Optimization of Three-, Four- and Five-layer Shrink-fitted Compound Cylinders

In this paper, using an analytical method, the optimum design formulas for three-, four- and five-layer compound cylinders under internal pressure are derived. The formulas can be used for obtaining the minimum weight of the compound cylinder for a specific internal pressure. In the optimization procedure, using Tresca’s yield criterion, maximum shear stress that occurs simultaneously in inner radiuses of all layers is minimized. The formulas for optimum values of contact radiuses, contact pressures and radial interferences are derived. First, optimum design formulas of three-layer compound cylinders are derived. Then these formulas are generalized for four- and five-layer compound cylinders. It is concluded that compound cylinders with a larger number of layers have higher internal pressure capacity with a specific weight. This is due to the fact that by increasing the number of layers, shear stress distribution of compound cylinder is more uniform across the wall thickness and the material is used more efficiently. Three examples are presented to show the effectiveness of the proposed method.

Keywords:

compound cylinder , optimization , multilayer , internal pressure