A practical evaluation approach towards form deviation for two-dimensional contours based on coordinate measurement data

Abstract

A precise evaluation of the form deviations of two-dimensional (2D) engineering contours is of essential importance in precision manufacturing. In this paper, we propose a practical approach towards evaluating form deviations of 2D contour profiles based on coordinate measurement data. Using this approach, a 2D contour is divided into straight and curved parts. Each straight part is directly presented by the original definition of the part; and each curved part is further represented by its optimal interpolation circular arc segments whose interpolation accuracy can be specified arbitrarily. The approximate contour curve consisting of the straight and circular arc segments has the fewest interpolation segments under the condition of satisfying the pre-specified interpolation accuracy. The form deviation of a measured point is defined as the distance from the point to its corresponding straight or circular segment. The geometrical form deviation of the contour profile is evaluated using the least square method. It has been demonstrated that the difference between the deviation definitions, relative to the original contour or to the approximate contour, is not larger than the pre-specified accuracy value for circular arc interpolation. Therefore, the evaluation precision of the form deviation can be sufficiently guaranteed. The approach is easy and convenient for engineering applications. The effectiveness and the efficiency of the approach are verified with a practical example of a planar cam contour in the paper.