A high-precision measurement method for moment of inertia based on torsion pendulum method

Abstract

The precise determination of moment of inertia (MOI) holds paramount importance in investigating the rotational dynamics of an object. Based on the torsion pendulum system, a novel high-precision measurement method for MOI is developed by using the constant force in this paper. Firstly, the extreme response characteristics of a torsional pendulum measurement system under a constant force are discussed in detail in this paper, and the relationships between the system damping ratio, natural frequency, MOI and the extremal characteristic points of the system response are determined through the linear regression analysis. By applying the superposition principle, the MOI for the object being measured can be computed. As the performance of the constant force source is the key to ensure the measurement accuracy, this paper develops an electromagnetic force source, which consists of a coil and a permanent magnet, and the electromagnetic force variation law with the relative position of the coil and permanent magnet is investigated by utilizing a high-precision electronic balance, and then the optimal relative position is determined to reduce the impact of the relative position on the electromagnetic force. Furthermore, the high-precision electromagnetic force driving equation at the optimal position is acquired by utilizing the least square method. Finally, this paper develops a novel torsional measurement device for the MOI and successfully achieves high-precise measurement of the MOI for the target object using the proposed measurement method. The measurement experiment for MOI of a target object indicates that the corresponding measurement relative error is 0.297%, thereby confirming the effectiveness and high precision of the proposed measurement approach.