Abstract
Nowadays, the use of freeform surfaces in various functional applications has become more widespread. Multi-sensor coordinate measuring machines (CMMs) are becoming popular and are produced by many CMM manufacturers since their measurement ability can be significantly improved with the help of different kinds of sensors. Moreover, the measurement accuracy after data fusion for multiple sensors can be improved. However, the improvement is affected by many issues in practice, especially when the measurement results have bias and there exists uncertainty regarding the data modelling method. This paper proposes a generic data modelling and data fusion method for the measurement of freeform surfaces using multi-sensor CMMs and attempts to study the factors which affect the fusion result. Based on the data modelling method for the original measurement datasets and the statistical Bayesian inference data fusion method, this paper presents a Gaussian process data modelling and maximum likelihood data fusion method for supporting multi-sensor CMM measurement of freeform surfaces. The datasets from different sensors are firstly modelled with the Gaussian process to obtain the mean surfaces and covariance surfaces, which represent the underlying surfaces and associated measurement uncertainties. Hence, the mean surfaces and the covariance surfaces are fused together with the maximum likelihood principle so as to obtain the statistically best estimated underlying surface and associated measurement uncertainty. With this fusion method, the overall measurement uncertainty after fusion is smaller than each of the single-sensor measurements. The capability of the proposed method is demonstrated through a series of simulations and real measurements of freeform surfaces on a multi-sensor CMM. The accuracy of the Gaussian process data modelling and the influence of the form error and measurement noise are also discussed and demonstrated in a series of experiments. The limitations and some special cases are also discussed, which should be carefully considered in practice.
Highlights
Nowadays, modern optical components with freeform surfaces are widely used since they have the advantages of excellent optical performance and functionalities [1]
Coordinate machines (CMMs) equipped multiple sensors popular in the high‐endmeasuring precision metrology market since theirwith measurement ability are canbecoming be enhanced by in the high-end precision metrology market since their measurement ability can be enhanced by incombining the high‐end precision metrology market since their measurement can be enhanced by the datasets measured by different sensors
Development a data modelling for datasets measured by different sensors and an appropriate data fusion method are the key issues for measurement withby multi‐sensor
Summary
Modern optical components with freeform surfaces are widely used since they have the advantages of excellent optical performance and functionalities [1]. Due to the high accuracy requirement and geometrical complexity of freeform surfaces, their design and manufacture are challenges, but their measurement is a challenge since the measurement process needs to characterize the machined freeform surfaces to determine the conformance with the design. The coordinate measuring machine (CMM) [2] is one of the most important geometrical measurement devices. Equipped with the most widely used touch trigger probe with high repeatability, it provides traceable and accurate measurement results over a relatively large measurement range, and is well accepted in the industry for coordinate measurement due to its flexibility and accuracy [3].
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