On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Simulation and material calibration of ultra high strength steel (UHSS) S960 welded joint under static tensile test utilizing finite element method (FEM)

The aim of this work was to calibrate the material properties including strength and strain values for different material zones of ultra-high strength steel (UHSS) welded joints under monotonic static loading. The UHSS is heat sensitive and softens by heat due to welding, the affected zone is heat affected zone (HAZ). In this regard, cylindrical specimens were cut out from welded joints of Strenx® 960 MC and Strenx® Tube 960 MH, were examined by tensile test. The hardness values of specimens’ cross section were measured. Using correlations between hardness and strength, initial material properties were obtained. The same size specimen with different zones of material same as real specimen were created and defined in finite element method (FEM) software with commercial brand Abaqus 6.14-1. The loading and boundary conditions were defined considering tensile test values. Using initial material properties made of hardness-strength correlations (true stress-strain values) as Abaqus main input, FEM is utilized to simulate the tensile test process. By comparing FEM Abaqus results with measured results of tensile test, initial material properties will be revised and reused as software input to be fully calibrated in such a way that FEM results and tensile test results deviate minimum. Two type of different S960 were used including 960 MC plates, and structural hollow section 960 MH X-joint. The joint is welded by BöhlerTM X96 filler material. In welded joints, typically the following zones appear: Weld (WEL), Heat affected zone (HAZ) coarse grained (HCG) and fine grained (HFG), annealed zone, and base material (BaM). Results showed that: The HAZ zone is softened due to heat input while welding. For all the specimens, the softened zone’s strength is decreased and makes it a weakest zone where fracture happens while loading. Stress concentration of a notched specimen can represent the properties of notched zone. The load-displacement diagram from FEM modeling matches with the experiments by the calibrated material properties by compromising two correlations of hardness and strength.

Napakäämityn murtovakokestomagneettitahtikoneen suunnittelu

Diplomityössä tutustutaan napakäämittyihin murtovakokestomagneettitahtikoneisiin sekä syvennytään niiden suunnitteluun analyyttisen laskennanavulla. Analyyttisen laskennan haasteena on perinteisesti käytettyjen kestomagneettitahtikoneiden laskentayhtälöiden sovittaminen murtovakokäämityille kestomagneettitahtikoneille. Työn lopussa analyyttisen laskennan tuloksia verrataan kenttälaskentaohjelmalla saatuihin tuloksiin. Tärkeimmät analyyttiset yhtälöt sekä laskentamallin rakenne on esitetty työssä.

A novel procedure for establishing clinching parameters for high strength steel sheet

The building industry has a particular interest in using clinching as a joining method for frame constructions of light-frame housing. Normally many clinch joints are required in joining of frames.In order to maximise the strength of the complete assembly, each clinch joint must be as sound as possible. Experimental testing is the main means of optimising a particular clinch joint. This includes shear strength testing and visual observation of joint cross-sections. The manufacturers of clinching equipment normally perform such experimental trials. Finite element analysis can also be used to optimise the tool geometry and the process parameter, X, which represents the thickness of the base of the joint. However, such procedures require dedicated software, a skilled operator, and test specimens in order to verify the finite element model. In addition, when using current technology several hours' computing time may be necessary. The objective of the study was to develop a simple calculation procedure for rapidly establishing an optimum value for the parameter X for a given tool combination. It should be possible to use the procedure on a daily basis, without stringent demands on the skill of the operator or the equipment. It is also desirable that the procedure would significantly decrease thenumber of shear strength tests required for verification. The experimental workinvolved tests in order to obtain an understanding of the behaviour of the sheets during clinching. The most notable observation concerned the stage of the process in which the upper sheet was initially bent, after which the deformation mechanism changed to shearing and elongation. The amount of deformation was measured relative to the original location of the upper sheet, and characterised as the C-measure. By understanding in detail the behaviour of the upper sheet, it waspossible to estimate a bending line function for the surface of the upper sheet. A procedure was developed, which makes it possible to estimate the process parameter X for each tool combination with a fixed die. The procedure is based on equating the volume of material on the punch side with the volume of the die. Detailed information concerning the behaviour of material on the punch side is required, assuming that the volume of die does not change during the process. The procedure was applied to shear strength testing of a sample material. The sample material was continuously hot-dip zinc-coated high-strength constructional steel,with a nominal thickness of 1.0 mm. The minimum Rp0.2 proof stress was 637 N/mm2. Such material has not yet been used extensively in light-frame housing, and little has been published on clinching of the material. The performance of the material is therefore of particular interest. Companies that use clinching on a daily basis stand to gain the greatest benefit from the procedure. By understanding the behaviour of sheets in different cases, it is possible to use data at an early stage for adjusting and optimising the process. In particular, the functionality of common tools can be increased since it is possible to characterise the complete range of existing tools. The study increases and broadens the amount ofbasic information concerning the clinching process. New approaches and points of view are presented and used for generating new knowledge.

