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A slotted disc spring consists of two segments: a coned disc segment and a number of lever arm segments. In this study, a load-displacement formula for the slotted disc spring is newly developed in the form of energy method by considering both rigid and bending deflections of the two segments. This formula is developed with the aim to further improve the SAE formula which is limited to a straight slotted disc spring. The coned and the lever arm angles of the straight slotted disc spring are the same. They are different for a bended slotted disc spring. Because of this limitation, it is geometrically impractical to employ the SAE formula for a bended slotted disc spring. To achieve the goal of this study, new calculations based on geometric and material properties inputs are developed for a bended slotted disc spring. A firm background study based on the theory of Almen is presented in developing new load-displacement calculations for a bended slotted disc spring.

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Geometric parameter design is an important stage in any product design. For example, by varying any of its geometric parameters, a slotted disc spring will show various defined nonlinear load-displacement behaviors. Therefore, these geometric parameters must be precisely designed to ensure the output spring design possesses a nonlinear load-displacement behavior that satisfies particular nonlinear criteria. More importantly, various engineering designs benefit from nonlinear behavior in order to meet certain engineering design requirements. Since each nonlinear spring application requires a unique load-displacement function, the spring geometric parameters must be precisely custom designed. However, there is no specific algorithm available to calculate such geometric design parameterization. The aim of this study is to propose a generalized algorithm for a slotted disc spring geometric design that ensures the output design exhibits identical load-displacement function with any prescribed one. A predicted geometric design algorithm for a slotted disc spring is proposed in this study. The design is characterized by a prescribed load-displacement function obtained from numerical model in the previous literature. The key feature of our proposed algorithm is that, the identified meeting point, which is defined from a prescribed function, can be used as a target point to match the predicted function with the prescribed function. Our proposed algorithm manipulates the slope characteristics of the established slotted disc spring numerical formulation to tune the predicted nonlinear function. This enables a geometric parameter design to be achieved. Improvements to the proposed geometric parameters were done by searching the best combination of optimum variables that produce minimum least mean square error between the prescribed and proposed nonlinear functions. The obtained numerical results demonstrate the effectiveness of the proposed algorithm to parameterize the geometric parameters for a slotted disc spring design.