Global Local Finite Element Method in Gear Stress Analysis (Analytical Solution and Global Local Domain).

Abstract

A Global Local Finite Element Method (GLFEM) has been applied to the analysis of the gear tooth stress field. The GLFEM is a numerical analysis technique in which finite element solutions and classical analytical ones (global function) are superposed in the global local domain on the basis of the energy principle. Hence, the reliability of the GLFEM greatly depends on which solution is used for the global function and/or which portion is selected for the global local domain. In the present paper, therefore, such effects on calculated stress field are discussed. Consequently, it is confirmed that Kelvin's solution is the most convenient one. Furthermore, the Lagrangian constraint is used for guaranteeing continuity of displacement on the boundary between the global local and local domains, but the constraint is not achieved sufficiently. Hence, sufficiently large area must be taken for the global local domain.