is based on the assumption of half-infinite space according to Hertz’s contact theory. However, the geometry of a ball bearing is complex and so JHM is not able to determine the bearing deflection accurately. For the traditional flow rate determination of membrane-type restrictor, the membrane deflections are determined by using elastic formula first. Then the membrane deflections are substituted into the fluid formula from laminar flow theory to determine the restrictor flow rate. However, the traditional formula, neglecting the influence of the coupling of membrane and oil film, is not able to determine the flow rate accurately. Hence, this study applies FEM with penalty function method and coupling analysis method to determine the bearing deflection and restrictor flow rate, respectively. The FEM results are verified by comparing to the experiment results. However, the bearing deflection and restrictor flow rate determinations by using FEM need longer computer time than traditional formula. Furthermore, this study uses FEM results and curve fitting to modify the load-contact deflection relationship from Hertz theory and membrane deflection-pressure relationship from elastic formula, thus making the modified formula results consistent with the FEM results.