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1
Sprężystoplastyczny kontakt toczny z materiałami gradientowymi
Myśliński A., Chudzikiewicz A.
Prace Naukowe Politechniki Warszawskiej. Mechanika
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2015
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z. 267
19--24
PL
Praca poświęcona jest numerycznemu wyznaczeniu maksymalnego naprężenia na brzegu kontaktu w zagadnieniu kontaktu tocznego. Naprężenie to powoduje szybkie zużycie powierzchni znajdujących się w kontakcie. Chociaż zagadnienie kontaktowe najczęściej rozważane jest jako sprężyste uważa się, że przyczyny zużycia powierzchni kontaktowych powodowane są pojawiającymi się odkształceniami plastycznymi. Badania eksperymentalne oraz symulacje numeryczne wskazują, że pokrycie powierzchni w kontakcie warstwą materiału gradientowego może zredukować kontaktowe naprężenia mechaniczne i cieplne. W pracy zostanie rozważone zagadnienie kontaktu tocznego pomiędzy sprężysto plastycznym ciałem a sztywnym kołem przy założeniu, że jedna z powierzchni jest pokryta materiałem gradientowym, którego własności zmieniają się wraz z jego grubością. Zjawisko kontaktu obejmujące tarcie i przepływ ciepła generowanego przez tarcie jest opisane sprzężonym układem równań sprężysto-plastycznego oraz przewodnictwo cieplnego. Pół-gładka metoda Newtona jest wykorzystana jako metoda obliczeniowa. Rozkłady temperatury i naprężenia na brzegu kontaktu są wyznaczone i przedyskutowane.
EN
The determination of maximal contact stress generating the rolling contact fatigue is one of the main goals in modeling wheel-rail dynamics. This damaging process is linked to plasticity usually neglected in wheel-rail contact models. Numerous laboratory and numerical experiments indicate that the use of a coating graded material layer attached to the conventional steel body can reduce the magnitude of contact and/or thermal stresses. Therefore in this paper we solve numerically the wheel-rail contact problem assuming the existence of a small layer on the rail. The mechanical and thermal properties are changing with its depth. The contact problem includes friction, frictional heat generation as well as heat transfer across the contact surface and wear. This contact problem is governed by the coupled elastoplatic and heat conductive equations. Temperature and stress distributions on the contact boundary are provided and discussed.
2
Content available Thermoelastic wheel-rail contact problem for a multi-layer structure
Chudzikiewicz A., Myśliński A.
Vibrations in Physical Systems
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2014
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Vol. 26
41--48
EN
Wheel-rail thermoelastic contact problem is analysed and numerically solved in the paper. The surface of the rail is assumed to consist from layers having distinct constant material parameters and a functionally graded material layer between. Thermal and mechanical properties of the graded layer are dependent on its depth rather than constant as it is considered in the literature. Numerous laboratory experiments indicate that graded materials layers or coatings covering the conventional steel body can reduce the magnitude of contact and/or thermal stresses as well as the noise and the rolling contact fatigue. The contact phenomenon includes friction as well as frictional heat generation and wear. Quasistatic numerical approach is used to solve numerically this contact problem. Numerical results are provided and discussed.
3
Modelowanie przepływu ciepła w procesach szlifowania powierzchni roboczych narzędzi do kształtowania plastycznego
Moszczyński L., Myśliński A.
Prace Naukowe Politechniki Warszawskiej. Mechanika
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2013
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z. 253
129--134
PL
W pracy zagadnienie przepływu ciepła w procesie szlifowania powierzchni rozważono jako zagadnienie dyfuzji i konwekcji opisane parabolicznym równaniem różniczkowym zamiast złożonym układem sprzężonym równań hiperboliczno-parabolicznych. Podano rozwiązania zagadnienia parabolicznego w postaci całkowej opisujące rozkład temperatury w strefie kontaktu między powierzchniami. Do wyznaczenia wartości całek zaproponowano nową metodę symulacji polegającą na naprzemiennym (ang. staggered) całkowaniu w czasie zamiast standardowych algorytmów znanych z literatury.
EN
In the paper the heat transfer problem during the surface grinding process has been considered as the diffusion and convection problem governed by a parabolic equation rather than by complex coupled system of hyperbolic and parabolic equations. The sultions to the parabolic problem in the integral form describing the temperature distribution in the contact zone between the surfaces have been provided. In order to calculate the values of these integrals numerically new simulation method based on staggered integration in time has been proposed rather than standards algorithm from the literature.
4
Content available remote Rolling contact problems with nonhomogeneous materials
Chudzikiewicz A., Myśliński A.
Vibrations in Physical Systems
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2012
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Vol. 25
103--108
EN
Numerous laboratory experiments indicate that graded materials layers or coatings covering the conventional steel body can reduce the magnitude of contact and/or thermal stresses as well as the noise and the rolling contact fatigue. The paper is concerned with the numerical solution of the wheel-rail elastic contact problem assuming that the surface of the rail consists from layers having distinct constant material parameters and a functionally graded material layer between them which mechanical properties are dependent on its depth. The contact phenomenon includes friction as well as wear. Quasistatic numerical approach is used to solve numerically this problem. Numerical results are provided and discussed.
5
Content available Topology optimization of quasistatic contact problems
Myśliński A.
International Journal of Applied Mathematics and Computer Science
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2012
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Vol. 22, no. 2
269-280
EN
This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.
6
Content available remote Radial basis function level set method for structural optimization
Myśliński A.
