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1

Profile design of noncircular belt pulleys

Krawiec P., Marlewski A.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 2

561--570

EN

During design of the envelope of a noncircular belt pulley one should take into account several conditions resulting from kinematics and geometry of the uneven-running strand transmission. Design of proper values of pitches for a belt pulley, which enable good cooperation between the belt pulley and the belt, should be carefully done. In available Polish literature and catalogues offered by belt manufacturers, one can find only detailed dimensions of belts with a trapezoidal profile. Information on other profiles is insufficient for full description of geometrical features of belt pulley teeth as well as to design tools for machining belt pulleys. Manufacturers of belt pulleys and belts give only necessary data to submit a purchase order. The paper presents a digitization process (scanning) of geometry of the envelope of circular belt pulleys with non-standard profiles; this scanning has been done with the application of coordinate measuring machines. The obtained information on geometrical features of tooth profiles has been numerically analysed. As a result of this analysis, the mathematical description has been obtained. Finally, noncircular belt pulleys with different tooth profiles have been designed and manufactured.

2

Using a CAS to visualize some images of lines mapped via the harmonic cross-ratio

Korczak E., Marlewski A.

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

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2012

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Vol. 23

11--19

EN

Let K be a cubic curve in the projective space P 3 and let T1 and T2 be points determining a bisecant T1T2 of K. We fix a point A on K and a point B≠A which does not lay on K, and such that T1T2 ≠AB. We are interested in the set of points X generated by the equation (T1, T1; M, X) = –1 where M denotes the point at which AB meets the bisecant T1T2. So we consider the line congruence of order 1 and of class 3 in the aspect of the harmonic cross-ratio. We derive theoretic formulas for the set of X ‘s and we go on in the harmonic case– then the set of X ’s is a conic. We use the computer algebra system Derive 5 from Texas Instruments, Inc., USA, to produce visualizations of the images of resulting curves.

PL

Niech K będzie krzywą przestrzenną rzędu trzeciego w przestrzeni rzutowej P 3 i niech M będzie dowolnym punktem tej przestrzeni nieleżącym na K. W wiązce prostych, której wierzchołkiem jest M, znajduje się dokładnie jedna bisekanta. Punkty, w których przecina ona krzywą K, oznaczamy przez T1 i T2. Tematem pracy jest zbadanie miejsc geometrycznych punktów X i T1T2, dla których dwustosunek (T1, T2; M, X) = –1, gdy punkt M przebiega prostą, którą wyznaczają ustalone punkt krzywej K i punkt, który na K nie leży. Badanie to przeprowadzamy przy użyciu programu Derive 5 for Windows (Texas Instruments, Inc.).

3

Determination of the Coefficient of Friction between Compressed Sawdust and Steel at High Temperature Conditions

Malujda I., Marlewski A.

Machine Dynamics Research

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2011

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Vol. 35, No. 2

38-46

EN

The purpose of this paper is to present the methodology of experimental testing of the friction coefficient between compressed sawdust and steel at increased temperature. The subject has been inspired by practical engineering experience in the design of machines for compression of natural materials classified as biomass, such as sawdust. Sawdust is a structurally complex material and investigation of its interaction with components of agglomerating machines is a prerequisite for determining the optimum parameters of the compression process. The paper presents a special test facility developed by the authors for experimental testing of the friction coefficient in loose materials subjected to the effect of heat. Moreover, it presents the experimentally determined values of the friction coefficients for various sawdust types as a function of temperature. The output of the research relates to the processes involved in compression of natural waste materials to obtain renewable sources of energy - environment-friendly fuels.

4

Arctangent Approximation of the Thermal Diffusivity Coefficient in Wood Hot Rolling Process

Malujda I., Marlewski A.

Machine Dynamics Research

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2011

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Vol. 35, No. 2

20-28

EN

Basing on the measurements of the thermal conductivity A. of beech wood in the temperature λ varying in the range 40-160°C we worked out the arctangent approximation of λ = λ(υ). In this paper we combine it with some formulae for the specific heat capacity cp = cp(υ) and this way we get AK and AS (K as Kirillov, S as Simpson-TenWolde) descriptions of the thermal diffusivity α = λ/(ρ-cp), where the density p remains constant. We provide these functions in all three anatomical directions of wood and this way we have the approximate formulae for the diffusivity α staying in the almost general onedimensional free heat conduction equation. Having this formula we are able to solve numerically this differential equation and, in consequence, we can optimize the hot rolling process to plasticize beech wood layer or sawdust briquettes.

5

Spline description of non-typical gears for belt transmissions

Krawiec P., Marlewski A.

