A Bipartite Graph for Estimating Measurement Uncertainty on Five-Axis Machining Centres

Abstract

The essential source of errors in machining on five-axis milling centres are errors caused by the improper calibration of a machine tool, setup errors and a process plan which is not designed optimally. For the multilateral machining of the complex, precise parts of machines, a process plan should include, before and during the process, coordinate measurements by means of a touch probe in order to verify previously made surfaces or to determine accurately the position and orientation of a local coordinate system. The uncertainty of these measurements is connected with the estimate precision of performing the manufactured parts. This paper presents a tool devised for determining the uncertainty of the results of coordinate measurements by a simulation method, which is also useful at the stage of machine tool calibration. A basis of this method is a bipartite graph with a tree structure. Transitions in the graph constitute a set of elementary measurement activities and analytical activities which determine the uncertainty of the position and orientation of respective geometric features and abstract objects. Based on the results of the conducted simulation tests it is possible to build analytical models for the rapid determination of measurement uncertainty. The tool devised is aimed at vector dimensioning and therefore it enables simple extension, including integration with geometric dimensioning and tolerancing. This paper includes an example of applying the method devised, which confirms its practicability.

Keywords

• measurement uncertainty
• calibration
• simulation method
• bipartite graph
• setup data