Error compensation and uncertainty evaluation of CMMs based on kinematic error models and gaussian processes

Abstract

Given the increasing demand for precision engineering applications, the evaluation of measurement error and uncertainty has been the focus of intensive research to meet the requirements of precision manufacturing processes. Systematic errors of mechanical components affect the accuracy of the production parts. It is therefore best to analyse the geometric accuracy of machine tools before production processes begin. This proposed method is based on simulation in the MATLAB programme, which investigates the influence of the geometric errors of the Coordinate Measuring Machine (CMM) on the calibration. The advantages of this measurement procedure are reduced physical measuring times, reduced measurement uncertainties as well as volumetric measurement, and compensation for CMM geometric errors. In this research, theoretical modelling of the local, kinematic error model and the Gaussian Process (GP) model are presented and explored in depth. These proposed methods are simulations providing an integrated virtual environment in which user can generate the inspection path planning for specific tasks and evaluate the errors and uncertainty associated with the measurement results, all without the need to perform a number of physical CMM measurements. The estimated errors and uncertainty can serve as rapid feedback for users before performing actual measurements or as a prior evaluation of the results of the CMM calibrations. The estimation of CMM geometric errors are usually described using 21 kinematic errors which consist of three positional and three rotational error functions for each of the three axes, along with three squareness errors. This assumes that the method to estimate of these kinematic errors can be generated by performing an artefact measurement such as for a hole or a ball plate in the numbers of the positions of the CMM working region and then matching the kinematic errors to the measured changes in artefact geometry. The process validation of a local, kinematic error model and a GP model has been determined with the design and analysis of CMM measurement using a ball plate as an artefact, calculating the percentage error to compare their effective results. This research project has led to the following contribution to knowledge: Mathematical model development for making effective choices regarding the local, kinematic error model and GP model is performed and formulated; this is verified by particular kinematic errors of the CMM measurements, presenting high accuracy and reliability of the error and uncertainty evaluation performance. The improvement achieved by the proposed method over the traditional approaches between the simulated datasets and actual CMM data measurements has been demonstrated. The numerical simulations with a well-designed strategy providing accurate estimates of the CMM kinematic errors using only a nominal CMM calibration with a ball plate have been validated and evaluated in both approaches. The influences of kinematic errors affected through the measurement process of the CMM on the calibration have been investigated.