Reducing Polynomial Coefficients in CMM Calibration
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing calibration methods for coordinate measuring machines require a high number of reference measured values and are time-consuming, often leading to significant measurement deviations, especially when correcting nonlinearities outside supported measurement points.
Innovation Solution
A method that reduces the number of polynomial coefficients used in calibration by iteratively eliminating coefficients with strong statistical dependence, optimizing the calibration data to improve accuracy and robustness, especially for nonlinear measuring errors, using a polynomial transformation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a high number of polynomial coefficients are used in calibration, then measurement precision is improved, but calibration time increases significantly
Solution Approach 1:
The patent extracts and eliminates redundant polynomial coefficients from the calibration model by identifying and removing coefficients with high statistical dependence (correlation > threshold). This reduces the number of coefficients that need to be determined during calibration, directly reducing calibration time while maintaining measurement precision for the remaining essential coefficients.
Solution Approach 2:
The patent changes the parameter set by dynamically selecting which polynomial coefficients to retain based on statistical analysis of their interdependencies. By transforming the full set of polynomial coefficients into a reduced set based on correlation thresholds, the calibration process becomes faster while preserving the essential measurement correction capabilities.
2Measurement precision
If polynomial transformation is used to correct nonlinearities, then measurement precision is improved at supported points, but new nonlinear measurement deviations are introduced at unsupported points
Solution Approach 1:
The patent removes polynomial coefficients that create harmful interpolation artifacts - specifically those with high statistical dependence that cause oscillations and new nonlinearities at unsupported measurement points. By extracting only the essential independent coefficients, the transformation corrects nonlinearities at supported points without introducing spurious deviations elsewhere.
Solution Approach 2:
The patent converts the statistical dependence information, which could be seen as a problem causing redundancy, into a useful criterion for selecting the optimal subset of polynomial coefficients. By using correlation analysis, the method identifies which coefficients to eliminate, transforming the potential harm of redundant coefficients into a systematic approach for creating a more reliable, compact calibration model.
Data Source
AI summary
A reference measurement object having known properties is used for the purpose of calibrating a coordinate measuring machine. A plurality of reference measured values are picked up on the reference measurement object. Calibration data are determined using the reference measured values and using the known properties of the reference measurement object. The calibration data comprises a first number of polynomial coefficients that are selected to correct nonlinear measuring errors using at least one polynomial transformation. The first number of polynomial coefficients is reduced in an iterative method to a lesser second number, with a plurality of pairs of polynomial coefficients being formed and with a polynomial coefficient of a pair being eliminated in each case when a statistical dependence between the polynomial coefficients of the pair is greater than a defined threshold value.