Constant and variable amplitude fatigue strength of high strength steel welds treated with ultrasonic impact treatment

Hitsattujen rakenteiden väsymiskestävyyttä pystytään parantamaan jälkikäsittelymenetelmillä, joistayksi, ultraäänikäsittely muokkaa hitsin geometriaa ja aiheuttaa puristusjäännösjännitystilan. Tässä tutkimuksessa verrataan kokeellisesti kuormaa kantamattoman hitsatun ja ui -käsitellyn rivan väsymislujuutta toisiinsa. Tutkimusohjelmaan kuuluu kahta teräslajia ja sekä vakio - että vaihtuva - amplitudista kuormitusta. Ultraäänikäsittelyllä saavutetaan väsymiskestoiän parantuminen vakio - ja vaihtuva - amplitudisella kuormituksella. Perusaineen lujuudella ei ole merkittää vaikutusta väsymislujuuteen kun liitos on hitsatussa tilassa. Tällöin väsymiskestävyyden määrää hitsin rajaviivan jännityskeskittymä. Ultraäänikäsitellyn hitsatunliitoksen väsymiskestävyys on suurempi korkeamman lujuuden omaavilla teräksillä. Tästä syystä korkealujuuksisten terästen käyttö ultraäänikäsiteltynä väsyttävästi kuormitetuissa kevytrakenteissa on perusteltua.

Kestomagneettitahtikoneen lämpömallinnus

Sähkökoneenterminen suunnittelu on yhtä tärkeätä kuin koneen sähköisten piirien ja magneettipiirin mitoitus, koska koneen lämpenemä määrää koneesta saatavan tehon. Pääosasähkökoneista suunnitellaan edelleen ns. perimätiedon avulla, jossa tukeudutaanvalmiiksi koeteltuihin ratkaisuihin ja kokemusperäiseen tietoon tiettyjen rakenteiden toimivuudesta. Perinteisin menetelmin uusia konerakenteita suunniteltaessa ei pystytä saamaan luotettavaa tietoa uusien ratkaisuiden toimivuudesta. Etenkin hitaasti pyörivien ja suuren vääntötiheyden omaavien kestomagneettitahtikoneiden jäähdytyksen mitoitus on ongelmallista. Siten tarve kehittää analyyttisiä työkaluja lämpenemän mallinnukseen on perusteltua. Tässä työssäperehdytään suuren tehotiheyden omaavien kestomagneettikoneiden urakoon ja virrantiheyden valintaan termisen mitoituksen kannalta. Työn tavoitteena on laatia yksinkertainen analyyttinen työkalu urakoon ja virrantiheyden valintaan. Työkaluavoidaan hyödyntää jo koneensuunnittelun alkuvaiheessa.

Gas-liquid mass transfer in bubbly flow: Estimation of mass transfer, bubble size and reactor performance in various applications

Gas-liquid mass transfer is an important issue in the design and operation of many chemical unit operations. Despite its importance, the evaluation of gas-liquid mass transfer is not straightforward due to the complex nature of the phenomena involved. In this thesis gas-liquid mass transfer was evaluated in three different gas-liquid reactors in a traditional way by measuring the volumetric mass transfer coefficient (kLa). The studied reactors were a bubble column with a T-junction two-phase nozzle for gas dispersion, an industrial scale bubble column reactor for the oxidation of tetrahydroanthrahydroquinone and a concurrent downflow structured bed.The main drawback of this approach is that the obtained correlations give only the average volumetric mass transfer coefficient, which is dependent on average conditions. Moreover, the obtained correlations are valid only for the studied geometry and for the chemical system used in the measurements. In principle, a more fundamental approach is to estimate the interfacial area available for mass transfer from bubble size distributions obtained by solution of population balance equations. This approach has been used in this thesis by developing a population balance model for a bubble column together with phenomenological models for bubble breakage and coalescence. The parameters of the bubble breakage rate and coalescence rate models were estimated by comparing the measured and calculated bubble sizes. The coalescence models always have at least one experimental parameter. This is because the bubble coalescence depends on liquid composition in a way which is difficult to evaluate using known physical properties. The coalescence properties of some model solutions were evaluated by measuring the time that a bubble rests at the free liquid-gas interface before coalescing (the so-calledpersistence time or rest time). The measured persistence times range from 10 msup to 15 s depending on the solution. The coalescence was never found to be instantaneous. The bubble oscillates up and down at the interface at least a coupleof times before coalescence takes place. The measured persistence times were compared to coalescence times obtained by parameter fitting using measured bubble size distributions in a bubble column and a bubble column population balance model. For short persistence times, the persistence and coalescence times are in good agreement. For longer persistence times, however, the persistence times are at least an order of magnitude longer than the corresponding coalescence times from parameter fitting. This discrepancy may be attributed to the uncertainties concerning the estimation of energy dissipation rates, collision rates and mechanisms and contact times of the bubbles.

