Determining the conformance between geometric deviations and desired design specifications is a major goal in precision surface machining. The degree of conformity is estimated using coordinate metrology to quantify the geometric accuracy of the fabricated part. Often, the geometric deviations observed in the final machined parts are caused by inherent machining process errors, including geometric imperfections, thermal effects, dynamic errors, and operational errors. Since these machining errors cannot be avoided it is necessary to predict and then to compensate for their geometric effects in a systematic closed-loop machining process. In this research, a technique for the automated inspection of geometric deviations is investigated and the corresponding compensation scheme for closed-loop machining processes is developed. The method constructs optimum substitute geometries from the discrete measured points. It then uses the information to automatically generate appropriate machining instructions that compensate for observed geometric deviations. The proposed approach exploits a new fitting method, Maximum Conformance to Tolerance (MCT), which maximizes the capability of compensation for the surface regions with unacceptable geometric deviations, and minimizes the total amount of the required compensation on the actual machined surface. Since the multivariable optimization problem defined by MCT is highly nonlinear, a search method for capturing an appropriate set of data points from the machined surface is developed, which significantly enhances computational stability and reduces uncertainty of the MCT estimation. The developed search algorithm specifies location and number of the measurements based on the continuity of the probability density function of geometric deviations, which is estimated by Parzen Windows, a nonparametric pattern recognition technique.

Furthermore, a novel method to generate the proper compensating machining instructions, based on the geometric deviations evaluated by MCT, is developed. The technique, called Local Compensating Transformation (LCT), uses the Voronoi Diagram and Delaunay Triangulation to model the surface geometry and determine a distribution of the geometric deviations. For each unsatisfactory region of the surface, LCT searches for the optimum local transformations of the corresponding machining instructions. This provides a unified approach, which generates the compensating piecewise tool paths for the next phase of machining independent of the complexity and properties of the nominal geometry.

Illustrative case studies and simulations have been performed using the developed methodology, to validate its performance using a variety of the geometries with different degrees of complexity and tolerance specification. It has been observed that the developed techniques are efficient and stable and, that the geometric deviations resulting from the quasistatic machining errors can be reduced up to 94%. The proposed methodology was used in closed-loop machining with a Computer Numerical Control (CNC) milling machine and a Coordinate Measuring Machine (CMM) with a tactile probing system. Results have successfully shown up to a 74% reduction in the final product’s geometric deviations. The methodology is flexible for any type of the nominal geometry of the workpiece and any configuration of the machine tools. Furthermore, it can be implemented in different cases of closed-loop machining including the on-line inspection, intermittent inspection and the production of repetitive parts. KEYWORDS:​ Surfac