40 resultados para finite element analysis (FEA)


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It is commonly observed that complex fabricated structures subject tofatigue loading fail at the welded joints. Some problems can be corrected by proper detail design but fatigue performance can also be improved using post-weld improvement methods. In general, improvement methods can be divided into two main groups: weld geometry modification methods and residual stress modification methods. The former remove weld toe defects and/or reduce the stress concentrationwhile the latter introduce compressive stress fields in the area where fatigue cracks are likely to initiate. Ultrasonic impact treatment (UIT) is a novel post-weld treatment method that influences both the residual stress distribution andimproves the local geometry of the weld. The structural fatigue strength of non-load carrying attachments in the as-welded condition has been experimentally compared to the structural fatigue strength of ultrasonic impact treated welds. Longitudinal attachment specimens made of two thicknesses of steel S355 J0 have been tested for determining the efficiency of ultrasonic impacttreatment. Treated welds were found to have about 50% greater structural fatigue strength, when the slope of the S-N-curve is three. High mean stress fatigue testing based on the Ohta-method decreased the degree of weld improvement only 19%. This indicated that the method could be also applied for large fabricated structures operating under high reactive residual stresses equilibrated within the volume of the structure. The thickness of specimens has no significant effect tothe structural fatigue strength. The fatigue class difference between 5 mm and 8 mm specimen was only 8%. It was hypothesized that the UIT method added a significant crack initiation period to the total fatigue life of the welded joints. Crack initiation life was estimated by a local strain approach. Material parameters were defined using a modified Uniform Material Law developed in Germany. Finite element analysis and X-ray diffraction were used to define, respectively, the stress concentration and mean stress. The theoretical fatigue life was found to have good accuracy comparing to experimental fatigue tests.The predictive behaviour of the local strain approach combined with the uniformmaterial law was excellent for the joint types and conditions studied in this work.

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The future of high technology welded constructions will be characterised by higher strength materials and improved weld quality with respect to fatigue resistance. The expected implementation of high quality high strength steel welds will require that more attention be given to the issues of crack initiation and mechanical mismatching. Experiments and finite element analyses were performed within the framework of continuum damage mechanics to investigate the effect of mismatching of welded joints on void nucleation and coalescence during monotonic loading. It was found that the damage of undermatched joints mainly occurred in the sandwich layer and the damageresistance of the joints decreases with the decrease of the sandwich layer width. The damage of over-matched joints mainly occurred in the base metal adjacent to the sandwich layer and the damage resistance of the joints increases with thedecrease of the sandwich layer width. The mechanisms of the initiation of the micro voids/cracks were found to be cracking of the inclusions or the embrittled second phase, and the debonding of the inclusions from the matrix. Experimental fatigue crack growth rate testing showed that the fatigue life of under-matched central crack panel specimens is longer than that of over-matched and even-matched specimens. Further investigation by the elastic-plastic finite element analysis indicated that fatigue crack closure, which originated from the inhomogeneousyielding adjacent to the crack tip, played an important role in the fatigue crack propagation. The applicability of the J integral concept to the mismatched specimens with crack extension under cyclic loading was assessed. The concept of fatigue class used by the International Institute of Welding was introduced in the parametric numerical analysis of several welded joints. The effect of weld geometry and load condition on fatigue strength of ferrite-pearlite steel joints was systematically evaluated based on linear elastic fracture mechanics. Joint types included lap joints, angle joints and butt joints. Various combinations of the tensile and bending loads were considered during the evaluation with the emphasis focused on the existence of both root and toe cracks. For a lap joint with asmall lack-of-penetration, a reasonably large weld leg and smaller flank angle were recommended for engineering practice in order to achieve higher fatigue strength. It was found that the fatigue strength of the angle joint depended strongly on the location and orientation of the preexisting crack-like welding defects, even if the joint was welded with full penetration. It is commonly believed that the double sided butt welds can have significantly higher fatigue strength than that of a single sided welds, but fatigue crack initiation and propagation can originate from the weld root if the welding procedure results in a partial penetration. It is clearly shown that the fatigue strength of the butt joint could be improved remarkably by ensuring full penetration. Nevertheless, increasing the fatigue strength of a butt joint by increasing the size of the weld is an uneconomical alternative.

