5. Radially Constrained Disk Springs

In the current chapter, the calculation of disk springs is studied with free sliding edges and edges with constrained radial motion. The disk springs with constant material thickness are studied using the models of thin and moderately thick isotropic shells. The variation formulations are used to derive load–displacement formulas for the disk springs with different constraints on radial movement on the inner and outer surfaces. The kinematic hypothesis is used for the shell models of conical shells. The motivating feature of the presented theory is its ability to calculate the cup springs with free gliding edges and the edges with constrained radial motion. The equations developed here are based on general assumptions and are suitable for disk springs made of isotropic materials, such as spring steel and light metal alloys. The advantage of the methodology is the derivation of closed-form solutions for several common restrictions on the radial motion of the inner and outer edges. The developed formulas are recommended for industrial calculations of free and restricted disk springs.