Virtuaaliprototyypin käyttö roottorin dynamiikan analysoinnissa

Työn tavoitteena oli selvittää kaupallisen dynamiikansimulointiohjelmiston soveltuvuus roottoridynamiikan analysointiin. Työssä keskityttiin erityisesti roottorin dynamiikkaan vaikuttavien epäideaalisuuksien mallintamiseen. Simulointitulosten tarkkuutta selvitettiin mittauksilla. Lisäksi vertailtiin yleiskäyttöisen dynamiikan simulointiohjelmiston ja roottoridynamiikan erikoisohjelmiston teoriaa. Tutkittava roottori oli paperikoneen putkitela. Telan joustavuus kuvattiin elementtimenetelmällä ratkaistujen moodien avulla. Elementtimallissa huomioitiin telan vaipan seinämänpaksuusvaihtelu, joka vaikuttaa telan massa- ja jäykkyysjakaumaan. Dynamiikkaohjelmistossa mallinnettiin telan tuennasta tulevat herätteet. Dynamiikkaohjelmistona käytettiin ADAMS:ia ja FEM-ohjelmana ANSYS:stä. Tuloksista havaittiin käytetyn menetelmän soveltuvan roottoridynamiikan analysointiin ja roottorin epäideaalisuuksien mallintamiseen. Simulointimallilla saatiin esille murtolukukriittiset pyörimisnopeudet ja telan kriittinen pyörimisnopeus vastasi hyvin mittaustuloksia.

Sähkökäyttöisen konejärjestelmän vuorovaikutteinen simulointi

Työn tavoitteena oli toteuttaa simulointimalli, jolla pystytään tutkimaan kestomagnetoidun tahtikoneen aiheuttaman vääntömomenttivärähtelyn vaikutuksia sähkömoottoriin liitetyssä mekaniikassa. Tarkoitus oli lisäksi selvittää kuinka kyseinen simulointimalli voidaan toteuttaa nykyaikaisia simulointiohjelmia käyttäen. Saatujen simulointitulosten oikeellisuus varmistettiin tätä työtä varten rakennetulla verifiointilaitteistolla. Tutkittava rakenne koostui akselista, johon kiinnitettiin epäkeskotanko. Epäkeskotankoon kiinnitettiin massa, jonka sijaintia voitiin muunnella. Massan asemaa muuttamalla saatiin rakenteelle erilaisia ominaistaajuuksia. Epäkeskotanko mallinnettiin joustavana elementtimenetelmää apuna käyttäen. Mekaniikka mallinnettiin dynamiikan simulointiin tarkoitetussa ADAMS –ohjelmistossa, johon joustavana mallinnettu epäkeskotanko tuotiin ANSYS –elementtimenetelmäohjelmasta. Mekaniikan malli siirrettiin SIMULINK –ohjelmistoon, jossa mallinnettiin myös sähkökäyttö. SIMULINK –ohjelmassa mallinnettiin sähkökäyttö, joka kuvaa kestomagnetoitua tahtikonetta. Kestomagnetoidun tahtikoneen yhtälöt perustuvat lineaarisiin differentiaaliyhtälöihin, joihin hammasvääntömomentin vaikutus on lisätty häiriösignaalina. Sähkökäytön malli tuottaa vääntömomenttia, joka syötetään ADAMS –ohjelmistolla mallinnettuun mekaniikkaan. Mekaniikan mallista otetaan roottorin kulmakiihtyvyyden arvo takaisinkytkentänä sähkömoottorin malliin. Näin saadaan aikaiseksi yhdistetty simulointi, joka koostuu sähkötoimilaitekäytöstä ja mekaniikasta. Tulosten perusteella voidaan todeta, että sähkökäyttöjen ja mekaniikan yhdistetty simulointi on mahdollista toteuttaa valituilla menetelmillä. Simuloimalla saadut tulokset vastaavat hyvin mitattuja tuloksia.

Virtuaaliprototyypin käyttö roottorin dynamiikan analysoinnissa

Työn tavoitteena oli selvittää kaupallisen dynamiikansimulointiohjelmiston so-veltuvuus roottoridynamiikan analysointiin. Työssä keskityttiin erityisesti rootto-rin dynamiikkaan vaikuttavien epäideaalisuuksien mallintamiseen. Simulointitu-losten tarkkuutta selvitettiin mittauksilla. Lisäksi vertailtiin yleiskäyttöisen dyna-miikan simulointiohjelmiston ja roottoridynamiikan erikoisohjelmiston teoriaa. Tutkittava roottori oli paperikoneen putkitela. Telan joustavuus kuvattiin ele-menttimenetelmällä ratkaistujen moodien avulla. Elementtimallissa huomioitiin telan vaipan seinämänpaksuusvaihtelu, joka vaikuttaa telan massa- ja jäykkyysja-kaumaan. Dynamiikkaohjelmistossa mallinnettiin telan tuennasta tulevat herätteet. Dynamiikkaohjelmistona käytettiin ADAMS:ia ja FEM-ohjelmana ANSYS:stä. Tuloksista havaittiin käytetyn menetelmän soveltuvan roottoridynamiikan ana-lysointiin ja roottorin epäideaalisuuksien mallintamiseen. Simulointimallilla saa-tiin esille murtolukukriittiset pyörimisnopeudet ja telan kriittinen pyörimisnopeus vastasi hyvin mittaustuloksia.

