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1
Content available remote Mathematical simulation of heat generation at a cutting-tool surface during stock removal processes
Mzad Hocine
Engineering Transactions
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2021
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Vol. 69, iss. 4
423--436
EN
The heat generated in various cutting zones significantly influences machining, affects tool wear, and thereby reduces tool life. In this paper, a spline cubic interpolation is used to estimate the transient heat flux imposed on the surface of a carbide cutting tool during stock removal, at constant thermal properties and cutting velocity. Interpolation of instantaneously measured temperature data set by the polynomial of lowest possible degree that passes through the points of the dataset is obtained. A high-precision remote-sensing infrared thermometer is used to measure the temperature at the surface. For friction shear stress determination, a mounted sensing system detects strain gauges signals and computes them in the form of forces on the display screen. From thermal behavior point of view the final result is notably interesting: it highlights the feature of non-proportionality in temperature/heat flux variation.
2
Content available Application of the polynomial interpolation method for determining performance characteristics of a diesel engine
Stoeck T., Abramek K. F.
Metrology and Measurement Systems
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2014
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Vol. 21, nr 1
157--168
EN
The article shows the methodology and calculation procedures based on Lagrange polynomial interpolation which were used to determine standard performance characteristics of the Polish production engine, type ANDORIA 4CTi90-1BE6. They allow to simplify the experimental research by maintaining a minimum number of measurement points and estimating the remaining data in an analytical way. The methods presented are convenient when it comes to the practical side because they eliminate the need for exploration of mathematical equations describing the various curves, which can be cumbersome and time consuming in the case of nonautomated accounts. The results of analysis were applied to actual experimental results, indicating sufficient accuracy of the resulting approximations. As a result, procedures may be used in bench testing of a similar profile, especially with repeated cycles of the experiment, such as optimization of operating parameters of combustion engines.
3
Content available Usefulness of nonlinear interpolation and particle filter in Zigbee indoor positioning
Zhang X., Guo H., Wu H., Uradziński M.
Geodesy and Cartography
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2014
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Vol. 63, no. 2
219--233
EN
The key to fingerprint positioning algorithm is establishing effective fingerprint information database based on different reference nodes of received signal strength indicator (RSSI). Traditional method is to set the location area calibration multiple information sampling points, and collection of a large number sample data what is very time consuming. With Zigbee sensor networks as platform, considering the influence of positioning signal interference, we proposed an improved algorithm of getting virtual database based on polynomial interpolation, while the pre-estimated result was disposed by particle filter. Experimental result shows that this method can generate a quick, simple fine-grained localization information database, and improve the positioning accuracy at the same time.
PL
Kluczem do algorytmu pozycjonowania wykorzystującego metodę fingerprinting jest ustanowienie skutecznej bazy danych na podstawie informacji z radiowych nadajników referencyjnych przy wykorzystaniu wskaźnika mocy odbieranego sygnału (RSSI). Tradycyjna metoda oparta jest na przeprowadzeniu kalibracji obszaru lokalizacji na podstawie wielu punktów pomiarowych i otrzymaniu dużej liczby próbek, co jest bardzo czasochłonne.
4
Content available The use of Newton’s method for interpolation in the bench testing of compression-ignition engine unit injector systems
Stoeck T., Osipowicz T.
Combustion Engines
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2014
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R. 53, nr 4
32--39
EN
The paper presents the methodology for calculations based on the Newton’s method which was used to determine the characteristics of test unit injector systems. It allowed simplification of the research process by preserving a minimum number of measuring points and estimation of other data analytically. Results were compared with the real experimental results obtaining satisfactory accuracy of approximations. The proposed methodology was adapted to a standard spreadsheet so that changes in pre-set parameters and required computations could be made on a regular basis, which in addition shortened the time of their performance.
PL
W artykule przedstawiono metodykę obliczeń opartą na metodzie Newtona, którą zastosowano do wyznaczenia charakterystyk probierczych pompowtryskiwaczy. Umożliwiła ona uproszczenie procesu badawczego przez zachowanie minimalnej liczby punktów pomiarowych i oszacowanie pozostałych danych w sposób analityczny. Rezultaty odniesiono do rzeczywistych wyników doświadczalnych, uzyskując zadowalającą dokładność przybliżeń. Proponowaną metodykę zaadaptowano do standardowego arkusza kalkulacyjnego, dzięki czemu zmianę parametrów zadanych i wymagane obliczenia prowadzono na bieżąco, co dodatkowo skróciło czas ich realizacji.