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Työssä on tutkittu kylmämuovattujen nelikulmaisten putkipalkkien K-liitosten mallinnusta epälineaarisella elementtimenetelmällä. Työn tärkeimpänä tavoitteena on ollut kehittää putkipalkin osien materiaalimalleja siten, että liitosten kestävyyttä voidaan tutkia laboratoriokokeiden ohella luotettavasti myös elementtimenetelmällä. Toisena tavoitteena on ollut tutkia, voidaanko putkipalkkien liitosten mitoitusohjeita turvallisesti soveltaa kylmämuovatuille putkipalkeille, joissa valmistusprosessi aiheuttaa muutoksia materiaaliominaisuuksiin, erityisesti muodonmuutoskykyyn. Työssä tehtyjen laboratoriokokeiden ja elementtianalyysien perusteella elementti-menetelmä on käyttökelpoinen työkalu putkipalkkiliitosten staattista kestävyyttä määritettäessä, kun materiaalimallit on määritetty oikein. Erityisesti liitoksen käyttö-rajatilan mukaisen kestävyyden laskennassa elementtimenetelmällä saadaan hyvin laboratoriokokeita vastaavia tuloksia. Tehdyt laboratoriokokeet osoittavat myös, että Eurocode 3:n mukaisia putkipalkkien liitosten mitoitusohjeita voi turvallisesti käyttää kylmämuovatuille putkipalkeille.

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Työssä on tutkittu elementtimenetelmän avulla kylmämuovattujen nelikulmaisten putkipalkkien materiaalimallin kehittämistä ja putkipalkkien X-liitosten jäykkyyden ja äärikestävyyden määrittämistä. Työn tavoitteena on tutkia kylmämuovauksen vaikutuksia putkipalkkiprofiilin materiaaliominaisuuksiin materiaalikokeiden ja elementtianalyysien avulla sekä kehittää putkipalkille anisotrooppista materiaalimallia. Työssä määritettyjä materiaalimalleja on sovellettu X-liitosten elementtimalleihin, joiden käyttäytymistä on verrattu äärikestävyyskokeiden tuloksiin. Tutkimuksen perusteella Eurocode 3:n mitoitusohjeita voidaan turvallisesti soveltaa kylmämuovattujen putkipalkkien X-liitosten laskennassa. Työssä tehtyjen materiaalikokeiden ja elementtianalyysien perusteella materiaalin anisotrooppisuuden vaikutus liitoksen kestävyyteen on vähäistä, ja putkipalkin pituussuuntaista materiaalimallia voidaan soveltaa myös kehäsuuntaisille materiaaliominaisuuksille. Materiaalikokeiden simulointi osoittaa, että elementtimenetelmää voidaan käyttää materiaalimallin määrittämisen apuvälineenä.

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Within the latest decade high-speed motor technology has been increasingly commonly applied within the range of medium and large power. More particularly, applications like such involved with gas movement and compression seem to be the most important area in which high-speed machines are used. In manufacturing the induction motor rotor core of one single piece of steel it is possible to achieve an extremely rigid rotor construction for the high-speed motor. In a mechanical sense, the solid rotor may be the best possible rotor construction. Unfortunately, the electromagnetic properties of a solid rotor are poorer than the properties of the traditional laminated rotor of an induction motor. This thesis analyses methods for improving the electromagnetic properties of a solid-rotor induction machine. The slip of the solid rotor is reduced notably if the solid rotor is axially slitted. The slitting patterns of the solid rotor are examined. It is shown how the slitting parameters affect the produced torque. Methods for decreasing the harmonic eddy currents on the surface of the rotor are also examined. The motivation for this is to improve the efficiency of the motor to reach the efficiency standard of a laminated rotor induction motor. To carry out these research tasks the finite element analysis is used. An analytical calculation of solid rotors based on the multi-layer transfer-matrix method is developed especially for the calculation of axially slitted solid rotors equipped with wellconducting end rings. The calculation results are verified by using the finite element analysis and laboratory measurements. The prototype motors of 250 – 300 kW and 140 Hz were tested to verify the results. Utilization factor data are given for several other prototypes the largest of which delivers 1000 kW at 12000 min-1.

