Non-Linear Journal Bearing Model for Analysis of Superharmonic Vibrations of Rotor Systems

A rotating machine usually consists of a rotor and bearings that supports it. The nonidealities in these components may excite vibration of the rotating system. The uncontrolled vibrations may lead to excessive wearing of the components of the rotating machine or reduce the process quality. Vibrations may be harmful even when amplitudes are seemingly low, as is usually the case in superharmonic vibration that takes place below the first critical speed of the rotating machine. Superharmonic vibration is excited when the rotational velocity of the machine is a fraction of the natural frequency of the system. In such a situation, a part of the machine’s rotational energy is transformed into vibration energy. The amount of vibration energy should be minimised in the design of rotating machines. The superharmonic vibration phenomena can be studied by analysing the coupled rotor-bearing system employing a multibody simulation approach. This research is focused on the modelling of hydrodynamic journal bearings and rotorbearing systems supported by journal bearings. In particular, the non-idealities affecting the rotor-bearing system and their effect on the superharmonic vibration of the rotating system are analysed. A comparison of computationally efficient journal bearing models is carried out in order to validate one model for further development. The selected bearing model is improved in order to take the waviness of the shaft journal into account. The improved model is implemented and analyzed in a multibody simulation code. A rotor-bearing system that consists of a flexible tube roll, two journal bearings and a supporting structure is analysed employing the multibody simulation technique. The modelled non-idealities are the shell thickness variation in the tube roll and the waviness of the shaft journal in the bearing assembly. Both modelled non-idealities may cause subharmonic resonance in the system. In multibody simulation, the coupled effect of the non-idealities can be captured in the analysis. Additionally one non-ideality is presented that does not excite the vibrations itself but affects the response of the rotorbearing system, namely the waviness of the bearing bushing which is the non-rotating part of the bearing system. The modelled system is verified with measurements performed on a test rig. In the measurements the waviness of bearing bushing was not measured and therefore it’s affect on the response was not verified. In conclusion, the selected modelling approach is an appropriate method when analysing the response of the rotor-bearing system. When comparing the simulated results to the measured ones, the overall agreement between the results is concluded to be good.

Vibrations in Rotating Machinery Arising from Minor Imperfections in Component Geometries

Vibrations in machines can cause noise, decrease the performance, or even damage the machine. Vibrations appear if there is a source of vibration that excites the system. In the worst case scenario, the excitation frequency coincides with the natural frequency of the machine causing resonance. Rotating machines are a machine type, where the excitation arises from the machine itself. The excitation originates from the mass imbalance in the rotating shaft, which always exists in machines that are manufactured using conventional methods. The excitation has a frequency that is dependent on the rotational speed of the machine. The rotating machines in industrial use are usually designed to rotate at a constant rotational speed, the case where the resonances can be easily avoided. However, the machines that have a varying operational speed are more problematic due to a wider range of frequencies that have to be avoided. Vibrations, which frequencies equal to rotational speed frequency of the machine are widely studied and considered in the typical machine design process. This study concentrates on vibrations, which arise from the excitations having frequencies that are multiples of the rotational speed frequency. These vibrations take place when there are two or more excitation components in a revolution of a rotating shaft. The dissertation introduces four studies where three kinds of machines are experiencing vibrations caused by different excitations. The first studied case is a directly driven permanent magnet generator used in a wind power plant. The electromagnetic properties of the generator cause harmonic excitations in the system. The dynamic responses of the generator are studied using the multibody dynamics formulation. In another study, the finite element method is used to study the vibrations of a magnetic gear due to excitations, which frequencies equal to the rotational speed frequency. The objective is to study the effects of manufacturing and assembling inaccuracies. Particularly, the eccentricity of the rotating part with respect to non-rotating part is studied since the eccentric operation causes a force component in the direction of the shortest air gap. The third machine type is a tube roll of a paper machine, which is studied while the tube roll is supported using two different structures. These cases are studied using different formulations. In the first case, the tube roll is supported by spherical roller bearings, which have some wavinesses on the rolling surfaces. Wavinesses cause excitations to the tube roll, which starts to resonate at the frequency that is a half of the first natural frequency. The frequency is in the range where the machine normally operates. The tube roll is modeled using the finite element method and the bearings are modeled as nonlinear forces between the tube roll and the pedestals. In the second case studied, the tube roll is supported by freely rotating discs, which wavinesses are also measured. The above described phenomenon is captured as well in this case, but the simulation methodology is based on the flexible multibody dynamics formulation. The simulation models that are used in both of the last two cases studied are verified by measuring the actual devices and comparing the simulated and measured results. The results show good agreement.

