Practical design equations for rectangular wire helical springs

Helical springs are used for many mechanisms. Rectangular wire helical springs are used in machines that require large spring loads, such as press machines, die machines, injection molding machines, construction machines, and load testing machines. Design formulas for the rectangular wire helical springs were given by Liesecke. However, pitch angle of the helical spring is neglected in his formulas, and they are inconvenient because we have to read factors used in the formulas from graphs. And, Shimizu et al. derived a theoretical equation, but there are still differences between values calculated by the equations and the FEM analysis results although a trend is consistent. And, the practical design equations are desired to be simple. Therefore, in this paper, simple practical design equations of the spring constant and the maximum shear stress are derived by using a fractional expression to FEM results by focusing on that the displacement and the stress generated in the helical spring are mainly caused by a tortional moment to the spring wire. Errors of the spring constant equations to the FEM results are less than 3 percents and errors of the maximum shear stress equation to the FEM results are less than 3.5 percents. Therefore, these equations are very useful for the practical design of the rectangular wire helical springs.