An Investigation of the Bending of Rotating Torsion-Bar Springs

摘要

The first three critical angular velocities, omega 1, omega 2 and omega 3 for torsion-bar-springs having representative rectangular and circular cross sections are plotted versus length of spring. In order to make circular and rectangular cross-sections comparable, three cases have been chosen, each of which gives, for the designated geometries, equal angles of twist per unit length for equal twisting moments. It can be seen that the second critical angular velocity is somewhat greater than twice that of the first and that the third critical angular velocity is correspondingly higher; this points to the value of pre-shaping the spring to conform to a mode shape higher than the first. The importance of spring length in determining critical angular velocities is also apparent.