Determining the Range of Applicability of Analytical Methods for Belleville Springs and Novel Approach of Calculating Quasi-Progressive Spring Stacks

This study investigates the accuracy of analytical methods for Belleville springs by comparing their results with finite element method (FEM) models to determine their applicability. Both well-established approaches, such as the Almen–Laszlo and Muhr–Niepage methods, and modern techniques, including Zheng’s energy method, Ferrari’s method, and Leininger’s approach, were analyzed. The findings identified areas of consistency between analytical methods and FEM models, leading to the development of an algorithm for selecting the appropriate computational method for different types of Belleville springs. This research also examined the practical application ranges of Belleville springs, considering their structures and operating conditions, while assessing the effects of friction forces on individual springs and different stacks. Differences between hysteresis observed in FEM models and the results from analytical formulas were highlighted. A lack of analytical methods for determining the characteristics of spring assemblies with quasi-progressive behavior was identified, leading to the proposal of a novel algorithm for their calculation. The proposed method was validated using a specific example, confirming its accuracy. Future research directions were outlined to develop a universal computational approach for assemblies of Belleville springs with varying configurations and spring types.