PSI - Issue 75

Robert Goraj et al. / Procedia Structural Integrity 75 (2025) 691–708 Goraj / StructuralIntegrity Procedia (2025)

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[14]. A higher SP can also be achieved by design optimizations [15],[16] and by applying of lightweight structures[17],[18]. Following these trends, mechanical based considerations dealing with a rotor shaft and a bearing cap of a permanent magnet (PM) synchronous motor are recently reported [19]. A mass reduction of these components is obtained based of a parametric analytical model and verified by FEM computations. In [20] a rotor design of a synchronous reluctance motors is considered. Here, an optimal rotor topology was achieved considering the von Mises stress and the radial deflection coupled with peak values of motor torque, motor power and efficiency. Other design approaches, that consider multi-physical (electromagnetic, thermal, mechanical) phenomena occurring in PM motors, are documented in [21], [22]. The mechanical stress on rotating components (shaft, PMs, iron core) and the critical rotor speed are here estimated based on rotor dynamics and structural 3D FEM analyses. Structural and vibration analyses for a surface mounted PM machine for an aerospace application are performed in [23]. An estimation of the tensile stresses in critical components (rotor hub, PM retention sleeve) has contributed to a better understanding of the fatigue limits of selected materials. Obtained resonance frequencies of torsional, axial, and flexural oscillation modes were considered in the final definition of the rotor design. An analytical model considering mechanical stresses in a PM retention sleeve is elaborated in [24]. It enables a quick design of non axisymmetric geometries consisting of orthotropic materials (e. g. fiber reinforced composites) and includes body forces, surface forces and interference induced stresses. The current work gives a humble contribution to the SP increasing through dimensioning of mechanical components. The dimensioning object is a bearing cap of an PM synchronous motor. The cap is subject to vibrations induced by the propeller pull force (referred as a thrust force). The vibrations cause mechanical stress in the cap, which results in wear of the component. The cap is dimensioned for sustaining 1E7 load cycles. The optimal material utilization of the bearing cap is obtained based on the following calculation methodology: • The bearing cap structure is represented by Timoshenko beams (referred as bearing spokes)[25], [26]. • The interaction of mechanical components is approximated with the lumped mass coupled damped oscillators. The vibration behavior is described using a set of differential equations, which are transferred to the Laplace domain and used for the formulation of a parametric (second moment of area dependent) semi analytical (SA) model[27],[28]. • Static and dynamic analyses - both in the frequency and in the time domain - are performed using the derived parametric SA model. The calculation output is the mechanical stress occurring in the bearing cap[29]. • Based on the mechanical stress, fatigue calculations are performed according to the FKM analytical strength assessment guideline of the Cooperative Research Association for Mechanical Engineering (FKM, Frankfurt/Germany). The output is an optimal second moment of area of the bearing spokes (corresponding to the optimal material utilization)[30], [31], [32]. • The SA structural results are verified using FEM and the fatigue results are verified using commercial software. A calculational strength proof for the allowed number of stress cycles is delivered. 2. Mathematical model Fig. 1 shows a simplified geometry of a bearing cap. A propeller (1) is directly connected to the rotor shaft (2). The rotor shaft is supported by an infinitely stiff bearing connection (3). The connection is joined to four H-profile bearing cap spokes (4). The spokes are connected to the stator (5) of an electric motor. The EM is fixed to the aircraft at the mounting pads consisting of four dampers (6). The overall mass of all rotating components (shaft, propeller, rotor of an EM) equals m 1 . The mass of all stationary components (a stator of an EM, housing) equals m 2 . The masses oscillate in the axial direction ( x -direction) due to the excitation force u x (t) coming from the propeller.