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This paper is a literature review which describes the construction of state of the art of permanent magnet generators and motors constructing and discusses the current and possible application of these machines in industry. Permanent magnet machines are a well-know class of rotating and linear electric machines used for many years in industrial applications. A particular interest for permanent magnet generators is connected with wind mills, which seem to be becoming increasingly popular nowadays. Geared and direct-driven permanent magnet generators are described. A classification of direct-driven permanent magnet generators is given. Design aspects of permanent magnet generators are presented. Permanent magnet generators for wind turbines designs are highlighted. Dynamics and vibration problems of permanent magnet generators covered in literature are presented. The application of the Finite Element Method for mechanical problems solution in the field of permanent magnet generators is discussed.

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Työssä perehdyttiin azimuth potkurilaitteen rakenteelliseen kestävyyteen vaikuttaviin seikkoihin. Työn tavoitteena oli tutkia eri rakenneratkaisuja ja yksityiskohtia sekä niiden vaikutusta koko potkurilaitteen toimintaan. Potkurilaitteiden lujuustekninen tarkastelu sisälsi rakenteen eheyden tarkistuksen mekaanisten kuormitusten alla kuin myös värähtelykäyttäytymisen tutkimisen. Tarkastelun pääsääntöinen kohde oli potkurilaitteen alarunko, eli laivan ulkopuolelle jäävä osa. Diplomityö oli osa kahden uuden potkurilaitteen kehitysprojektia. Projektissa esiin tulleita rakennemuutoksia vertailtiin vanhoihin, jo toteutettuihin rakenneyksityiskohtiin. Lisäksi tutkittiin olemassa olevien rakenneratkaisujen hyödyntämistä uusissa laitteissa. Huomiota kiinnitettiin myös hitsien muotoiluun ja näiden mitoituskäytäntöihin. Rungon ehyyttä koskevat laskelman ovat hyvin pitkälti suoritettu elementtimenetelmää apuna käyttäen. Elementtimenetelmää varten luotiin useita malleja kattaen kokonaisia potkurilaittee runkoja kuin myös sen yksittäisiä osia. Elementtimenetelmän avulla saatuja tuloksia vertailtiin käytettävissä oleviin mittaustuloksiin. Työssä havaittiin potkurilaitteen rungon mitoittavaksi tekijäksi staattisessa tilanteessa muodostuvan voimansiirtolinja ja siinä sijaitsevien hammaspyörien siirtymät. Tämän seurauksena rungon taipumat ovat määräävämpiä geometrian kannalta kuin materiaalien sallitut jännitykset.

