應用流阻網路法於靜壓軸承特性分析及靜態剛度最佳化設計

Analysis and Optimal Design for Static Stiffness of Hydrostatic Bearing by Using Resistance Network Method

王亞平(Yea-Ping Wang)

指導教授 ： 康 淵

中原大學/工學院/機械工程研究所/博士(2008年)

https://doi.org/10.6840/cycu200800133

摘要

本文探討靜壓頸軸承採用毛細管節流器及單向薄膜節流器，在不同的油腔數目( )及位移率( )時，節流器參數(毛細管： ，單向薄膜： )、單向薄膜順從係數( )及油腔長度比( )，對承載(無因次承載： ，有因次承載： )及靜剛度(無因次靜剛度： ，有因次靜剛度： )的影響。
本文使用流阻網路法建立各油腔的流量平衡方程式，聯立求解前述之方程式，得各油腔的壓力比，進而計算靜壓頸軸承的承載及靜剛度，最後，利用遺傳基因演算法及全域搜尋法，以最大靜剛度為目標函數求最佳化之設計參數。流阻網路法是指多油腔系統中，潤滑油在相鄰兩油腔間的流動有如網路般的交互影響，其流量( )正比於相鄰兩油腔之間的壓差( )，反比於相鄰兩油腔間之液阻( )。
本文的分析結果顯示，採用毛細管節流器之靜壓頸軸承，（1）油腔數目較多時，選用較小的油腔長度比；（2）靜態負荷較大時，選用較小之節流參數；（3）油腔數目相同且位移率較大時，選用較小的油腔長度比及適度調整各油腔之節流參數；以上三種情形均可提高靜剛度。採用單向薄膜節流器之靜壓頸軸承，經最佳化分析，得到在適當的節流參數範圍以及適當的薄膜順從係數，可獲得具有無限大靜剛度涵義的極大值。

關鍵字

靜剛度 ； 最佳化設計 ； 靜壓頸軸承 ； 流阻網路法

並列摘要

This thesis studies the influence of restriction parameters: (capillary: , membrane: ), membrane compliance ( ) and recess length ratio ( ) and numbers of recess on the load capacity (without unit: , with unit: ) and stiffness (without unit: , with unit: ) of a hydrostatic bearing with capillary and membrane compensators via different recess number ( ) and displacement rate( ).
The flow resistance network method is used by this study to establish the flow continuity equations for all recesses. The pressure ratio of recess can be solved by these equations, then the load capacity and stiffness of the hydrostatic bearing can be obtained. The maximal static stiffness of oil film is defined as the cost function, and the optimum parameters can be designed by genetic algorithms and global domain searching method. The flow resistance network means the flow rate interaction of a multi-recess system is established by the energy equations, which is the flow rate proportionates the pressure difference ( ) between two different recesses, and inverse proportionates the flow resistance ( ).
The simulations results indicate that the bearing with capillary compensator can increase the static stiffness of oil film with the following conditions: (1) the smaller recess length ratio is needed under more recesses number condition. (2) The smaller restriction parameters are needed under heavier load capacity condition. (3) With the same recess number, the smaller recess length ratio and appropriate restriction parameters are needed under more displacement rate condition. The simulations results also indicate that the bearings with membrane compensator can obtain the theoretical near infinite stiffness of oil film with appropriate restriction parameters and membrane compliance.

並列關鍵字

Optimal ； Resistance Network Method ； Hydrostatic Bearing

參考文獻

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3. Kher, A. K., Cowley, A., The design and performance characteristics of a capillary compensated hydrostatic journal bearing. 8th Machine Tool Development and Research Conf., Manchester. 1967; pp. 397-418.

4. Hunt, J. B., Ahmed, K. M., Load capacity, stiffness and flow characteristics of a hydrostatically lubricated six pocket journal bearing supporting a rotating spindle. Proc. ImechE. 1968; 182:53-62.

5. Davies, P. B., A general analysis of multi-recess hydrostatic journal bearings. Proc. ImechE. 1969; 184:1-10.