Exact shell solutions for conical springs. III. Belleville springs with variable thickness

Published: 25 January 2023| Version 2 | DOI: 10.17632/gtk67w9kp7.2
Vladimir Kobelev


In the current dataset, we examine the Belleville spring with the variable thickness. The thickness is assumed to be variable along the meridional and parallel coordinates of conical coordinate system. The calculation of the Belleville springs includes the cases of the free gliding edges and the edges on cylindric curbs, which constrain the radial movement. The equations developed here are based on common assumptions and are applicable to the industrial calculations. There are 10 models with the different thickness distributions of the material thickness over the radius of the surface. For each model, the three load cases were simulated. One load case represents the freely gliding edges of the spring. Another load cases constrain the radial movement of inner or outer edge of the middle surface. The input files in ANSYS APDL language are saved for each model and each load condition. All APDL files are in the archive ANSYS.zip. The APDL files are used for the simulation with program ANSYS. The EXCEL files in the archive telle3.1.zip represent the results of finite-element simulations with the program ANSYS 2023.R2. The vertical reactions on the inner edge are stored in the file telle3.1.zip. These EXCEL data will be imported in MAPLE source file. With this MAPLE source file the comparison between the closed form solutions and finite-element analysis is performed.


Steps to reproduce

For the calculations, the MAPLE 2020 code is provided. The code is executable with the MAPLE CAS of MAPLESOFT (615 Kumpf Drive Waterloo, ON Canada, N2V 1K8) using the version 2020.02 or above.


Universitat Siegen


Mechanics, Applied Mechanics, Automotive Mechatronics