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To investigate transverse vibration of the eccentric rotor in a 12/8 poles switched reluctance motor (SRM), a transverse analytical vibration model is built by finite element method (FEM) under the interaction of radial magnetic resultant and vibration displacement. External forces, including radial magnetic resultant and centrifugal force, are also derived in detail, according to the variation of airgap and current and other intermediate parameters with rotation angle.

The transverse vibration response of the eccentric rotor including radial magnetic resultant and vibration displacement is solved by Newmark-β method, after inputting the currents of three phase windings under angle position control strategy. The basic characteristics of radial magnetic resultant and vibration displacement are reflected in time and frequency domain.

The magnetic resultant vector of the eccentric rotor presents multi-petals star geometric shape. The frequency distribution of magnetic resultant relates to rotation speed, current waveform and the least common multiple of the stator and rotor teeth. However, the frequency distribution of the vibration displacement also relates closely to the first-order critical whirl speed of the rotor. When the rotor is running at certain speeds, it will display superharmonic resonance and show abundant displacement locus.

By using this analytical model and solving process proposed in this paper, the nonlinear coupled vibration response of the eccentric rotor in SRM can be analyzed and discussed rapidly; only the stator’s winding currents obtained by experiment or electromagnetic simulation is needed as input.

To propose an air‐gap element for electrical machine simulation which accounts for static and dynamic rotor eccentricity.

The air‐gap element technique is extended to account for a non‐centered rotor. The consistency, stability and convergence of the discretisation error are studied. A specialized efficient solution technique combining the conjugate gradient algorithm with fast Fourier transforms is developed.

The eccentric air‐gap technique offers better discretisation properties than the classical techniques based on remeshing. Thanks to the specialized solver, the computation times remain comparable.

The introduction of eccentricity in the air‐gap element used for finite element electrical machine simulation is a new development.

When rotor and stator teeth are close, the connecting air gap flux tube's cross-sectional area exceeds the tooth overlap area. This flux fringing effect is disregarded in the air gap permeance calculation of single-slice magnetic equivalent circuits (MECs) of electric motors with skewed rotors. This paper aims to extend an air gap permeance calculation method incorporating flux fringing for unskewed rotors to skewed and radially eccentric rotors.

Assuming axial independence, the unskewed air gap permeance is rotated according to the skew and integrated along the axial dimension, resulting in a first method. The integral is approximated analytically, resulting in a second method. Results are compared to a commonly used reference method and validated using a non-linear finite element method (FEM) simulation.

The proposed methods provide better alignment with the FEM validation compared to the reference method for skewed rotors and common rotor eccentricity, i.e. below 50% of the air gap length. The analytical method is shown to be competitive with the reference method regarding computational time cost.

Two novel air gap permeance methods are proposed for single-slice MECs with skewed rotors. Their characteristics are discussed and validated.

This paper aims to provide a precision assembly method to improve the aircraft engine quality of initial unbalance with the purpose of founding the process for mass eccentricity propagation and demonstration of assembly process. The proposed method can be used for assembly guidance, tolerance allocation and so on, especially for the assembly with a large number of rotors and the assembly requirements of initial unbalance and coaxiality in high precision.

This paper proposes a constrained optimization-build method to minimize initial unbalance of aircraft engine assembly, which takes amount of unbalance and concentricity of each rotor into account. A constrained nonlinear programming model is extracted by choosing the initial unbalance as the objective function, and choosing the coaxiality and assembly orientations as the nonlinear constraints. The initial unbalance is reduced stage-by-stage by controlling the assembly angle of each rotor.

The validity and accuracy of the proposed method is verified by the multistage rotors assembly through experiments run with the measuring instruments. Compared with the direct-build method, the initial unbalance of final assembly using proposed method is reduced by 22.2% in four rotors assembly.

Different from the geometric eccentricity propagation control methods to reduce the initial unbalance indirectly, this paper establishes mass eccentric propagation model in multistage rotors assembly of aircraft engine for the first time. It provides a new idea to establish the relationship between the amount of unbalance of each rotor and the initial unbalance of multistage rotors.

This paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap.

The superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP.

The radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results.

This paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method.

There is an unbalanced magnetic pull between the rotor and stator of the cage induction motor when the rotor is not concentric with the stator. These forces depend on the position and motion of the centre point of the rotor. In this paper, the linearity of the forces in proportion to the rotor eccentricity is studied numerically using time‐stepping finite element analysis. The results show that usually the forces are linear in proportion to the rotor eccentricity. However, the closed rotor slots may break the spatial linearity at some operation conditions of the motor.

The paper seeks to perform a detailed numerical study of flow over a generic fan‐wing airfoil and also attempts to modify the geometry for the improvement of the aerodynamic performance.

Advanced computational fluid dynamics (CFD) technique has been employed for evaluation of the aerodynamic performance (e.g. lift/drag ratio) of a model problem. Numerical investigation starts with sensitivity studies to minimize domain size influence and grid dependency, followed by time‐accurate transient calculations. A preliminary re‐design exercise has been performed by analyzing the results of a current design.

