Estimation of Uncertainty of Coordinate Measurements According to the Type B Method

Abstract

Abstract. The paper describes a new method for analytical estimation of the uncertainty component introduced by the CMM, including temperature influence. The uncertainty is estimated separately for each characteristic (dimension or geometrical deviation) given in the geometrical specification. The uncertainty is calculated directly, i.e. no analysis of the accuracy of determination of particular geometrical elements is performed. The fundamental condition enabling analytical estimation of the uncertainty is assumption that uncertainty of coordinate measurement depends on the differences of coordinates of characteristic points used to calculate particular deviation.

Geodetic method of the fuel tank form inspection

“…Different models were tested [1,11,8,9]. The following most important indicators came out from the calculation within the height network: height differences should be measured with a measurement uncertainty of 0.26-0.45 mm, the internal reliability, the average lower limit value of grave mistake, 2.5 mm, and the average coefficient of external reliability 6.0 (the effect of the undetected blunders [9, eq.…”

Coordinate measurement uncertainty: Models and standards

“…The analytical method of uncertainty evaluation developed by the authors is also based on transparent-box model. In the full version, it uses practically the same input data as the PTB (Physikalisch-Technische Bundesanstalt) version [7] of the simulation method [8][9][10][11]. The significant difference is that almost practically all component uncertainties are determined by the type B evaluation.…”

Analytical estimation of coordinate measurement uncertainty

“…[9][10][11]): in coordinate measurements it is necessary to evaluate the uncertainty separately for each characteristic (''characteristic'' is understood as particular dimensions and geometrical deviations), since the geometrical errors of a CMM are important source of measurement errors, the presented software (similarly as in computer simulation) uses commonly accepted kinematic model of a CMM (developed by PTB) and the associated model of error propagation; the identification of the geometrical errors can be done basing on the results of CMM calibration by means of ball-plate [4,12], each characteristic is presented in appropriate model by the use of minimal number of characteristic points of the measured workpiece; the characteristic points can be surface points, point of axis, centre point of sphere; the characteristic points of a surface represent the actual probing points -they are chosen from the contour of the probed surface; characteristic points of axes are centre points of circles -they are chosen close to extreme cross-sections of hole/shaft [11], the method includes analysis of influence of CMM errors on particular geometrical deviations direct -the model of particular characteristic uses all characteristic points of the workpiece, for both: datum features' points and toleranced features' points (in the computer simulation a decomposition of the measuring task is performed to evaluate uncertainty for particular characteristic -the first stage involves calculating associated geometrical elements from the probing points which include measurement errors, and in the second stage characteristics are calculated as relations between the geometrical elements [4]), the models of particular characteristics use different number (3)(4)(5)(6)(7)(8) of characteristic points; the points should be distributed according to the strategy used in the measurement and the good measurement practice, the models of particular characteristics are derived from the formulae for point-point, point-straight line and point-plane distance [10], each characteristic is defined by a formula presented in a form where it is a function of coordinates' differences' of characteristic points of the workpiece [11], measurement uncertainty of particular characteristics is calculated as combined uncertainty (uncertainty of indirect measurement) [9], for estimation component uncertainties of particular coordinates' differences of characteristic points the type B method is used [9], the uncertainty budget for the coordinates' differences includes influences of particular geometrical errors of CMM, probing system errors, errors connected with probing strategy and especially number of probing points, as well as temperature errors (the paper gives only the budget for geometrical errors of CMM).…”

“…The formula expressing the measured characteristic (coaxiality deviation), and more precisely distance of point S from straight line AB, as a function of coordinates' differences of workpiece characteristic points is in a form [11]:…”