Analytical study of the frequency response function of a nonlinear spring damper system

A spring damper system with a nonlinear damping element is investigated using the Volterra series method to study the system frequency response function (FRF) characteristics. The relationship between the FRF and the characteristic parameters of the nonlinear damper is determined to produce an analytical description for the system FRF. Simulation studies are used to verify the theoretical analysis. These results provide an important basis for the FRF based analysis and design of nonlinear spring damper systems in the frequency domain

Analytical modelling of modular and unequal tooth width surface-mounted permanent magnet machines

This paper presents simple analytical modelling for 2 types of 3-phase surface-mounted permanent magnet (SPM) machines such as modular and unequal tooth width (UNET) machines with different slot/pole number combinations. It is based on the slotless open-circuit air-gap flux density and the slotted air-gap relative permeance calculations. This model allows calculating the open-circuit air-gap flux density, phase flux linkage and back electromotive force (EMF), average torque of both the modular and UNET machines. Its accuracy has been validated by 2D finite element (FE) method. A flux focusing/defocusing factor has also been introduced to analyse the influence of flux gaps in alternate stator teeth of modular machines on the machine electromagnetic performances. It has been found that by properly choosing the slot/pole number combination and flux gap width, the open-circuit air-gap flux density, the winding factor and the flux focusing effect can all be improved. As a result, the performance of modular machine can be significantly boosted. The analytical and FE models have been validated by experiments

Space-time Characteristics and Experimental Analysis of Broadening First-order Sea Clutter in HF Hybrid Sky-surface Wave Radar

In high frequency (HF) hybrid sky-surface wave radar, the first-order sea clutter broadening is very complex and serious under the influence of ionosphere and bistatic angle, which affects the detection of ship target. This paper analyzes the space-time characteristics based on the HF sky-surface wave experimental system. We first introduce the basic structure, working principle and position principle based on our experimental system. Also analyzed is the influence of ionosphere and bistatic angle on the space-time coupling characteristics of broadening first-order sea clutter and the performance of space-time adaptive processing (STAP). Finally, the results of theoretic analysis are examined with the experimental data. Simulation results show that the results of experiment consist with that of theoretic analysis

Influence of stator topologies on average torque and torque ripple of fractional-slot SPM machines with fully closed slots

This paper investigates the influence of concentrated winding configurations and stator core structures on torque performance of fractional-slot surface-mounted PM (SPM) machines. From analyzing the separated torque components of prototype SPM machines with 12-slots/10-poles (12S/10P) combination by frozen permeability (FP) method, it can be found that the torque ripple is closely related with local saturation in fully closed slot (FCS) machines. Besides, the heavier local saturation will also jeopardize the merit of using alternate teeth wound windings, such as obtaining higher average torque than electrical machines with all teeth wound windings. The further analysis of stator tooth relative permeability variation over one electrical period demonstrates that the major reason for torque ripple difference among these electrical machines with different stator topologies is the asymmetric saturation between the adjacent teeth. Both the subharmonic due to armature reaction (determined by winding connection and current value) and the asymmetry of stator core structure contribute to such asymmetric saturation. In order to more clearly verify this, the complementary slot/pole number combination (12S/14P) is also analyzed. The conclusion is effective for electrical machines with other slot/pole number combinations as well. Experiments have been carried out to validate the predictions

Design Guidelines for Fractional Slot Multi-Phase Modular Permanent Magnet Machines

This paper presents the design considerations for a fractional slot multi-phase modular permanent magnet (PM) machine with single-layer concentrated windings. The winding factors for various slot/pole number combinations are calculated to identify the optimal slot/pole number combinations for different phase numbers. In addition, the electromagnetic performance influenced by flux gaps (FGs), such as air-gap MMF, back-EMF, cogging torque, on-load torque and torque ripple, etc., are comprehensively investigated by using the 2-D finite element (FE) method. Several general rules with respect to the influence of FGs on multi-phase modular PM machines performance are established. The prototypes of modular PM machines are built and the finite element results are validated with experiments

Comparative Study of Fault Tolerant Switched Flux Permanent Magnet Machines

The fault tolerant capabilities are compared in this paper for the conventional double layer switched flux permanent magnet machine and its single layer counterparts, i.e. C-core, Ecore and modular. The comparison includes the inter-turn shortcircuit and irreversible demagnetization faults. A combination of Simulink and finite element models is used in the study. Based on the predictions, it is found that the modular topology produces the lowest short-circuit current and also has the best demagnetization withstand capability while the conventional one produces the highest short-circuit current and has the worst demagnetization withstand capability. The frozen permeability method is employed to separate the flux produced by armature current and magnets, and the results showed that, besides the influence of short-circuit current, the available magnet volume and magnetic circuit configuration play an important role in the demagnetization process. It is also found that removing half of the magnets, such as using C-core, E-core and modular topologies, generally improves the demagnetization withstand capability and also increases the torque per magnet volume. Measured results are also presented to validate the short-circuit current predictions and magnet demagnetization

