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Relevant bibliographies by topics / Winding numbers

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Academic literature on the topic 'Winding numbers'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 June 2025

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Journal articles on the topic "Winding numbers"

1

GRIDIN, Vladimir M. "Brushless DC Motors with a Three-Section Winding and Two Inductors." Elektrichestvo 1, no. 1 (2021): 55–60. http://dx.doi.org/10.24160/0013-5380-2021-1-55-60.

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Two brushless DC motors (BLDC) with a three-section armature windiщ and two cylindrical inductors-magnets are considered. One motor has an ordinary drum-type armature windiщ, and numbers of radial poles in its two inductors differ from each other by a factor of three. The other motor has a toroidal armature winding, and the numbers of radial poles in its two inductors differ from each other by a factor of two. An expression for the distribution of the resulting armature winding magnetic induction over the air gap circumference is given. The optimal relationships between the parameters of two inductors are determined. Expressions are obtained for the ratios of the electromagnetic torques of the considered motors and for the known BLDC motor with a conventional three-section armature winding and a composite inductor consisting of an inner magnetically soft bushing and external poles formed by magnets. The compared machines have the same number of power transistors and are made with the same dimensions of their electromechanical parts, and their armature windings consume the same power from the power source. It has been found that the electromagnetic torque in the considered motor with the ordinary armature winding is approximately a factor of 1.37 greater than in the known motor with a three-section armature winding, whereas in the motor with a toroidal armature winding it is smaller by about a factor of 1.1, i.e., insignificantly. However, the electromagnetic torque pulsation in the motor with a toroidal winding and three power transistors is approximately 3%, whereas in the known motor with three and six power transistors its values are approximately equal to 8 and 4.5%, respectively. The considered motors with simpler cylindrical inductors can compete with the known BLDC motors.

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2

Chernov (Tchernov), V. V., and Y. B. Rudyak. "On generalized winding numbers." St. Petersburg Mathematical Journal 20, no. 5 (2009): 837–49. http://dx.doi.org/10.1090/s1061-0022-09-01075-9.

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3

Shin, Homin, and Junghwan Chang. "Characteristics Analysis of Doubly Fed Magnetic Geared Motor Considering Winding Frequency Conditions." Energies 11, no. 10 (2018): 2564. http://dx.doi.org/10.3390/en11102564.

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The magnetic geared motor, which has improved torque density because of the magnetic gearing effect, has been researched. However, its narrow operating region due to the operating mechanism by the magnetic gearing effect and field flux by the PM is a challenge that needs to be overcome. Whereas, the doubly fed magnetic geared motor (DFMGM) can extend the operating region because of the double stator and double winding structure with the individual frequency control of the current fed to the inner and outer windings. However, two rotating magnetic fields, which are produced by the inner and outer winding flux, exist at the air-gap, and the large numbers of space harmonic components of the modulated flux density are produced at the air-gaps. These space harmonic components, which are produced by the winding MMF, influence not only the back-EMF of the winding but also the performances of the operating torque. Besides, the inner and outer windings affect each other in the back-EMF, and its characteristics appears differently in the inner and outer windings. Thus, in this paper, the structure, operating strategy, and basic characteristics according to the frequency condition in the inner and outer windings are presented.

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KNUDSEN, CARSTEN. "TOPOLOGICAL WINDING NUMBERS FOR PERIOD-DOUBLING CASCADES." International Journal of Bifurcation and Chaos 06, no. 01 (1996): 185–87. http://dx.doi.org/10.1142/s0218127496001934.

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We define the topological winding number for unimodal maps that share the essential properties of that of winding numbers for forced oscillators exhibiting period-doubling cascades. It is demonstrated how this number can be computed for any of the periodic orbits in the first period-doubling cascade. The limiting winding number at the accumulation point of the first period-doubling cascade is also derived. It is shown that the limiting value for the winding number ω∞ can be computed as the Farey sum of any two neighbouring topological winding numbers in the period-doubling cascade. The derivations are all based on symbolic dynamics and simple combinatorics.

