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This paper aims to establish a piecewise Maxwell stress analytical model of bearingless switched reluctance motor (BSRM) for the full rotor angular positions. The proposed model varies from the existing models, which are only applicable to the partial-overlapping positions of stator and rotor poles. By extending the applicable rotor angular positions, this model provides a basic analytical model for the multi-phase excitation control of BSRM.

The full rotor angular positions are classified into the partial-overlapping positions and the non-overlapping positions. At first, two different air gap subdividing methods are proposed, respectively, for the two-position ranges. Then, different integration paths are selected accordingly. Furthermore, two approximate methods are presented to calculate the average flux density of each air gap subdivision. Finally, considering the mutual coupling between the two perpendicular radial suspension forces, a piecewise Maxwell stress analytical model is derived for the full rotor angular positions of BSRM.

A piecewise Maxwell stress analytical model of BSRM is built for the full rotor angular positions, and applicable to the multi-phase excitation mode of BSRM. For the partial-overlapping positions and the non-overlapping positions, two sets of air gap subdividing methods, integration paths and approximate calculation methods of air gap flux densities are proposed, respectively. The accuracy and reliability of the proposed model are verified by the finite element method.

The piecewise Maxwell stress analytical model of BSRM for the full rotor angular positions is proposed for the first time. The novel air gap subdividing methods, integration paths, approximate calculation methods of air gap flux densities and the coupling between the two radial suspension forces are adopted to improve the modeling accuracy. As the applicable range of rotor angular position is extended, this model overcomes the limitation of the existing models only for single-phase excitation mode and contributes to the accurate control of BSRM multi-phase excitation mode.

This paper aims to present a prototype of a capacitive angular-position sensor which exploits advantages of flexible/printed electronics. The novelty of the sensor is that the capacitor structure is placed at the circumference of the rotor and stator, that it posses two channels (capacitor structures) electrically shifted for p/4 and that the rotor is common for both channels. The electrodes of the sensing capacitor are digitated, providing a triangular transfer function.

This sensor prototype consists of two flexible inkjet-printed silver electrodes forming a cylindrical capacitor structure. One of them is wrapped around the stator and another is wrapped around the rotor part of a simple mechanical platform used to precisely adjust the angular displacement.

The capacitance as a function of angular position was measured using an inductance capacitance impedance (LCZ) Meter, and results are presented for a full-turn measurement range. The experimental results are compared with analytical ones and very good agreement has been achieved.

The proposed capacitive sensor structure can be used as an absolute or an incremental encoder with different resolutions, and it can be applied in automotive industry or robotics.

THE present paper gives, in abbreviated form, the theory of blade motion and of static and dynamic stability of single‐rotor helicopters. Limitations of space do not permit of full discussion and the article should be taken as only an introduction to the somewhat complex problems of helicopter stability and control.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

THE balancing of rotating parts can be effected either on a balancing machine, or by means of vibration measurements carried out on the completed assembly.

AIRCRAFT of the type known under the Registered Trade Mark “Autogiio,” have means for controllably tilting the rotor axis in relation to the body in one or more substantially vertical planes about real or virtual pivot axes, any such pivot axis being located above the centre of gravity of the aircraft, below the point of intersection of the rotor axis with the projection of the line of resultant aerodynamic action of the rotor on a plane containing both the rotor axis and the shortest distance between the rotor axis and the pivot axis, and offset from the rotor axis in the direction of the aerodynamic reaction line. Figs. 2 and 5 show diagrammatically an aircraft having a body b, a rotor comprising blades r, r, connected by horizontal hinges a, a, to a rotor hub having an axis of rotation 0, 0. Lines 0–0, 1–1, 2–2, etc., represent the projections on the plane of the paper of the aerodynamic reaction lines corresponding to successively reduced angles of incidence of the rotor, line 0–0 representing the reaction line for an angle of incidence of 90 deg. corresponding to vertical descent, line 5–5 representing that corresponding to a small angle of incidence corresponding to maximum flight speed. These projection lines intersect at a focal point f1, the height of which above the hinges a, a depends upon the degree of separation thereof, this height being zero when the hinges a, a are coaxial and intersect the axis of rotation. The transverse axis about which the rotor may be tilted is shown at p2 and is disposed below the point f1 and forward of the axis of rotation 0, 0. In the limiting case where the hinges a, a are coaxial p2 may pass through the point of intersection of the hinges with the axis 0–0. Fig. 5 shows how the longitudinal pivot axis p5 for lateral tilting of the rotor is displaced from the axis of rotation 0–0 in the direction of the aerodynamic reaction line, i.e., in the direction of the re‐treating blade. The transverse pivot p2 for longitudinal rotor tilting is located rearwardly of the centre of gravity, the perpendicular from the centre of gravity on the pivot making an angle of the order of 6 deg. with the perpendicular to the longitudinal body axis. Means may also be provided for bodily displacing the rotor longitudinally of the aircraft whereby the attitude of the body to the line of flight may be controlled in the plane of symmetry, independently of the flying speed and of the position of the centre of gravity. In one embodiment, Fig. 6, a pyramid of struts 36 supports a rotor comprising blades 38 secured to a hub 37 by horizontal pivots 39, links 40, and vertical pivots 41. Hub 37 is mounted on an axis member 78, Figs. 9 and 10, pivotally mounted on pyramid 36 by means of a transverse pivot 42 and a longitudinal pivot 43, Fig. 8. Pyramid struts 36 are bolted to an apex member 71 incorporating a fork 72, Fig. 10, carrying transverse pivot 42 on which is rotatably mounted an intermediate member incorporating an offset backward projection constituting the longitudinal pivot 43 and a downward projection 76 which serves to limit rocking of member 74 about the pivot 42 by co‐operation with the sides of a shot 71x formed in apex member 71. Rocking movement of axis member 78 in pivot 43 is limited by integral lugs 80 which embrace the projection 76. Movements of part 74 about pivot 42 and of axis member 78 about pivot 43 are damped by spring‐loaded friction discs 148, 153 respectively, the pressure on which may be varied by adjusting their respective nuts 151, 156. As shown in Fig. 9, an internal expanding rotor brake and rotor starting gear are associated with the axis member 78, the latter gear including a dog clutch permitting over‐running of the rotor with respect to the drive shaft. Means for controlling the rotor tilting movements comprise levers 48, 52 respectively associated with the intermediate member 74 and the axis member 78. Lever 48 is coupled to a bell crank 46, Fig. 6, by a rod 47, and lever 52 is coupled to a lever 50, Fig. 8, on a longitudinal rock shaft 49 by rod 51, bell crank 46 and rock shaft 49 being operated by a conveniently arranged control column 44. Rods 47, 51 are tubular and are connected to their respective levers 48, 52 by resilient connections comprising columns of rubber rings 106, Fig. 9, which bear against abutments 107 fixed in the bore of the rod and against a collar 108 formed on a slidable rod 109 which is connected to the operating lever by a forked shackle 110, in the case of rod 47, and by a shackle 111 and an eyed swivel 112, Fig. 10, in the case of rod 51. Means are provided for imposing an elastic bias on either control: these comprise in the case of the fore‐and‐aft control two lengths 116 of shock absorber elastic, Fig. 11, coupled at one end to a lever 115 on shaft 113 of bell crank 46, and at the other by cables 117 to an adjustable lever 119 working in a quadrant 120. Similarly, shock absorbers 123 are coupled to a lever 122 on rock shaft 49 and are connected by cables 124, Fig. 12, passed round pulleys 126 to a lever 127 mounted on a subsidiary rock shaft 128, the angular position of which is controlled by a ratchet lever 129, Fig. 11. Shackles 118 are adjustable for varying the initial stress in elastics 116 and turnbuckles 125 are placed in the run of cables 124. In addition to control column 44, a rudder bar 55 is provided operating a rudder 54, Fig. 6, and a steerable tail wheel 64, and a lever 62 for adjusting a tail plane 57. All these controls may be locked in any adjusted position, lever 62 by a ratchet 63 and the remainder by means of friction clamps 141, 142, 143 respectively, Figs. 11 and 12. Clamp 141 locks a slotted lever 140 fast on rock shaft 49 to a fixed fuselage member. Similarly clamp 135 co‐operates with a slotted plate 134, linked by rod 133 to a lever, 132, on rock shaft 113. Clamp 143 co‐operates with a slotted plate 142, inserted in the run of a rudder cable 56x.

