A New Method for the Calculation of Characteristics of Disc Springs with Trapezoidal Cross-Sections and Rounded Edges

In the European standards specifying disc spring manufacturing, geometry, shape and characteristic, an edge rounding is prescribed. Common methods for the calculation of disc spring characteristics, even in these standards, are based on a rectangular cross-section. This discrepancy can lead to a considerable divergence of the computed characteristic from the characteristic determined by testing. In literature, this divergence has not yet been examined with regard to rounded edges. In this paper, a new method addressing this problem is introduced. For this purpose, the geometry of idealized disc springs is parameterized. Based on four edge radii and two angles of the inner and outer faces, equations to compute the initial cone angle and the lever arm are introduced. These equations are used to formulate an algorithm to adapt other computation methods to non-rectangular cross-sections and rounded edges. The method is applied to the formulas by Almen-Laszlo, Curti-Orlando, Zheng and those by Kobelev. FE simulations of disc springs with rounded edges and a non-rectangular cross-section were used to verify the new formulas. The results show that the introduced method can be applied to known characteristic computation methods and result in a model expansion taking cross-section variations into account. The adjusted characteristics show more accurate alignment to the FE simulation for the cross-section variations investigated. These findings not only close the geometric gap between the manufacturing guidelines and the computation on an analytical basis, they also define a new parameter space for designs of disc springs and a corresponding force computation method to optimize spring characteristics.