Issue34

F. Curà et alii, Frattura ed Integrità Strutturale, 34 (2015) 447-455; DOI: 10.3221/IGF-ESIS.34.50 449 simulate the presence of the whole gear. The gear is loaded with a force on the highest point of single tooth contact (HPSTC). Tab. 1 resumes the test cases considered for the 2D FEM analysis. Test Case Bending Force [N] Speed [rpm] 1 1619 0 2 0 10000 3 1619 10000 4 3238 10000 5 8095 10000 6 12952 10000 Table 1 : Test cases considered for the first 2D FEM analysis (the wheel is a full gear). Crack propagation studies have been performed by means of 3D extended finite element models (XFEM) [12]. In this case the entire gear geometry has been considered. XFEM region has been created by defining three zones near the tooth root where the crack has been hypothesized to propagate; the average elements size in each region is respectively: 1.6mm, 0.6mm and 0.3mm. An elliptical crack has been inserted at one extremity of the tooth width (with principal axis dimensions respectively: 0.1mm and 0.25mm), see Fig. 2. Each simulation consists in 15 propagation steps, with an increment of crack length equal to 0.3mm at step; the Paris’ law has been used as propagation law. The load has been placed as a force distributed along a line on the tooth width at the HPSTC, in combination with centrifugal load. The hub diameter has been clamped. Figure 2 : 3D extended finite element model (XFEM). Propagations have been calculated in gears with different rim thicknesses and web thicknesses (respectively defined by the backup ratio m b = B/m and the web ratio m w = W /L, where B is the rim thickness, m is the gear module, W is the web thickness and L is the face width, see Fig. 3) [12, 14], in order to evaluate if these geometric parameters may affect the contribution of the centrifugal load on crack propagation direction. Fig. 3 shows the meaning of the geometric parameters backup ratio (m b ) and web ratio (m w ). A so called full gear is a wheel whose web thickness is equal to the face width (m w = 1). Tab. 2 resumes the XFEM simulation run in this work.