Mathematical modeling of the aluminum extrusion process to support the development of a virtual optimization software package

在过去的几年里，Castool(一家挤压行业的工具设计和制造商)开发了一种名为Vos(可视化优化软件)的软件工具。该软件最初的目的是帮助挤压工厂根据他们正在挤压的合金和型材来优化其挤出机的生产率。虽然最初的目的是使用VOS来帮助优化和预测生产率，但现实是，VOS最终更像是一个包含历史信息的模具数据库。关于挤压变量与所需压力和出口温度之间关系的定量知识才是唯一的。Castool已经开始从VOS中整合一些更有用的东西，这些VOS将告诉挤出机他们可以预期的任何型材、模具、坯料和印刷机设置的组合的生产率，但是仍然缺乏关于这些变量之间关系的定量知识。最初，Castool打算将实际的压力数据(来自布兰普顿的Almag)转换为温度和速度，但这是如此近似，不太可能有很大的用处。Castool打算继续这种从压力到温度的转换，但很难从ALMAG获得好的信息。Castool现在想做的是开发一个简单、快速、几乎实时的参数模型，包括变量，挤压比、坯料温度、容器温度，并预测最大速度以及模压和挤压出口温度。本研究的重点是建立一个数学模型，在一定范围内准确地预测温度和挤压载荷，以便建立模具温度、挤压比、挤压速度和坯料温度之间的关系

Over the last couple of years, Castool (a tool designer and manufacturer for the extrusion industry) havedeveloped a software tool called VOS (Visual Optimization Software). The original purpose for this softwarewas to assist extrusion plants in optimizing the productivity of their extruders based on the alloy and profilethey were extruding. Although the original intent was to use the VOS to help optimize and predictproductivity, the reality is that VOS has ended up more as a die database with historical information. What islacking is the quantitative knowledge of the relationship between the extrusion variables and the pressurerequired and exit temperature. Castool has started to put together something more useful from the VOS whichwill tell the extruder what productivity they can expect for any combination of profile, die, billet and pressset-up however the still lack quantitative knowledge on the relationship between these variables.Initially, Castool was going to convert real pressure data (from Almag in Brampton) into temperature andtherefore speed, but this is so approximate that it is unlikely to be of great use. Castool intend to continue thisconversion of pressure to temperature but had difficulties getting good information from Almag.What Castool would like to do now is develop a simple and fast, almost real-time, parametric models with thevariables, extrusion ratio, billet temperature, container temperature and predict maximum speed and diebearing and extrusion exit temperatures.The focus of this research will be to develop a mathematical model to accurately predict the temperature andextrusion load for a range of cases so that correlations between the tooling temperature, extrusion ratio, ramspeed and billet temperature can be made with respect to extrudate temperature upon exit and pressure during