Measurement of Torsional Natural Frequencies, Moments of Inertia and Torsional Stiffness of Shafts

This paper presents a method to measure torsional natural frequencies and to calculate moment of inertia and torsional stiffness of a shaft. The concepts of equivalent mass moment of inertia and equivalent torsional stiffness are used to model the shaft. The method applies two identical accelerometers to measure the frequency response functions (FRFs) on two symmetric positions about the shaft. Adding these two FRFs, the bending components of the FRFs are canceled, whereas the torsional components of the FRFs are retained and enhanced. Hence, the torsional natural frequencies of the shaft can be found. By attaching a uniform hollow disk firmly to the free end of the shaft and measuring the new FRFs of the system with the disk, the moment of inertia and torsional stiffness of the shaft can be calculated.