ESTIMATION OF MEASUREMENT UNCERTAINTY WITH THE USE OF UNCERTAINTY DATABASE CALCULATED FOR OPTICAL COORDINATE MEASUREMENTS OF BASIC GEOMETRY ELEMENTS

The paper presents a method for estimating the uncertainty of optical coordinate measurement based on the use of information about the geometry and the size of measured object as well as information about the measurement system, i.e. maximum permissible error (MPE) of the machine, selection of a sensor, and also the required measurement accuracy, the number of operators, measurement strategy and external conditions contained in the developed uncertainty database. Estimation of uncertainty is done with the use of uncertainties of measurements of basic geometry elements determined by methods available in the Laboratory of Coordinate Metrology at Cracow University of Technology (LCM CUT) (multi-position, comparative and developed in the LCM CUT method dedicated for non-contact measurements) and then with the use of them to determine the uncertainty of a given measured object. Research presented in this paper are aimed at developing a complete database containing all information needed to estimate the measurement uncertainty of various objects, even of a very complex geometry based on previously performed measurements.


INTRODUCTION
Together with growing importance of optical coordinate measuring systems, and expanding area of their applications grows the need to systematize the issue of uncertainty of measurements done with the use of them.The measurement result given without information about the uncertainty of its obtaining, from a technical point of view, has of little importance.The issue of measurement uncertainty is constantly tested and improved in relation to needs of machines and instruments market development [1][2][3][4][5][6].
To face problems associated with the measurement uncertainty issue especially in industrial practice in the Laboratory of Coordinate Metrology have been designed a cycle of studies aimed at developing advanced database of uncertainties together with the methodology of its effective use.Uncertainties included in the database are provided from measurements of profiles surfaces models produced in a technology of Fused Deposition Modeling (FDM) with the use of machine developed in the LCM CUT, which are then used for estimating the uncertainty of a real measurement.The measurement uncertainty is estimated basing on similarities with the uncertainty database in case of following factors: • geometry, size of measured object, • MPE -maximum permissible error of the machine, • required measurement accuracy, • sensor type, • measurement strategy, • the number of operators, • external conditions (especially temperature).
At the present stage of research, optical coordinate measuring systems available in the Labo-ratory of Coordinate Metrology and elements of basic geometry are used to verify the correctness of taken assumptions.The use of uncertainty database significantly reduces the time needed to obtain the uncertainty for real measurement, and what's more it allows the estimation of uncertainty in situations when it is not possible -for example because of lack of appropriate standards.

Optical coordinate measuring systems
Research with the use of optical coordinate measuring systems available in the Laboratory of Coordinate Metrology are aimed at possessing data from measurements of printed models of geometrical elements.The above-mentioned systems are presented in Figure 1 Coordinate Measuring Machine (CMM) LK V10.7.6 SL of Nikon Metrology, Articulated Arm Coordinate Measuring Machine (AA CMM) 73SI (both CMM and AA CMM are equipped with optical probe heads) and optical system SMARTTECH 3D -SCAN3D qualify 10 Mpi operating by white light.Measurements are carried out in accordance with procedures developed on the basis of standards (among others [7][8][9][10]) and many years of experience of the LCM team.In the next step appropriate measurement uncertainties are determined and with the use of them developed database is composed.

Measured object models
To make maximally complete measurement an uncertainty database is possible to be created without generating significant costs associated with the purchase of special standards, to create models of geometric elements the Fused Deposition Modelling (FDM) technology belonging to the group of rapid prototyping methods is use.This technology is mainly used for 3D printing (modelling, prototyping).It operates by laying down material in layers in that case a plastic filament.In the Laboratory of Coordinate Measurements for production of models uses a printer of 500×500×500 mm workspace, constructed there.Because of it a broad measuring base composed of among other elements is obtained quickly.They included the following ones:

Database use
The purpose of the developed database is to allow the operator the estimation of the uncertain- The database stores information about the coordinate measuring system and measuring task together with corresponding uncertainties.Each record in the database refers to a particular machine and to a particular measurement performed with the use of this machine together with the uncertainty determined for this measurement.Currently, the records are carried out work to improve the selection algorithm for typing of corresponding to the real measurement information from the database and for estimating the measurement uncertainty based on them.The comparison results with the correlation coefficients for each of found information in the database to performed measurement (the degree of a compliance).Finally, estimated measurement uncertainty is calculated as a weighted mean value from uncertainties for which similarities with the real measurement have been detected [15].

