Numerical simulation of the coil spring and investigation the impact of tension and compression to the spring natural frequencies

This work is a comparison of the calculated and experimental natural frequencies of coil springs under the action of axial tension-compression. To calculate the coil springs, the finite element form of a single coil is proposed. The initial stiffness matrix and initial mass matrix are calculated by the differential equations of Kirchhoff-Clebsch. The co-rotational approach of single coil finite element is provided to make it applicable for calculating the changing stiffness matrix and changing mass matrix of the coil springs with initial deformations. The frequency and the form shape of the nature oscillation of coil spring are calculated as well. In addition, the comparison with experiment results show the high accuracy.