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Kahane, Jean-Pierre. "Winding numbers and summation processes." Complex Variables and Elliptic Equations 55, no. 8-10 (2010): 911–22. http://dx.doi.org/10.1080/17476930903568381.

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Kahane, Jean-Pierre. "Winding numbers and fourier series." Proceedings of the Steklov Institute of Mathematics 273, no. 1 (2011): 191–95. http://dx.doi.org/10.1134/s0081543811040080.

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ANTIPOV, Viktor N., Andrey D. GROZOV, and Anna V. IVANOVA. "The Use of Concentrated Windings for High-Power Synchronous Wind Generators." Elektrichestvo 4, no. 4 (2021): 50–57. http://dx.doi.org/10.24160/0013-5380-2021-4-50-57.

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Low-power machines were commonly considered as the main application field of concentrated windings. However, a lot of paper have recently been published, which address both the theory of these windings and specific cases of their application for large synchronous machines. The article presents an analysis of the parameters of concentrated windings having various configurations intended for use in high-power gear and gearless wind generators. In assessing the winding, not only the high winding factor value was taken into account, but also the star of slot EMFs, harmonic spectra of the MMFs and EMFs, the cogging torque component and torque pulsation under load, as well as emerging losses. It is shown that the well-known advantages of concentrated windings over distributed windings can be fully realized by choosing the appropriated numbers of slots and poles.

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Abouelsaood, Ahmed. "Gauge transformations with fractional winding numbers." Physical Review D 54, no. 4 (1996): 2889–98. http://dx.doi.org/10.1103/physrevd.54.2889.

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9

Söderberg, B. "Circle maps and reciprocal winding numbers." Journal of Mathematical Physics 29, no. 4 (1988): 837–42. http://dx.doi.org/10.1063/1.527980.

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10

Jurkovic, Sinisa, and Elias G. Strangas. "Comparison of PMAC Machines for Starter-Generator Application in a Series Hybrid-Electric Bus." International Journal of Vehicular Technology 2011 (April 6, 2011): 1–11. http://dx.doi.org/10.1155/2011/275785.

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This paper presents a comparative study of outer rotor PMAC machine candidates for starter-generator application in hybrid bus with series power train configuration. PMAC machines with interior and surface mount permanent magnets are considered and compared, although a complete analysis is only carried out for the SPM. Different design aspects such as concentrated versus distributed windings as well as interior and exterior rotor structures are evaluated. Different slot numbers per pole per phase configurations for concentrated winding PMAC machines are also examined. Comparison and evaluation of the machines is based on their performance which included evaluation of winding and iron losses, magnet losses, and maximum torque capability as well as the size and weight of the machines.

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Dissertations / Theses on the topic "Winding numbers"

1

Dimitroglou, Rizell Georgios. "Winding numbers and attaching Riemann surfaces." Thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120618.

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Faulkner, Michael. "Phénomènes émergents et topologiques dans les systèmes BKT sur réseau." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL0984/document.

