Measurement Mechanism And Realization Method Of Moment Of Inertia For Tiny Objects

The moment of inertia has important theoretical significance in the fields of spaceflight,industrial engineering and so on,so it is necessary to realize accurate measurement of moment of inertia.However,for the moment of inertia of small objects(100g-500g),there is no suitable measurement method at present.Some test systems have lower accuracy due to friction or mass deviation,while some test systems have more auxiliary equipment,resulting in complicated operation and introducing new errors.Based on the actual needs and subject research,this paper studies and constructs a measuring system for the center of mass and moment of inertia of small objects to realize convenient and fast high-precision measurement.In this paper,the principle of rotational inertia measurement methods such as torsion pendulum method,linear pendulum method and complex pendulum method is analyzed,the advantages and disadvantages of different measurement methods and their respective applicable conditions are compared,and the most appropriate complex pendulum method for measuring rotational inertia of small objects is selected.According to the mathematical model of the center of mass and the complex pendulum method,the relationship between the moment of inertia and the complex pendulum period is obtained.The error analysis is carried out on the established model,and the proportion of periodic measurement error,quality measurement error and length measurement error in the total error is studied,as well as the variation law of each error with the parameters of the test system such as structural parameters and materials.According to the analysis result and the requirement of mechanical design rigidity,the mechanical structure design of the measuring device is carried out,the appropriate structural parameters are selected to reduce the error,and the air bearing is used to replace the ball bearing to reduce the friction force.After that,the static analysis and topology optimization of the mechanical structure are carried out.According to the nature of the complex pendulum,the measurement of the center of mass of the measured object is realized by using the moment of inertia measurement system,avoiding the tedious operation and the error caused by themeasurement of the two devices.In view of the accuracy of centroid measurement,the measurement error caused by centroid deviation is reduced through two measurements rotated 180 degrees and error compensation means,so as to ensure the measurement accuracy.Finally,the physical processing and the test system construction are carried out,and the accuracy of the test system is verified by standard parts.The experimental data show that the measurement accuracy of the center of mass of the test system can reach ± 1 mm and the measurement accuracy of the moment of inertia is 1.0 %.The measuring device meets the requirements of stability,reliability and high precision for measuring the center of mass and moment of inertia of small objects.