Direct-on-line axial flux permanent magnet synchronous generator static and dynamic performance

In distributed energy production, permanent magnet synchronous generators (PMSG) are often connected to the grid via frequency converters, such as voltage source line converters. The price of the converter may constitute a large part of the costs of a generating set. Some of the permanent magnet synchronous generators with converters and traditional separately excited synchronous generators couldbe replaced by direct-on-line (DOL) non-controlled PMSGs. Small directly networkconnected generators are likely to have large markets in the area of distributed electric energy generation. Typical prime movers could be windmills, watermills and internal combustion engines. DOL PMSGs could also be applied in island networks, such as ships and oil platforms. Also various back-up power generating systems could be carried out with DOL PMSGs. The benefits would be a lower priceof the generating set and the robustness and easy use of the system. The performance of DOL PMSGs is analyzed. The electricity distribution companies have regulations that constrain the design of the generators being connected to the grid. The general guidelines and recommendations are applied in the analysis. By analyzing the results produced by the simulation model for the permanent magnet machine, the guidelines for efficient damper winding parameters for DOL PMSGs are presented. The simulation model is used to simulate grid connections and load transients. The damper winding parameters are calculated by the finite element method (FEM) and determined from experimental measurements. Three-dimensional finite element analysis (3D FEA) is carried out. The results from the simulation model and 3D FEA are compared with practical measurements from two prototype axial flux permanent magnet generators provided with damper windings. The dimensioning of the damper winding parameters is case specific. The damper winding should be dimensioned based on the moment of inertia of the generating set. It is shown that the damper winding has optimal values to reach synchronous operation in the shortest period of time after transient operation. With optimal dimensioning, interferenceon the grid is minimized.

Fractional slot permanent magnet synchronous motors for low speed applications

This study compares different rotor structures of permanent magnet motors with fractional slot windings. The surface mounted magnet and the embedded magnet rotor structures are studied. This thesis analyses the characteristics of a concentrated two-layer winding, each coil of which is wound around one tooth and which has a number of slots per pole and per phase less than one (q < 1). Compared to the integer slot winding, the fractional winding (q < 1) has shorter end windings and this, thereby, makes space as well as manufacturing cost saving possible. Several possible ways of winding a fractional slot machine with slots per pole and per phase lessthan one are examined. The winding factor and the winding harmonic components are calculated. The benefits attainable from a machine with concentrated windingsare considered. Rotor structures with surface magnets, radially embedded magnets and embedded magnets in V-position are discussed. The finite element method isused to solve the main values of the motors. The waveform of the induced electro motive force, the no-load and rated load torque ripple as well as the dynamic behavior of the current driven and voltage driven motor are solved. The results obtained from different finite element analyses are given. A simple analytic method to calculate fractional slot machines is introduced and the values are compared to the values obtained with the finite element analysis. Several different fractional slot machines are first designed by using the simple analytical methodand then computed by using the finite element method. All the motors are of thesame 225-frame size, and have an approximately same amount of magnet material, a same rated torque demand and a 400 - 420 rpm speed. An analysis of the computation results gives new information on the character of fractional slot machines.A fractional slot prototype machine with number 0.4 for the slots per pole and per phase, 45 kW output power and 420 rpm speed is constructed to verify the calculations. The measurement and the finite element method results are found to beequal.

A novel approachfor assessing the fatigue strength of ultrasonic impact treated welded structures.

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.

Effect of Mechanical and Geometric Mismatching on Fatigue and Damage of Welded Joints

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.

Materiaalimallin määrityksestä kylmämuovattujen putkipalkkien K-liitosten FE-analyysissä

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.

Kylmämuovattujen putkipalkkien X-liitosten äärikestävyyden ja jäykkyyden määrittäminen sekä materiaalimallin kehittäminen

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.

High-Speed Solid-Rotor Induction Machine – Electromagnetic Calculation and Design

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.

Literature review on permanent magnet generators design and dynamic behavior

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.

Azimuth thrusterin rungon lujuustekninen tarkastelu

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.