Logging residues from regeneration fellings for biofuel production - a GIS-based availability and supply cost analysis

Finland has large forest fuel resources. However, the use of forest fuels for energy production has been low, except for small-scale use in heating. According to national action plans and programs related to wood energy promotion, the utilization of such resources will be multiplied over the next few years. The most significant part of this growth will be based on the utilization of forest fuels, produced from logging residues of regeneration fellings, in industrial and municipal power and heating plants. Availability of logging residues was analyzed by means of resource and demand approaches in order to identify the most suitable regions with focus on increasing the forest fuel usage. The analysis included availability and supply cost comparisons between power plant sites and resource allocation in a least cost manner, and between a predefined power plant structure under demand and supply constraints. Spatial analysis of worksite factors and regional geographies were carried out using the GIS-model environment via geoprocessing and cartographic modeling tools. According to the results of analyses, the cost competitiveness of forest fuel supply should be improved in order to achieve the designed objectives in the near future. Availability and supply costs of forest fuels varied spatially and were very sensitive to worksite factors and transport distances. According to the site-specific analysis the supply potential between differentlocations can be multifold. However, due to technical and economical reasons ofthe fuel supply and dense power plant infrastructure, the supply potential is limited at plant level. Therefore, the potential and supply cost calculations aredepending on site-specific matters, where regional characteristics of resourcesand infrastructure should be taken into consideration, for example by using a GIS-modeling approach constructed in this study.

Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

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.

Messaging Application Engine for Symbian Platform

Tämä diplomityö kuvaa viestintä sovelluksen ytimen kehitystyön Symbian-alustalle. Koko sovelluksen vaatimuksena oli vastaamattomiin puheluihin vastaaminen ennalta määritellyillä tekstiviesteillä käyttäjän määrittelemien sääntöjen mukaisesti. Ei-toiminnallisia vaatimuksia olivat resurssien käytön vähentäminen ja uudelleenkäytön mahdollistaminen. Täten tämän työn tavoitteena oli kehittää ydin, joka kapseloi sovelluksen sellaisen toiminnallisuuden, joka on käyttöliittymästä riippumatonta ja uudelleenkäytettävää. Kehitystyössä ohjasi Unified Process, joka on iteroiva, käyttötapauksien ohjaama ja arkkitehtuurikeskeinen ohjelmistoprosessi. Se kannusti käyttämään myös muita teollisuudenalan vakiintuneita menetelmiä, kuten suunnittelumalleja ja visuaalista mallintamista käyttäen Unified Modelling Languagea. Suunnittelumalleja käytettiin kehitystyön aikana ja ohjelmisto mallinnettiin visuaalisesti suunnittelun edistämiseksi ja selkiyttämiseksi. Alustan palveluita käytettiin hyväksi kehitysajan ja resurssien käytön minimoimiseksi. Ytimen päätehtäviksi määrättiin viestien lähettäminen sekä sääntöjen talletus ja tarkistaminen. Sovelluksen eri alueet, eli sovelluspalvelin ja käyttöliittymää, pystyivät käyttämään ydintä ja sillä ei ollut riippuvuuksia käyttöliittymätasolle. Täten resurssien käyttö väheni ja uudelleenkäytettävyys lisääntyi. Viestien lähettäminen toteutettiin Symbian-alustan menetelmin. Sääntöjen tallettamiseen tehtiin tallennuskehys, joka eristää sääntöjen sisäisen ja ulkoisen muodon. Tässä tapauksessa ulkoiseksi tallennustavaksi valittiin relaatiotietokanta. Sääntöjen tarkastaminen toteutettiin tavanomaisella olioiden yhteistoiminnalla. Päätavoite saavutettiin. tämä ja muut hyviksi arvioidut lopputulokset, kuten uudelleenkäytettävyys ja vähentynyt resurssien käyttö, arveltiin juontuvan suunnittelumallien ja Unified Processin käytöstä. Kyseiset menetelmät osoittivat mukautuvansa pieniinkin projekteihin. Menetelmien todettiin myös tukevan ja kannustavan kehitystyön aikaista oppimista, mikä oli välttämätöntä tässä tapauksessa.

A Development and Application of a Three-Dimensional Model for a CFB Gasifier

The developing energy markets and rising energy system costs have sparked the need to find new forms of energy production and increase the self-sufficiency of energy production. One alternative is gasification, whose principles have been known for decades, but it is only recently when the technology has become a true alternative. However, in order to meet the requirements of modern energy production methods, it is necessary to study the phenomenon thoroughly. In order to understand the gasification process better and optimize it from the viewpoint of ecology and energy efficiency, it is necessary to develop effective and reliable modeling tools for gasifiers. The main aims of this work have been to understand gasification as a process and furthermore to develop an existing three-dimensional circulating fluidized bed modeling tool for modeling of gasification. The model is applied to two gasification processes of 12 and 50 MWth. The results of modeling and measurements have been compared and subsequently reviewed. The work was done in co-operation with Lappeenranta University of Technology and Foster Wheeler Energia Oy.