Development of a simulation tool for torsional vibration of branched power transmission system

In this master's thesis a mechanical model that is driven with variable speed synchronous machine was developed. The developed mechanical model simulates the mechanics of power transmission and its torsional vibrations. The mechanical model was developed for the need of the branched mechanics of a rolling mill and the propulsion system of a tanker. First, the scope of the thesis was to clarify the concepts connected to the mechanical model. The clarified concepts are the variable speed drive, the mechanics of power transmission and the vibrationsin the power transmission. Next, the mechanical model with straight shaft line and twelve moments of inertia that existed in the beginning was developed to be branched considering the case of parallel machines and the case of parallel rolls. Additionally, the model was expanded for the need of moreaccurate simulation to up to thirty moments of inertia. The model was also enhanced to enable three phase short circuit situation of the simulated machine. After that the mechanical model was validated by comparing the results of the developed simulation tool to results of other simulation tools. The compared results are the natural frequencies and mode shapes of torsional vibration, the response of the load torque step and the stress in the mechanical system occurred by the permutation of the magnetic field that is arisen from the three phase short circuit situation. The comparisons were accomplished well and the mechanical model was validated for the compared cases. Further development to be made is to develop the load torque to be time-dependent and to install two frequency converters and two FEM modeled machines to be simulated parallel.

Improving Dynamic Characteristics of Open-loop Controlled Log Crane

The improvement of the dynamics of flexible manipulators like log cranes often requires advanced control methods. This thesis discusses the vibration problems in the cranes used in commercial forestry machines. Two control methods, adaptive filtering and semi-active damping, are presented. The adaptive filter uses a part of the lowest natural frequency of the crane as a filtering frequency. The payload estimation algorithm, filtering of control signal and algorithm for calculation of the lowest natural frequency of the crane are presented. The semi-active damping method is basedon pressure feedback. The pressure vibration, scaled with suitable gain, is added to the control signal of the valve of the lift cylinder to suppress vibrations. The adaptive filter cuts off high frequency impulses coming from the operatorand semi-active damping suppresses the crane?s oscillation, which is often caused by some external disturbance. In field tests performed on the crane, a correctly tuned (25 % tuning) adaptive filter reduced pressure vibration by 14-17 % and semi-active damping correspondingly by 21-43%. Applying of these methods require auxiliary transducers, installed in specific points in the crane, and electronically controlled directional control valves.

