Measurement of time-varying moment of inertia based on Hilbert transform

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.