A procedure to estimate parameters of a line segment taking into account its representation through pi circuits: Theoretical development

The objective of this paper is to show an alternative methodology to estimate per unit length parameters of a line segment of a transmission line. With this methodology the line segment parameters can be obtained starting from the phase currents and -voltages in receiving and sending end of the line segment. If the line segment is represented as being one or more pi circuits whose frequency dependent parameters are considered lumped, its impedance and admittance can be easily expressed as functions of the currents and voltages at the sending and receiving end. Because we are supposing that voltages and currents at the sending and receiving end of the tine segment (in frequency domain) are known, it is possible to obtains its impedance and admittance and consequently its per unit length longitudinal and transversal parameters. The procedure will be applied to estimate the longitudinal and transversal parameters of a small segment of a single-phase line that is already built.

A procedure to estimate parameters of a line segment taking into account its representation through π circuits: Theoretical development

The objective of this paper is to show an alternative methodology to estimate per unit length parameters of a line segment of a transmission line. With this methodology the line segment parameters can be obtained starting from the phase currents and voltages in receiving and sending end of the line segment. If the line segment is represented as being one or more π circuits whose frequency dependent parameters are considered lumped, its impedance and admittance can be easily expressed as functions of the currents and voltages at the sending and receiving end. Because we are supposing that voltages and currents at the sending and receiving end of the line segment (in frequency domain) are known, it is possible to obtains its impedance and admittance and consequently its per unit length longitudinal and transversal parameters. The procedure will be applied to estimate the longitudinal and transversal parameters of a small segment of a single-phase line that is already built. © 2006 IEEE.

Some considerations about a new procedure to derive transmission line parameters concerning three-phase lines

The paper shows an alternative methodology to calculate transmission line parameters per unit length and to apply it in a three-phase line with a vertical symmetry plane. This procedure is derived from a general procedure where the modal transformation matrix of the line is required. In this paper, the unknown modal transformation matrix requested by general procedure is substituted by Clarke's matrix. With the substitution that is shown in the paper, the transmission line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency dependent transmission line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a non-transposed three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulation results for typical frequency spectra of switching transients (10 Hz to 10 kHz). Results have shown that procedure has © 2006 IEEE.

Mutual coupling modeling in transmission lines directly in the phase domain

This paper describes a computational model based on lumped elements for the mutual coupling between phases in three-phase transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile of the currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2011 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model. © 2012 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model © 2003-2012 IEEE.

Equivalent representation of mutual coupling in transmission lines by discrete element

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2003-2012 IEEE.

Um modelo de linha de transmissão bifásica desenvolvido diretamente no domínio das fases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimação dos parâmetros de linha de transmissão a partir de um segmento de linha discretizado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Damage detection in beams by using artificial neural networks and dynamical parameters

In this paper is presented a multilayer perceptron neural network combined with the Nelder-Mead Simplex method to detect damage in multiple support beams. The input parameters are based on natural frequencies and modal flexibility. It was considered that only a number of modes were available and that only vertical degrees of freedom were measured. The reliability of the proposed methodology is assessed from the generation of random damages scenarios and the definition of three types of errors, which can be found during the damage identification process. Results show that the methodology can reliably determine the damage scenarios. However, its application to large beams may be limited by the high computational cost of training the neural network.

Modal transformation obtained from Clarke's matrix - Asymmetrical three-phase case

Some constant matrices can be used as phase-mode transformation matrices for transposed three-phase transmission lines. Clarke's matrix is one of these options. Its application as a phase-mode transformation matrix for untransposed three-phase transmission lines has been analyzed through error and frequency scan comparisons. Based on an actual untransposed asymmetrical three-phase transmission line example, a correction procedure is applied searching for better results from the Clarke's matrix applicaton as a phase-mode transformation matrix. The error analyses are carried out using Clarke's matrix and the new transformation matrices obtained from the correction procedure. Applying Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. If the the corrected transformation matrices are used, the relative values of the off-diagonal elements are decreased. Based on the results of these analyses, the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2007 IEEE.

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space