非线性阻尼条件下物体转动惯量测量研究

Measurement of a moment of inertia of a sample piece under nonlinear damping condition

为了实现非线性阻尼条件下物体转动惯量的测量,分析非线性阻尼对扭摆运动的影响,建立了扭摆运动的非线性微分方程,利用Hilbert变换计算扭摆运动的瞬时无阻尼固有频率和瞬时阻尼系数,从而求出被测物体的转动惯量。通过增加被测物体的面积来增强非线性阻尼的效果,利用基于扭摆法的转动惯量测量系统对阻尼样件进行了测量。实验结果表明:在非线性阻尼条件下,阻尼样件转动惯量测量的相对误差小于1%。

In order to measure the moment of inertia of a sample piece under nonlinear damping condition, the influence of nonlinear damping on the movement of a torsion pendulum was analyzed. The nonlinear motion equation of the torsion pendulum was established. The moment of inertia of a sample piece was calculated with instantaneous undamped natural frequency and the instantaneous decay coefficient of the torsion pendulum computed using Hilbert transformation. In order to increase the effect of the nonlinear damping, the damping paddles were used to increase the area of the sample piece. The moment of inertia of the sample piece was measured with a system based on a torsion pendulum. The experimental results showed that the relative error of the moment of inertia of the sample piece is less than 1% under condition of nonlinear damping.