Journal of Theoretical and Applied Mechanics

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2011

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Vol. 49 nr 2

355-367

EN

The usage of noncircular gears makes possible to get better characteristics of the transmission. This problem is widely studied in the case of regular noncircularity, e.g., when a gear is of an elliptical or cycloidal shape. In this study, there are taken into account non-typical irregular gears. The design of such gears involves more advanced techniques, in particular there has to be applied a numerical treatment to get a mathematical description of the gear profile. In the paper, we discuss a parametric spline interpolation of the third degree and we give an example of such approximation. We also present a prototype drive making that the belt transmission has changeable kinematical features.

PL

Zastosowanie nieokrągłych kół zębatych powala uzyskać lepsze charakterystyki przełożenia. Przypadki, gdy koła nieokrągłe mają kształty regularne, np. eliptyczny lub cykloidalny, zostały już szeroko przebadane. W tej pracy są poddane analizie nietypowe nieregularne koła zębate. Projektowanie takich kół wymaga bardziej zaawansowanych technik, w szczególności podejścia numerycznego w celu uzyskania matematycznego opisu profilu koła. W pracy omawiamy interpolację parametryczną za pomocą funkcji sklejanych stopnia trzeciego i stosujemy ją do uzyskania odpowiedniego opisu. Ponadto prezentujemy prototypowy napęd, w którym zostało zastosowane przedmiotowe nieregularne koło nieokrągłe. Zastosowanie tego koła w przekładni cięgnowej sprawia, że ma ona zmienne cechy kinematyczne.

6

Some properties of four topologies in real linear spaces and three classes related to them

Jankowski L., Marlewski A.

Commentationes Mathematicae

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2009

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Vol. 49, [Z] 2

107-137

EN

In the paper there are invesigated the core topology, τ_1, the directional topology, τ_2, the Klee topology, τ_3, and the finite topology, τ_0, as well as the generalizations τ1(n), τ2(n) and τ3(n) of τ1, τ2 and τ3, respectively. These generalizations are obtained when in the definition of a given topology the condition concerning straight lines is replaced by the analogous condition concerning linear varieties of dimension n, where n ∈ N. There are stated the inclusions between these topologies, the characterization with the respect to separation axioms. There are answered the questions: when considered topological spaces are Baire, sequential and Frechet? There are formulated criteria for the compactness and sequentially compactness of sets, for the convergence of sequences. There is stated the characterization of curves. Till now these problems were undertaken only in particular cases and for some topologies τ1, τ2, τ3 and τ0. For all considered topologies as well as for a certain class (including linear topologies) there are characterized the components of open sets; it is shown that every such component is the arcwise connected component and the quasi-component. In the paper there is also discussed the problem: what is it obtained when in the definition of the topology τ2(n) instead of R there is an other topological space?

7

A note on the core topology and three other ones

Jankowski L., Marlewski A.

Fasciculi Mathematici

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2005

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Nr 36

49-63

EN

In the paper there are considered the topologies defined in real linear spaces: the core topology, the topology generated by the family of directionally continuous functions, and the topology defined by Klee in [7]. The notion of the last one is extended to infinite dimensional case by means of the finite topology investigated by Kakutani and Klee [5]. Some properties of the finite topology are proved. The main result says that every one of considered topologies contain essentially the next one in the order listed above.

8

Suites periodiques generees par des involutions et des antiinvolutios de l'espace projectif complexe a n dimensions

Knitter K., Marlewski A.

Zeszyty Naukowe. Geometria / Politechnika Poznańska

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2002

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Nr XXII

53-63

EN

In an n-dimensional complex projective space there are considered pairs of (anti)involutions generating cyclic collineations of arbitrary order. There are obtained canonical matrix representations of such involutions and tbere is proved the theorem on decomposition of any cyclic collineation into two antiinvolutions.

9

Model obrazu gleb uprawnych w zakresie optycznym

Cierniewski J., Piekarczyk J., Marlewski A.

Archiwum Fotogrametrii, Kartografii i Teledetekcji

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2000

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Vol. 10

30-1--30-12

PL

Omówiony w niniejszej pracy model, opisujący dwukierunkowe odbicie od powierzchni gleb poddanych zabiegom uprawowym, wykorzystano do ilościowego określenia wpływu rozmycia przez deszcz powierzchni zaoranych i bronowanych na tle oddziaływania kierunkowości tych zabiegów względem pozycji Słońca. Dane modelowane wskazują, że wpływ deszczu uwidacznia się najwyraźniej w kierunkach odsłonecznych. Świeżo wykonana orka zapewnia większą zmienność wskaźnika znormalizowanego odbicia NR w funkcji kąta zenitalnego obserwacji niż świeżo wykonane bronowanie. Wskaźnik NR jest o 5-25% wyższy dla świeżo wykonanej orki niż dla świeżo wykonanego bronowania. Z kolei w stosunku do tego ostatniego zabiegu, powierzchnie zaorane i bronowane rozmyte przez odpowiednio intensywny deszcz cechują się o 5-10% niższym NR. Podobnie silny jak wpływ' deszczu na zmienność wskaźnika NR ma kąt oświetlenie bruzd świeżo zaoranych powierzchni.