METHODS
In research three methods for determining the measurement uncertainty were used: • Multi-position method, • Comparative method, • OPTI-U method (Optical Uncertainty) -developed in the Laboratory of Coordinate Metrology dedicated for determining the uncertainty of optical coordinate measurements.

Multi-position method
Multi-position method involves using a variety of factors, combining the use of the non-calibrated measuring object with frequently repeated measuring strategy [11,12]. where

Comparative method
The comparative method involves making measurements of the calibrated standard of a form and size closed to the measured object [11,12].

OPTI-U method
OPTI-U method is a method developed in the Laboratory of Coordinate Metrology with the partly use of components of multi-position method, and of methods known in the metrology as R&R [1].It is aimed at determining the uncertainty of optical coordinate measurements [13].

OPTI-U method
OPTI-U method is a method developed in the Laboratory of Coordinate Metrology the partly use of components of multi-position method, and of methods known in metrology as R&R [1].It is aimed at determining the uncertainty of optical coord measurements [13].

The principle of the measurement uncertainty database use
The purpose of the developed database is to allow the operator the estimation of uncertainty of realized measuring task by the use of data collected in it.The basic princip the measurement uncertainty database operation scheme is presented in Fig. 3. (

RESULTS
The measurement was carried out with the use of coordinate measuring machine LK V10.7.6 SL of Nikon Metrology company equipped with a linear scanner LC60Dx.A measurement object was the internal and external diameter of the cylinder (Fig. 4a).As a standard a reference ring of a diameter of 28 mm was used (Fig. 4b), and as a reference measurement, the results from cylinder and standard measurements with the use of Zeiss machine were used (Fig. 4c).
Data in the form of point clouds were developed in Focus 10 program, with the use of filtration methods available in the program (Fig. 5).For developing the results, all methods for determining of measurement uncertainty presented in chapter 2 (Multi-position, comparative and developed in the LCM CUT method dedicated for non-contact measurement -OPTI-U) were used (Table 1).
Presented results show the impact of the used measurement method on the measurement result and on the uncertainty of its obtaining.During measurement, equal filters (in the software dedicated to optical measurements) and equal measurement conditions were used.To make the more extensive commentary, all stages of research have to be complete.Obtained uncertainties are used to create a part of the database for analogous measurements.

Fig. 2 .Fig. 3 .
Fig. 2. The process of sinusoidal surface standard projecting process with the use of FDM technology on a machine modelled in the LCM -extension factor depended on effective degrees of freedom, u c -uncertainty component depended on standard [mm], u p -uncertainty component depended on the used procedure [mm], u w -uncertainty component depended on measured object [mm], u b -uncertainty component depended on systematic error [mm].
where: E Lcomponent of error of length measurement, mm, E Dcomponent of ave error for external or internal diameter measurement or for a flat surface [mm], E component of used software [mm], E Scomponent of matching of "points clouds" [mm] extension factor depended on effective degrees of freedom, u AVuncertainty compo depended on machine operator [mm], u EVuncertainty component depended on gauge [m u CALuncertainty component depended on calibration value [mm], u CTEuncerta component depended on calibration temperature [mm].

Fig. 4 .Fig. 5 .
Fig. 4. Measurement carried out with the use of coordinate measuring machine LK V10.7.6 SL of Nikon Metrology company equipped with a linear scanner LC60Dx a) measurement of the object b) measurement of the standard, c) the reference measurement of the object and the standard with the use of Zeiss machine

Table 1 .
Results of measurements performed with the use of optical probe head with uncertainties developed with methods used in the LCM