Method of estimating temperature distribution history

Abstract

A method is provided for estimating a temperature distribution history in the case of line-heating flat-plate steel by high frequency induction. The method of estimating the temperature distribution history includes a first step of measuring a history of temperature distribution that is generated when a test piece of sheet steel is spot-heated; a second step of analyzing an induction current distribution that is generated when the sheet steel is spot-heated; a third step of expressing the induction current distribution by an approximation equation of the initial induction current distribution at an initial temperature and temperature dependent correction factor of the initial induction current distribution, and identifying the initial induction current distribution and the temperature dependent correction factors based on the temperature distribution history and the induction current distribution; a fourth step of analyzing internal heat generation from the initial induction current distribution, the temperature dependent correction factor, and a temperature dependency of electrical resistivity of the sheet steel; and a fifth step of analyzing the temperature distribution history generated during the line heating by applying the internal heat generation to the sheet steel while the internal heat generation is being moved. According to the method, the temperature distribution history in the case where the flat-plate steel is line-heated by high frequency induction can be efficiently estimated at high precision.

The invention claimed is: 
     
       1. A method of estimating a temperature distribution history implemented by an apparatus for estimating temperature distribution history of heated sheet steel for forming three-dimensional curved surfaces, comprising:
 a first step of measuring, without electromagnetic analysis, a history of temperature distribution that is generated when a test piece of sheet steel is spot-heated by high-frequency induction; 
 a second step of obtaining an induction current distribution, which is generated when the sheet steel is spot-heated by the high-frequency induction, by using finite element analysis; 
 a third step of expressing the induction current distribution by an approximation equation of an initial induction current distribution at an initial temperature and temperature dependent correction factors of the initial induction current, wherein the initial induction current distribution and the temperature dependent correction factors are identified based on the temperature distribution history obtained in the first step and the induction current distribution obtained in the second step; 
 a fourth step of obtaining internal heat generation from the initial induction current distribution, the temperature dependent correction factors obtained in the third step, and a temperature dependency of electrical resistivity of the sheet steel; 
 a fifth step of obtaining the temperature distribution history generated during the line heating by the finite element analysis by applying the internal heat generation that is obtained in the fourth step to the sheet steel while the internal heat generation is being moved; and 
 automating forming of a three dimensional curved surface based on the temperature distribution history; 
 wherein said apparatus is a computer that includes a processor and a non-transitiory computer readable medium containing computer instructions for causing the processor to perform at least the second to fifth steps wherein: 
 in the third step, the induction current distribution I(r, z, T) is expressed by the following approximation equation (1) of the initial induction current distribution Io(r, z) at the initial temperature (To) and the temperature dependent correction factors w(T) of the initial induction current, and the initial induction current distribution Io(r, z) and the temperature dependent correction factors w(T) are identified based on the temperature distribution history obtained in the first step and the induction current distribution obtained in the second step,
     I ( r, z, T )= Io ( r, z ) w ( T )   (1)
 
 
 r z denoting the position of the sheet steel, and T denoting the tem erature of the sheet steel; and 
 in the fourth step, the internal heat generation W is obtained by the finite element analysis based on the following equation (2) from the initial induction current distribution Io(r, z) and the temperature dependent correction factor w(T) obtained in the third step and the temperature dependency R(T) of electrical resistivity of the sheet steel,
     W = Io ( r, z ) 2   w ( T ) 2   R ( T ).   (2)
 
 
 
     
     
       2. The method according to  claim 1 , wherein in the fifth step, the internal heat generation is applied to the sheet steel as the internal heat generation moves in a straight line or in a curve with respect to a main surface of the sheet steel. 
     
     
       3. The method according to  claim 2 , wherein in the fifth step, the internal heat generation is applied to the sheet steel as the internal heat generation moves at constant speed or at varying speed with respect to the sheet steel. 
     
     
       4. The method according to  claim 3 , wherein in the first step, the sheet steel is spot-heated by a high-frequency induction coil. 
     
     
       5. The method according to  claim 2 , wherein in the first step, the sheet steel is spot-heated by a high-frequency induction coil. 
     
     
       6. The method according to  claim 1 , wherein in the fifth step, the internal heat generation is applied to the sheet steel as the internal heat generation moves at constant speed or at varying speed with respect to the sheet steel. 
     
     
       7. The method according to  claim 6 , wherein in the first step, the sheet steel is spot-heated by a high-frequency induction coil. 
     
     
       8. The method according to  claim 1 , wherein in the first step, the sheet steel is spot-heated by a high-frequency induction coil.