Obtaining discrete data is inseparably connected with losing information on surface properties. In contact measurements, the ball tip functions as a mechanical-geometrical filter. In coordinate measurements the coordinates of the measurement points of a discrete distribution on the measured surface are obtained. Surface geometric deviations are represented by a set of local deviations, i.e. deviations of measurement points from the nominal surface (the CAD model), determined in a direction normal to this surface. The results of measurements depend both on the ball tip diameter and the grid size of measurement points. This article presents findings on the influence of the ball tip diameter and the grid size on coordinate measurement results along with the experimental results of measurement of a free-form milled surface, in order to determine its local geometric deviations. One section of the surface under research was measured using different measurement parameters. The whole surface was also scanned with different parameters, observing the rule of selecting the tip diameter d and the sampling interval T in the ratio of 2:1.
Geometric deviations of free-form surfaces are attributed to many phenomena that occur during machining, both systematic (deterministic) and random in character. Measurements of free-form surfaces are performed with the use of numerically controlled CMMs on the basis of a CAD model, which results in obtaining coordinates of discrete measurement points. The spatial coordinates assigned at each measurement point include both a deterministic component and a random component at different proportions. The deterministic component of deviations is in fact the systematic component of processing errors, which is repetitive in nature. A CAD representation of deterministic geometric deviations might constitute the basis for completing a number of tasks connected with measurement and processing of free-form surfaces. The paper presents the results of testing a methodology of determining CAD models by estimating deterministic geometric deviations. The research was performed on simulated deviations superimposed on the CAD model of a nominal surface. Regression analysis, an iterative procedure, spatial statistics methods, and NURBS modelling were used for establishing the model.