This paper presents an optimal method for rotordynamic simulation of induction motors, including the effects of unbalanced magnetic pull (UMP). The developed simulation method containing the UMP model is simple but still accurate for the actual design process of induction motors. The UMP model is simplified by using the magnetizing current without calculation of the rotor current. The effects of the slot opening and saturation are initially incorporated into the model by using the Carter factor. To improve the accuracy of the model, the magnetizing current is calculated by the finite element analysis (FEA), and the proposed correction factor is also built into the model. Moreover, mixed eccentricity is modeled and applied to the time step rotordynamic simulation for considering the actual rotor eccentricity condition. Based on the developed UMP and eccentricity models, rotordynamic simulation methods within the induction motor design process are proposed and tested in a standard four-pole induction motor. The simulation results show that inclusion of the UMP force reduces the critical speeds and generates electromagnetic excitation. The study further shows that the effects of UMP vary with a change in static eccentricity, dynamic eccentricity, slip, and bearing stiffness. Finally, based on the results, a utilization plan of the developed methods is proposed.

In large rotor-bearing systems, the rolling element bearings act as a considerable source of subcritical vibration excitation. Simulation of such rotor bearing systems contains major sources of uncertainty contributing to the excitation, namely the roundness profile of the bearing inner ring and the clearance of the bearing. In the present study, a simulation approach was prepared to investigate carefully the effect of varying roundness profile and clearance on the subcritical vibration excitation. The FEM-based rotor-bearing system simulation model included a detailed description of the bearings and asymmetricity of the rotor. The simulation results were compared to measured responses for validation. The results suggest that the simulation model was able to capture the response of the rotor within a reasonable accuracy compared to the measured responses. The bearing clearance was observed to have a major effect on the subcritical resonance response amplitudes. In addition, the simulation model confirmed that the resonances of the 3rd and 4th harmonic vibration components in addition to the well-known 2nd harmonic resonance (half-critical resonance) can be significantly high and should thus be taken into account already in the design phase of large subcritical rotors.

Design of High Speed (HS) electric machines is an iterative process that requires a multidisciplinary design team to accomplish the required performance. In this study, a design space method (DSM) is developed to streamline conceptual designing of a high-speed and high-power electric machine. The method uses analytical equations and a rotordynamic model to determine geometrical dimensions based on the application requirements. These dimensions create a feasible baseline design for the particular application. However, considering the dimensions as design variables and using the baseline design as a starting point, a multidimensional combination and interaction of the design variables and the correlated output for the particular topology of motor and performance range can be further studied for design exploration and optimization purposes. The study includes a test case where the baseline dimensions are determined and compared to an existing machine from literature, and then further explored to identify the sensitivity of different outputs with respect to different design variables. The method enables rapid design iterations, rotordynamics and rotor mass optimization. The baseline design can be also used as a starting point for the detailed design.

Development and verification of frequency domain solution methods for rotor-bearing system responses caused by rolling element bearing waviness, Mechanical Systems and Signal Processing, 163 (2022) 108117.

The mounting of a rotating machine affects the dynamic behavior of the machine. Typically in large machines, the support structures have lower stiffness on the actual site than in the acceptance tests conducted by the manufacturers. In this research, a method is developed for the support stiffness identification for an in-situ machine using a simulation-data-driven, deep learning algorithm. The novel approach aims to utilize transfer learning to first teach the deep learning algorithm using vibration response data generated from a simulation model of the rotor-bearing-support system, and then test it with measured response. To validate the stiffness estimation of the algorithm for multiple cases, an experimental test rig is used where the horizontal support stiffness can be varied through a range of values. The results from the deep learning algorithm are compared with simpler algorithms such as Linear regression (LR), Artificial Neural Network (ANN), and Support vector regression (SVR) for benchmarking. The models are trained with filtered frequency domain response, and challenges due to measurement uncertainty are analyzed. With proposed pre-processing steps of the frequency domain response and outlier elimination, the deep learningbased virtual sensor can predict the support stiffness with reasonable accuracy, where the limiting factor is the data quality and lack of excitation at critical speed frequencies.

Mass unbalance is one of the most prominent faults that occurs in rotating machines. The identification of unbalance in the case of large flexible rotors is crucial because in industrial applications such as paper machines and roll grinders, high vibrations can adversely affect the quality of the end product. The objective of this research is to determine the unbalance location, magnitude and phase for a large flexible rotor with few measured coordinates. To this end, an established force-based method comprising of modal expansion and equivalent load minimization is applied. Due to the anisotropic behavior of the test rotor, the force method required at least six measured coordinates to predict the unbalance with an error of 4 to 36%. To overcome this limitation, an alternate method, eliminating the use of modal expansion, is proposed. Here, displacements generated by varying the location of a reference unbalance along the rotor axis, are compared to measured displacements to detect the unbalance location. Furthermore, instead of force-based fault models, the minimization of displacements at measured locations determines the unbalance parameters. The test case in this study is the guiding roll of a paper machine and its different unbalance states. The algorithm is tested initially with a simulation-based model and then validated with an experimental set up. The results show that the displacement method can locate the unbalance close to the actual location and it can predict the unbalance magnitude and phase with only two measured coordinates. Lastly, using measured data from 15 measurement points across the tube section of the test rotor, a comparison shows how the selection of the two measured locations affects the estimation accuracy.

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Mass unbalance is a major concern in modern day rotating machinery. For single and double disc rotor bearing systems, model based techniques have been used to identify the unbalance. The aim of this research is to predict the unbalance in a similar way for a paper machine's tube roll using its virtual model. In this case study, the rotor is a large diameter continuous tube with thin walls and without any mounted disc. To identify the unbalance magnitude and phase, modal expansion and equivalent load minimization by least squares is used. The distributed equivalent load is sorted using two different methods. The first method considers only the isolated maximum load. In the second method, the load at all the nodes are taken into account. This first method is tested on a single disc rotor bearing system from literature and the unbalance parameters were predicted with good accuracy. However, for the paper machine's tube roll, due to its continuous structure, the equivalent load is distributed more evenly across the rotor. Therefore the second method is able to predict the unbalance parameters with better accuracy.