Chapter Eight - TORSIONAL VIBRATION

Abstract

This chapter presents an analysis of torsional vibration. The analysis of torsional vibration is concerned not with displacements but with the rotations of masses about their centers of mass. Therefore, the polar moment of inertia of the mass is the parameter used instead of the mass itself. For simplicity, it is referred to as the inertia of the mass and has the units of kg. m2. Vibration of the rotating mass gives rise to a vibratory load known as the inertia torque. The restoring torque provided by the shaft itself can similarly be called the vibratory shaft torque. The shaft is, thus, a torsional spring with a stiffness expressed in units of Nm/rad. If a torsionally vibrating damper is included in the system, its damping coefficient (damping rate) will be expressed in units of Nm/(rad/s), that is, Nms/rad. Usually torsional vibration is concerned with circular shafts, the stiffnesses of which often need to be obtained from the physical dimensions of the system components. This process is carried out using the simple relations for torsional stiffness and shaft twist.