Multi-objective optimization of an energy-efficient diaphragm spring for clutch applications

This study presents a deterministic multi-objective framework for the energy-efficient design of a diaphragm spring for automotive clutch applications. The proposed methodology is based on the direct feasible-set approach and similarity theory, enabling synthesis-level optimal-rational design within a closed dimensionless parameter space. Unlike stochastic search-based optimization methods, the developed framework constructs a complete information set of admissible design solutions and identifies rational configurations through adaptive constraint management. The multi-objective analysis demonstrates the absence of a globally optimal solution and justifies the concept of optimal-rational design. The synthesized configurations achieve up to + 22% increase in compressive force, - 12% reduction in material volume, and improved stiffness characteristics compared to the reference configuration. To ensure mechanical admissibility, the analytical synthesis model is validated through nonlinear finite element analysis incorporating geometric nonlinearity and localized elastoplastic behavior. The peak equivalent stress reaches 2244 MPa but remains confined to highly localized regions with equivalent plastic strain below 0.004. Experimental validation under full actuator displacement (17 mm) confirms stable nonlinear behavior, ± 2% force variation over 5000 cycles, and moderate thermal rise (10-12 °C). Energy efficiency is quantitatively assessed through hysteresis analysis, revealing a 25% reduction in mechanical energy dissipation per cycle and improved mechanical efficiency. The strong agreement between analytical predictions, FEM simulations, and experimental measurements confirms the predictive reliability of the proposed deterministic optimization framework. The developed approach provides a transparent and computationally efficient methodology for energy-efficient diaphragm spring synthesis and can be extended to other nonlinear elastic components in transmission systems.