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1

Holonomicity analysis of electromechanical system on the example of simple switched reluctance motor

Wciślik M., Suchenia K.

Computer Applications in Electrical Engineering

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2015

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Vol. 13

330--339

EN

The paper deals with a single-phase reluctance motor used to test the motion equations of an electromechanical system. The identification of the motor electric parameters as a function of the rotation angle of the rotor was carried out using AC 50 Hz voltage source. A mechanical part of the system was designed as a physical pendulum containing the motor rotor and a metal bar mounted on the rotor axis. The parameters of the mechanical part were measured during the pendulum oscillations. The work presents the characteristics and motion equation parameters of the motor dynamics. The reluctance motor motion equation does not fullfil the power balance. The parameters of the motion equations obtained from the experiment and from the second order Lagrange’a equations are compared. The derivation of motion equation, together with a discussion of holonomicity of electromechanical systems is also presented.

2

Dynamic model of the drum of the washing machine SAMSUNG WF0804

Buśkiewicz J., Pittner G.

Vibrations in Physical Systems

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2012

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Vol. 25

89--95

EN

The paper deals with vibrations of the washing machine Samsung WF0804. The motion equations of the washing machine drum were derived. The vibration of the drum caused by the unbalanced mass was examined. The presented analysis will make up the basis for experimental studies aimed at validating the theoretical model and finding the most effective way of balancing of the drum vibration.

3

Numerical and experimental vibration analysis of domestic washing machine drum

Buśkiewicz J., Pittner G., Barczewski R.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 3

765-777

EN

The vibration of a drum of the washing machine Samsung WF0804 caused by the unbalanced mass attached to the rotating unit was examined. The motion equations of the washing machine drum were derived. The stand for experimental measurement was presented. The numerical results were compared with experimental measurements. General conclusions were mode. The analysis will make up the basis for experimental studies aimed at finding the most effective way of balancing drum vibrations.

4

Oil aging influence on the slide journal bearing lubrication

Miszczak A., Sikora G.

Journal of KONES

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2010

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Vol. 17, No. 2

327-333

EN

In this study authors solve the fundamental set of equations of the hydrodynamic theory of lubrication, namely are: the continuity equation, conservation of momentum and conservation of energy for the case of stationary slide bearings lubrication with a thixotropic lubricant. Adoption of assumption of steady flow loads in the considered phenomenon to the changes absence of the flow parameters in a short time period i.e. in one hour. In the constitutive equation is assumed that the stress tensor is a function of strain tensor, dynamic viscosity of oil and hydrodynamic pressure. Dynamic viscosity decreases in a long period of time of workf. ex. after 10 000 by 20 000 kilometres. In a thin layer of oil film, density and thermal conductivity was assumed to be constant. Authors define the lubricant's dynamic viscosity as a product of viscosity changes in temperature, pressure and time eta = eta(T).eta(p).eta(t). In the analysis of hydrodynamic lubrication, Authors consider a Journal bearing of finite length, with the smooth sleeve with a full circumferential angle. Fundamental equations are written in dimensionless form and estimated according to the theory of a thin boundary layer. Prepared in this way equations of motion can be solved by various methods. Authors propose to solve the motion equations with a method of small parameter. The small parameter method we define the unknown functions in a form of uniformly convergent power series expanded in the neighbourhood of the small parameters. In most used cases, absolute value of the small parameter is less than unity. These functions are substituted into simultaneous fundamental equations, then the series are multiplied using Cauchy's method. Comparing coefficients with the same exponents of small parameter, simultaneous set of differential equation is acquired, from which next approximations of unknown functions are appointed. With so obtained equations, the equation that allows assigning hydrodynamic pressure and hydrodynamic pressure corrections resulting from taking into account the impact of pressure, temperature and ageing in viscosity changes of the lubricant successively can be assigned.

5

Introduction to dynamic modeling of rack stackers for high-bay warehouse

Hajdu S., Tiba Z.

Zeszyty Naukowe Politechniki Poznańskiej. Budowa Maszyn i Zarządzanie Produkcją

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2009

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Nr 10

15-23

EN

Results of this paper indicated that there are many ways of modelling the planar vibration of single mast rack stacker machines, which approximate features of a real structure with different accuracy. These models are usable well for control examinations and for linear control design. However, by the determination of the model, besides the accuracy, the model shouldn't be too complicated and calculation demanding.

6

Analiza dynamiki ładowarki czołowej dla fazy obrotu czerpaka w pryzmie ośrodka ziarnistego

Boryga M., Graboś A.

