Prediction of Mechanical States in Wound Capacitors

The problem of determining the mechanical states inside wound capacitor rolls is addressed through the application of two dimensional, linear elasticity. Allowances are made for heterogeneous wound construction of the capacitor, orthotropic material behavior of the capacitor constitutents, and arbitrary winding tension. A key element in the formulation is the derivation of material properties for a wound, orthotropic layer which is equivalent in behavior to a stack of dissimilar piles such as are actually wound on the capacitor simultaneously during one turn of the mandrel. The dissimilar plies are necessary by virtue of the conductor and dielectric materials which must be present in a capacitor. The derivation of predictive equations is based on winding the equivalent layer on an appropriate mandrel, followed by a recovery of the individual ply responses. The capability to explicitly calculate the winding tensions which would be necessary to produce a required wound tension dependence upon capacitor radius is also developed. Numerical results for typical capacitor design and construction are presented, and justification for the application of optimization theory in capacitor development is demonstrated.