Marek Lis

A general form of the mathematical model for the analysis of transient states of complex electro-mechanical systems with distributed parameters

In the paper a literature review concerning development and application of mathematical models for the analysis of transient states of complex electro-mechanical systems with distributed parameters is presented. Special attention is paid to real-life systems and to presentation of results of digital simulations. In the paper the assumptions for the analysis of transient states of complex electro-mechanical systems in the context of occurrence of vibrations in the rotation transmission system. A general form of the mathematical model for the analysis of transient states of electro-mechanical systems is given, which makes it possible to describe in the continuous form the system of rotation transmission for any of its components. The final form of the equations of the mathematical model, which makes it possible to carry out the digital simulations and to obtain the results as 3D planes that depict the vibrations in reference to time and to real fragments of rotation transmission chain for chosen quantities under examination, is presented.

Modelowanie matematyczne pracy generatorów indukcyjnych w złożonych układach energetycznych

In the paper a general mathematical model of an electric power set is presented. The set consists of induction generators, transformers and batteries of capacitors. On the basis of the abovementioned mathematical model the transient processes in the electric power set were analyzed for various operation states. Classical methods were applied in order to formulate the state differential equations. The results of computer simulation numerical calculations are presented as graphs. (Mathematical modeling work of induction generators in composite energy systems) Słowa kluczowe: zasada Hamiltona-Ostrogradskiego, Euler-Lagrange’a system, zespól elektryczny, transformator mocy

Development of a method to determine the dependencies of load moments and elastic moments on element parameters during the rolling process for dynamical states of a drive system for the rolling machine- roller table

The article presents general dependencies for the design of the load torque of a hot-rolling mill stand with respect to the rolling parameters. For the analysis of the electromechanical system a computer-aided model of an induction asynchronous motor taking into account iron losses has been developed. A simplified version of the mathematical model of rolling for a single mill stand has been assumed. The calculation results have been presented as time dependencies. On the basis of the calculation results the characteristics of the rolling process with respect to the maximum values of the elastic moments on motor clutches and the clutch coupling the mill stand on the thickness of the rolled component as well as the dependency of the maximum elastic moments on the connections as well as the dependency of the average value of currents of mill stand stator on thickens of the rolled product are presented.

Mathematical model for analysis of dynamical states of a drive system containing rolling mill and roller table including the selected parameters of a rolling process

In the paper the structure of the electromechanical system containing a rolling mill and a roller table is presented. A two-mass system is under consideration. The second type Lagranges equation is used in order to formulate the equations of the abovementioned drive system including the electrical motor of a rolling mill and the electrical motors of a roller table as well as the mechanical system with its elasticity and variable masses of the rolled element and the transported element. The temperature dependency of a specific gravity and a deformation factor for a detail is taken into account. The transformation of mathematical model given in general form into computational equations was carried out. Moreover, the simulation of the exemplary dynamical states were made. The constructional-exploitative parameters of rolling mill - roller table set were taken into account. The results of simulation are presented as graphs of time changes of the selected variables.

Mathematical model of electric drive for rolling mill

In the paper the analysis of electromechanical processes in drive system for rolling mill with rigid torque transmission is presented. The abovementioned drive system, that bases on lumped parameters, consists of two high-power induction motors driving the rolls of rolling mill. The method based on the modification of Hamiltons principle was used in order to formulate the state differential equations. The numerical simulations of rolling-mill operation are made for three examples. The results are presented as graphs. Streszczenie. W pracy poddano analizie procesy elektromechaniczne w ukladzie napedowym walcarki o sztywnej transmisji ruchu. Badany uklad sklada sie z dwoch silnikow indukcyjnych duzej mocy, ktore napedzają cylindry walcarki. System rozpatruje sie jako uklad o parametrach skupionych. Dla formowania rozniczkowych rownan stanu wykorzystano metode, ktora bazuje na modyfikacji zasady Hamiltona. Przeprowadzono symulacje numeryczne pracy ukladu walcarki dla trzech przypadkow obliczeniowych. Wyniki przedstawiono w postaci graficznej (Model matematyczny napedu elektrycznego walcarki).

A mathematical model of a single-mass electromechanical system taking into account the temperature effect on system parameters on the example of mill stand

In the paper a general form of a mechanical system of a single mill stand cooperating with a rolling transportation line with electro-rolls is presented. The dependencies of the influence of temperature on Young elasticity modulus and the dependencies of steel density on temperature of components being transported, as well as the dependencies of the plasticity of the transported piece of metal on temperature. A generalized mathematical model of a single-mass mechanical system is formulated. The generalized model has been transformed and supplemented with the relationships influencing the values of forces occurring in the rotation transmission system that result from the dependencies of the transported material on temperature.