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1

Analysis of the effect of inertial forces of the electrolyte flow on the ECM machining effects of curvilinear rotary surfaces

Sawicki Jerzy, Paczkowski Tomasz, Zdrojewski Jarosław

Archive of Mechanical Engineering

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2022

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LXIX, nr 4

645--666

EN

This paper presents an analysis of the impact of inertial forces of the electrolyte flow in an interelectrode gap on the effects of ECM process of curvilinear rotary surfaces. Considering a laminar flow in the interelectrode gap, the equations of the flow of the mixture of electrolyte and hydrogen in the curvilinear orthogonal coordinate system have been defined. Two classes of equations of motion have been formulated, which differ in the estimates referred to the components of velocity and pressure, and which were analytically solved using the method of perturbation. Using the machined surface shape evolution equation, the energy equation, and the analytical solutions for velocity and pressure, the ECM-characteristic distributions have been determined: of mean velocity, pressure, mean temperature, current density, gas phase concentration, the gap height after the set machining time for the case when there is no influence of inertial forces, the effect of centrifugal forces and, at the same time, centrifugal and longitudinal inertial forces.

2

Magnetohydrodynamic flow of viscous fluid in a slot between fixed surfaces of revolution

Sawicki J.

Polish Maritime Research

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2017

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nr 3

78--85

EN

The paper considers stationary magnetohydrodynamic flow of viscous fluid in the slot between fixed curvilinear surfaces of revolution exposed to azimuthal magnetic field. To solve the problem, the equations of boundary layer in the curvilinear coordinate system. x,θ,y , were applied. The equations of the boundary layer were solved analytically with the use of the small-parameter method. The formulas determine the field of velocity and pressure.

3

Ferromagnetic flow of viscous fluid in a slot between fixed surfaces of revolution

Sawicki J.

Polish Maritime Research

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2016

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nr 4

99--104

EN

In this paper the steady laminar flow of viscous incompressible ferromagnetic fluid is considered in a slot between fixed surfaces of revolution having a common axis of symmetry. The boundary layer ferromagnetic equations for axial symmetry are expressed in terms of the intrinsic curvilinear orthogonal coordinate system x, θ ,y.The method of perturbation is used to solve the boundary layer equations. As a result, the formulae defining such parameters of the flow as the velocity components vx, vy, and the pressure , were obtained.

4

Zastosowania metody perturbacji do oszacowania wartości własnych układów dynamicznych o parametrach niepewnych

Liszka T.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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2003

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z. 101

231-238

PL

Metoda perturbacji pozwala na szybkie oszacowanie wartości własnych w układach poddanych zaburzeniom. Uogólniając tę metodę na liczby przedziałowe, można wykorzystać ją do oszacowania wszystkich wartości własnych przedziałowego zadania własnego [A]x = lambda[B]x, a także zadania własnego drugiego stopnia lambda do potęgi 2[A]x + lambda[B]x+[C]x=0. W teorii konstrukcji tę metodę możemy wykorzystać do oszacowania częstości drgań własnych wielowymiarowych układów dynamicznych o parametrach niepewnych oraz częstości drgań swobodnych w układach z tłumieniem.

EN

Method of perturbation makes possible quick estimation of eignvalues of systems under disturbances. Extension of this method over interval numbers gives possibility to estimate all eigenvalues of interval generalized eigenvalue problem [A]x = lambda[B]x and second degree eigenvalue problem lambda power 2 [A]x + lambda[B]x + [C]x = 0. In theory of structures this method can be used for eigenfrequency estimation of multidimensional dynamic systems with interval parameters and frequency of free vibration in systems with damping.