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（挤压行业的工具设计师和制造商）开发了一种名为VOS（可视化优化软件）的软件工具。该软件的最初目的是帮助挤压厂根据他们正在挤压的合金和型材优化其挤压机的生产率。虽然最初的目的是使用VOS来帮助优化和预测生产力，但现实是VOS最终更像是一个包含历史信息的数据库。缺乏的是对挤出变量与所需压力和出口温度之间关系的定量认识。Castool已经开始从VOS中收集一些更有用的东西，这些东西将告诉挤出机他们对型材，模具，钢坯和压力机设置的任何组合所期望的生产率，但是仍然缺乏这些变量之间关系的定量知识。最初，Castool打算将真实的压力数据（来自Brampton的Almag）转换为温度和速度，但这是非常近似的，不太可能有很大的用处。Castool打算继续这种压力到温度的转换，但很难从Almag获得准确的信息。Castool现在想做的是开发一个简单、快速、几乎实时的参数化模型，包括挤压比、坯料温度、容器温度等变量，并预测最大速度、模压和挤压出口温度。本研究的重点将是开发一个数学模型，以准确预测一系列情况下的温度和挤压负荷，以便在模具温度、挤压比、冲压速度和坯料温度之间建立与挤出温度和挤出过程中的压力之间的相关性

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