A Novel Mathematical Formulation for Density-based Topology Optimization Method Considering Multi-Axis Machining Constraint

TL;DR

This paper introduces a new density-based topology optimization method that incorporates multi-axis machining constraints using a Heaviside-based mathematical formulation, enabling the design of manufacturable freeform structures.

Contribution

The paper presents a novel mathematical formulation for topology optimization that explicitly considers multi-axis machining restrictions, extending applicability to 5-axis and 2.5D milling processes.

Findings

Successfully applied to compliance minimization problems

Demonstrated effectiveness through 2D and 3D numerical examples

Enhanced control of void region sizes with filter techniques

Abstract

This paper proposes a novel density-based method for structural design considering restrictions of multi-axis machining processes. A new mathematical formulation based on Heaviside function is presented to transform the design field into a geometry which can be manufactured by multi-axis machining process. The formulation is developed for 5-axis machining, which can be also applied to 2.5D milling restriction. The filter techniques are incorporated to effectively control the minimum size of void region. The proposed method is demonstrated by solving the compliance minimization problem for different machinable freeform designs. Several two and three-dimensional numerical examples are presented and discussed in detail.