• CN:11-2187/TH
  • ISSN:0577-6686

›› 2012, Vol. 48 ›› Issue (20): 22-26.

• 论文 • 上一篇    下一篇

基于Hilbert变换的时变转动惯量测量研究

赵岩;张晓琳;王军;唐文彦   

  1. 哈尔滨工业大学电气工程及自动化学院
  • 发布日期:2012-10-20

Measurement of Time-varying Moment of Inertia Based on Hilbert Transform

ZHAO Yan;ZHANG Xiaolin;WANG Jun;TANG Wenyan   

  1. School of Electrical Engineering and Automation, Harbin Institute of Technology
  • Published:2012-10-20

摘要: 针对时变转动惯量测量的问题,建立基于扭摆法的时变转动惯量测量模型,提出基于Hilbert变换的时变转动惯量计算方法。根据分析动力学的原理,利用第二类拉格朗日方程建立基于时变转动惯量的单自由度扭摆运动方程。对物体的角位移信号进行Hilbert变换并构造解析信号。利用角位移信号的瞬时角频率和包络信号计算扭摆运动的瞬时无阻尼固有频率。根据瞬时无阻尼固有频率求出物体的转动惯量。利用基于气浮转台的扭摆系统,对转动惯量线性变化的试验样件进行转动惯量测量。由于测量系统采用气浮转台,因此,消除机械摩擦力对转动惯量测量的影响。试验结果表明,试验样件的转动惯量测量值的相对误差小于0.5%,从而验证基于Hilbert变换的时变转动惯量测量方法的有效性。

关键词: Hilbert变换, 扭摆法, 时变系统, 转动惯量

Abstract: In order to measure the time-varying moment of inertia, the measurement model based on torsion pendulum is established and the calculation method of moment of inertia based on Hilbert transform is proposed. According to the principle of analytical dynamics, the differential equation of the torsion pendulum is presented using the second Lagrange equation. The analytic signal is calculated by the Hilbert transform of the angular displacement signal. The instantaneous undamped natural frequency is computed by the instantaneous angular frequency and the envelope signal. The time-varying moment of inertia is calculated by the instantaneous undamped natural frequency of the torsion pendulum. The torsion pendulum system based on air-turntable is used to measure the time-varying moment of inertia of the test object. With the introduction of the air-turntable, the influence of friction force can be reduced. The experimental result shows that the relative measurement error of the time-varying moment of inertia is less than 0.5%, which indicates the validity of the measurement method.

Key words: Hilbert transform, Moment of inertia, Time-varying system, Torsion pendulum

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