Inżynieria Rolnicza

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2005

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R. 9, nr 8

39--47

PL

Przedstawiono sposób modelowania oraz wyniki komputerowej symulacji ruchu ładowarki czołowej T-426 z uwzględnieniem obciążeń zewnętrznych ogniwa roboczego (czerpaka). Siły i momenty sił bezwładności obliczono wykorzystując równania Newtona-Eulera. Siły i momenty sił oddziaływań członów obliczono z równań równowagi sił i momentów sił działających na każdy wydzielony człon łańcucha kinematycznego ładowarki. Dla sekwencji obrotu czerpaka w pryzmie ośrodka ziarnistego wyznaczono przebiegi zmian w czasie wybranych kinematycznych i dynamicznych charakterystyk ruchu.

EN

Paper described the modeling procedure and computer simulation results of the T-426 front loader motion, considering external loads of the working element (bucket). The forces and inertial force moments were calculated using the Newton–Euler equation. Forces and moments of elements’ reactions were calculated on the basis of balance equations of the forces and moments acting on each separated element in the kinematic chain of loader. For the sequences of bucket turn into granular medium heap the time dependent changes of selected kinematic and dynamic motion characteristics were determined.

7

Energetyczne kryterium poprawności równań ruchu i weryfikacja ich rozwiązań w zagadnieniach dynamiki maszyn

Strzałko J.

Zeszyty Naukowe. Rozprawy Naukowe / Politechnika Łódzka

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1998

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Z. 249

1-155

PL

W pracy przedstawiono propozycję kontrolowania poprawności numerycznych rozwiązań równań ruchu dla układów mechanicznych zachowawczych i niezachowawczych, o stałej i zmiennej masie, we współrzędnych uogólnionych i quasi-współrzędnych. Proponowana metoda polega na sprawdzaniu poziomu energii w analizowanym układzie. Zastosowanie metody weryfikacji procesu rozwiązania w obliczeniach numerycznych polega na uzupełnieniu równań ruchu dodatkowym równaniem różniczkowym opisującym zmiany całkowitej energii i śledzeniu przebiegu bilansu energii dostarczanej do układu, produkowanej i rozpraszanej w układzie oraz oddawanej do otoczenia. Równanie bilansu zmian energii zapisywane jest za pomocą pewnej funkcji, której pochodna spełnia warunek C(t) = 0. Wskaźnikiem dokładności rozwiązania jest przebieg zmian funkcji C(t), która winna zachowywać stałą wartość w czasie. Podany jest sposób wyprowadzenia funkcji C(t] dla układów holonomicznych opisanych równaniami Lagrange'a Il-go rodzaju, dla układów z więzami kinematycznymi opisanych równaniami Lagrange'a Il-go rodzaju z mnożnikami Lagrange'a, dla układów o zmiennej masie i konfiguracji opisanych równaniami Nielsena oraz dla układów analizowanych przy wykorzystaniu równań Boltzmanna-Hamela. Konkretne przykłady zastosowań dotyczą modeli maszyn roboczych.

EN

In this work the suggestion to control the correctness of numerical solutions of motion equations for any mechanical systems (conservative and non-conservative, time varying and non-varying mass, with generalized coordinates and quasi coordinates) has been presented. The application examples refer first of all to machine models: cranes, excavators, car lifts, etc. The presented method of the correctness control of motion equations is the development of Kane and Levinson conception. The proposed method is based on the testing of the energy level in the analyzed systems. The application of solution process' verification method in numerical calculation is based on completing the motion equation by the additional differential equation which would describe the changes in total energy and would follow the energy balance process (the energy that is supplied, produced and diffused to the system, or emitted to surroundings). The balance equation of energy changes is presented by means of the function C(t) the derivative of which follows the condition C(t) = 0. The accuracy solution indicator is the process of changes in C(t) function the value of which should remain constant in time. All changes in the function during equation integration with 'step by step' method signal the solution error. These errors may result from errors in algorithm (formally incorrect or too simplified equation), in program (divergent procedures) or in data (badly selected integration step, etc.). In this thesis the way to derive the C(t) function - necessary to balance the energy has been presented for holonomic system described by Lagrange equation of the second kind for systems with kinematical constraints described by Lagrange equation of the second kind Lagrange multipliers, for systems with varying mass and configuration described by Nielsen equation and for systems analyzed when applying Boltzmann-Hamel equation.