3. “Equivalent Columns” for Helical Springs

In this chapter the helical spring is substituted by a flexible rod that is located along the axis of helix. This rod possesses the same mechanical features, as the spring itself. Its bending, torsion and compression stiffness are equal to the corresponding stiffness of the helical spring. This rod is known as an “equivalent column” of the helical spring. The “equivalent column” equations are considerable easier to handle than the original equations of the helical spring. The integral spring properties, as an axial and transversal stiffness, buckling loads, fundamental frequencies could be directly determined using the “equivalent column” equations. In contrast, the local properties, like stresses in the wire or contact forces, could be evaluated only with the more complicated equations of the helical elastic rod.

In this chapter the stability and transversal vibrations of the spring are studied from the unified point of view, which is based on the “equivalent column” concept. Buckling refers to the loss of stability up to the sudden and violent failure of straight bars or beams under the action of pressure forces, whose line of action is the column axis. This concept is applied for the stability of helical springs.

An alternative approach method is based on the dynamic criterion for the spring stability. The equations for transverse (lateral) vibrations of the compressed coil springs were derived. This solution expresses the fundamental natural frequency of the transverse vibrations of the column as the function of the axial force, as well as the variable length of the spring.