Torsion pendulum measurement method for time varying moment of inertia

Abstract A time-varying moment of inertia (MOI) measurement model based on the torsion pendulum method is studied. According to the principle of dynamics, the motion equation of torsion pendulum with single degree of freedom is established by using the second Lagrange equation modeling, which indicates the time-varying MOI can be obtained by the instantaneous undamped natural frequency of torsional pendulum motion and the torsion bar coefficient. Among them, the instantaneous frequency is calculated by the instantaneous angular frequency and envelope signal of angular displacement using Hilbert transform. The torsion bar coefficient is calibrated by the standard weight with known MOI, and has been compensated by temperature. Based on air floating turntable, the torsion pendulum system is built to measure the MOI of fine sand in the funnel, which can minimize the effects of mechanical friction. The relative error of MOI between calculating the result and measuring the value is less than 0.65%, which verifies the effectiveness of the proposed time varying temperature compensation method.