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1
Content available remote Unified mega algorithm for partial recurrence reynolds solution
Wierzcholski K. Ch.
Journal of Applied Computer Science
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2012
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Vol. 20, nr 1
81-101
EN
The main scientific topic of the presented paper concerns the method of the determination and calculations of the general and particular numerical solutions of a Reynolds partial recurrence equation with variable coeffcients in curvilinear orthogonal coordinates for curvilinear boundary conditions, and an indication the new applications of the abovementioned solutions in applied and theoretical mechanics. A general space of discrete solution was derived and determined for various orthogonal coordinates. From the mathematical point, the presented method of the solution of modified Reynolds equation leads this problem to resolving the partial recurrence non-homogeneous, linear equation of the second order with variable coeffcients. The formulae and the calculation algorithm derived in this chapter are utilized in numerical calculations.
2
Content available remote Pseudo-Gaussian Density Functions for Gap Height Between Two Surfaces
Wierzcholski K. Ch., Nowakowska K.
Journal of Applied Computer Science
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2010
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Vol. 18, nr 2
79-90
EN
The presented paper formulates the sequence of pseudo-Gaussian distributions where are presented the mathematical results of standard deviation and probability density function derivations for bio-and micro-bearing gap height on the basis of Mow, Dowson, Cwanek, Wierzcholski experimental results. The mathematical derivation of the optimum probability density functions and least standard deviation are illustrated in two cases. The first case relates to the height of the gap if vibration and unsteady load causes the random changes. The second case relates to the height of the gap if the asperities of the cartilage surface roughness cause the random changes. Author formulates one Theorem and some Corollaries where the sequence of pseudo-Gaussian-distributions are derived. The presented proof shows, that such sequence is convergent to the Gaussian distribution in infinity.
3
Content available remote Mathematical Implementation Into Computer Calculations
Wierzcholski K. Ch.
Journal of Applied Computer Science
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2010
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Vol. 18, nr 1
117-135
EN
This paper presents the implementation of mathematical and logical formulae into computer Matlab 7:3 Professional Program as artificial intelligence component applied for determination of control and memory of micro-bearing operating parameters. Effcient functioning of slide microbearings is requisite for the intelligent features to which belongs memory with simultaneously capability of the processes control. Artificial intelligence of micro-bearing denotes the creating the mathematical and logical models to describe pressures, load carrying capacities, friction, phenomena and friction coeffcients in the form of modified partial diferential equations.
4
Content available remote Fuzzy Logic Tools in Intelligent Micro-Bearing Systems
Wierzcholski K. Ch.
Journal of Applied Computer Science
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2009
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Vol. 17, nr 2
123-131
EN
Fuzzy logic is a mathematical object with defined multivalued function which has values in closed set [0,1]. In classical case mentioned function has only two values namely zero and one. This paper presents the fuzzy logic tools in intelligent micro-bearing systems. Presented in this paper artificial intelligence (AI) for micro-bearings systems determines the friction forces and wear value. Moreover by virtue of fuzzy logic theory, the AI creates a new formal dependences between micro-bearing shapes and friction forces and wear effects during the exploitation process.
5
Content available remote Hydrodynamic pressure, carrying capacities, friction forces in biobearing gap
Wierzcholski K.Ch.
Acta of Bioengineering and Biomechanics
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2009
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Vol. 11, nr 2
31-44
EN
The present paper deals with the calculations of the pressure distributions, carrying capacities and friction forces derivations in a super- thin layer of biological synovial fluid inside the slide biobearing gap limited by a spherical, conical, cylindrical, parabolic, hyperbolic bone heads. There are also described unsteady and random flow conditions of the bio-bearing lubrication with the changes of the dynamic viscosity of the synovial fluid in the gap height in general.
6
Content available remote Comparison between impulsive and periodic non-Newtonian lubrication of human hip joint
Wierzcholski K. Ch.
Engineering Transactions
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2005
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Vol. 53, iss. 1
69-114
EN
This paper shows numerical comparisons between lubrication of human hip joint gap in unsteady impulsive and periodic motion. We assume that spherical bone head in human hip joint moves at least in two directions namely in circumference and meridian directions. Basic equations describing synovial fluid flow in human hip joint are solved on the analytical and numerical way. Numerical calculations are performed in Mathcad 11 Professional Program, taking into account the method of Finite Differences. This method satisfies stability of numerical solutions of partial differential equations and gives real values of pressure and capacity forces occurring in human hip joints.
7
Content available remote Hip joint lubrication after injury in stochastic description of optimum standard deviations
Wierzcholski K. Ch.