Control and Cybernetics
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2010
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Vol. 39, no 3
627-645
EN
This paper is concerned with simultaneous topology and shape optimization of elastic contact problems. The structural optimization problem for an elastic contact problem consists in finding such topology as well as such shape of the boundary of the domain occupied by the body that the normal contact stress is minimized. Shape and topological derivatives formulae of the cost functional obtained using material derivative and asymptotic expansion methods, respectively, are recalled. These derivatives are employed to formulate the necessary optimality condition and to calculate a descent direction in a numerical algorithm. Level set based method is employed in numerical algorithm for tracking the evolution of the domain boundary on a fixed mesh and finding an optimal domain. In order to increase the efficiency of the level set based numerical algorithm, the radial basis function approach is used to solve the equation governing domain boundary evolution. Numerical examples are provided and discussed.
7
Content available Quasistatic approach to wheel - rail contact problems with elastic graded materials
Chudzikiewicz A., Myśliński A.
Archives of Transport
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2010
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Vol. 22, iss. 1
43-59
EN
Graded materials are generally two - phase composities with continously varying volume fraction. Numerous experiments indicate that used as the coatings attached to the conventional steel body and interfacial zones they can reduce the magnitude of mechanically and/or thermally induced stresses. In this paper the wheel - rail contact problem including friction and wear is considered. The rail is assumed to be covered with a coating. The mechanical properties of the coating material depend on its distance to the rail surface and are governed by power law. In the paper quasistatic approach to solve numerically this rolling contact problem is employed. This approach is based on the assumption that for the observer moving with the rolling wheel the displacement of the rail is independent on time. Finite element method is used as a discretization method. Numerical results are provided and discussed.
PL
Materiały gradientowe są w ogólnym przypadku dwufazowymi kompozytami, których fazy zmieniają się w sposób ciągły. Liczne eksperymenty badawcze wskazują, że materiały te wykorzystane jako pokrycie konstrukcji wykonanych ze stali lub jako warstwy pośrednie pomiędzy powierzchniami w kontakcie redukują naprężenia mechaniczne lub termiczne. W artykule rozważa się zagadnienie kontaktu tocznego koło - szyna ze zjawiskiem tarcia oraz zużycia. Zakłada się, że szyna jest pokryta sprężystym materiałem gradientowym. Własności mechaniczne tego materiału zależą od jego odległości od powierzchni szyny i opisane są funkcją potęgową. W pracy wykorzystuje się podejście quasistatyczne do numerycznego rozwiązania zagadnienia kontaktu tocznego. Podejście to opiera się na założeniu, że dla obserwatora poruszającego się wraz z toczącym się kołem przemieszczenie szyny nie zależy od czasu. Metoda elementu skończonego jest wykorzystana jako metoda dyskretyzacji. Przedstawiono i przedyskutowano wyniki eksperymentów numerycznych.
8
Content available remote On thermoviscoelastic wheel-rail contact problems
Chudzikiewicz A., Myśliński A.
Vibrations in Physical Systems
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2004
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Vol. 21
119--122
EN
This paper is concerned with the numerical solution of wheel - rail rolling contact problems. The unilateral dynamic contact problem between a viscoelastic body and a rigid foundation is considered. The contact with Coulomb friction law occurs at a portion of the boundary of the body. The contact condition is described in velocities. The friction coefficient is assumed to be bounded and suitable small. A frictional heat generation and heat transfer across the contact surface as well as Archard's law of wear in contact zone are assumed. The equlibrium state of this contact problem is described by the coupled hyperbolic variational inequality of the second order and a parabolic equation. To solve numerically this contact problem we will decouple it into mechanical and thermal parts. Finite difference and finite element methods are used to discretize the contact problem. The Augmented Lagrangian technique combined with the active set method are employed to solve the discretized contact problem. Numerical examples are provided.
9
Content available remote Shape optimization of thermoviscoelastic contact problems
Myśliński A.
Control and Cybernetics
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2003
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Vol. 32, no 3
611-627
EN
This paper is concerned with a shape optimization problem of a viscoelastic body in unilateral dynamic contact with a rigid foundation. The contact with Coulomb friction is assumed to occur at a portion of the boundary of the body. The nonpenetration condition is described in terms of velocities. The thermal deformation is taken into account. Using the material derivative method as well as the results concerning the regularity of solutions to dynamic variational thermoviscoelastic problem the directional derivative of the cost functional is calculated. A necessary optimality condition is formulated.
10
Content available Fictitious domain approach for numerical solution of elliptic problems
Myśliński A., Żochowski A.
Control and Cybernetics
|
2000
|
Vol. 29, no 1
305-323
EN
In the paper the numerical aspects of the fictitious domain method for elliptic problems are considered. Theoretical results concerning the equivalence of original and embedded domain elliptic problems as well as the convergence of discretization are recalled. The dependence of accuracy of numerical solutions to elliptic problems on the approximation of boundary conditions as well as on the order of shape functions are disscussed. The numerical examples are provided.
11
Content available remote On Thermoelastic Rolling Contact Problems in Wheel-Rail Systems
Chudzikiewicz A., Myśliński A.
Machine Dynamics Problems
|
1998
|
Vol. 20
91-100
EN
The paper deals with the numerical solution of a class of rolling contact problems with the temperature fields as an additional component. The wheel-rail system serves as an example. We consider contact with Coulomb friction between the rigid wheel and an elastic rail fixed to a rigid fundation. We assume a frictional heat generation and heat transfer through the contact area. In the paper we propose a quasistatic approach to solve this contact problem. The system is described by an elliptic variational inequality and a parabolic equation. To solve this problem numerically we will decouple it into mechanical and thermal parts. Numerical examples showing the influence of the temperature field on the normal contact force distribution and the length of the contact zone are provided.
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