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Cette thèse s'intéresse aux phénomènes électrostatiques émergents dans les modèles magnétiques toroïdaux bi-dimensionnels à symétrie XY, fournissant ainsi un support pour de plus amples recherches dans le domaine de la transition de phase Berezinskii-Kosterlitz-Thouless (BKT).Dans de nombreux systèmes bi-dimensionnels, dont le modèle bi-dimensionnel XY du magnétisme, la transition BKT contrôle la dissociation thermique de paires de défauts topologiques liés. Le modèle XY est analogue au gaz de Coulomb bi-dimensionnel, à ceci près qu'il peut être simulé sans avoir à modéliser les interactions à longue distance du système Coulombien. Cette thèse élucide ce paradoxe en démontrant que l'approximation de Villain appliquée au modèle XY est strictement équivalente au modèle électrostatique de Maggs-Rossetto (MR) appliqué au système Coulombien bi-dimensionnel.Cette équivalence est utilisée pour sonder la transition BKT par l'application de l'algorithme MR au gaz de Coulomb bi-dimensionel. En simulant le système Coulombien, il est prouvé que les fluctuations dans l'organisation des charges autour du tore sont activées à la température de transition BKT. Ces fluctuations du champ électrique indiquent ainsi la phase de haute température de la transition.Il est ensuite montré que l'exposant critique effectif de la théorie de Bramwell-Holdsworth (BH) peut être mesuré dans les films d'hélium 4 superfluide, qui correspondent à des gaz de Coulomb effectifs dans la limite de systèmes de grandes tailles finies<br>This thesis addresses the emergent electrostatics of two-dimensional, toroidal magnetic models that possess XY symmetry, providing a platform for novel investigations into the Berezinskii-Kosterlitz-Thouless (BKT) phase transition.The BKT transition drives the thermal dissociation of bound pairs of topological defects in many two-dimensional systems, including the two-dimensional XY model of magnetism. The XY model is closely analogous to the two-dimensional Coulomb gas, but can be simulated without computing the long-range interactions of the Coulombic system. This thesis elucidates this paradox by showing that Villain's approximation to the XY model is strictly equivalent to the Maggs-Rossetto (MR) electrostatic model when applied to the two-dimensional Coulomb gas.The mapping is used to probe the BKT transition through the application of the MR algorithm to the two-dimensional Coulomb gas. By simulating the Coulombic system, fluctuations in the winding of charges around the torus are shown to turn on at the BKT transition temperature. These topological-sector fluctuations in the electric field therefore signal the high-temperature phase of the transition.It is then shown that the effective critical exponent of Bramwell-Holdsworth (BH) theory can be measured in superfluid 4He films, which correspond to effective Coulomb gases in the limit of large but finite system size. With the Coulombic system taken as the base BKT system, it is inferred that BH theory is a general property of BKT systems

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Aru, Juhan. "Géométrie du champ libre Gaussien en relation avec les processus SLE et la formule KPZ." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1007/document.

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Cette thèse porte sur la géométrie du champ libre Gaussien. Le champ libre Gaussien est un objet central en théorie quantique des champs et représente entre autre les fluctuations naturelles d'un potentiel électrique ou d’un modèle de dimères. La thèse commence dans le discret avec la démonstration d'un principe de Donsker en dimension plus grande que 1. Ce résultat est établi grâce à une nouvelle façon de représenter le champ libre en exprimant son gradient comme la partie gradient d'un champ de bruits blancs. Ensuite, les processus d'exploration du champ libre - ou ensembles locaux - introduits par Schramm-Sheffield sont étudiés en détail. Ces ensembles locaux généralisent de façon naturelle le concept de temps d'arrêt. On formalise cette théorie d'une nouvelle manière en procédant par analogie au cas 1D. Pour mieux comprendre le comportement du champs libre près des points d'intersection des ensembles locaux, un étude fine des oscillations du champ libre 2D près du bord s'avère utile. Enfin, la partie principale de cette thèse étudie des processus d'explorations particuliers – les processus SLE qui sont couplés naturellement avec le champ libre. On peut donner par exemple un sens aux lignes de niveau en utilisant le processus SLE_4 (Schramm-Sheffield). Nous avons utilisé ce couplage pour mieux comprendre la relation dite de KPZ qui intervient dans la théorie de la gravité quantique de Liouville. A l ‘aide de résultats fins sur l’enroulement des SLEs, nous avons montré comment adapter la relation de KPZ à la famille ci-dessus de processus d’explorations du champ libre. On peut interpréter ces résultats aussi comme une description de la géométrie du champ libre près des ces lignes d’exploration<br>In this thesis we study the geometry of the Gaussian free field (GFF). After a gentle general introduction, we describe what we call the Hodge decomposition of the white noise – a way to represent the white noise vector field as a sum of a gradient and a rotation of independent GFFs. This decomposition gives rise to the Donsker invariance principle for the GFF.Next, we revisit from a slightly different angle the theory of so-called local sets of the GFF, introduced by Schramm and Sheffield. These random sets allow one to study the geometry of the GFF in a Markovian way. We also go a step further in describing the behaviour of the field near the boundary of possibly several local sets. The first chapter ends with a study of boundary oscillations of the GFF.The GFF is only a generalized function, yet it comes out that one can still make sense of it as a „random landscape“. In particular, Schramm and Sheffield gave meaning to the level lines of the GFF in terms of a coupling with SLE_4 process. In chapter 2 we study this coupling and describe the existent proofs and a non-proof of measurability of the SLE_4 process in this coupling. The rest of this chapter contains one of the most technical parts of the thesis – we obtain fine estimates on the winding of the SLE curves, conditioned to pass closely by a fixed point.This technical work is put in use in chapter 3, where we study the so called KPZ relation. In this context, the KPZ formula relates fractal dimensions of sets under the Euclidean geometry and under the „quantum geometry“ given by the exponential of the GFF. So far the KPZ formula was derived for planar sets independent of the quantum geometry. Here, we determine the KPZ formulas for sets that are naturally coupled with the quantum geometry – for the flow and level lines of the GFF. The family of KPZ formulas obtained resemble but still differ from the KPZ formula for independent sets

