The Calculation of the Volumetric Properties of Sweep-Generated Solids Via Line Integration

A key issue in the geometric and mechanical analyses of machine elements with complex shapes such as turbine blades and bevel gears is the accurate and economic computation of their volumetric properties, namely, volume, centroid coordinates, and inertia tensor. A method is proposed here for the computation of these properties that is applicable to sweep-generated solids based only on their 2D generating contour and their sweeping parameters. Thus, the direct 3D calculations of the volumetric properties of such solids are reduced to simple 2D calculations. Comparisons of numerical results are presented, which show that the volumetric properties of this class of solids can be effectively performed in a computationally reduced fashion which, additionally, enhances the accuracy of the computed values.