Contribution to new calculations of preheating and differentiation temperatures using Lagrange interpolation

Abstract

This paper presents a chronology of how the critical cooling time and preheating temperature in welding have been determined so far. The author of this paper introduces a new approach in calculating preheating temperature using prior art experience as well as his long-term research results in the field of welding. Earlier solutions were based on Rosenthal's 2D and 3D model for calculating the critical cooling time and the corresponding preheating temperature and the improved expressions used by the British Standard. This paper uses the necessary experience in thermal and the corresponding disciplines of mathematics. Problems that occur and prevent efficient obtaining of solvable expressions in a simple and elementary way, the author of this paper solves in a completely new and inventive way.