模型不确定转子系统动力学降阶模型构建方法  

Construction method of dynamic reduced order model for model uncertain rotor systems

作　　者：励精为治 刘保国[1,2] 刘彦旭 张义彬[1] LI Jingweizhi;LIU Baoguo;LIU Yanxu;ZHANG Yibin(School of Mechanical and Electrical Engineering,Henan University of Technology,Zhengzhou 450001,China;Henan Key Laboratory for Super Abrasive Grinding Equipment,Zhengzhou 450001,China)

机构地区：[1]河南工业大学机电工程学院,河南郑州450001 [2]河南省超硬磨料磨削装备重点实验室,河南郑州450001

出　　处：《机电工程》2025年第3期472-480,共9页Journal of Mechanical & Electrical Engineering

基　　金：国家自然科学基金资助项目(12072106)。

摘　　要：转子系统进行动力学建模时引入的不确定因素会使其产生模型不确定性,而采用模型不确定建模法建立的动力学模型通常维数较高。本征正交分解(POD)能够从系统中提取出主要的特征信息,从而在降低模型维数的同时,保留其关键的动力学特性。因此,针对转子系统不确定动力学模型维数较高的问题,基于POD方法,提出了一种模型不确定转子系统动力学降阶模型的构建方法。首先,建立了转子系统确定性动力学模型,计算了确定模型的临界转速和振型;然后,根据确定模型的低阶振型和实验振型,对不确定模型的散度参数进行了识别;最后,采用非参数建模法和POD方法建立了模型不确定转子系统动力学的降阶模型,搭建了转子实验台,将不确定降阶模型得到的振动响应均值与实验测得的振动响应进行了对比研究。研究结果表明:当转速在3000 r/min~4000 r/min内,模型不确定降阶模型得到的振动响应均值与实测结果更为接近,差异不超过10%,证明该降阶模型对转子系统动力学特性的描述具有准确性和可靠性。研究结果为高维复杂转子系统的动力学建模方法和更高转速工况下振动特性的预测提供了理论参考。Uncertain factors introduced during the dynamic modeling of rotor systems can generate model uncertainties,and the dynamic models established using model uncertainty modeling methods are typically high-dimensional and structurally complex.The proper orthogonal decomposition(POD)can extract the primary characteristic information from the system,thereby reducing the model dimension while preserving its key dynamic properties.To address the issue of high model dimension in the dynamic modeling of uncertain rotor systems,a method for constructing a reduced order dynamic model of uncertain rotor systems was proposed based on POD.Firstly,a deterministic dynamic model of the rotor system was established,and the critical speeds and vibration modes of the deterministic model were calculated.Then,the dispersion parameter of the uncertain mode of the rotor system was identified based on the low-order vibration modes of the deterministic model and the experimental vibration modes.Finally,a non-parametric modeling method and the POD method were used to establish a reduced order dynamic model of the uncertain rotor system.Utilizing an established rotor test rig,a comparative study was conducted between the mean vibration responses obtained from the uncertain reduced order model and experiments.The research results show that within a rotational speed range from 3000 r/min to 4000 r/min,the mean vibration responses derived from the uncertain reduced-order model are in closer proximity to the experimental measurements,with discrepancies not exceeding 10%,it proves that the reduced order model is accurate and reliable in describing the dynamic characteristics of the rotor system.The research results provide theoretical insights for dynamic modeling of high-dimensional complex rotor systems and prediction of vibration characteristics under high-speed operating conditions.

关 键 词：本征正交分解 转动机件 转子系统 模型不确定 降阶模型 动力学特性 散度参数识别 

分 类 号：TH133[机械工程—机械制造及自动化]