Theoretical Analysis and Simulations of Vertically Vibrated Granular Materials

The dynamical properties ofshaken granular materials are important in many industrial applications where the shaking is used to mix, segregate and transport them. In this work asystematic, large scale simulation study has been performed to investigate the rheology of dense granular media, in the presence of gas, in a three dimensional vertical cylinder filled with glass balls. The base wall of the cylinder is subjected to sinusoidal oscillation in the vertical direction. The viscoelastic behavior of glass balls during a collision, have been studied experimentally using a modified Newton's Cradle device. By analyzing the results of the measurements, using numerical model based on finite element method, the viscous damping coefficient was determinedfor the glass balls. To obtain detailed information about the interparticle interactions in a shaker, a simplified model for collision between particles of a granular material was proposed. In order to simulate the flow of surrounding gas, a formulation of the equations for fluid flow in a porous medium including particle forces was proposed. These equations are solved with Large Eddy Simulation (LES) technique using a subgrid-model originally proposed for compressible turbulent flows. For a pentagonal prism-shaped container under vertical vibrations, the results show that oscillon type structures were formed. Oscillons are highly localized particle-like excitations of the granular layer. This self-sustaining state was named by analogy with its closest large-scale analogy, the soliton, which was first documented by J.S. Russell in 1834. The results which has been reportedbyBordbar and Zamankhan(2005b)also show that slightly revised fluctuation-dissipation theorem might apply to shaken sand, which appears to be asystem far from equilibrium and could exhibit strong spatial and temporal variations in quantities such as density and local particle velocity. In this light, hydrodynamic type continuum equations were presented for describing the deformation and flow of dense gas-particle mixtures. The constitutive equation used for the stress tensor provides an effective viscosity with a liquid-like character at low shear rates and a gaseous-like behavior at high shear rates. The numerical solutions were obtained for the aforementioned hydrodynamic equations for predicting the flow dynamics ofdense mixture of gas and particles in vertical cylindrical containers. For a heptagonal prism shaped container under vertical vibrations, the model results were found to predict bubbling behavior analogous to those observed experimentally. This bubbling behavior may be explained by the unusual gas pressure distribution found in the bed. In addition, oscillon type structures were found to be formed using a vertically vibrated, pentagonal prism shaped container in agreement with computer simulation results. These observations suggest that the pressure distribution plays a key rolein deformation and flow of dense mixtures of gas and particles under vertical vibrations. The present models provide greater insight toward the explanation of poorly understood hydrodynamic phenomena in the field of granular flows and dense gas-particle mixtures. The models can be generalized to investigate the granular material-container wall interactions which would be an issue of high interests in the industrial applications. By following this approach ideal processing conditions and powder transport can be created in industrial systems.

Torque vibration model of axial-flux surface-mounted permanent magnet synchronous machine

In order that the radius and thus ununiform structure of the teeth and otherelectrical and magnetic parts of the machine may be taken into consideration the calculation of an axial flux permanent magnet machine is, conventionally, doneby means of 3D FEM-methods. This calculation procedure, however, requires a lotof time and computer recourses. This study proves that also analytical methods can be applied to perform the calculation successfully. The procedure of the analytical calculation can be summarized into following steps: first the magnet is divided into slices, which makes the calculation for each section individually, and then the parts are submitted to calculation of the final results. It is obvious that using this method can save a lot of designing and calculating time. Thecalculation program is designed to model the magnetic and electrical circuits of surface mounted axial flux permanent magnet synchronous machines in such a way, that it takes into account possible magnetic saturation of the iron parts. Theresult of the calculation is the torque of the motor including the vibrations. The motor geometry and the materials and either the torque or pole angle are defined and the motor can be fed with an arbitrary shape and amplitude of three-phase currents. There are no limits for the size and number of the pole pairs nor for many other factors. The calculation steps and the number of different sections of the magnet are selectable, but the calculation time is strongly depending on this. The results are compared to the measurements of real prototypes. The permanent magnet creates part of the flux in the magnetic circuit. The form and amplitude of the flux density in the air-gap depends on the geometry and material of the magnetic circuit, on the length of the air-gap and remanence flux density of the magnet. Slotting is taken into account by using the Carter factor in the slot opening area. The calculation is simple and fast if the shape of the magnetis a square and has no skew in relation to the stator slots. With a more complicated magnet shape the calculation has to be done in several sections. It is clear that according to the increasing number of sections also the result will become more accurate. In a radial flux motor all sections of the magnets create force with a same radius. In the case of an axial flux motor, each radial section creates force with a different radius and the torque is the sum of these. The magnetic circuit of the motor, consisting of the stator iron, rotor iron, air-gap, magnet and the slot, is modelled with a reluctance net, which considers the saturation of the iron. This means, that several iterations, in which the permeability is updated, has to be done in order to get final results. The motor torque is calculated using the instantaneous linkage flux and stator currents. Flux linkage is called the part of the flux that is created by the permanent magnets and the stator currents passing through the coils in stator teeth. The angle between this flux and the phase currents define the torque created by the magnetic circuit. Due to the winding structure of the stator and in order to limit the leakage flux the slot openings of the stator are normally not made of ferromagnetic material even though, in some cases, semimagnetic slot wedges are used. In the slot opening faces the flux enters the iron almost normally (tangentially with respect to the rotor flux) creating tangential forces in the rotor. This phenomenon iscalled cogging. The flux in the slot opening area on the different sides of theopening and in the different slot openings is not equal and so these forces do not compensate each other. In the calculation it is assumed that the flux entering the left side of the opening is the component left from the geometrical centre of the slot. This torque component together with the torque component calculated using the Lorenz force make the total torque of the motor. It is easy to assume that when all the magnet edges, where the derivative component of the magnet flux density is at its highest, enter the slot openings at the same time, this will have as a result a considerable cogging torque. To reduce the cogging torquethe magnet edges can be shaped so that they are not parallel to the stator slots, which is the common way to solve the problem. In doing so, the edge may be spread along the whole slot pitch and thus also the high derivative component willbe spread to occur equally along the rotation. Besides forming the magnets theymay also be placed somewhat asymmetric on the rotor surface. The asymmetric distribution can be made in many different ways. All the magnets may have a different deflection of the symmetrical centre point or they can be for example shiftedin pairs. There are some factors that limit the deflection. The first is that the magnets cannot overlap. The magnet shape and the relative width compared to the pole define the deflection in this case. The other factor is that a shifting of the poles limits the maximum torque of the motor. If the edges of adjacent magnets are very close to each other the leakage flux from one pole to the other increases reducing thus the air-gap magnetization. The asymmetric model needs some assumptions and simplifications in order to limit the size of the model and calculation time. The reluctance net is made for symmetric distribution. If the magnets are distributed asymmetrically the flux in the different pole pairs will not be exactly the same. Therefore, the assumption that the flux flows from the edges of the model to the next pole pairs, in the calculation model from one edgeto the other, is not correct. If it were wished for that this fact should be considered in multi-pole pair machines, this would mean that all the poles, in other words the whole machine, should be modelled in reluctance net. The error resulting from this wrong assumption is, nevertheless, irrelevant.

