There are still significant challenges in the accurate positioning of optical freeform surfaces on the machine tool and the measurement instrument due to the high accuracy requirement and their complex shapes. This paper proposes a Fiducial-aided On-machine Positioning method (FAOPM) that combines on-machine measurement and off-machine measurement to precisely position optical freeform surfaces during the precision manufacturing cycle including rough machining, fine machining, measurement, and error compensation. The FAOPM makes use of fiducials which are firstly measured on a coordinate measuring machine with nanometric accuracy to generate a Fiducial-aided Computer Aided Design (FA-CAD) of the designed optical surface, then the developed on-machine measuring device obtains the accurate positions of the fiducials after remounting in the machining coordinate system. Finally the relative position of the workpiece is identified so that the associated cutting paths and compensation tool path can be easily generated. Several optical freeform surfaces were experimentally machined to prove the capability of the proposed method. The results indicate that the positions of the workpiece during the precision manufacturing and measurement cycle were precisely achieved and the form accuracy of the optical freeform surfaces was remarkable improved based on the FAOPM.
Form characterization of a machined optical freeform surface demands accurate alignment of the sampled measured data points on the machined surface, and they are compared with the designed geometry of the surface through positioning. In this paper, a fiducial-aided robust positioning method (FAPM) is developed which attempts to evaluate freeform surfaces with high efficiency and precision. The FAPM method makes use of fiducials as reference datum to form a fiducial-aided computer-aided design (FA-CAD) of the freeform surface which not only establishes an inherent surface feature, but also links the different coordinate systems among design coordinate frame, machine tool, and measurement instrument. To verify the capability of the proposed method, a series of experiments were conducted. Compared with the traditional freeform measurement method (e.g., least squares method), the results indicate that the robustness and accuracy of the measurement is significantly enhanced by the FAPM.
Achieving high form accuracy of optical freeform surfaces in machining is extremely difficult due to their geometric complexity. A positioning or repositioning process is necessary for fabricating optical freeform surfaces during the machining and measuring processes. The concept of fiducial-aided calibration and positioning (FACP) has been developed to provide high-precision relative position data among different coordinate frames to minimize the repositioning errors. This paper attempts to establish an uncertainty analysis model to evaluate the uncertainty and reliability of the FACP method. Firstly, two kinds of the most-used configurations of the FACP systems available for carrying out experiments in both machining and measuring machines are designed with consideration of four main factors. Secondly, a linear transforming model is developed to connect different coordinate frames among the machine tool, on-machine measuring system and off-machine measurement instrument with high precision. Hence, all the uncertainties associated with the FACP method are considered, and a modified chi-squared technique is used to identify the relationship between these uncertainties. Experimental work has been conducted on two machine tools with different on-machine probing systems. The results show that the transformation uncertainty is very small in the proposed linear transforming model, while the final accuracy of the FACP system is sensitive to the measurement results obtained from the on-machine measuring system.
In this paper, a fiducial-aided reconfigurable artefact is presented for estimating volumetric errors of a multi-axis machine tools. The artefact makes use of an adjustable number of standard balls as fiducials to build a 3D artefact which has been calibrated on a coordinate measuring machine (CMM). This 3D artefact shows its reconfigurability in its number of fiducials and their locations according to the characteristics of workpieces and machine tools. The developed kinematics of the machine tool was employed to identify the volumetric errors in the working space by comparing the information acquired by the on-machine metrology with that by the CMM. Experimental studies are conducted on a five-axis ultra-precision machine tools mounted with the 3D artefact composed of five standard spheres. Factors including the gravity effect and measurement repeatability are examined for the optimization of the geometry of the artefact. The results show that the developed 3D artefact is able to provide information of the volume occupied by the workpiece.
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