Mathematical Tools for Building Setup-Maps to Optimally Locate Each Casting in a Machining Fixture: Case Study With Minimum Wall Thickness

Abstract

A novel combination of mathematical tools underlies a method to lower cost of the first fixture-setup required to finish-machine surfaces on large castings or weldments where components will be attached. The computer-aided design (CAD) model, tolerance specifications, process plan, and design of the fixture, including configuration of the locators, are given. The math tools are used to build algorithms for a digital model, the Setup-Map© (S-Map©), that predictively captures all allowable locator adjustments needed to position and orient each part in its fixture before machining begins. The S-Map in this paper is generated for a case-study design, a cast valve-body with two to-be-machined (TBM) features, but the math tools are general so the same methods could be applied directly, or easily adapted, to other designs and fixture schemes. Geometric variations at the TBM features are represented with Tolerance-Maps© (T-Maps©) that are constructed with higher-dimensional linear half-spaces. The T-Maps are shifted to be aligned with, and offset from, one-sided simulated envelopes derived from scans of corresponding features on each casting. Linear programming identifies the setup-point that is chosen to most evenly distribute the required amount of machining over all the TBM features. Inverse kinematics of parallel robots is used to convert the setup-point to custom settings at the fixture locators for each casting. The half-space construction enables the identification of TBM features that have insufficient material and require repair. The algorithms were validated with 13 castings.