Design of porthole aluminium extrusion dies through mathematical formulation

TL;DR

This paper presents a mathematical formulation for designing porthole aluminium extrusion dies by analyzing extensive geometric data and applying regression techniques, aiming to encapsulate design experience into a predictive model.

Contribution

It introduces a statistical regression-based mathematical model for porthole die design, validated on a typical four-cavity die case, enabling generalized application and further research.

Findings

Regression analysis effectively models die geometries.

Discarding non-significant variables improves model accuracy.

The model summarizes extensive design experience into a single expression.

Abstract

A mathematical approach to solve the porthole die design problem is achieved by statistical analysis of a large amount of geometric data of successful porthole die designs. Linear and logarithmic regression are used to analyse geometrical data of 596 different ports from 88 first trial dies. Non-significant variables or high correlated variables are discarded according to knowledge of the extrusion process and statistical criteria. This paper focuses on a validation model for a typical case of porthole dies: four cavities and four ports per cavity dies. This mathematical formulation is a way of summarizing in a single expression the experience accumulated in a large number of designs over time. A broad way of research is open to generalise this model or extend it to other types of porthole dies.