用于柔性转子主动控制的等几何Timoshenko梁模型及其数值验证

发布时间：2018-02-07 11:43

  本文关键词： 等几何方法 柔性转子模型 Timoshenko梁 振动控制 磁悬浮轴承　出处：《西安交通大学学报》2016年10期 　论文类型：期刊论文

【摘要】：为了克服采用标准有限元方法建立的转子模型自由度多不便直接用于控制器设计的问题,结合等几何分析方法的精度高、自由度少的特点,提出了把低阶等几何Timoshenko梁模型运用到柔性转子的主动控制中,并进行了数值验证。首先,给出了半离散等几何模型及在主动控制中作为转子控制输入信号的各类边界条件;其次,分别对比了高、低阶等几何模型的奇异值响应以及简支条件下的高、低阶模型的数值解与理论解;最后,在采用磁悬浮轴承支撑和给定分布不平衡力扰动的条件下,对转子进行了分散比例微分(PD)仿真控制。结果表明:所采用的低阶模型的奇异值响应在前6阶临界转速范围内与高阶模型基本一致;高阶模型的前10阶模态频率很好地吻合了理论解,低阶模型前4阶模态频率误差在0.2%以内;高、低阶等几何梁模型下的转子不平衡振动位移稳态响应的差别很小,该误差可看成工作转速下的同频小扰动。低阶等几何梁模型在低频范围的高精度验证了该方法所得低阶模型直接用于控制器设计的可行性。
[Abstract]:In order to overcome the problem that the degree of freedom of rotor model established by standard finite element method can not be directly used in controller design, combined with the characteristics of high precision and less degree of freedom of isometric analysis method, The low order isometric Timoshenko beam model is applied to the active control of the flexible rotor, and the numerical results are given. Firstly, the semi-discrete geometric model and the boundary conditions used as the input signal of the rotor control are given. Secondly, the singular value responses of high and low order geometric models and the numerical and theoretical solutions of high and low order models under simply supported conditions are compared respectively. The distributed proportional differential (PDD) simulation control of the rotor is carried out. The results show that the singular value response of the low order model is basically consistent with that of the higher order model in the first 6 order critical speed range. The first 10 order modal frequencies of the high order model are in good agreement with the theoretical solution. The error of the first 4 order modal frequencies of the lower order model is less than 0.2%, and the difference in the steady state response of the rotor unbalanced vibration displacement under the high and low order isometric beam model is very small. The error can be regarded as a small disturbance of the same frequency at the working speed, and the high accuracy of the low-order isometric beam model in the low frequency range verifies the feasibility of using the low-order model directly in the controller design.
【作者单位】： 西安交通大学能源与动力工程学院;
【基金】：国家自然科学基金资助项目(51236006) 中央高校基本科研业务费专项资金资助项目(XJJ2013002)
【分类号】：O347.6;O241.82
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本文编号：1494298