Aerodynamical instability of web

Diplomityön tavoitteena oli tutkia miten ilman turbulenttisuus vaikuttaa tasaisesti liikkuvan rainan tilaan. Yhtenä sovelluskohteena teollisuudessa voidaan mainita esimerkiksi leiju-kuivain. Tiedetään, että konenopeuksien kasvu ja siitä johtuva ilmavirran nopeuden kasvu aiheuttaa voimavaikutuksia rainaan ja voi aiheuttaa lepatusta. Lepatus johtaa dynaamiseen epästabiilisuuteen, joka voidaan havaita, kun lineaarinen systeemi tulee epävakaaksi ja joh-taa epälineaariseen, rajoitettuun värähtelyyn. Lepatus huonontaa tuotteiden laatua ja voi johtaa ratakatkoihin. Työssä on esitetty tietoa ilman ja rainan vuorovaikutuksesta, jota hyödyntämällä voidaan kehittää yksinkertaistettu malli, jonka avulla liikkuvaa rainaa voidaan simuloida kuivaimes-sa. Kaasufaasin virtausyhtälöt on ratkaistu eri turbulenttimalleja käyttäen. Myös viskoelas-tisen rainan muodonmuutosta on tarkasteltu. Koska rainalle ei ole kirjallisuudesta saatavilla tarkkoja fysikaalisia ja mekaanisia arvoja, näitä ominaisuuksia testattiin eri arvoilla, jotta rainan käyttäytymistä jännityksen alaisena voidaan tarkastella. Näiden ominaisuuksien tun-teminen on ensiarvoisen tärkeää määritettäessä rainan aeroviskoelastista käyttäytymistä. Virtaussimulointi on kallista ja aikaa vievää. Tämä tarkoittaa uusien tutkimusmenetelmien omaksumista. Tässä työssä vaihtoehtoisena lähestymistapana on esitetty yksinkertaistettu malli, joka sisältää ilman ja rainan vuorovaikutusta kuvaavat ominaisuudet. Mallin avulla saadaan tietoa epälineaarisuuden ja turbulenssin vaikutuksesta sekä monimutkaisesta yh-teydestä stabiilisuuden ja ulkoisesti aikaansaadun värähtelyn sekä itse aiheutetun värähtelyn välillä. Työn lopussa on esitetty havainnollinen esimerkki, jolla voidaan kuvata olosuhteita, jossa rainan tasainen liike muuttuu epävakaaksi. Kun turbulenttisuudesta johtuva painevaih-telu ylittää tietyn rajan, rainan värähtely kasvaa muuttuen satunnaisesta järjestäytyneeksi. Saaduttulokset osoittavat, että turbulenttisuudella on suuri vaikutus eikä sitä voi jättää huomioimatta. Myös rainan viskoelastiset ominaisuudet tulee huomioida, jotta rainan käyt-täytymistä voidaan kuvata tarkasti.

Smooth height/age curves from stem analysis with linear programming

[Abstract]

Linear prediction application for modelling the relationships between a large number of stand characteristics of Norway spruce stands

Abstract

Dynamic Model of a Small Once-Through Boiler

In this study, a model for the unsteady dynamic behaviour of a once-through counter flow boiler that uses an organic working fluid is presented. The boiler is a compact waste-heat boiler without a furnace and it has a preheater, a vaporiser and a superheater. The relative lengths of the boiler parts vary with the operating conditions since they are all parts of a single tube. The present research is a part of a study on the unsteady dynamics of an organic Rankine cycle power plant and it will be a part of a dynamic process model. The boiler model is presented using a selected example case that uses toluene as the process fluid and flue gas from natural gas combustion as the heat source. The dynamic behaviour of the boiler means transition from the steady initial state towards another steady state that corresponds to the changed process conditions. The solution method chosen was to find such a pressure of the process fluid that the mass of the process fluid in the boiler equals the mass calculated using the mass flows into and out of the boiler during a time step, using the finite difference method. A special method of fast calculation of the thermal properties has been used, because most of the calculation time is spent in calculating the fluid properties. The boiler was divided into elements. The values of the thermodynamic properties and mass flows were calculated in the nodes that connect the elements. Dynamic behaviour was limited to the process fluid and tube wall, and the heat source was regarded as to be steady. The elements that connect the preheater to thevaporiser and the vaporiser to the superheater were treated in a special way that takes into account a flexible change from one part to the other. The model consists of the calculation of the steady state initial distribution of the variables in the nodes, and the calculation of these nodal values in a dynamic state. The initial state of the boiler was received from a steady process model that isnot a part of the boiler model. The known boundary values that may vary during the dynamic calculation were the inlet temperature and mass flow rates of both the heat source and the process fluid. A brief examination of the oscillation around a steady state, the so-called Ledinegg instability, was done. This examination showed that the pressure drop in the boiler is a third degree polynomial of the mass flow rate, and the stability criterion is a second degree polynomial of the enthalpy change in the preheater. The numerical examination showed that oscillations did not exist in the example case. The dynamic boiler model was analysed for linear and step changes of the entering fluid temperatures and flow rates.The problem for verifying the correctness of the achieved results was that there was no possibility o compare them with measurements. This is why the only way was to determine whether the obtained results were intuitively reasonable and the results changed logically when the boundary conditions were changed. The numerical stability was checked in a test run in which there was no change in input values. The differences compared with the initial values were so small that the effects of numerical oscillations were negligible. The heat source side tests showed that the model gives results that are logical in the directions of the changes, and the order of magnitude of the timescale of changes is also as expected. The results of the tests on the process fluid side showed that the model gives reasonable results both on the temperature changes that cause small alterations in the process state and on mass flow rate changes causing very great alterations. The test runs showed that the dynamic model has no problems in calculating cases in which temperature of the entering heat source suddenly goes below that of the tube wall or the process fluid.

