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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.

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.

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.

The purpose of this paper is to focus on the mechanical bearing load caused by the unbalanced magnetic pull (UMP), which is studied in detail. The applied approach is based on an analysis of static and dynamic eccentricities at different positions and different amplitudes. The influence of the operating points is calculated to show the effective bearing load for machines operating at different speeds. The decreasing lifetime of the applied bearings is examined and evaluated in detail.

To evaluate the proposed methodology a permanent magnet synchronous machine (PMSM) with buried magnets is used. To consider effects of slotting and saturation, a finite element (FE) model is employed. The Monte Carlo method is used to determine the most likely amplitudes of the eccentricities. Calculating the UMP for all possible operating points using a control strategy for the machine and coupling this results with a drive cycle, determines the effective force acting on the bearing.

It has been shown that the position of the eccentricity has a not significant influence on the behavior of the UMP and may therefore be neglected. The amplitude of the eccentricity vector influences the amplitude of the UMP including all harmonic force components. For technical relevant eccentricities, the influence is approximately linear for the average and the dominant harmonics of the UMP. In most cases, it is sufficient to displace the rotor at an arbitrary position and amplitude. It is sufficient to simulate one type of eccentricity (static or dynamic) with an arbitrary value of displacement (rotor or stator) to evaluate all possible airgap unbalances. Using stochastic simulations of the eccentricity amplitudes enables an a priori design and lifetime estimation of bearings.

This paper gives a close insight on the effect of mechanical bearing load caused by rotor eccentricities. The effect of the position of the eccentricity vector, the operational range and a drive cycle are considered. A stochastic simulation and an empirical lifetime model of one bearing gives an example of using this methodological approach.

Deals with the problem of the electromagnetic torque calculation in the case of either nonuniformity of the air‐gap or eccentricity of the rotor. The electromagnetic field distributions have been evaluated for drag‐cup motors. An analytical model has been introduced for linear motor based on the variation method for magnetic flux density magnitudes. The total torque and its components have been evaluated for the motors chosen. The decrease of the electromagnetic torque and increase of eddy‐current losses have been discussed due to either rotor circular asymmetry or its eccentricity.