W artykule przedstawiono zmodyfikowane stanowisko do badań przyczepności występującej pomiędzy ogumionym kołem jezdnym a nawierzchnią drogi. Stanowisko to umożliwia pomiar poziomej reakcji wzdłużnej przy poślizgu koła wynoszącym 100 %. Znając pionową siłę nacisku koła jezdnego na nawierzchnię drogi, wyznaczono współczynnik przyczepności, którego zmienność w czasie przedstawiono na wykresie.
EN
The article presents a modified test stand for the traction between the tire wheel and the road surface. This position allows you to measure the horizontal longitudinal reaction with a wheel slip of 100%. Knowing the vertical force of the contact wheel on the surface of the road, the coefficient of adhesion was determined, the variability of which is shown in the graph over time.
Zjawisko indukcji elektromagnetycznej jest obecnie wykorzystywane w wielu gałęziach przemysłu. Najpowszechniej stosowane jest do uzupełniania energii w telefonach komórkowych, jak również w szczoteczkach do zębów a nawet pojazdach. W artykule omówiony został aspekt teoretyczny zjawiska indukcji oraz projekt realizowany na Politechnice Łódzkiej mający na celu wykorzystanie tego zjawiska przy konstrukcji napędu elektrycznego samochodu osobowego wyposażonego fabrycznie w napęd spalinowy. Zjawisko indukcji elektromagnetycznej opisane jest prawem Faradaya, które stwierdza, że zmienny w czasie strumień indukcji pola magnetycznego jest w stanie wytworzyć siłę elektromotoryczną w obwodzie elektrycznym. To samo prawo stosuje się również w przypadku indukcji wzajemnej, gdzie jedna cewka z zewnętrznym źródłem prądu przemiennego powoduje poprzez zmienne pole magnetyczne powstanie prądu w drugim obwodzie znajdującym się blisko pierwszego. Zaimplementowanie zjawiska w pojeździe elektrycznym polega na skonstruowaniu elementów tworzących cewkę nadaw-czą, podłączoną do sieci elektrycznej oraz cewkę odbiorczą zainstalowaną w samochodzie i zasilającą silnik. Praktycznym rozwiązaniem tego zadania może być system MOVITRANS® opracowany przez firmę SEW Eurodrive. Posiada on gotowe koncepcje urządzeń nadawczych i odbiorczych oraz elementów pośrednich przesyłu energii. Współpraca Politechniki Łódzkiej z SEW Eurodrive w tej kwestii została już nawiązana i pierwszych wyników można spodziewać się wkrótce.
EN
Nowadays, the electromagnetic induction phenomenon is used in numerous branches of industry. The most commonly it is applied to charging mobile phones as well as electrical toothbrushes and even cars. The project which is carried out at The Lodz University of Technology is aimed at using the phenomenon for construction of the electrical propulsion for the Smart car initially produces with the internal combustion engine. The electromagnetic induction phenomenon is described by the Faraday’s Law. It says that a varying magnetic flux is able to create an electromotive force in the electric circuit. The same law is applied in case of the mutual induction phenomenon where one coil connected to an external source of alternating current, by means of the varying magnetic flux, is able to generate current in another coil located near the first one. Practical application of the phenomenon in the car consists in constructing elements making the transmitting coil connected to the power grid and the receiving coil installed in the car. An useful solution of this task can be the MOVITRANS® system designed by the SEW Eurodrive Company. The system consists of ready-to-use concepts of receiving and transmitting devices as well as all necessary connecting components to make the energy transmission possible. Cooperation of The Lodz University of Technology with the SEW Eurodrive Company has been already established and first findings can be expected in the nearest future.
W artykule omówiony został projekt realizowany na Politechnice Łódzkiej, którego celem było zaadaptowanie istniejącego stanowiska badawczego, tak aby umożliwiało wykonanie pomiaru tarcia (przyczepności) opony przy poślizgu koła jezdnego 100%. Nawiązano do pojęć takich jak poślizg, siła tarcia (przyczepności) oraz współczynnik przyczepności. Zagadnienia te były kluczowe dla określenia warunków jakie zmodyfikowane stanowisko powinno spełniać. Omówiona została dotychczasowa konstrukcja stanowiska a następnie przedstawiono wykonane zmiany konstrukcyjne.
EN
Paper discussed the project realized at the Lodz University of Technology which aim was to adapt already existing test stand so that it enables measurements of the tire friction (tire adhesion) during 100% slippage conditions. Firstly, several terms connected directly with the topic of wheel (as the combination of tire and rim) and its kinematics were presented including slippage, friction force and adhesion (friction) coefficient of the tire. They were crucial from the point of view of the conditions that the rebuilt stand shall fulfill. Secondly, the already existing stand was described. This part of the work included description of three different configurations of the stand existing so far. Three different phases of the wheel’s motion together with the phenomena accompanying them that were tested on the stand were also presented. The last stage concerned the project part itself and included construction of the frame holding the electric motor and the balance frame holding the mass which reduces the wheel pressure force on the road. Finally, when the test stand in new configuration was ready, validating measurements were performed. As the result, it was concluded that rebuilt measuring construction enable one to examine the friction phenomenon between tire and road during 100% slippage. The obtained values of the friction coefficient were corresponding to the expected ones. Some interesting dependencies were also observed, for instance presumable influence of the increasing (over some value) tire temperature during measurement on friction coefficient. However, to validate it some modifications in the test stand construction are recommended for the future.
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There are examples of several types of investigations available for beginners: 1. search for patterns 2. iterating a certain procedure and analysing the results, 3. looking for exceptions, or special cases in a pattern, 4. generalizing given problem.
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Here we present two different problems for investigation: counting the routes on a cubic grid and counting the paths on a chessboard. In both investigations we can use two different strategies: a) the strategy "of jumping" and b) the strategy "of going step- by-step", The first strategy leads to combinatorial formulas and the second to number triangles. We feel the strategy of "going step-by-step" is more important at this moment.
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Problems in the curriculum have existed since ancient times, if not earlier. For example, an Egyptian mathematical manuscript (the Ahmes Papyrus) consisting of a collection of problems, was written about 1650 B.C. This has not changed in nearly 4000 years. The central idea of problems has been a common to school mathematics historically and to school mathematics today. Traditionally, when we have spoken about problems we have meant word problems and especially so-called story problems. From our contemporary view, these are only one particular kind of problem. These are problems with the help of which we present pupils with a pseudo - real world. Through this type of problem we present students with a situation or a task and in the form of a question with a goal that the student must achieve. We can say that these are „goal - aimed" problems, or in contemporary terminology closed problems. We require that the student choose some previously learned algorithm (if he/she knows more than one), and with this perform a calculation. They are often placed at the end of a set of algorithmic exercises and with help of them we practise what we have just learned. In many countries today, as in our own, these problems are of central importance, and it is by solving such problems that we can assess the student. Here is a typical example of a story problem when we must calculate with fractions: Story problem: On a trip at the end of school year there were 25 pupils. 3/5 of them are girls. How many girls and how many boys participated in the trip? A great change occurred in the concept of the problem when we began to consider the relationship between the student and a problem. Reys et al. (1984) argued that „a problem involves a situation in which a person wants something and does not know immediately what to do to get it". In this explanation of a problem, it is very important that the pupil wants to achieve the goal. If for example, we give to our student the task of making a present for his/her mother for Mothers' Day, it is problem for him/her only if they want to do it (in this new approach).
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