主动控制压电旋转悬臂梁的参数振动稳定性分析

唐冶; 王涛; 丁千

doi:10.6052/0459-1879-19-211

主动控制压电旋转悬臂梁的参数振动稳定性分析

doi: 10.6052/0459-1879-19-211

唐冶^*†,,
王涛^*,
丁千^*2),

^* 天津大学机械工程学院,天津 300072
^† 安徽工程大学机械与汽车工程学院,安徽芜湖 241000

基金项目: 1) 国家自然科学基金项目(51575378);1) 国家自然科学基金项目(11902001);1) 国家自然科学基金项目(11972245);中国博士后科学基金项目(2018M641643);安徽省自然科学基金项目(1908085QA13)

详细信息

通讯作者:
丁千

中图分类号: O322
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出版历程
- 收稿日期: 2019-08-02
- 刊出日期: 2019-11-18

STABILITY ANALYSIS ON PARAMETRIC VIBRATION OF PIEZOELECTRIC ROTATING CANTILEVER BEAM WITH ACTIVE CONTROL

Tang Ye^{*†
,},
Wang Tao^*,
Ding Qian^{*2)
,}

^* School of Mechanical Engineering, Tianjin University,Tianjin 300072,China
^† School of Mechanical and Automotive Engineering, Anhui Polytechnic University, Wuhu 241000,Anhui, China

摘要

摘要: 在工程实际中旋转机械由于制造和加工误差,装配的不均匀性等原因,往往会脉动运行,这将使得机械系统发生参数振动. 当脉动参数满足一定关系时,这种参数振动将会失稳,进而影响机械结构的正常运转. 本文针对这一问题,引入压电材料对脉动旋转悬臂梁系统的振动进行控制,研究主动控制悬臂梁系统的参数振动优化设计问题,采用 Hamilton 变分原理与一阶 Galerkin 离散相结合的方法,建立了受速度反馈传感器主动控制的压电旋转悬臂梁的一阶近似线性控制方程. 运用多尺度方法,得到了压电旋转悬臂梁系统在发生1/2亚谐波参数共振时稳定性边界的控制方程,并利用直接分析方法验证了解析摄动解的正确性. 将摄动解中临界阻尼比和轮毂角速度脉动幅值的无量纲参数作为评价系统稳定性能的指标. 通过数值算例,分析了轮毂半径、轮毂角速度平均值和脉动幅值、梁长以及速度传感器的反馈增益系数对系统稳定性区域的影响. 研究结果表明,梁长、轮毂半径、脉动幅值会降低系统稳定性,反馈增益系数可以提高系统稳定性,而轮毂角速度平均值与系统稳定性之间有非单调的关系. 为进一步设计压电旋转机械结构提供了理论依据.
- 压电旋转悬臂梁 /
- 主动控制 /
- 参数振动 /
- 稳定性 /
- 多尺度法
Abstract: In engineering application, rotating machines tend to be pulsating operation due to the errors of manufacturing and processing as well as the non-uniformity of assembly, which may cause parametric vibration of the system. Furthermore, if the pulsation parameters satisfy a certain relationship, the parametric vibration will cause the system to lose stability, which furtherly affects the normal operation of mechanical structures. In view of this problem, the piezoelectric material is introduced to suppress vibration of rotating cantilever beam subjected to parametric exciting. The problem about the parametric optimization and design of rotating cantilever beam with active control is studied in this paper. The first order approximate linear equation governing the piezoelectric rotating cantilever beam controlled by velocity feedback sensor is established based on the Hamilton' principle combining with the first-order Galerkin discretization method. Then, the multi-scale method is applied to obtain the governing equation of stability boundary of the piezoelectric rotating cantilever system with the 1/2 sub-harmonic parametric resonance. The correctness of the perturbation solution is verified by the direct analysis method. The critical damping ratio and the dimensionless parameter of pulsating amplitude of hub angular velocity in the perturbation solution are regarded as the indicators to evaluate the system stability. Numerical examples are presented to illustrate the effects of the hub radius, the average value and pulsating amplitude of hub angular velocity, the beam length and the feedback gain coefficient of velocity sensor on the dynamic stability. The results show that the stable region can be increased with the decrease of the beam length, the hub radius and pulsating amplitude of hub angular velocity, but the raise of the feedback gain coefficient, moreover, the relation between the average value of hub angular velocity and the stability is not monotonous. It provides a reference for the further design of piezoelectric rotating machinery structure.
- piezoelectric rotating cantilever beam /
- active control /
- parametric vibration /
- stability /
- multi-scale method

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