Simulation tests of the method for determining a CAD model of free-form surface deterministic deviations

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.