预估校正Galerkin方法及其在大型转子-轴承系统中的应用

Predictor-corrector Galerkin method with its application in a large-scale rotor-bearing system

根据非线性Galerkin方法和后处理Galerkin方法的思路,提出了用于大型非线性动力系统降阶的预估校正Galerkin方法。在模态坐标下,将大型非线性动力学系统分成‘主子系统’,‘从属子系统’和‘可忽略子系统’。略去‘可忽略子系统’的影响,发展一种新颖的预估校正算法综合处理‘主子系统’和‘从属子系统’,以达到降维和节省计算时间的目的。以某200MW汽轮机组低压转子的有限元模型作为分析对象,通过比较系统的动力学特性验证新方法的精度和效果。结果表明:新方法可在不影响精度的前提下,大幅缩减计算时间。

Based on nonlinear Galerkin method and post-processing Galerkin method,a predictor-corrector Galerkin method was proposed to deal with order reductions of a large-scale nonlinear dynamic system.In modal coordinates,a large-scale nonlinear dynamic system was split into a 'dominant' subsystem,a 'slave' subsystem and a 'negligible' subsystem.Neglecting the effects of the 'negligible' subsystem,a novel predictor-corrector algorithm was developed to deal with the 'dominant' subsystem and the 'slave' subsystem.In such a way,a lower reduced-order system could be obtained to maintain the precision and save the computing time.A low-pressure rotor-bearing model of a 200MW turbine set was given to illustrate the precision and efficiency of the predictor-corrector Galerkin method compared with the standard Galerkin method.It was shown that the method gives a considerable increase in precision but a lower computational cost.