5
Content available A subinterval-based method for circuits with fractional order elements
Sowa M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 3
449--454
EN
The paper deals with the solution of problems that concern fractional time derivatives. Specifically the author’s interest lies in solving circuit problems with so called fractional capacitors and fractional inductors. A numerical method is proposed that involves polynomial interpolation and the division of the entire time interval (for which computations are performed) into subintervals. Analytical formulae are derived for the integro-differentiation according to the Caputo fractional derivative. The rules that concern the subinterval dynamics throughout the computation are also presented in the paper. For exemplary linear circuit problems (AC and transient) involving fractional order elements the solutions have been obtained. These solutions are compared with ones obtained by means of traditional methods.
6
Content available Algorytm upraszczania linii z wykorzystaniem interpolacji
Kozioł K.
Roczniki Geomatyki
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2013
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T. 11, z. 3(60)
45--59
PL
W publikacji autor przedstawia nowy algorytm upraszczania, dokonujący zamiany łamanej pierwotnej na krzywą poprzez proces interpolacji. W wyniku działania algorytmu punkty na krzywej rozmieszczane są zależnie od skali mapy tworząc łamaną uogólnioną. Dodatkowo w rozmieszczaniu uwzględnia się: punkty ekstremalne krzywej zgodne z normą rozpoznawalności rysunku oraz punkty charakterystyczne. Nowy algorytm porównano z najczęściej stosowanymi algorytmami upraszczania: Douglasa - Peukera, Visvalinghama i Whyatta, Wanga oraz Chrobaka. W porównaniach badano: liczbę wierzchołków łamanych po uproszczeniu, strzałki jako najkrótsze odległości od wierzchołków usuniętych łamanej pierwotnej do boków łamanej uproszczonej oraz różnicę pomiędzy długością łamanej pierwotnej z długościami po uproszczeniu łamanych. Porównanie wykazało, że wyniki nowego algorytmu cechują się: najmniejszą liczbą usuwanych wierzchołków, najkrótszymi strzałkami, najmniejszą różnicą długości pierwotnej do długości uproszczonych, najmniejszymi średnimi błędami strzałek łamanej po upraszczaniu oraz największymi rozstępami skali pierwotnej do uogólnianej. Cechy nowego algorytmu zwiększają procent automatyzacji procesu upraszczania, a zwiększenie rozstępu skal ma szczególne znaczenie w Wielorozdzielczych/ Wieloreprezentacyjnych Bazach Danych.
EN
The paper presents a new line simplification algorithm for converting the original polyline into a curve. The arrangement of points on the curve depends on the scale of the map. The critical points of the curve, according to the recognisability norm were also taken into consideration. The proposed algorithm is compared to the most widely used simplification algorithms. As it has been proven in the comparison, the results of the new algorithm show the smallest number of deleted vertices, the shortest bows, and the smallest difference between the lengths of the original polygonal curve and the simplified curve. Those features increase the automation of the simplification process.
7
Median algorithm to the interpolation of 2-D digital data
Kornatowski E.
Poznan University of Technology Academic Journals. Electrical Engineering
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2010
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No. 61
17-25
8
Calculation of reflector profile using Hermite interpolation
Wandachowicz K.
Poznan University of Technology Academic Journals. Electrical Engineering
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2010
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No. 62
161-169
EN
A computational design optimisation process is used to generate luminaire reflector geometry that achieves a set luminous intensity distribution. Reflector profile is calculated using polynomial interpolation. The shape-preserving Hermite interpolation is discussed and compared with other piecewise cubic interpolation. The direct search optimisation strategy is used and compared with the analytical solution to the problem.
9
Content available Mathematical description of the external characteristics of compression-ignition engine
Stoeck T.
