转子系统二次降维及其在非线性转子动力学分析中应用

Dimension reduction for high-dimensional dynamic systems is a difficult technological problem, attracting the long-term attention of researchers in the aear of nonlinear dynamics. The dimension of actual engineering systems is very high and affected by nonlinear factors, the dimension of the results obtained by the dimension reduction method for the first time is still high, the qualitative analysis of the reduced system is very difficult. So the dimension reduction technology for the second time should be proposed to reduce the dimension of the system again. This proposal focuses on the study of rotor system of the aero-engine, Craig-Bampton(CB)modal synthesis mtheod is applied to reduce the dimension of aero-engine’s complex rotor system model estabilished by the finite element method for the first time. The proper orthogonal decomposition(POD)method is used for dimension reduction of the rotor model for the second time based on the proper orthogonal mode(POM)energy estimation method. The dynamic behaviors of this reduced model are analyzed. The rotor system with rub-imapct is selected as experimental verification object, the singularity of the reduced system model obtained by the second dimension reduction is analyzed, and the bifurcation behaviors in the engineering parameter domains are studied. The efficiency of the proposed second dimension reduction method to the rotor system is verified via the simulation experiment.

高维非线性动力学系统降维是非线性动力学领域研究人员长期关注的技术难题。实际工程系统模型由于维数过高并且受到非线性因素的影响，对其进行一次降维后的结果维数仍然很高，很难对简化系统进行定性分析。因此需要提出二次降维技术，再次对其进行降维。本项目以航空发动机转子系统为研究对象，对于有限元方法建立的航空发动机复杂转子系统实体模型，应用Craig-Bampton(CB)模态综合法进行一次降维；基于本征正交模态(POM)能量判别法，再用本征正交分解(POD)方法对模型进行二次降维；然后以此降维模型对系统动力学特性进行分析。以碰摩故障转子系统为实验验证对象，对二次降维得到的简化系统进行奇异性分析，研究其在工程参数域内的分岔特性。对提出的二次降维方法进行模拟试验验证，以证明其对于转子系统的有效性。

高维非线性动力学系统降维是非线性动力学领域研究人员长期关注的技术难题。本项目以航空发动机转子系统为研究对象，对于有限元方法建立的航空发动机复杂转子系统实体模型，提出了转子系统二次降维技术，应用Craig-Bampton (CB) 模态综合法进行一次降维；基于本征正交模态 (POM) 能量判别法，再用本征正交分解 (POD) 方法对模型进行二次降维；然后以此降维模型对系统动力学特性进行分析。以碰摩故障转子系统为实验验证对象，对二次降维得到的简化系统进行奇异性分析，研究其在工程参数域内的分岔特性，揭示了碰摩故障的非线性动力学行为。对提出的二次降维方法进行了模拟试验验证，证明了其对于转子系统的有效性。本项目执行期间发表SCI论文20篇，受理发明专利6项，参加国际会议5次，国内会议16次。