汽轮机组的数学机械化建模与算法分析

Mechanized Mathematics Modelling and Algorithm Analysis for a Turbine Set

对于大型汽轮发电机组,描述系统运行状态的微分方程相对复杂且维数很高,为对其进行解析分析,首先应用模态综合法建模得到降阶后的微分方程组,经代数变换后应用数学机械化方法进行解析建模分析。由于参加消元的节点位移变量均是线性变量,故消元时可保留油膜力表达式的非线性成分不变,这样就得到了维数相对较低且等式右端含有非线性油膜力表达式的代数方程组。为实现具有上述特点的代数方程组的求解,提出了既不同于解析法又与经典数值算法不完全相同的微分控制算法思想,据此实现对复杂汽轮发电机组转子系统的建模及对节点位移响应的分析与预测。

For a large turbine generator set, considering higher order and higher dimension of nonlinear differential equations governing the motion of its rotor-bearing system, the mechanized mathematics can be used as a means of modeling and analyzing rotor-bearing system after reducing order of differential equations by component mode method, in order to obtain the analyzed solutions of the turbine set. Lower dimension algebraic equations included nonlinear oil force expressions are obtained, because the nonlinear parts of oil force expressions can be remained after eliminating the linear coupling variable of node displacements of rotor-bearing system of the turbine set. Differential control method（DCM） that was different to both analyzed method and typical numerical method is presented. According to proposed method the model of complex turbine set is described and node displacement response of set is analyzed and predicted.