Synthesis of Adequate Mathematical Description of Rolling Mill Motion

Abstract

Synthesis of adequate mathematical description of the main mechanical line of rolling mill are considered. The four-mass model with weightless elastic connections is chosen as mathematical model of dynamic system of the main mechanical line of the rolling mill. The problem was reduced to solution of integral equation of the first kind (to unsteady problem). The methods of obtaining of the steady solutions are suggested. Synthesis of the adequate mathematical descriptions with unitary model of external load are suggested. The metal rolling was executed with using of real experimental measurements as an example.

Inverse Problems for Dynamic Systems: Classification and Solution Methods

“…The function in Equation 2is presented approximately. In some cases is defined from experiment [4,5], in other cases this function represents the approxi-mation of the given function [12,15].…”

“…Other purposes in the solution of an inverse problem are not pursued. For example, in inverse problems [5,14] a ultimate goal is the obtaining of the adequate mathematical description of motion of dynamic system for the purposes of reception of the authentic forecast of motion. Any function from set of the possible…”

“…It is necessary to distinguish two opportunities: 1) function of initial data is obtained as a result of approximation of experimental measurements [4,5];…”

“…of initial data is obtained as a result of approximation some dependence which are given a priori g u [15]. In the first case the solution of an inverse problem can be used at synthesis of the adequate mathematical description of dynamic systems [4,5].…”

“…For the authentic forecast of motion of dynamic systems it is necessary to use the adequate mathematical description of physical process as an example [4,5]. One way to obtain such mathematical description is the solution of an inverse problems [4,5]. Besides, it is important that this description was steady against small changes of initial data of an inverse problem.…”