Analysis of torque and speed ripple producing non-idealities of frequency converters in electric drives

Electric motors driven by adjustable-frequency converters may produce periodic excitation forces that can cause torque and speed ripple. Interaction with the driven mechanical system may cause undesirable vibrations that affect the system performance and lifetime. Direct drives in sensitive applications, such as elevators or paper machines, emphasize the importance of smooth torque production. This thesis analyses the non-idealities of frequencyconverters that produce speed and torque ripple in electric drives. The origin of low order harmonics in speed and torque is examined. It is shown how different current measurement error types affect the torque. As the application environment, direct torque control (DTC) method is applied to permanent magnet synchronous machines (PMSM). A simulation model to analyse the effect of the frequency converter non-idealities on the performance of the electric drives is created. Themodel enables to identify potential problems causing torque vibrations and possibly damaging oscillations in electrically driven machine systems. The model is capable of coupling with separate simulation software of complex mechanical loads. Furthermore, the simulation model of the frequency converter's control algorithm can be applied to control a real frequency converter. A commercial frequencyconverter with standard software, a permanent magnet axial flux synchronous motor and a DC motor as the load are used to detect the effect of current measurement errors on load torque. A method to reduce the speed and torque ripple by compensating the current measurement errors is introduced. The method is based on analysing the amplitude of a selected harmonic component of speed as a function oftime and selecting a suitable compensation alternative for the current error. The speed can be either measured or estimated, so the compensation method is applicable also for speed sensorless drives. The proposed compensation method is tested with a laboratory drive, which consists of commercial frequency converter hardware with self-made software and a prototype PMSM. The speed and torque rippleof the test drive are reduced by applying the compensation method. In addition to the direct torque controlled PMSM drives, the compensation method can also beapplied to other motor types and control methods.