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Halfar, Tomáš. "Zlepšení energetických parametrů asynchronních strojů malého výkonu." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-219929.

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The master’s thesis Improvement power parameter of small induction motors deals with issues of lowering the losses of small induction motors. The first part introduces with design and principles of operation of induction motors. Also introduces to theoretical problematic of losses, their lowering and measuring. In the practical part there are results of the measuring the losses in the induction motor ATAS Elektromotory Náchod a.s. T22VT512 (71-0512). There are proposed methods of increasing the efficiency of induction motor due to measuring and their verification in the Maxwell software. The last part is dedicated to measuring the losses of prototype motor from ATAS and comparison of results with previous motor.

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Chen, Han-Ting, and 陳漢庭. "Zak Phase and Winding Number." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/vy7jeb.

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碩士<br>國立臺灣大學<br>物理學研究所<br>107<br>A well known property of topological insulators is the existence of robust edge states. We use the SSH model to illustrate the robustness of the zero energy edge state under arbitrary perturbations. Also, it is known that the polarization is proportional to the Zak phase. By summing over the Zak phase of all the energy bands, the total Zak phase is shown to be always an integer multiple of 2pi even if there is no chiral symmetry. Therefore, we may relate the total Zak phase and the winding number, and we may generalize the bulk-edge correspondence to systems without chiral symmetry.

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谷村, 省吾, and Shogo TANIMURA. "Zero-mode, winding number and quantization of abelian sigma model in (1+1) dimensions." Thesis, 1995. http://hdl.handle.net/2237/15640.

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Books on the topic "Winding numbers"

1

Roe, John. Winding around: The winding number in topology, geometry, and analysis. American Mathematical Society, 2015.

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2

Warde, J. D. Joint stock companies' manual: For the use of shareholders, directors and officers of companies, and the general public; containing practical information as to the steps to be taken and the proofs to be furnished in applying for a charter of incorporation under the acts of the province of Ontario and the Dominion of Canada, relating to the formation of joint companies by letters patent : together with information respecting the organization, management, carrying on and winding up of such companies, and a number of forms and by-laws suitable for the use thereof. 3rd ed. Hunter, Rose, 1985.

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1974-, Nelson Sam, ed. Quandles: An introduction to the algebra of knots. American Mathematical Society, 2015.

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Kachelriess, Michael. Anomalies, instantons and axions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0017.

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The axial anomaly is derived both from the non-invariance of the path-integral measure under UA(1) transformations and calculations of specific triangle diagrams. It is demonstrated that the anomalous terms are cancelled in the electroweak sector of the standard model, if the electric charge of all fermions adds up to zero. The CP-odd term F̃μν‎Fμν‎ introduced by the axial anomaly is a gauge-invariant renormalisable interaction which is also generated by instanton transitions between Yang–Mills vacua with different winding numbers. The Peceei–Quinn symmetry is discussed as a possible explanation why this term does not contribute to the QCD action.

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White, Ruth. Mr. Windbag in the Line Country: Learn About Letters & Numbers. Rhythms Productions, 1999.

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Dignam, Alan, and John Lowry. 17. Corporate rescue and liquidations in outline. Oxford University Press, 2018. http://dx.doi.org/10.1093/he/9780198811831.003.0017.