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A high-speed and high-voltage solid-rotor induction machine provides beneficial features for natural gas compressor technology. The mechanical robustness of the machine enables its use in an integrated motor-compressor. The technology uses a centrifugal compressor, which is mounted on the same shaft with the high-speed electrical machine driving it. No gearbox is needed as the speed is determined by the frequency converter. The cooling is provided by the process gas, which flows through the motor and is capable of transferring the heat away from the motor. The technology has been used in the compressors in the natural gas supply chain in the central Europe. New areas of application include natural gas compressors working at the wellheads of the subsea gas reservoir. A key challenge for the design of such a motor is the resistance of the stator insulation to the raw natural gas from the well. The gas contains water and heavy hydrocarbon compounds and it is far harsher than the sales gas in the natural gas supply network. The objective of this doctoral thesis is to discuss the resistance of the insulation to the raw natural gas and the phenomena degrading the insulation. The presence of partial discharges is analyzed in this doctoral dissertation. The breakdown voltage of the gas is measured as a function of pressure and gap distance. The partial discharge activity is measured on small samples representing the windings of the machine. The electrical field behavior is also modeled by finite element methods. Based on the measurements it has been concluded that the discharges are expected to disappear at gas pressures above 4 – 5 bar. The disappearance of discharges is caused by the breakdown strength of the gas, which increases as the pressure increases. Based on the finite element analysis, the physical length of a discharge seen in the PD measurements at atmospheric pressure was approximated to be 40 – 120 m. The chemical aging of the insulation when exposed to raw natural gas is discussed based on a vast set of experimental tests with the gas mixture representing the real gas mixture at the wellhead. The mixture was created by mixing dry hydrocarbon gas, heavy hydrocarbon compounds, monoethylene glycol, and water. The mixture was chosen to be more aggressive by increasing the amount of liquid substances. Furthermore, the temperature and pressure were increased, which resulted in accelerated test conditions. The time required to detect severe degradation was thus decreased. The test program included a comparison of materials, an analysis of the e ects of di erent compounds in the gas mixture, namely water and heavy hydrocarbons, on the aging, an analysis of the e ects of temperature and exposure duration, and also an analysis on the e ect of sudden pressure changes on the degradation of the insulating materials. It was found in the tests that an insulation consisting of mica, glass, and epoxy resin can tolerate the raw natural gas, but it experiences some degradation. The key material in the composite insulation is the resin, which largely defines the performance of the insulation system. The degradation of the insulation is mostly determined by the amount of gas mixture di used into it. The di usion was seen to follow Fick’s second law, but the coe cients were not accurately defined. The di usion was not sensitive to temperature, but it was dependent upon the thermodynamic state of the gas mixture, in other words, the amounts of liquid components in the gas. The weight increase observed was mostly related to heavy hydrocarbon compounds, which act as plasticizers in the epoxy resin. The di usion of these compounds is determined by the crosslink density of the resin. Water causes slight changes in the chemical structure, but these changes do not significantly contribute to the aging phenomena. Sudden changes in pressure can lead to severe damages in the insulation, because the motion of the di used gas is able to create internal cracks in the insulation. Therefore, the di usion only reduces the mechanical strength of the insulation, but the ultimate breakdown can potentially be caused by a sudden drop in the pressure of the process gas.

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Bone strain plays a major role as the activation signal for the bone (re)modeling process, which is vital for keeping bones healthy. Maintaining high bone mineral density reduces the chances of fracture in the event of an accident. Numerous studies have shown that bones can be strengthened with physical exercise. Several hypotheses have asserted that a stronger osteogenic (bone producing) effect results from dynamic exercise than from static exercise. These previous studies are based on short-term empirical research, which provide the motivation for justifying the experimental results with a solid mathematical background. The computer simulation techniques utilized in this work allow for non-invasive bone strain estimation during physical activity at any bone site within the human skeleton. All models presented in the study are threedimensional and actuated by muscle models to replicate the real conditions accurately. The objective of this work is to determine and present loading-induced bone strain values resulting from physical activity. It includes a comparison of strain resulting from four different gym exercises (knee flexion, knee extension, leg press, and squat) and walking, with the results reported for walking and jogging obtained from in-vivo measurements described in the literature. The objective is realized primarily by carrying out flexible multibody dynamics computer simulations. The dissertation combines the knowledge of finite element analysis and multibody simulations with experimental data and information available from medical field literature. Measured subject-specific motion data was coupled with forward dynamics simulation to provide natural skeletal movement. Bone geometries were defined using a reverse engineering approach based on medical imaging techniques. Both computed tomography and magnetic resonance imaging were utilized to explore modeling differences. The predicted tibia bone strains during walking show good agreement with invivo studies found in the literature. Strain measurements were not available for gym exercises; therefore, the strain results could not be validated. However, the values seem reasonable when compared to available walking and running invivo strain measurements. The results can be used for exercise equipment design aimed at strengthening the bones as well as the muscles during workout. Clinical applications in post fracture recovery exercising programs could also be the target. In addition, the methodology introduced in this study, can be applied to investigate the effect of weightlessness on astronauts, who often suffer bone loss after long time spent in the outer space.