Journal of KONES
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2010
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Vol. 17, No. 2
445-450
EN
In this paper is presented a calculation procedure based on Lagrange's interpolation formuła which has been used for describing the external characteristics of compression-ignition engine of the 359 type. The characteristic curves of specific fuel consumption and exhaust gas smokiness were chosen as an example, which had been obtained during examinations on engine test bed for a drive unitfuelled with four types of fuel. Measurements were carried out on a standard engine test bed which is part of laboratory facilities of the Department of Automotive Vehicles Operation, Western Pomeranian University of Technology in Szczecin. The study object was an unsupercharged four-stroke engine of domestic production of the 359 type. It is a six-cylinder compression-ignition drive unit with direct fuel injection system. Interpolating polynomials determined analytically for respective characteristics have been presented in the graphical form, while experimental examination results necessary for obtaining them have been additionally tabulated. The presented methodology allows simplification of particular experiment stages by giving possibility to estimate analytically the missing data and with preservation of a minimum number of measuring points. With small corrections, it may be used in similar examinations on other engine test beds. Its application should support the planning of particular experiment stages but does not, in any case, replace it since determination of engine characteristic curves is possible through research only.
10
Content available Application of interval interpolation for the description of compression-ignition engine performance characteristics
Stoeck T., Prajwowski K.
Archives of Transport
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2010
|
Vol. 22, iss. 3
349-357
EN
In this paper is presented a calculation method based on Lagrange's interpolation formula which has been used for mathematical description of the performance characteristics of a compression-ignition engine of the 359 type of the Polish production. Its application allows simplification of experimental tests through preservation of a minimum number of measuring points and estimation of other data analytically. In order to minimise the interpolation error occurring with polynomials of high degrees and constant node distances, the characteristics were approximated by spline functions with both solutions being shown comparatively in the graphical form. As calculation examples, the curves of specific fuel consumption and infrared radiation absorption coefficient were chosen, which had been obtained during examinations on engine test bench for a drive unit fuelled with four types of fuel. In addition, results of the experiment required for their determination were tabulated. The presented method may be used in further tests of a given engine as well as on other experimental benches, aiding long-lasting and expensive optimisation of operating parameters when using fuels of plant origin. Description of any performance characteristics by means of interval interpolation is convenient from the practical side and does not cause greater calculation problems since polynomials of low degrees are being used in the procedure.
PL
W artykule przedstawiono metodykę obliczeniową bazującą na interpolacji wielomianowej Lagrange'a, którą wykorzystano do matematycznego opisu charakterystyk zewnętrznych silnika o zapłonie samoczynnym produkcji polskiej typu 359. Jej zastosowanie pozwala na uproszczenie badań doświadczalnych poprzez zachowanie minimalnej ilości punktów pomiarowych i oszacowanie pozostałych danych w sposób analityczny. W celu zminimalizowania błędu interpolacji występującego przy wielomianach wysokich stopni i stałych odległościach węzłów, charakterystyki przybliżano funkcjami sklejanymi, przy czym oba rozwiązania pokazano porównawczo w formie graficznej. Jako przykłady obliczeniowe wybrano krzywe jednostkowego zużycia paliwa i współczynnika absorpcji promieniowania podczerwonego, które uzyskano w badaniach na hamowni silnikowej dla jednostki zasilanej czterema rodzajami paliw. Wyniki eksperymentu wymagane do ich wyznaczenia dodatkowo stabelaryzowano. Prezentowana metodyka może być wykorzystana w dalszych badaniach danego silnika, jak również na innych stanowiskach doświadczalnych, wspomagając długotrwałą i kosztowną optymalizację parametrów roboczych przy stosowaniu paliw pochodzenia roślinnego. Opisanie dowolnych charakterystyk zewnętrznych za pomocą interpolacji przedziałowej jest wygodne od strony praktycznej i nie przysparza większych trudności obliczeniowych, gdyż w procedurze wykorzystuje się wielomiany niskich stopni.
11
Content available remote The polynomial interpolation for technical experiments
Biernat G., Ciekot A.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2007
|
Vol. 6, nr 1
19-22
EN
In the article there are the interpolation of the empirical processes by polynomials of several variables.
12
Content available remote Wow defect reduction based on interpolation techniques
Maziewski P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2006
|
Vol. 54, nr 4
469-477
EN
In this paper the capacity of non-uniform sampling rate conversion techniques, invo1ving different interpolation methods, aimed at wow defect reduction, is examined. Involved are: linear interpolation, tour po1ynomial-based interpolation methods and the windowed sincbased method. The examined polynomial methods are: Lagrange interpolation, polynomial fitting with additional noise reduction, Hermitan and Spline. The performance of an artificially distorted audio signal, restored using non-uniform resampling, is evaluated on the basis of standard audio defect measurement criteria and compared for all of the aforementioned interpolation methods. The chosen defect descriptors are: total harmonic distortion, total harmonic distortion plus noise and signal to noise ratio.
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