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Titles in the Core Text series take the reader straight to the heart of the subject, providing focused, concise, and reliable guides for students at all levels. This chapter deals with the regulatory regime governing corporate rescue and liquidations. It first considers two procedures that were introduced by the Insolvency Act 1986 aimed at implementing the objective of corporate rescue: the administration order and the company voluntary arrangement, the former of which has been fundamentally reformed by the Enterprise Act 2002. It then discusses voluntary winding-up by companies, members, and creditors under the 1986 Act, as well as the grounds on which the court may initiate compulsory winding-up. The chapter also examines the consequences of a winding-up petition on dispositions of company property; winding-up in the public interest; the duties and functions of the liquidator; provisions allowing avoidance of transactions entered into prior to liquidation; the personal liability of directors under the Insolvency Act 1986; and distribution of surplus assets following liquidation. Finally, it outlines a number of amendments to the 1986 Act.

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Dignam, Alan, and John Lowry. 17. Corporate rescue and liquidations in outline. Oxford University Press, 2016. http://dx.doi.org/10.1093/he/9780198753285.003.1801.

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Titles in the Core Text series take the reader straight to the heart of the subject, providing focused, concise, and reliable guides for students at all levels. This chapter deals with the regulatory regime governing corporate rescue and liquidations. It first considers two procedures that were introduced by the Insolvency Act 1986 aimed at implementing the objective of corporate rescue: the administration order and the company voluntary arrangement, the former of which has been fundamentally reformed by the Enterprise Act 2002. It then discusses voluntary winding-up by companies, members, and creditors under the 1986 Act, as well as the grounds on which the court may initiate compulsory winding-up. The chapter also examines the consequences of a winding-up petition on dispositions of company property; winding-up in the public interest; the duties and functions of the liquidator; provisions allowing avoidance of transactions entered into prior to liquidation; the personal liability of directors under the Insolvency Act 1986; and distribution of surplus assets following liquidation. Finally, it outlines a number of amendments to the 1986 Act.

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Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. The Existence of Field Theories beyond the Perturbation Expansion. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0024.

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The standard model of fundamental interactions. A brief summary of the phenomenology of weak interactions. The construction of the electroweak theory and its experimental consequences. The deep inelastic scattering data as a motivation for quantum chromodynamics. Asymptotic freedom and the parton model. Quantum chromodynamics formulated on a space–time lattice. Non-trivial gauge field configurations and instantons. The meaning of the winding number. The strong CP problem and axions.

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French, Derek. 18. Remedies for maladministration. Oxford University Press, 2018. http://dx.doi.org/10.1093/he/9780198815105.003.0018.

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This chapter considers the remedies available when maladministration occurs, with emphasis on the existence of the company as a separate person. It examines circumstances where a wrong has been done to the company or to individual members, focusing on the proper claimant principle established in Foss v Harbottle (1843) 2 Hare 461, and the possible action that can be taken against company officers who have committed a wrong. It also explains the causes for which a member can file derivative claims; the right of a member to petition the court for relief under the Companies Act 2006 (CA 2006), part 30 (ss 994 to 999); the concept of winding up; the irregularity principle; and when the Secretary of State can intervene in maladministration cases. The chapter cites relevant legislation (Companies Act 1985, Insolvency Act 1986 and CA 2006) and a number of particularly significant court cases.

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French, Derek, Stephen W. Mayson, and Christopher L. Ryan. 18. Remedies for maladministration. Oxford University Press, 2016. http://dx.doi.org/10.1093/he/9780198778301.003.0018.

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This chapter considers the remedies available when maladministration occurs, with emphasis on the existence of the company as a separate person. It examines circumstances where a wrong has been done to the company or to individual members, focusing on the proper claimant principle established in Foss v Harbottle (1843) 2 Hare 461, and the possible action that can be taken against company officers who have committed a wrong. It also explains the causes for which a member can file derivative claims; the right of a member to petition the court for relief under the Companies Act 2006 (CA 2006), part 30 (ss 994 to 999); the concept of winding up; the irregularity principle; and when the Secretary of State can intervene in maladministration cases. The chapter cites relevant legislation (Companies Act 1985, Insolvency Act 1986, and CA 2006) and a number of particularly significant court cases.

