“Equivalent Columns” for Helical Spring

In this chapter, the coil spring is replaced by a flexible rod located along the axis of the coil. This rod has the same mechanical properties as the spring itself. Its bending, torsion, and compression stiffnesses are equal to the corresponding stiffnesses of the helical spring. This rod is known as the “equivalent column” of the coil spring. The “equivalent column” equations are much easier to handle than the original helical spring equations. The integral properties of the spring, such as axial and lateral stiffness, buckling loads, and natural frequencies, can be determined directly using the equivalent column equations. On the other hand, the local properties, such as stresses in the wire or contact forces, could only be evaluated 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 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 compressive forces whose line of action is the column axis. This concept is applied to the stability of helical springs. An alternative method of approach is based on the dynamic criterion of spring stability. The equations for transverse (lateral) vibrations of compressed helical springs have been derived. This solution expresses the fundamental natural frequency of the lateral vibrations of the column as a function of the axial force, as well as the variable length of the spring. This chapter is the third section of the first part, which studies the springs from the design point of view.