Bayesian methods for estimation, optimization and experimental design

Mathematical models often contain parameters that need to be calibrated from measured data. The emergence of efficient Markov Chain Monte Carlo (MCMC) methods has made the Bayesian approach a standard tool in quantifying the uncertainty in the parameters. With MCMC, the parameter estimation problem can be solved in a fully statistical manner, and the whole distribution of the parameters can be explored, instead of obtaining point estimates and using, e.g., Gaussian approximations. In this thesis, MCMC methods are applied to parameter estimation problems in chemical reaction engineering, population ecology, and climate modeling. Motivated by the climate model experiments, the methods are developed further to make them more suitable for problems where the model is computationally intensive. After the parameters are estimated, one can start to use the model for various tasks. Two such tasks are studied in this thesis: optimal design of experiments, where the task is to design the next measurements so that the parameter uncertainty is minimized, and model-based optimization, where a model-based quantity, such as the product yield in a chemical reaction model, is optimized. In this thesis, novel ways to perform these tasks are developed, based on the output of MCMC parameter estimation. A separate topic is dynamical state estimation, where the task is to estimate the dynamically changing model state, instead of static parameters. For example, in numerical weather prediction, an estimate of the state of the atmosphere must constantly be updated based on the recently obtained measurements. In this thesis, a novel hybrid state estimation method is developed, which combines elements from deterministic and random sampling methods.

Tactile-Proprioceptive Robotic Grasping

Robotic grasping has been studied increasingly for a few decades. While progress has been made in this field, robotic hands are still nowhere near the capability of human hands. However, in the past few years, the increase in computational power and the availability of commercial tactile sensors have made it easier to develop techniques that exploit the feedback from the hand itself, the sense of touch. The focus of this thesis lies in the use of this sense. The work described in this thesis focuses on robotic grasping from two different viewpoints: robotic systems and data-driven grasping. The robotic systems viewpoint describes a complete architecture for the act of grasping and, to a lesser extent, more general manipulation. Two central claims that the architecture was designed for are hardware independence and the use of sensors during grasping. These properties enables the use of multiple different robotic platforms within the architecture. Secondly, new data-driven methods are proposed that can be incorporated into the grasping process. The first of these methods is a novel way of learning grasp stability from the tactile and haptic feedback of the hand instead of analytically solving the stability from a set of known contacts between the hand and the object. By learning from the data directly, there is no need to know the properties of the hand, such as kinematics, enabling the method to be utilized with complex hands. The second novel method, probabilistic grasping, combines the fields of tactile exploration and grasp planning. By employing well-known statistical methods and pre-existing knowledge of an object, object properties, such as pose, can be inferred with related uncertainty. This uncertainty is utilized by a grasp planning process which plans for stable grasps under the inferred uncertainty.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Process modeling method for electric accessories manufacturing enterprise

The theoretical research of the study focused to business process management and business process modeling, the goal was to found a new business process modeling method for electrical accessories manufacturing enterprise. The focus was to find few options for business process modeling methods where company could have chosen the best one for its needs The study was carried out as a qualitative research with an action study and a case study as the most important ways collect data. In the empirical part of the study examples of company’s processes modeled with the new modeling method and process modeling process are presented. The new way of modeling processes improves especially visual presentation of the processes and improves the understanding how employees should work in the organizational interfaces of the process and in the interfaces between different processes. The results of the study is a new unified way to model company’s processes, which makes it easier to understand and create the process models. This improved readability makes it possible to reduce the costs that were created from the unclear old process models.

LVDC power distribution system: computational modelling

In the doctoral dissertation, low-voltage direct current (LVDC) distribution system stability, supply security and power quality are evaluated by computational modelling and measurements on an LVDC research platform. Computational models for the LVDC network analysis are developed. Time-domain simulation models are implemented in the time-domain simulation environment PSCAD/EMTDC. The PSCAD/EMTDC models of the LVDC network are applied to the transient behaviour and power quality studies. The LVDC network power loss model is developed in a MATLAB environment and is capable of fast estimation of the network and component power losses. The model integrates analytical equations that describe the power loss mechanism of the network components with power flow calculations. For an LVDC network research platform, a monitoring and control software solution is developed. The solution is used to deliver measurement data for verification of the developed models and analysis of the modelling results. In the work, the power loss mechanism of the LVDC network components and its main dependencies are described. Energy loss distribution of the LVDC network components is presented. Power quality measurements and current spectra are provided and harmonic pollution on the DC network is analysed. The transient behaviour of the network is verified through time-domain simulations. DC capacitor guidelines for an LVDC power distribution network are introduced. The power loss analysis results show that one of the main optimisation targets for an LVDC power distribution network should be reduction of the no-load losses and efficiency improvement of converters at partial loads. Low-frequency spectra of the network voltages and currents are shown, and harmonic propagation is analysed. Power quality in the LVDC network point of common coupling (PCC) is discussed. Power quality standard requirements are shown to be met by the LVDC network. The network behaviour during transients is analysed by time-domain simulations. The network is shown to be transient stable during large-scale disturbances. Measurement results on the LVDC research platform proving this are presented in the work.

Spontaneous Focusing on Numerosity in the Development of Early Mathematical Skills

The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.