Research On Nonlinear Problems In Moment Of Inertia Measurement Based On Torsion Pendulum

The moment of inertia (MOI) expresses the inertia of the rigid body duringrotation. The MOI measurement has important practical significance because theMOI is measured in the industrial fields such as aircraft, automobile, machinery,instrumentation. The existing MOI measurement technique is suitable for linearmeasurement systems. Due to the complicated shape and large size of measurementobjects, there exist nonlinear factors in the MOI measurement. With the wideapplication of composite material and alloy material, nonlinear factors appear in theMOI measurement because of the nonlinear characteristic of the material. Thenonlinear factors affect the accuracy of MOI measurement.In order to improve the accuracy of MOI measurement, the influence ofnonlinear factors on the MOI measurement based on torsion pendulum is considered.The time-varying and time invariant MOI measurement models based on thenonlinear dynamic systems are described. The influence of the nonlinear factors onthe MOI measurement is analyzed. The MOI calculation method for the nonlineardynamic system is presented. The MOI measurement system based on torsionpendulum is established. The validity of MOI measurement model and calculationmethod is verified by the experimental results. The main contents are as follows:The influence of nonlinear factors on the MOI measurement is considered. Thetime-varying and time invariant MOI measurement models based on nonlineardynamic systems are established by the principal of analytical dynamics. For thequantitative analysis of the MOI measurement model, the approximate analyticalsolution is computed by the solving method of nonlinear differential equation. Thenumerical solution is used to validate the analytical solution. The influence of thenonlinear factors on the MOI measurement is analyzed by the numerical simulationmethod, which provides theoretical basis for the MOI accurate measurement.The functional relationship between MOI and instantaneous undamped naturalfrequency is determined by the time-frequency analysis method based on Hilberttransformation. The MOI calculation method based on Hilbert transform ispresented. The analytical signal is formed by the Hilbert transform of the angulardisplacement signal. The MOI is calculated by the instantaneous undamped natural frequency which is computed by the analytical signal. This method is suitable forthe calculation of the time-varying and time invariant MOI under the condition ofnonlinear system. For different MOI measurement models，the correctness of theMOI calculation method based on Hilbert transform is verified by the numericalsimulation method.In order to ensure the accuracy of MOI measurement, the influence of the endeffect in Hilbert transform on the MOI measurement is analyzed. The signalextension is used to inhibit the end effect. In order to reduce the effect of the noiseon the MOI measurement, the finite impact response (FIR) filter based on Kaiserwindow is designed. It is used to filter the experimental signal before the MOIcalculation.In order to verify the validity of MOI measurement model and calculationmethod, the MOI measurement system based on torsion pendulum is established.The experimental samples with time invariant and time-varying MOI are designed.The experimental samples can make torsion pendulum movement by the air-hoveredturntable. The angular displacement signal is measured by the gating sensor.According to the nonlinear model of MOI measurement, the MOI of theexperimental samples is calculated by the calculation method based on the Hilberttransform. The experimental results show that the MOI measurement results basedon the nonlinear model are better than the results based on the linear model. So theexperimental results verify the validity of the nonlinear measurement model. Theexperimental results show that the accurate calculation of time invariant and thetime-varying MOI is achieved by the method presented by this paper. So theexperimental results verify the validity of the MOI calculation method presented bythis paper.