Design and implementation of FPGA-based LQ control of active magnetic bearings

The need for high performance, high precision, and energy saving in rotating machinery demands an alternative solution to traditional bearings. Because of the contactless operation principle, the rotating machines employing active magnetic bearings (AMBs) provide many advantages over the traditional ones. The advantages such as contamination-free operation, low maintenance costs, high rotational speeds, low parasitic losses, programmable stiffness and damping, and vibration insulation come at expense of high cost, and complex technical solution. All these properties make the use of AMBs appropriate primarily for specific and highly demanding applications. High performance and high precision control requires model-based control methods and accurate models of the flexible rotor. In turn, complex models lead to high-order controllers and feature considerable computational burden. Fortunately, in the last few years the advancements in signal processing devices provide new perspective on the real-time control of AMBs. The design and the real-time digital implementation of the high-order LQ controllers, which focus on fast execution times, are the subjects of this work. In particular, the control design and implementation in the field programmable gate array (FPGA) circuits are investigated. The optimal design is guided by the physical constraints of the system for selecting the optimal weighting matrices. The plant model is complemented by augmenting appropriate disturbance models. The compensation of the force-field nonlinearities is proposed for decreasing the uncertainty of the actuator. A disturbance-observer-based unbalance compensation for canceling the magnetic force vibrations or vibrations in the measured positions is presented. The theoretical studies are verified by the practical experiments utilizing a custom-built laboratory test rig. The test rig uses a prototyping control platform developed in the scope of this work. To sum up, the work makes a step in the direction of an embedded single-chip FPGA-based controller of AMBs.

Rullaussylinterin ja painotelan mallinnus kiinnirullaimen simulointiin

Diplomityössä tutkitaan kaupallisen simulointiohjelmiston soveltuvuutta nykyaikaisen kiinnirullaimen dynamiikan tutkimiseen. Kiinnostuksen kohteena on erityisesti kahden telan välinen nippi, sekä siinä tapahtuvat värähtelyt. Työssä mallinnetaan rullaussylinterin ja telapainolaitteen simulointimallit. Rullaussylinterin simulointimalli yhdistetään Lappeenrannan teknillisessä korkeakoulussa mallinnettuun tampuuritelan simulointimalliin, jolloin nippikontaktin tutkiminen on mahdollista. Simuloituja tuloksia verrataan todellisella laitteella tehtyihin mittauksiin sekä elementtimenetelmällä laskettuihin tuloksiin. Diplomityön mekaniikka mallinnetaan ADAMS-ohjelmistossa monikappaledynamiikan keinoin. Toimilaitteiden sekä säätöjärjestelmien kuvaukseen käytetään MATLAB Simulink-ohjelmistoa. Telojen joustavuuden mallinnuksessa käytetään hyväksi keskittyneiden massojen periaatetta. Järjestelmän hydraulipiirit mallinnetaan keskittyneiden paineiden teorian mukaisesti ja toimilaitteiden mallinnuksessa käytetään puoliempiiristä mallinnustekniikkaa. Työssä havaitaan monikappaledynamiikan soveltuvan kiinnirullaimen dynamiikan tutkimiseen. Kahden diplomityön tuloksena laaditun nippimallin avulla voidaan kuvata rullaustapahtumassa vaikuttavat voimat oikein. Värähtelymittausten perusteella voidaan tehdä karkeita johtopäätöksiä, mallin toimivuuden arvioimiseksi värähtelyjen kuvaamisessa, joskin mallin havaitaan vaativan lisätutkimusta ja kehitystyötä.

Maastoajoneuvon korin teräsrakenteiden värähtelyominaisuuksien FEM-analysointimenetelmien kehittäminen

