Homogenization Modeling and Effective Mechanical Constants for EM Composite Conductor with Cooling Channel

Abstract

A homogenization modeling to predict the effective mechanical properties of electric machinery composite conductor consisting of metallic core with cooling channel, and multi-layer of insulating materials was presented. A two-level homogenization scheme to model complex composite with multi-phase materials and the validation of using finite element method was developed. Composite cylinder assembly model was adopted in the Level 1 homogenization for the metallic core and the cooling channel was analyzed as a fiber void with null material properties. The effective mechanical properties of the composite insulation layers were homogenized by smearing the properties of the multiple insulation layers of bonding, insulation and insulationfiber-reinforced composite. Level 2 homogenization derived nine effective mechanical constants for conductor through a combined homogenization sequences. The good comparisons between the analytical predictions and the results obtained from the finite element analyses demonstrated the applicability of the model.

Asymptotic Homogenization and Numerical Implementation to Predict the Effective Mechanical Properties for Electromagnetic Composite Conductor

“…These comparisons are presented in Figure 4 for EM composite conductor without a cooling channel, and Figure 5 for EM composite conductor with a cooling channel, respectively. The results of effective mechanical properties of the EM composite conductor predicted based on the asymptotic homogenization theory and the developed 3DHOMOG program agree well with the results predicted by analytical model and standard finite element model reported in [3][4][5], thus demonstrate the applicability of the asymptotic homogenization theory to predict the effective properties and the unit cell structural anisotropy of the EM composite conductor. However, the asymptotic homogenization theory can offer additional advantage of global-local analysis for conduct design, as pointed out before.…”

“…Calculation of the constitute relation of the phase 3 glass-epoxy composite was reported in [3]. Results of using the asymptotic homogenization theory, its finite element implementation, and the developed computational algorithm 3DHOMOG are compared with the results from the available analytical and numerical models reported in authors' early paper [5]. These comparisons are presented in Figure 4 for EM composite conductor without a cooling channel, and Figure 5 for EM composite conductor with a cooling channel, respectively.…”

“…An attempt of using both analytical and numerical approaches to predict the effective mechanical constants for the above EM composite conductor was reported in [3][4][5]. In the reported work, the homogenization of the heterogeneous EM conductor was achieved from a two-level homogenization hierarchy scheme.…”

“…The Level 2 homogenization scheme was further applied to calculate the overall effective mechanical constants of the conductor through a combined sequence of homogenization from a hybrid displacement and traction-prescribed boundary conditions applied to the representative conduct unit cell. Although good agreements can be observed between the predictions based on the reported homogenization model and the finite element model [3][4][5], there are some limitations and inherent errors that need to be considered in applying these models to predict the composite effective modules. Such limitations and errors were caused by, for example, the upper and lower bound errors that resulted from the prescribed different boundary conditions [7], and the effect of the boundary and representative element size in the finite element prediction [8].…”

“…Therefore, the application of the asymptotic homogenization makes it possible to investigate the conductor structural mechanical behavior, stress and deformation at both the global (macro-structural) level and local (micro-structural) level, thus enables the analyses at a detailed level of individual constituents including geometries and properties for failure analysis. In addition, the asymptotic homogenization does not have an inherent bound error and the boundary effect in the effective constant calculation comparing to the analytical and numerical models reported in [3][4][5]. However, although its theory has been well developed, the numerical implementation of the asymptotic homogenization has been very limited due to the complicity of the computational algorithm.…”