隐函数求解法在单供气孔静压气体球轴承参数优化中的应用

摈弃不可压缩流简化,在已知承载力的条件下,以最大静刚度为设计准则,建立了显含单供气孔静压气体球轴承3个结构参数和隐含轴承刚度的隐式方程。利用隐函数的导数及矩阵的正定性,讨论了隐函数极值存在的条件。在约束条件中加入了小孔节流器的实现条件、稳定性工作条件及加工制造限制条件等。编制MATLAB程序求解了隐函数极值及其对应的轴承结构参数取值,计算结果与使用不可压缩流简化得到的显式刚度方程的优化参数完全一致。

Application of implicit function solving method in optimization of externally pressurized spherical gas bearing with single orifice

The implicit expression of the stiffness which includes three structure parameters of externally spherical gas bearing with single orifice was established in accordance with the design criteria of the largest stiffness with the known load.Making use of the derivative of implicit function and the matrix positive definiteness,the paper discusses the conditions of the existence of the implicit function extreme.By including the conditions of orifice compensation,stable working conditions and the restrictions on manufacture processing and others as the constraints,MATLAB program was established for calculating the extreme value of the implicit function and the corresponding bearing structure parameters.The results are consistent with the optimized structural parameters obtained by using simplified incompressible flow assumptions.