Genetic Algorithm-Based Inverse Design of Slotted Disc Springs Through Load–Displacement Matching

Abstract

The load–displacement characteristic is a primary design requirement for a slotted disc spring, but the geometry that produces a prescribed nonlinear response is often unknown. This study couples Schremmer’s analytical formulation with a Genetic Algorithm (GA) that minimizes the least mean square (LMS) curve error. The outer diameter was fixed at 152.40 mm to preserve the benchmark installation, while the tongue width and 12-slot topology were retained to isolate the continuous inverse problem. A one-factor-at-a-time analysis ranked the normalized sensitivities as transition diameter (approximately 8.35), thickness (1.69), inner diameter (1.47), slot length (0.76), and cone height (0.67); the indices for slot count, tongue width, and slot width were below 0.05. Because slot length is dependent, transition diameter, inner diameter, thickness, and cone height were optimized. The GA achieved LMS = 0.017, compared with 43.677 for the earlier inverse method. The four optimized dimensions differed from their targets by approximately 0.78%, 4.00%, 1.06%, and 1.18%, respectively. This result verifies computational recovery within the shared analytical benchmark only; no finite element or experimental validation was performed. The method is therefore a preliminary screening tool, and finite element verification, manufacturability assessment, and prototype testing are required before engineering implementation.