Tämä diplomityö on tehty Patria Vehicles Oy:n toimeksiannosta. Patria Vehicles Oy:n tuotantoon kuuluvat vaativiin maasto-olosuhteisiin soveltuvat sotilasajoneuvot. Tutkimuksen tarkoituksena oli kehittää menetelmäohjeet, kuinka FEM-analyysillä voidaan tutkia tuotekehitysvaiheessa ajoneuvon korin teräsrakenteiden värähtelyominaisuuksia ja dynaamista käyttäytymistä. Tutkimuksessa on käytetty Ideas-FEM-ohjelmistoa. Dynaamisten ongelmien ratkaisemiseksi on ymmärrettävä rakenteiden dynaamista käyttäytymistä. Rakenteiden käyttäytymistä ja muodonmuutoksia on tutkittava kriittisillä ominaistaajuuksilla. Tutkimuksessa on selvitetty, kuinka ajoneuvon elementtimallilla voidaan tehdä ominaisvärähtely- ja vastelaskentaa. Ominaisvärähtelylaskennalla selvitetään rakenteen ominaismuodot ja -taajuudet. Vastelaskennalla tutkitaan erilaisten herätteiden vaikutuksia ajoneuvon dynaamiseen käyttäytymiseen ja määritetään herätteistä rakenteeseen aiheutuvat vasteet ja herätteiden siirtyvyys rakenteessa. Lisäksi tutkitaan herätteiden aiheuttamia todellisia jännityksiä ja siirtymiä, jotta saadaan selville rakenteen todelliset rasitukset. Analyyseillä voidaan tutkia, kuinka ajoneuvon korirakennetta on jäykistettävä ja vaimennettava, jotta siinä ei esiinny haitallista melua ja värähtelyä.

Älykkäiden ohjausjärjestelmien käyttö puutavarakuormaimen väsymiskestoiän parantamisessa

Työn tavoitteena oli tutkia älykkäiden ohjausjärjestelmien käyttöä mekatronisen koneen väsymiskeston parantamisessa. Älykkäiden järjestelmien osalta työssä keskityttiin lähinnä neuroverkkojen ja sumean logiikan mahdollisuuksien tutkimiseen. Tämän lisäksi työssä kehitettiin väsymiskestoikää lisäävä älykkäisiin järjestelmiin perustuva ohjausalgoritmi. Ohjausalgoritmi liitettiin osaksi puutavarakuormaimen ohjausta. Ohjaimen kehittely suoritettiin aluksi simulointimallien avulla. Laajemmat ohjaimen testaukset suoritettiin laboratoriossa fyysisen prototyypin avulla. Tuloksena puutavarakuormaimen puomin väsymiskestoikäennuste saatiin moninkertaistettua. Väsymiskestoiän parantumisen lisäksi ohjainalgoritmi myös vaimentaa kuormaimen värähtelyä.

Development of Servo Hydraulics of Veneer Lathe

Diplomityö tehtiin kansainväliseen, mekaanisen puunjalostusteollisuuden koneita, tuotantojärjestelmiä ja tehtaita toimittavaan yritykseen. Diplomityön tarkoituksena oli kartoittaa syitä viilusorvin teräpenkin asemoinnissa esiintyneisiin värähtelyongelmiin ja tutkia ratkaisuja niiden voittamiseksi, sekä sorvausvoimien määrittäminen. Diplomityön teoreettisessa osassa tutustuttiin viilusorvin, erityisesti sen hydraulisten servojärjestelmien rakenteeseen ja toimintaan sekä viilunsorvaukseen. Teräpenkin syötön servojärjestelmää tutkittiin teoreettisesti johtamalla suljetun piirin siirtofunktiot “asema/käsky” ja “virhe/voima” ja tulostamalla niiden taajuusvaste-kuvaajat, joista tutkittiin parametrien vaikutuksia järjestelmän toimintaan. Tulokset vahvistettiin simuloimalla. Todettiin nykyisen järjestelmän värähtelyongelmien johtuvan pääasiassa hydrauliöljyn joustosta sylinterissä. Parannuksina ehdotettiin suurempaa sylinterin halkaisijaa ja viskoosikitkakertoimen suurentamista. Diplomityön kokeellisessa osassa mitattiin viilusorvin servojärjestelmien toimilaitteissa esiintyviä voimia ja niiden perusteella laskettiin varsinaiset sorvausvoimat. Lisäksi tutkittiin teräpenkin syötön ja muiden servojärjestelmien asemointitarkkuutta sorvauksen aikana. Mittauksia varten diplomityössä suunniteltiin ja hankittiin kannettava mittausjärjestelmä.

