Inertia property determination by spectrum analysis of damped oscillation detection signal

Abstract

Oscillation method is the most effective approach to determine the inertia properties of rigid bodies. This paper proposes a new signal processing method to determine the moment of inertia (MoI) accurately in the presence of high frictional damping when using a torsion pendulum setup. A mathematical model of damped oscillation is established, and the analytic form of Fourier transformation of the damped torsional oscillation is derived. A formula for calculating the MoI in relation to the dominant frequency and damping ratio is also derived. An algorithm regarding periodic extension and normalization of torsional oscillation signal is proposed to calculate the dominant frequency and damping ratio of torsional oscillation in the frequency domain. The feasibility and accuracy of this algorithm are verified by both numerical simulations and measurement experiments. The experimental results show that the proposed method has good measurement repeatability, and the relative error of measurement is within 0.80%.