Surrogate Vibration Modeling Approach for Design Optimization of Electric Machines

Data-Driven Electrical Machines Structural Model Using the Vibration Synthesis Method

“…The presented data-driven model can capture both in-plane and out-of-plane mode shapes, whereas the model in [13] uses a semi-analytical approach where the modal frequencies are obtained from FEA and the displacement is computed analytically, thus being able to capture only global mode-shapes, having less accuracy than a full FEA method, such as the vibration-synthesis. The model presented in [14] is similar to the proposed model because it uses FEA for data generation and a zeros/poles FRF identification. The authors in [14] use the impulse FRF generated by a unit force for the model construction, while in the present case, the FRFs are unitary forces-shapes generated by harmonic forces.…”

“…The model presented in [14] is similar to the proposed model because it uses FEA for data generation and a zeros/poles FRF identification. The authors in [14] use the impulse FRF generated by a unit force for the model construction, while in the present case, the FRFs are unitary forces-shapes generated by harmonic forces. This implies that to preserve the air-gap force spectrum, attention has to be paid to the number of discretizations per tooth length (as shown in [5]), and the time to generate the data increases with the number of teeth.…”

“…number of pole pairs, slots and winding), and the computational time needed to generate the model does not increase with the number of teeth, but with the number of unitary-force shapes applied. Also, the current method is used early in the design cycle, where only the stator is considered for the vibration transmission path, without the presence of housing and additional structural damping elements specifically designed to mitigate NVH issues, whereas the authors in [14] consider the full machine assembly.…”

“…The purpose of building the data-driven model is to decrease the electrical machine vibration computational time at the design-stage, while maintaining FEA accuracy, and having the possibility of fast and accurate system-level analysis. To determine the computational advantage over FEA, a computational efficiency factor for the unitary force-shape responses is introduced k ctr that describes the relative reduction in computation time, similar to the one presented in [14]. By using the unitary-force shape approach, the computational time needed to obtain data for one design sample used for building the data-driven models is relative equivalent to that used for one standard FEA computation (the unitary force shape computation time is two orders of magnitude higher compared to the zeros/poles identification time thus, it is considered negligible), all things being equal: the same number of unitary force-shape responses, the same number of output nodes, and the same frequency range and frequency steps used in both cases.…”

“…A surrogate model [13] based on the semi-analytical approach is proposed [3], but this can only capture global modal behavior. The only data-driven structural dynamics model, known to the authors, that can capture both global and local mode-shapes uses the vibration impulse responses of the Switched Reluctance Machine (SRM) that are fitted to a Look-up Table (LUT) model using the Rational Fraction Polynomial (RFP) method [14].…”