PSI - Issue 31

Sanjin Braut et al. / Procedia Structural Integrity 31 (2021) 45–50 Sanjin Braut et al. / Structural Integrity Procedia 00 (2019) 000–000

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2.3. Material characteristics The rotor steel lamination used both in the stator and rotor stacks was made of electrical steel M270–50A. Table 1 shows basic mechanical properties of the rotor lamination material. Gao et al. (2010) gives additionally stress fatigue properties for stress ratios R = S min /S max = 0.05 and R = 0.3 which good cover the stress history in the critical rotor region. The S–N parameters are expressed in terms of Basquin equation, Čakmak et al. (2019), ( ) 2 b a f f S S N = ′ (1) Where b is fatigue strength exponent and S f ´ is the fatigue strength coefficient. The following parameter values for the baseline S–N curve were taken in this analysis: S f ´ = 673.25 MPa and b = – 0.09559.

Table 1. Basic mechanical properties of M270-50A. Material Density, kg/m 3 Young modulus, MPa

Poisson’s ratio

Yield strength, MPa

Ultimate strength, MPa

Specific heat, J/(kg C)

Thermal expansion, 1/K

Thermal conductivity, W/(m K)

M270-50A

7650

180 000

0,3

352

478

460

1.2e-5

39

2.4. Thermo-mechanical FEM analysis Although the rotor stack is made of lamination sheets where each can be modeled with 2D shell finite elements (FE), Božić et al. (2010), Božić et al. (2011) and Božić et al. (2018), due to dominantly in plane stress character (Gao et al. 2010) i.e. within each laminate layer simplification rotor is assumed as homogeneous 3D body. Therefore, transient thermos-mechanical analysis was done in Ansys 2020 R2 using 3D finite elements. To reduce the computational effort required for such a transient thermal and transient mechanical sequential calculations (Cazin et al 2020.), the 3D-model is limited only to the rotor structure. The model is additionally reduced by taking advantage of the symmetry and periodicity conditions. Hence, only one rotor pole was considered. Although not necessary, the same mesh was used for thermal and for structural simulation consisting of HEX20 and WED 15 finite elements. The mesh was optimized to meet the recommended element quality, especially in the expected critical area. The one rotor pole model with an axial length of 70 mm, an inner radius of 110 mm and an outer radius of 142 mm is meshed with 8200 finite elements with 46586 nodes. The rotor losses are removed by convection in the air gap and at the rotor front surface (next to the cooling fan). It was modeled with convection boundary condition set. Due to the relatively low rotor losses and a short active rotor stack length, 65 mm, heating of the cooling air in the air gap can be neglected. Therefore, the air gap temperature applied with the convection boundary condition is assumed to be constant and equal to the ambient air temperature i.e. 22 °C. The contact between upper surfaces of permanent magnets and rotor iron are modeled as no-separation contacts, Vukelić et al. (2020). Adhesive layers in contact surfaces are neglected in the mechanical model, but their effect is included in a form of thermal contact resistance. In the second part of analysis, i.e. transient structural, body loads due to the temperature distribution are imported from the previous thermal analysis. Additionally a rotational speed data from the race track measurements are included to simulate stresses caused by centrifugal force. Figure 1 shows the simulation results. In Fig. 1a) presents equivalent (von Mises) rotor lamination stresses and temperature for the most critical position, magnet pocket upper filet during 3 laps drive. Distribution of von Mises equivalent stresses in the rotor structure at t = 1500 s is shown in Fig 1 b).