# Sensitivity Analysis and Filtering of Machinable Parts Using Density-Based Topology Optimization
## 1 Introduction
### Study Description and Novelty  
Density-based TO is the most popular method in commercial packages such as Altair Hyperworks suite [22], Ansys suite [23], Dassault Systemes suite [24], and PTC suite [25]. This manuscript analyzes the two main parameters involved in the TO process: the penalty and filter radius. This study aims to determine the best parameters for obtaining manufacturable results with minimal interpretation for three-axis machining. This research aims to assist designers in making informed decisions and saving time in the preprocessing and simulation phases.  
A wide range of values is considered for the mentioned parameters along with calculation times, discreteness, and machinability of the results. All these data are ordered and presented later in this study. It is important to note that other studies [1; 16; 26] make remarkable contributions in this area, but none of them are specifically oriented to a concrete manufacturing method and are often limited to a short set of values for the studied parameters. Other works [27; 28] concentrate on achieving these manufacturable parts by adding filters and additional constraints to the TO process, but a more direct application is sought in the present paper.  
The given text describes the development of a novel analysis tool that can assess the machinability of a part for a three-axis machine. This tool is later applied as a filter to automatically modify the non-extra-constrained part, making it more machinable and less interpretable. MatLab(r) R2023a is used for the ease of use of the scientific and designer communities and to allow the replication of the research results.  
The structure of the paper is organized as follows:  
* The initial section discusses the chosen parameter value criteria, along with the load case and material parameters of the main study case for the sensitivity analysis.
* Following that, the parameters used for analyzing the results are presented and explained, with particular emphasis on the measure of the discreteness and the evaluation of the machinability,
* Subsequently, the results of the 92 simulations are presented and analyzed, allowing conclusions related to the aim of the study to be obtained.
* The machining filter is presented and verified through different verification tests.
* Finally, the conclusions drawn from the study and potential avenues for future research are presented.  
In summary, novelty is given in two fields: the extensive sensitivity analysis of a 3D case and the machining analysis and filter. Regarding this last topic, this document includes a machining analysis tool that identifies whether an element is manufacturable via three-axis machining. It calculates the global machinability as a result, achieving a 100% fully machinable design. This analysis tool is used for the machining filter and the sensitivity analysis. Finally, a novel machining filter is presented in combination with the machining analysis tool. It takes into account the density threshold for displaying the elements and does not require big changes in the sensitivity analysis. These are differentiable points with respect to existing machining filters [27; 28; 29].