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Tässä työssä tutkittiin eri mitoitusmenetelmien soveltuvuutta hitsattujen rakenteiden vä-symislaskennassa. Käytetyt menetelmät olivat rakenteellinen jännityksen menetelmä, te-hollisen lovijännityksen menetelmä ja murtumismekaniikka. Lisäksi rakenteellisen jänni-tyksen määrittämiseksi käytettiin kolmea eri menetelmää. Menetelmät olivat pintaa pitkin ekstrapolointi, paksuuden yli linearisointi ja Dongin menetelmä. Väsymiskestävyys määritettiin kahdelle hitsiliitoksen yksityiskohdalle. Laskenta tehtiin käyttäen elementtimenetelmää rakenteen 3D-mallille. Tutkittavasta aggregaattirungosta oli olemassa FE-malli mutta alimallinnustekniikkaa hyödyntämällä pystyttiin yksityiskohtai-semmin tutkimaan vain pientä osaa koko rungon mallista. Rakenteellisen jännityksen menetelmä perustuu nimellisiin jännityksiin. Kyseinen mene-telmä ei vaadi geometrian muokkausta. Yleensä rakenteellisen jännityksen menetelmää käytetään hitsin rajaviivan väsymislaskennassa, mutta joissain tapauksissa sitä on käytetty juuren puolen laskennassa. Tässä työssä rakenteellisen jännityksen menetelmää käytettiin myös juuren puolen tutkimisessa. Tehollista lovijännitystä tutkitaan mallintamalla 1 mm fiktiiviset pyöristykset sekä rajaviivalle että juuren puolelle. Murtumismekaniikan so-veltuvuutta tutkittiin käyttämällä Franc2D särön kasvun simulointiohjelmaa. Väsymislaskennan tulokset eivät merkittävästi poikkea eri laskentamenetelmien välillä. Ainoastaan rakenteellisen jännityksen Dongin menetelmällä saadaan poikkeavia tuloksia. Tämä johtuu pääasiassa siitä, että menetelmän laskentaetäisyydestä ei ole tietoa. Raken-teellisen jännityksen menetelmällä, tehollisen lovijännityksen menetelmällä ja murtumis-mekaniikalla saadaan samansuuntaiset tulokset. Suurin ero menetelmien välillä on mal-linnuksen ja laskennan vaatima työmäärä.

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Nykyinen Eurocode 3 suunnitteluohjeen rakenneputkiliitoksia käsittelevä osio vaatii S500 suurlujuusteräksestä valmistettujen liitosten mitoituksen yhteydessä käytettäväksi reduk-tiokerrointa 0.8. Tämä on varsin konservatiivinen mitoituspa, joka vähentää merkittävästi lujemman teräslaadun käyttämisestä saavutettavaa hyötyä. Tämän työn pääasiallinen ta-voite on laboratoriotestein selvittää S500 lujuusluokan rakenneputkiliitosten todellinen äärikapasiteetti ja verrata sitä nykyisen mitoitusohjeen mukaiseen kapasiteettiin. Tässä työssä tutkitut liitokset ovat valmistettu poikkileikkaukseltaan nelikulmaisista kyl-mämuovatuista rakenneputkista. Koesarja koostui kahdeksasta X-liitoksesta, sekä kymme-nestä K-liitoksesta. Kaikki testit suoritettiin huoneenlämmössä, LUT Koneen teräsrakenne-laboratoriossa. Laboratoriotestien lisäksi rakenteen käyttäytymistä tutkittiin epälineaarisen elementtimenetelmän avulla ja näitä tuloksia verrattiin kokeellisiin tuloksiin. Sekä testien että FE–analyysin perusteella voidaan todeta, että S500 lujuusluokan terästä käytettäessä ei Eurocode 3:n mukaisen reduktiokertoimen käytölle ole perusteita.