Acta of Bioengineering and Biomechanics
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2005
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Vol. 7, nr 2
51-79
EN
The lubrication parameters of rough and used cartilage surface in human hip joint changes suddenly after its injury. Stochastic changes of the roughness of the surfaces of the head of bone and stochastic changes of the load imply the random changes of gap height. Hence, the pressure distributions and capacity as well as friction forces and friction coefficients radically decrease or increase in several microseconds after trauma. These changes are very difficult to measure, hence an appropriate numerical research in this field is very important. In order to obtain correct numerical results, we have to perform calculations using stochastic description with optimum standard deviations.
8
Content available remote Viscoelastic lubrication of human hip joint for impulsive motion after injury
Wierzcholski K.Ch.
Tribologia
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2004
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nr 2
53-80
EN
This paper presents analytical and numerical solutions of velocity components for synovial fluid flow and pressure and capacities in spherical hip joint gap for hydrodynamic unsteady viscoelastic lubrication in a few or several dozen microseconds after impulse. These parameters of lubrication have very important changes in very short time and are not measurable in experimental way in the time of several microseconds. Therefore analytical and numerical results presented in this paper are necessary in the therapy after trauma.
PL
Tematem niniejszej pracy są parametry smarowania lepkosprężystą cieczą synowialną stawu biodrowego człowieka w czasie kilku lub kilkunastu, a nawet kilkudziesięciu mikrosekund po doznanym urazie. W niniejszej pracy rozpatruje się urazy wywołujące zmniejszenie lub zwiększenie wysokości i zmiany kształtu szczeliny stawu, które to zmiany po pewnym określonym czasie po doznanym urazie mogą zaniknąć. W konsekwencji takich urazów i to w bardzo krótkim czasie, rzędu mikrosekund, następują bardzo istotne zmiany parametrów smarowania. Mamy tu na uwadze zmiany rozkładów wartości ciśnienia i sił nośnych. Takie zmiany warunków smarowania nieustalonego mają - zdaniem traumatologów i ortopedów - istotny wpływ na trwałe lub czasowe uszkodzenie stawu, a wiedza na temat tych zmian ma decydujące znaczenie na trafne postawienie diagnozy i dalsze leczenie zachowawcze lub operacyjne. Ponieważ decydujący okres, w którym dokonują się wspomniane zmiany smarowania, trwa zaledwie kilka, kilkanaście lub kilkadziesiąt mikrosekund, stąd pomiar tych zmian jest bardzo kosztowy, utrudniony, a nawet niemożliwy ze względu na krótki czas, tym bardziej, że w sytuacji urazu i towarzyszącego mu bólu trudno jest natychmiastowo sięgnąć po przyrządy pomiarowe. Wobec powyższego analityczno-numeryczne wyznaczanie wartości ciśnienia siły nośnej w stawie biodrowym człowieka w czasie kilku lub kilkudziesięciu mikrosekund po urazie dokonanym przez siłę, jest zdaniem autora bardzo celowe. Przedstawione wyniki badań wzbogacą z pewnością bazę niezbędnych danych, potrzebną ortopedom w diagnozie i terapii.
9
Content available Viscoelastic lubrication of spherical slide bearing in impulsive unsteady motion
Wierzcholski K. Ch.
Polish Maritime Research
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2004
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nr 4
9-21
EN
This paper presents numerical and semi-analytical solutions of oil velocity components and pressure distributions in spherical unsymmetrical gap of slide bearing. A hydrodynaŹmic unsteady lubrication during oil flow with viscoelastic properties is here considered. In the case of various driving systems on ships the bearings with spherical journals and spherical sleeves or slide bearings with spherical bits operate often under impulsive unsteady motions. Many impurities appearing in service leads to viscoelastic properties of the oil. During service of transport machines it is necessary to adjust the shaft location respective to the sleeve in order to make optimizing the convergent lubricating film possible. Such conditions are effectively satisfied in bearings with spherical journals. The presented numerical calculations were perforŹmed by means of the Mathcad 2000 Professional Program and the method of finite differences. This method satisfies stability conditions of numerical solutions of capacity forces occurring in spherical bearings.
10
Content available remote Numerical contribution to the viscoelastic magnetic lubrication of human joint in periodic motion
Wierzcholski K. Ch.
