Analysis of air bearing torsion pendulum moment of inertia measurements including nonlinear oscillation and damping

For precise measurement of the moment of inertia (MOI) of asymmetric objects, using an air bearing torsional pendulum, the nonlinearity of the torsion bar and the damping effect caused by the interaction between air and sample need to be included in the analysis. The instantaneous undamped natural frequency and instantaneous damping coefficient of the motion are obtained from the Hilbert transform of the angular displacement signal and are used for data fitting to calculate the MOI. Measurements for algorithm verification were made using a special sample with large windvanes to increase the damping effect. The nonlinear analysis of the MOI experimental results indicated a relative error of less than 0.1% compared with 0.3% for classical linear analysis of the data.