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The power rating of wind turbines is constantly increasing; however, keeping the voltage rating at the low-voltage level results in high kilo-ampere currents. An alternative for increasing the power levels without raising the voltage level is provided by multiphase machines. Multiphase machines are used for instance in ship propulsion systems, aerospace applications, electric vehicles, and in other high-power applications including wind energy conversion systems. A machine model in an appropriate reference frame is required in order to design an efficient control for the electric drive. Modeling of multiphase machines poses a challenge because of the mutual couplings between the phases. Mutual couplings degrade the drive performance unless they are properly considered. In certain multiphase machines there is also a problem of high current harmonics, which are easily generated because of the small current path impedance of the harmonic components. However, multiphase machines provide special characteristics compared with the three-phase counterparts: Multiphase machines have a better fault tolerance, and are thus more robust. In addition, the controlled power can be divided among more inverter legs by increasing the number of phases. Moreover, the torque pulsation can be decreased and the harmonic frequency of the torque ripple increased by an appropriate multiphase configuration. By increasing the number of phases it is also possible to obtain more torque per RMS ampere for the same volume, and thus, increase the power density. In this doctoral thesis, a decoupled d–q model of double-star permanent-magnet (PM) synchronous machines is derived based on the inductance matrix diagonalization. The double-star machine is a special type of multiphase machines. Its armature consists of two three-phase winding sets, which are commonly displaced by 30 electrical degrees. In this study, the displacement angle between the sets is considered a parameter. The diagonalization of the inductance matrix results in a simplified model structure, in which the mutual couplings between the reference frames are eliminated. Moreover, the current harmonics are mapped into a reference frame, in which they can be easily controlled. The work also presents methods to determine the machine inductances by a finite-element analysis and by voltage-source inverters on-site. The derived model is validated by experimental results obtained with an example double-star interior PM (IPM) synchronous machine having the sets displaced by 30 electrical degrees. The derived transformation, and consequently, the decoupled d–q machine model, are shown to model the behavior of an actual machine with an acceptable accuracy. Thus, the proposed model is suitable to be used for the model-based control design of electric drives consisting of double-star IPM synchronous machines.

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Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

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Tässä työssä suunniteltiin lappeenrantalaisen Astex Oy:n tilauksesta liikkuvan työkoneen runkorakenne. Työ tehtiin Lappeenrannan teknillisen yliopiston teräsrakenteiden laboratoriossa. Suunniteltava rakenne kuului linkkuohjattuun, noin 5000 kg painoiseen trukkitraktoriin. Lähtökohtana rakenteen suunnittelulle olivat tilaajan asettamat rakenteen geometriaan ja suorituskykyyn liittyvät reunaehdot ja rajoitteet. Uuden rakenteen suunnittelussa hyödynnettiin myös tilaajatahon kehittelemää vastaavan tyyppistä prototyyppirakennetta. Rakenteen suunnitteluprosessi koostui neljästä eri vaiheesta. Suunniteltavan rakenteen lähtökohtana olleelle prototyyppirakenteelle suoritettiin koneen käytönaikaisia venymäliuskamittauksia rakenteen kuormitushistorian selvittämiseksi. Mittauksista saatujen tulosten perusteella määritettiin kuormitukset uudelle suunniteltavalle rakenteelle. Määritettyjä kuormituksia hyödyntäen ideoitiin, suunniteltiin ja mallinnettiin uusi tilaajan vaatimuksia vastaava rakenne. Uudelle rakenteelle suoritettiin lujuusanalyysit FE-analyysiä hyödyntäen. Uuden rakenteen suunnittelussa kiinnitettiin huomiota rakenteen hyvään valmistettavuuteen ja suunniteltiin rakenneratkaisut tilaajataholle mahdollisimman optimaalisiksi. Suunnittelu- ja mallinnustyö tehtiin Solidworks 2014 ohjelmistolla. Rakenteen lujuustekniset tarkastelut sisälsivät rakennedetaljien analyyttistä mitoitusta ja laskentaa. FE-laskennalla selvitettiin rakenteen ääri- ja väsymiskestävyys. Laskenta sisälsi koko rakenteen globaaleja tarkasteluja, sekä eri kriittisten rakennedetaljien yksityiskohtaisempia analyysejä. FE-laskennan pääpaino oli rakenteen väsymisanalyyseissä, jotka toteutettiin Hot-Spot- ja särönkasvumenetelmillä. Rakenteen FE-analyysien suorittamisessa käytettiin Femap, NxNastran ja Abaqus-ohjelmistoja.

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The design process of direct-driven permanent magnet synchronous machines (PMSMs) for a full electric 4 ´ 4 sports car is presented. The rotor structure of the machine consists of two permanent magnet layers embedded inside the rotor laminations thus resulting in some inverse saliency, where the q-axis inductance is larger than the d-axis one. An integer slot stator winding was selected to fully take advantage of the additional reluctance torque. The performance characteristics of the designed PMSMs were calculated by applying a twodimensional finite element method. Cross-saturation between the d- and q-axes was taken into account in the calculation of the synchronous inductances. The calculation results are validated by measurements.