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.

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.

Control of permanent magnet linear synchronous motor in motion control applications

The aim of the thesis is to study the principles of the permanent magnet linear synchronous motor (PMLSM) and to develop a simulator model of direct force controlled PMLSM. The basic motor model is described by the traditional two-axis equations. The end effects, cogging force and friction model are also included into the final motor model. Direct thrust force control of PMLSM is described and modelled. The full system model is proven by comparison with the data provided by the motor manufacturer.

Calculation of the critical crack size for cold form rectangular hollow section tube (CRHS) under bending load at -40º C temperature

To predict the capacity of the structure or the point which is followed by instability, calculation of the critical crack size is important. Structures usually contain several cracks but not necessarily all of these cracks lead to failure or reach the critical size. So, defining the harmful cracks or the crack size which is the most leading one to failure provides criteria for structure’s capacity at elevated temperature. The scope of this thesis was to calculate fracture parameters like stress intensity factor, the J integral and plastic and ultimate capacity of the structure to estimate critical crack size for this specific structure. Several three dimensional (3D) simulations using finite element method by Ansys program and boundary element method by Frank 3D program were carried out to calculate fracture parameters and results with the aid of laboratory tests (loaddisplacement curve, the J resistance curve and yield or ultimate stress) leaded to extract critical size of the crack. Two types of the fracture which is usually affected by temperature, Elastic and Elasti-Plastic fractures were simulated by performing several linear elastic and nonlinear elastic analyses. Geometry details of the weldment; flank angle and toe radius were also studied independently to estimate the location of crack initiation and simulate stress field in early stages of crack extension in structure. In this work also overview of the structure’s capacity in room temperature (20 ºC) was studied. Comparison of the results in different temperature (20 ºC and -40 ºC) provides a threshold of the structure’s behavior within the defined range.

Polymeeripinnoitteen aiheuttamat itseherätteiset värähtelyt nipillisessä telasysteemissä

Lukuisissa teollisuussovelluksissa materiaalien, kuten paperin ja teräslevyjen, muokkaamiseen käytettävät pyörivät nippitelat kärsivät aina erilaisten herätteiden synnyttämistä mekaanisista värähtelyistä, jotka voivat aiheuttaa virheitä valmistettaviin tuotteisiin. Tässä työssä tutkittiin viskoelastisia polymeerejä ja polymeeripinnoitteen nipilliseen telasysteemiin synnyttämiä haitallisia itseherätteisiä värähtelyjä. Työn polymeerejä käsittelevässä kirjallisuusosassa luotiin katsaus amorfisten polymeerien fysikaalisiin ominaisuuksiin. Kokeellisessa osuudessa tutkittiin tarkemmin kahden amorfisen telapinnoitepolymeerin termoreologisia ja mekaanisia ominaisuuksia suoritettujen DMTA-mittausten perusteella. Sovittamalla toisen polymeerin master-käyrään yleistetty lineaarisen standardiaineen malli saatiin selville polymeerin mekaaniset parametrit ja approksimaatio sen relaksaatiospektrille. Telapinnoitteen nipilliseen systeemiin synnyttämiä itseherätteisiä värähtelyjä ja niiden seurauksia tarkasteltiin kahdelle telalle ja polymeeripinnoitteelle kehitetyn analyyttisen mallin ja numeeristen laskujen avulla. Pinnoite mallinnettiin lineaarisen standardiaineen mukaisesti. Telasysteemin parametrit määritettiin DMTA-mittaustuloksista ja systeemiä vastaavasta koelaitteesta kokeellisella moodianalyysillä ja elementtimenetelmällä. Numeerisesta stabiilisuusanalyysistä ja liikeyhtälöiden integroinneista saadut tulokset kertovat telapinnoitteen aaltomaisista deformaatiomuodoista ja niiden synnyttämistä taajuusalueittain esiintyvistä epästabiileista värähtelyistä. Telasysteemi on epästabiili pinnoitedeformaatiokuvion systeemiin aiheuttaman herätevoiman taajuuden ollessa lähellä systeemin korkeampaa ominaistaajuutta. Numeerisista tuloksista voitiin ennustaa nopean ja hitaan barringin olemassaolo.

Applications and Markets of Linear Motors

A steady increase in practical industrial applications has secured a place for linear motors. They provide high dynamics and high positioning accuracy of the motor, high reliability and durability of all components of the system. Machines with linear motors have very big perspectives in modern industry. This thesis enables to understand what a linear motor is, where they are used and what situation there is on their market nowadays. It can help to understand reasonability of applying linear motors on manufacture and benefits of its application.

Centralized Motion Control of a Linear Tooth Belt Drive: Analysis of the Performance and Limitations

A centralized robust position control for an electrical driven tooth belt drive is designed in this doctoral thesis. Both a cascaded control structure and a PID based position controller are discussed. The performance and the limitations of the system are analyzed and design principles for the mechanical structure and the control design are given. These design principles are also suitable for most of the motion control applications, where mechanical resonance frequencies and control loop delays are present. One of the major challenges in the design of a controller for machinery applications is that the values of the parameters in the system model (parameter uncertainty) or the system model it self (non-parametric uncertainty) are seldom known accurately in advance. In this thesis a systematic analysis of the parameter uncertainty of the linear tooth beltdrive model is presented and the effect of the variation of a single parameter on the performance of the total system is shown. The total variation of the model parameters is taken into account in the control design phase using a Quantitative Feedback Theory (QFT). The thesis also introduces a new method to analyze reference feedforward controllers applying the QFT. The performance of the designed controllers is verified by experimentalmeasurements. The measurements confirm the control design principles that are given in this thesis.