Novel modular switched reluctance machines for performance improvement

Compared to non-modular machines, modular topologies become increasingly attractive due to their simplified manufacture process, better fault tolerant capability and potentially reduced material consumption. In order to maintain or even enhance the machine performance while achieving high fault tolerant capability, novel modular, single layer winding switched reluctance machines (SRMs) with different pole numbers are proposed, which are supplied by rectangular wave current with different conduction angles. The influences of the pole number and flux gap width between E-core segmented stators on the electromagnetic performance have been investigated in terms of self- and mutual inductances, electromagnetic torque, copper loss, iron loss, and radial force. It has been found that the modular structures with higher rotor pole numbers than stator slot numbers (12-slot/14-pole and 12-slot/16-pole SRMs) can maintain and even improve the average torque due to the nature of self- and mutual inductances. In addition, the torque ripple for modular machines are significantly reduced (below 50%), so do the iron loss and radial force, leading to higher efficiency albeit with potentially lower vibration and acoustic noise. Two prototypes with 12-slot/8-pole and 12-slot/14-pole combinations have been built with both non-modular and modular structures to validate the predictions in terms of inductances and static torques

Investigation on contribution of inductance harmonics to torque production in multiphase doubly salient synchronous reluctance machines

This paper investigates the contribution of each order inductance harmonic to the torque (both average torque and torque ripple) of multiphase doubly salient synchronous reluctance machines (DS-SRMs). Such machines are similar to switched reluctance machines but supplied with sinewave currents. The investigations in this paper are as follows: first, a general analytical torque model based on Fourier Series analysis of inductances has been built for machines with different phase numbers, slot/pole number combinations and also winding configurations. The instantaneous torque for DS-SRMs with any given phase number can then be accurately predicted. Using such model, contribution of each order inductance harmonic to torque can be investigated separately. It is found that the torque ripple frequency of the DS-SRM only depends on phase number. For example, for a m-phase machine, there will be m×kth order torque ripple if mod(mk,2)=0, where m is phase number and k is a natural number. This study also explains why certain phase numbers inherently produce lower torque ripple than others. The findings in this paper provide a future direction for potential torque ripple reduction methods either from machine design or advanced control. The simulations have been validated by experiments using a 6-phase DS-SRMs

Influence of adjacent teeth magnet polarities on performance of flux reversal permanent magnet machine

This paper provides a comprehensive analysis of performance difference among various kinds of flux reversal permanent magnet (FRPM) machines having different PM arrangements. Four PM arrangement types are firstly identified by the number and relative polarities of PMs on the stator teeth, and their influence on equivalent pole-pair number of armature winding and working harmonics of air-gap field is revealed. Then, the torque variation against rotor pole number of each PM arrangement is analyzed. Detailed electromagnetic performance of four PM arrangements with 14-pole rotor is compared. It shows that the FRPM machine, in which four PM pieces are mounted on each stator tooth and two adjacent magnets on different stator teeth are of opposite polarities, offers the highest torque density and the highest efficiency, which makes it promising in low-speed high-torque applications. In addition, four prototype machines are manufactured and tested to validate the findings

Performance comparison of doubly salient reluctance machine topologies supplied by sinewave currents

This paper comprehensively investigates the electromagnetic performance of 3-phase, 12-slot, and 8-pole switched reluctance machines (SRMs) with different winding configurations, i.e. double/single layer, short pitched (concentrated) and fully pitched (distributed). These SRMs are supplied by sinewave currents so that a conventional 3-phase converter can be employed, leading to behavior which is akin to that of synchronous reluctance type machines. Comparisons in terms of static and dynamic performances such as d- and q-axis inductances, on-load torque, torque-speed curve, efficiency map, etc. have been carried out using two-dimensional finite element method (2-D FEM). It is demonstrated for the given size of machine considered, that for same copper loss and without heavy magnetic saturation, both single and double layer mutually coupled SRMs can produce higher on-load torque compared to conventional SRMs. Additionally, double layer mutually coupled SRM achieved the highest efficiency compared to other counterparts. When it comes to single layer SRMs, they are more suitable for middle speed applications and capable of producing higher average torque while lower torque ripple than their double layer counterparts at low phase current. Two prototype SRMs, both single layer and double layer, are built to validate the predictions