Measurement of the Deflection Factor of Helical Springs

In the deflection formula of a coiled spring δ=η8DPn/Gd, the different values of correcting factor η have been obtained by several authors for the small values of index D/d. Authors made experiments in order to determine a dependable value of η using steel and piano wire helical springs.In the above formula, d, D and G are the constants determined uniquely if the type and the dimension of the spring are given as to the material. The number of effective coils n is N-2, N being the total number of coils, and δ is the deflection of the helical spring obtained under the action of axial load P.Two correcting factors were considered as follows:ηt is the correcting factor for the case where the total deflection of the spring is considered. η1 is the correcting factor when only one coil in the middle section of the spring is considered in relation to deflection.We conducted some experiments on helical springs with various materials, types and dimensions.First, the modulus of rigidity G of the wire was measured. Then the relation between load and deflection were obtained for the whole coils of spring and for the middle one coil with no effect of the ends. The changes of the diameter D of the coil under various loads were also measured.The results obtained are as follows:(1) ηt is smaller than unity for small values of D/d, but it become larger than unity for larger values of D/d.(2) η1 is smaller than ηt by about 0.02. And they all tend to become constant for large values of D/d.(3) The manner in which the values of η1 change matches well with the result given by Gohner.(4) It is concluded that as the deflection factor for small helical springs, Gohner's one may be properly used.