CFD predicted lift force agrees fairly well with the measurement data with about 6.55 per cent error, while drag force compares less favourably with about 12.59 per cent error. Both errors are generally acceptable for an engineering application of complex flow problems. Several key flow features observed previously by experiment have also been re‐produced by simulation, notably the eccentric vortex motions in the blade interior and the stream “jet” flow outside the blades near the exit. With the modified geometry, there is a considerable lift/drag ratio improvement of about 29.42 per cent. The possible reasons for such a significant improvement have been discussed.

As it is the first step towards the detailed flow analysis of this type of model, a simpler blade shape rather than “real” one has been used.

The paper provides a very useful source of information and could be used as guidance for further industry practice of unmanned aerial vehicles design.

This paper is valuable for both academic researchers and industry engineers, especially those working in the area of high‐lift wing design. The works presented are original.

When solving the cogging torque of complex electromagnetic structures, such as consequent pole hybrid excitation synchronous (CPHES) machine, traditional methods have a huge computational complexity. The notable feature of CPHES machine is the symmetric range of field-strengthening and field-weakening, but this type of machine is destined to be equipped with a complex electromagnetic structure. The purpose of this paper is to propose a hybrid analysis method to quickly and accurately solve the cogging torque of complex 3D electromagnetic structure, which is applicable to CPHES machine with different magnetic pole shapings.

In this paper, a hybrid method for calculating the cogging torque of CPHES machine is proposed, which considers three commonly used pole shapings. Firstly, through magnetic field analysis, the complex 3D finite element analysis (FEA) is simplified to 2D field computing. Secondly, the discretization method is used to obtain the distribution of permeance and permeance differential along the circumference of the air-gap, taking into account the effect of slots. Finally, the cogging torque of the whole motor is obtained by using the idea of modular calculation and the symmetry of the rotor structure.

This method is applicable to different pole shapings. The experimental results show that the proposed method is consistent with 3D FEA and experimental measured results, and the average calculation time is reduced from 8 h to 4 min.

This paper proposes a new concept for calculating cogging torque, which is a hybrid calculation of dimension reduction and discretization modules. Based on magnetic field analysis, the 3D problem is simplified into a 2D issue, reducing computational complexity. Based on the symmetry of the machine structure, a modeling method for discretized analytical models is proposed to calculate the cogging torque of the machine.

The purpose of this paper is to analyze the unbalanced magnetic pull (UMP) of the rotor of traction motor and the influence of the UMP on thermal characteristics of traction motor bearing.

The unbalanced magnetic pull on the rotor with different eccentricity was calculated by Fourier series expansion method. A bearing thermal analysis finite element model considering both the vibration of high-speed train caused by track irregularity and the UMP of traction motor rotor was established. The validity of the model is verified by experimental data obtained from a service high-speed train.

The results show that thermal failure of bearing subassemblies most likely occurs at contact area between the inner ring and rollers. The UMP of rotor of traction motor has a significant effect on the temperature of the inner ring and roller of the bearing. When the eccentricity is 10%, the temperature can even be increased by about 12°C. Therefore, the UMP of rotor of traction motor must be considered in thermal analysis of traction motor bearing.

In the thermal analysis of the bearing of the traction motor of high-speed train, the UMP of the rotor of the traction motor is considered for the first time

To present results of research closely linked with real life applications. It resumes work of a period of about two years.

Applying the finite‐element method (FEM) the impact of balancing kerfs in the bars of squirrel‐cage rotors of a small scale, mass series induction machine (IM) is studied. For the analysis and design optimization of the IM both, 2D electromagnetic, multi‐slice and 3D structure‐dynamic models are considered. Introducing and applying a novel 2D‐3D force‐transformation scheme, all possible balancing variants of the IM are studied in terms of electromagnetic and mechanical behaviour.

The obtained results lead to a significant improvement of the studied IM. In fact, it is found, that the method of balancing the rotor by carving the rotor bars results in higher unbalanced pull rather than reducing it. This is due to electromagnetic unbalance caused by balancing. Hence, the IM is no longer balanced in series production. This again leads to a major economic benefit.

Using the FEM for simulation of structure dynamic problems is often limited to how the boundary layers are handled. In real life materials are not “connected” but glued or clamped. Therefore, the behaviour can only be adopted by manipulating the material parameters derived from iterative parameter adoption by measurement.

Owing to the findings the IM is no longer balanced in series production, leading to a significant reduction of costs. In general, the applied methods can be used for the analysis and optimization of any kind of manufacturing or tolerance problem of electrical machines such as various kinds of eccentricity, punching kerfs, broken bars, magnetization errors in permanent‐magnet machines, etc.

This contribution gives a close insight of how to study the impact of manufacturing and tolerance problems of electric machinery, applying the method to an IM with balancing kerfs.