Acta of Bioengineering and Biomechanics
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2004
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Vol. 6, nr 1
61-82
EN
This paper presents the author's numerical contribution to unsymmetrical viscoelastic hydrodynamic lubrication of human joints with synovial fluid in periodically changed time and unsteady magnetic field. We assume that bone head in human joint moves in two directions, namely in circumference and meridian directions. Basic equations describing the flow of synovial fluid in human hip joint are solved analytically od numerically. Numerical calculations are performed in Mathcad 2000 Professional Program, taking into account the method of finite differences. This method satisfies stability of numerical solutions of partial differential equations and values of capacity forces occurring in human joints.
11
Content available remote Capacity of deformed human joint gap in time-dependent magnetic field
Wierzcholski K. Ch.
Acta of Bioengineering and Biomechanics
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2003
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Vol. 5, nr 1
43-65
EN
Analysis of carrying capacity of synovial unsymmetrical fluid flow in deformed, human joint gap, especially in hip joint, is presented. The following assumptions are taken into account: stationary, isothermal and incompressible synovial unsymmetrical fluid flow in time-dependent magnetic field rotation motion of bone head, squeeze of synovial fluid in human joint gap, changeable synovial non-Newtonian fluid viscosity, changeable and deformed gap height in human joint, and constant synovial fluid density. The simplified system of basic equations for pressure and synovial velocity distribution are analysed. Numerical and analytical formulae for capacity force taking into account conjugation fields of the stresses and deformations occurring in elastic cartilage and in synovial fluid obtained by virtue of theory of elasticity and fluid mechanics can be considered as the novely of this paper. Analytical solutions for he values of capacity forces allow easy numerical calculations, which may be very useful for medical diagnosis.
12
Content available remote Numerical view of pressure, capacity and compressive stress in human hip joint gap
Wierzcholski K.Ch.
Tribologia
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2002
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nr 2
765-777
EN
Numerical calculations of carrying capacity in human hip joint for synovial unsymmetrical fluid flow are presented in this paper. Following assumptions are taking into account: stationary, isothermal and incompressible synovial unsymmetrical non Newtonian fluid flow, rotational motion of bone head, squeezing of synovial fluid in changeable joint gap height, and constant synovial fluid density. Reynolds equations and capacity forces are presented in spherical co-ordinates. A new results obtained in this paper are numerical performances for pressure distribution and capacity calculated from surface integrals in spherical co-ordinates. Capacity formulae contain not only changeable height of bearing gap but also unsymmetrical flow of synovial fluid. Obtained in present paper numerical values may be very useful for medical diagnosis.
PL
W niniejszej pracy przedstawione zostały obliczenia numeryczne siły nośnej biodra człowieka dla niesymetrycznego rzeczywistego przepływu cieczy synowialnej w szczelinie stawu. Przyjęto następujące założenia: przepływ ustalony cieczy synowialnej, izotermiczny i nieściśliwy przepływ nienewtonowskiej cieczy smarującej, smarowanie wywołane ruchem obrotowym oraz poprzez wyciskanie w szczelinie, a także przyjęto stalą wartość gęstości cieczy synowialnej. W pracy posłużono się wyprowadzonym wcześniej równaniem Reynoldsa we współrzędnych sferycznych zarówno dla ruchu obrotowego, jak i dla wyciskania cieczy synowialnej przy uwzględnieniu specyficznych geometrycznych i fizycznych warunków panujących w szczelinie stawu biodrowego. Nowymi wynikami uzyskanymi w niniejszej pracy są numeryczne wartości rozkładu ciśnienia i siły nośnej. W obliczeniach numerycznych została uwzględniona zmienna wysokość szczeliny stawu biodrowego przy mimośrodowym usytuowaniu głowy kości względem chrząstki, a także przepływ niesymetryczny mazi stawowej. Uzyskane w niniejszej pracy wartości numeryczne ciśnienia, siły nośnej i naprężeń ściskających są przydatne w diagnostyce lekarskiej, a także dostarczają nowych propozycji rozwiązań tribologicznych współczesnej technice w budowie maszyn.
13
Content available remote Axisymmetrical flow of synovial fluid between curvilinear bone surfaces in human joints
Wierzcholski K. Ch.
Acta of Bioengineering and Biomechanics
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2000
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Vol. 2, nr 1
29-46
EN
Bone and cartilage co-operate in human joint. The gap between their surfaces is filled with synovial fluid. In this case, the solution of the lubrication problem should be based on actual, various geometry of co-operating surfaces of human joint. In this paper we consider a symmetrical flow of synovial fluid between spherical, hyperbolic and parabolic bone surfaces in human joint. In order to study the symmetrical flow of synovial fluid in joint gap, we obtain velocity components and hydrodynamic pressure distributions in final, dimensionless form.
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