ANALYSIS OF MOVEMENT OF EULER-BERNOULLI BEAM SUBJECTED TO AN IMPACT AT THE BEAM CENTER AFTER FREE DROPPING
Bruno Conti Franco1; Wang Chong2
1 Ibirubá Campus, Federal Institute of Rio Grande do Sul; 2 Applied Mechanics Group, Graduate Program in Engineering, Federal University of Pampa
Baixar PDF doi:10.20906/CPS/CILAMCE2015-0047
Resumo
Brazil is one of major producers of iron ore in the world. After the ore is explored, the first process of the production is to triturate iron ore. A rods mill is most common grinding equipment. These machines are of high maintenance costs due to constant fracture in the milling bars caused by the chock when the bar drops and impact with ores. To reduce such costs, mathematical and mechanical analysis for the fracture is necessary. As concerning crack propagation induced by the impact, the analysis is complex and difficult to be resolved. The numerical method most widely used to study the dynamic crack propagation is the Finite Element Method. Until now main commercial software such as ANSYS, ABAQUES and others, besides being expensive and required a lot of training for the use, are unable to model dynamic crack propagation caused by impact. On the other hand the Finite Difference Method is a numerical method of simple and widely used in scientific research. The aim of this work is to develop algorithm of finite difference method in order to model the vibration of a rod mill bar subjected to an impact. This algorithm will be extended to analyze the crack dynamic propagation in future. Based on by Centered Finite Difference Method (CFDM), we has discretized the general movement equation of the Euler-Bernoulli beam with the consideration of initial and boundary conditions and obtained numerical solutions of displacement, bending moment and shear of the bar in terms of time. We also have carried out the same modeling by using on the software ANSYS LS. Comparing the results from the CFDM with the one from the ANSYS, we find no significant differences between them and confirm that the algorithm developed in this work is credible, which can be used for the analysis of the crack dynamic propagation in future.
Palavras-chave: chock; Euler-Bernoulli beam; numerical solution; Centered Finite Difference Method