高速柔性转子系统动力特性稳健设计方法

高速柔性转子系统为控制其转子变形和多阶临界转速分布，常采用多支点支承方案，而转子-支承结构力学参数的分散性，使得转子动力特性设计成为多变量多目标非确定性优化问题。通过Lagrange法建立柔性转子运动方程，定义罚函数以定量描述多阶临界转速的分布特征，采用区间数学分析方法和遗传算法结合的方式，建立了基于临界转速分布特征优化及连接结构刚度损失控制的转子系统动力特性稳健设计方法。算例表明，通过将多阶临界转速集中于一定转速区间，并控制连接结构弯曲应变能分布比例，可有效减小转子通过多阶临界转速时的振动响应，降低转子动力特性对连接结构受力状态变化的敏感度，提高高速柔性转子系统动力特性的稳健性。 

Robust design method for dynamic properties of high-speed flexible rotor systems

In order to control the deformation of rotor and distribution of multiple critical speeds, it is common to adopt multi-support configuration, which indicates that the optimization is a multi-objective, multi-variable and non-deterministic problem, taking into account parameter uncertainties. An equation of motion for flexible rotor is derived with the aid of Lagrange equation. Penalty functions are introduced to quantitatively describe the distribution feature of multi-order critical speeds. A robust design method for dynamic properties of rotor is presented based on the optimization of critical speed distribution and stiffness loss control of joint structure with the combination of interval analysis method and genetic algorithm. A numerical example shows that by concentrating the multi-order critical speeds into a certain speed interval and controlling the bending strain energy proportion of joint structure, the vibration response passing through multi-order critical speeds and sensitivity of rotor dynamic properties to the change of joint structure stiffness loss are both reduced, thus improving the robustness of this type of rotor system.