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Book chapters on the topic "Winding numbers"

1

Felsager, Bjørn. "Smooth Maps—Winding Numbers." In Geometry, Particles, and Fields. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0631-6_10.

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Saller, Heinrich. "Circles and Winding Numbers." In Operational Symmetries. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58664-9_5.

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Fulton, William. "Applications of Winding Numbers." In Graduate Texts in Mathematics. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4180-5_4.

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Shakarchi, Rami. "Winding Numbers and Cauchy’s Theorem." In Problems and Solutions for Complex Analysis. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1534-9_4.

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Lang, Serge. "Winding Numbers and Cauchy’s Theorem." In Monographs in Computer Science. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-59273-7_4.

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Lang, Serge. "Winding Numbers and Cauchy’s Theorem." In Graduate Texts in Mathematics. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3083-8_4.

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Ullrich, David. "Logarithms, winding numbers and Cauchy’s theorem." In Complex Made Simple. American Mathematical Society, 2008. http://dx.doi.org/10.1090/gsm/097/05.

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Shevchenko, Ivan I. "Spectra of Winding Numbers of Chaotic Asteroidal Motion." In Chaos in Gravitational N-Body Systems. Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0307-4_36.

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Lee, Carl. "Winding numbers and the generalized lower-bound conjecture." In Discrete and Computational Geometry: Papers from the DIMACS Special Year. American Mathematical Society, 1991. http://dx.doi.org/10.1090/dimacs/006/13.

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Huggett, Stephen, and David Jordan. "Winding Number." In A Topological Aperitif. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-3694-1_6.

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Conference papers on the topic "Winding numbers"

1

Chen, Xiaorui, and Sara McMains. "Polygon Offsetting by Computing Winding Numbers." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85513.

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In this paper we present a simple new algorithm to offset multiple, non-overlapping polygons with arbitrary holes that makes use of winding numbers. Our algorithm constructs an intermediate “raw offset curve” as input to the tessellator routines in the OpenGL Utility library (GLU), which calculates the winding number for each connected region. By construction, the invalid loops of our raw offset curve bound areas with non-positive winding numbers and thus can be removed by using the positive winding rule implemented in the GLU tessellator. The proposed algorithm takes O((n + k)logn) time and O(n + k) space, where n is the number of vertices in the input polygon and k is the number of self-intersections in the raw offset curve. The implementation is extremely simple and reliably produces correct and logically consistent results.

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Quandt, Alexander. "Optical topological materials and winding numbers." In Active Photonic Platforms XII, edited by Ganapathi S. Subramania and Stavroula Foteinopoulou. SPIE, 2020. http://dx.doi.org/10.1117/12.2567486.

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Mukundan, Shruthi, Himavarsha Dhulipati, Guodong Feng, Jimi Tjong, and Narayan C. Kar. "Modeling and Analysis of Novel Star-Delta Winding Configuration with Odd Slot Numbers for Reduced Space Harmonics Using Winding Function." In 2019 IEEE International Electric Machines & Drives Conference (IEMDC). IEEE, 2019. http://dx.doi.org/10.1109/iemdc.2019.8785395.

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Hinton, Jantzen L., Paul A. Gross, Ramana V. Grandhi, and Arif S. Malik. "Using an Airy Function to Predict Stresses in Wound Metal Strip Having Asymmetric Thickness Profile." In ASME 2010 International Manufacturing Science and Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/msec2010-34162.

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This work analyzes the evolution of stresses during the rewinding of flat-rolled steels having asymmetric strip thickness profile (or wedge). When monitoring the stress distribution across the width of the sheet, control systems with strip flatness meters are unable to distinguish between “rolled-in” stresses and the stresses caused by winding. To avoid strip flatness defects, an efficient and accurate method was developed to separate the winding stress contribution from the overall stresses that are measured indirectly by a flatness control system. Commercial finite element software was first applied to determine in-plane evolution of stresses in a strip containing 2.4% wedge for various numbers of mandrel wraps during re-winding. The finite element analysis enabled a trend study that provided insight as to how the in-plane stresses in the rolled sheet evolve during the winding process. Coefficients of a 4th order polynomial Airy Stress Function were then obtained to predict the stresses according to the mandrel wrap number and planar spatial position on the strip. With this approach, only a single function is needed to predict the entire in-plane stress field. This paper illustrates development of the Airy Stress function as characteristics of the in-plane stresses during winding of strip with asymmetric thickness profile.

