An Optimum Design for Laminated Steel Leaf Springs

Abstract

This study presents an optimum design methodology for laminated semi-elliptic steel leaf springs used in vehicle suspension systems, with the primary objective of minimizing spring weight while satisfying structural, geometric, and dynamic requirements. Analytical expressions for bending stress, mid-span deflection, stiffness, and natural frequency are derived based on classical beam theory and expressed in non-dimensional form to enable a generalized and systematic optimization framework. The design variables considered include strip thickness, strip width, and number of leaves, while constraints are imposed on allowable bending stress, maximum deflection, bounded geometry, and natural frequency to ensure structural safety and acceptable ride comfort. The resulting nonlinear optimization problem is solved using MATLAB for a carbon steel (AISI 1020) leaf spring subjected to a specified vertical load. The optimized design consists of four steel strips with a width of approximately 75 mm and a thickness of about 7.5 mm, yielding a total spring weight of approximately 19 kg. The results demonstrate that significant weight reduction can be achieved without compromising stress limits, deflection requirements, or dynamic performance. The proposed methodology provides a reliable and efficient tool for the optimal design of steel laminated leaf springs and can be extended to other materials, loading conditions, and vehicle applications. The results obtained from this study have been compared with available numerical results obtained by FEA and a good agreement is aobtained.