Päällystyskoneiden runkojen värähtelyiden FE-analysoinnin kehittäminen

Työssä kehitettiin päällystyskoneen runkojen FE-analysointia erityisesti vastelaskennan kannalta, joskin myös ominaistaajuuslaskennan tarkentamiseksi esitettiin parannuksia. Työssä rajoitutaan harmonisten telaherätteiden aiheuttamien vasteiden analysointiin. . Työssä käsitellään värähtelyjen teoriaa ja tarkastellaan Abaqus-ohjelmiston (versio 5.8) laskentamenetelmiä vakiotilan värähtelyvasteen laskemiseksi. FEM-mallin rakenteeseen liittyen käsitellään perustuksien ja maaperän, konepalkin ja telaherätteiden mallintamista ja mallinnuksen laajuutta. Telaherätteitä käsitellään yksittäisen telan ja telojen samanvaiheisuuden kannalta. Samanvaiheisuutta tutkitaan työssä kehitetyllä summafunktiolla. Värähtelyjen mittaukseen FEM-mallien verifioimiseksi esitetään parannuksia. Nykyinen mallinnustapa käsitellään lyhyesti. Parannusehdotuksia kokeiltiin mallintamalla Rauma 400-päällystyskone ja vertaamalla tuloksia mitattuihin. Laskennan tulokset vastasivat vaihtelevasti mittaustuloksia, mittaustulosten puutteellisuus vaikeutti vertailua. Tulosten perusteella herätetiedon parantaminen on perusteltua ja mallin laajennus lisää todenmukaisuutta. Maaperän huomiointi vaikuttaa ennen kaikkea ominaistaajuuksiin ja muotoihin ja suora ratkaisutapa on käyttökelpoinen vasteen laskentamenetelmä otettaessa maaperä huomioon.

On the Analysis and Control of a Linear Synchronous Servomotor with a Flexible Load

Industry's growing need for higher productivity is placing new demands on mechanisms connected with electrical motors, because these can easily lead to vibration problems due to fast dynamics. Furthermore, the nonlinear effects caused by a motor frequently reduce servo stability, which diminishes the controller's ability to predict and maintain speed. Hence, the flexibility of a mechanism and its control has become an important area of research. The basic approach in control system engineering is to assume that the mechanism connected to a motor is rigid, so that vibrations in the tool mechanism, reel, gripper or any apparatus connected to the motor are not taken into account. This might reduce the ability of the machine system to carry out its assignment and shorten the lifetime of the equipment. Nonetheless, it is usually more important to know how the mechanism, or in other words the load on the motor, behaves. A nonlinear load control method for a permanent magnet linear synchronous motor is developed and implemented in the thesis. The purpose of the controller is to track a flexible load to the desired velocity reference as fast as possible and without awkward oscillations. The control method is based on an adaptive backstepping algorithm with its stability ensured by the Lyapunov stability theorem. As a reference controller for the backstepping method, a hybrid neural controller is introduced in which the linear motor itself is controlled by a conventional PI velocity controller and the vibration of the associated flexible mechanism is suppressed from an outer control loop using a compensation signal from a multilayer perceptron network. To avoid the local minimum problem entailed in neural networks, the initial weights are searched for offline by means of a differential evolution algorithm. The states of a mechanical system for controllers are estimated using the Kalman filter. The theoretical results obtained from the control design are validated with the lumped mass model for a mechanism. Generalization of the mechanism allows the methods derived here to be widely implemented in machine automation. The control algorithms are first designed in a specially introduced nonlinear simulation model and then implemented in the physical linear motor using a DSP (Digital Signal Processor) application. The measurements prove that both controllers are capable of suppressing vibration, but that the backstepping method is superior to others due to its accuracy of response and stability properties.

Active Damping and Energy Recovery in a Hydraulic Boom Controlled by an Electric Drive

The aim of the study is to obtain a mathematical description for an alternative variant of controlling a hydraulic circuit with an electrical drive. The electrical and hydraulic systems are described by basic mathematical equations. The flexibilities of the load and boom is modeled with assumed mode method. The model is achieved and proven with simulations. The controller is constructed and proven to decrease oscillations and improve the dynamic response of the system.