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Burton, Greg. "A Hybrid Approach to Polygon Offsetting Using Winding Numbers and Partial Computation of the Voronoi Diagram." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34303.

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In this paper we present a new, efficient algorithm for computing the “raw offset” curves of 2D polygons with holes. Prior approaches focus on (a) complete computation of the Voronoi Diagram, or (b) pair-wise techniques for generating a raw offset followed by removal of “invalid loops” using a sweepline algorithm. Both have drawbacks in practice. Robust implementation of Voronoi Diagram algorithms has proven complex. Sweeplines take O((n + k)log n) time and O(n + k) memory, where n is the number of vertices and k is the number of self-intersections of the raw offset curve. It has been shown that k can be O(n2) when the offset distance is greater than or equal to the local radius of curvature of the polygon, a regular occurrence in the creation of contour-parallel offset curves for NC pocket machining. Our O(n log n) recursive algorithm, derived from Voronoi diagram algorithms, computes the velocities of polygon vertices as a function of overall offset rate. By construction, our algorithm prunes a large proportion of locally invalid loops from the raw offset curve, eliminating all self-intersections in raw offsets of convex polygons and the “near-circular”, k proportional to O(n2) worst-case scenarios in non-convex polygons.

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Kim, Ju Hyung, Yingjie Li, Dheeraj Bobba, and Bulent Sarlioglu. "New perspective to understand winding configurations of even and odd numbers of pole flux-switching permanent magnent machine." In 2016 IEEE Transportation Electrification Conference and Expo (ITEC). IEEE, 2016. http://dx.doi.org/10.1109/itec.2016.7520250.

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Wu, Leilei, Ronghai Qu, and Dawei Li. "Influence of pole ratio and winding pole numbers on the performances and optimal parameters of the surface permanent magnet vernier machines." In 2014 XXI International Conference on Electrical Machines (ICEM). IEEE, 2014. http://dx.doi.org/10.1109/icelmach.2014.6960231.

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Veiga, Jose´ C., Carlos F. Cipolatti, Nelson Kavanagh, and David Reeves. "The Influence of Winding Density in the Sealing Behavior of Spiral Wound Gaskets." In ASME 2011 Pressure Vessels and Piping Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/pvp2011-57556.

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Spiral wound gaskets are used worldwide in piping and equipment flanges and can be manufactured in several combinations of materials, and in a wide range of dimensions, winding densities and shapes. This paper shows the sealability influence of winding densities, which are not specified by the current Spiral Wound B16.20 gasket standards, including flexible graphite filler thickness, height and number of windings. The effect of the flange rotation is also shown.

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Quinby, J. L., and B. F. Feeny. "Low-Frequency Phenomena in a Frictionally Excited Beam." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59779.

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A cantilevered beam was excited by a periodically reciprocating friction contact surface. Frequency sweeps revealed frequency regions of dynamic responses in the flexural direction of the beam. Chaotic and quasiperiodic responses were observed when the input frequency was fixed. The quasiperiodic responses sometimes were accompanied by beam oscillations normal to the friction surface. Extremely low frequencies were observed (up to over 100 times lower than the driver). Two-frequency quasiperiodicity was observed, and underlying circle maps were extracted. Winding numbers were matched to frequencies quantified in FFTs. Impending torus folding and intermittency were revealed. Three-frequency quasiperiodicity was also evident. A torus doubling bifurcation was documented.

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Park, Sang-Hyun, Ki-bum Park, Hyoung-Suk Kim, Gun-Woo Moon, and Myung-Joong Youn. "Cell-to-cell charge equalization converter using multi-winding transformer with reduced number of windings." In ECCE Asia (ICPE 2011- ECCE Asia). IEEE, 2011. http://dx.doi.org/10.1109/icpe.2011.5944606.

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