Mathematical model for determination of strand twist angle and diameter in stranded-wire helical springs

The twist angle of strands has a significant effect on the performance of stranded-wire helical springs. This paper proposes two models (a precise mathematical model and an approximate mathematical model) for calculation of the twist angle and the diameter of strands formed of an arbitrary number of wires. These two parameters can be derived from the screw pitch of strands and the diameter and number of their wires, regardless of the model used. In comparative and analytical studies, it was determined that for strands with the same number of wires, the larger the ratio of the screw pitch to the diameter of the wires is, the smaller the relative errors of the two models are. Only when the foresaid ratio is two times larger than the number of wires, the results of the approximate mathematical model can be acceptable. In other cases, the approximate mathematical model cannot be used. Finally, application software was developed for direct precise-mathematical-model calculation of the twist angle and diameter of strands formed of arbitrary wires.