The purpose of this paper is to apply a fast analytical model of the acoustic behaviour of pulse‐width modulation (PWM) controlled induction machines to a fractional‐slot winding machine, and to analytically clarify the interaction between space harmonics and time harmonics in audible electromagnetic noise spectrum.

A multilayer single‐phase equivalent circuit calculates the stator and rotor currents. Air‐gap radial flux density, which is supposed to be the only source of acoustic noise, is then computed with winding functions formalism. Mechanical and acoustic models are based on a 2D ring stator model. A method to analytically derive the orders and frequencies of most important vibration lines is detailed. The results are totally independent of the supply strategy and winding type of the machine. Some variable‐speed simulations and tests are run on a 700 W fractional‐slot induction machine in sinusoidal case as a first validation of theoretical results.

The influence of both winding space harmonics and PWM time harmonics on noise spectrum is exposed. Most dangerous orders and frequencies expressions are demonstrated in sinusoidal and PWM cases. For traditional integral windings, it is shown that vibration orders are necessarily even. When the stator slot number is not even, which is the case for fractional windings, some odd order deflections appear: the radial electromagnetic power can therefore dissipate as vibrations through all stator deformation modes, leading to a potentially lower noise level at resonance.

The analytical research does not consider saturation and eccentricity harmonics which can play a significant role in noise radiation.

The analytical model and theoretical results presented help in designing low‐noise induction machines, and diagnosing noise or vibration problems.

The paper details a fully analytical acoustic and electromagnetic model of a PWM fed induction machine, and demonstrate the theoretical expression of main noise spectrum lines combining both time and space harmonics. For the first time, a direct comparison between simulated and experimental vibration spectra is made.

THIS paper presents a summary of the method and results of a general investigation into the performance characteristics of ‘single’ autogyro and helicopter rotors, which was a preliminary to the establishment, by the firm the author serves, of a helicopter division.

The purpose of this paper is to focus on the analysis of the dynamic and periodic interaction between both fixed and rotating blade rows in a single‐stage turbomachine.

A numerical three‐dimensional (3D) simulation of the complete stage is carried out, using a commercial code, FLUENT, that resolves the 3D, unsteady turbulent flow inside the passages of a low‐speed axial flow fan. For the closure of turbulence, both Reynolds‐averaged Navier‐Stokes modeling and large eddy simulation (LES) techniques are used and compared. LES schemes are shown to be more accurate due to their good description of the largest eddy structures of the flow, but require careful near‐wall treatment.

The main goal is placed on the characterization of the unsteady flow structures involved in an axial flow blower of high reaction degree, relating them to working point variations and axial gap modifications.

Complementarily, an experimental facility was developed to obtain a physical description of the flow inside the machine. Both static and dynamic measurements were used in order to describe the interaction phenomena. A five‐hole probe was employed for the static characterization, and hot wire anemometry techniques were used for the instantaneous response of the interaction.

The paper describes development of a methodology to understand the flow mechanisms related to the blade‐passing frequency in a single rotor‐stator interaction.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.