Modeling And Identification Of Contour Features And Its Application

The measurement of geometrical contour features is an important problem in geometrical metrology. The geometrical parameters of a contour include its dimension, position, form error and form spectrum. These parameters caused in manufacturing process have great influence on the product performance, and must be inspected and controlled. The contour is continuous, but only some finite discrete sampling data can be sampled, so the estimating result based on these discrete data is only the approximative evaluations of the parameters. Generally speaking, the more the number of sampling points, the more exact the estimations. As increasing the number of sampling points, the efficiency of inspecting is surely reduced and its processing cost is increased as well, therefore, it is important to research and solve the problem of sampling strategy, including how to choose the number and optimal distribution of sampling points, and how to analysis the uncertainty of estimated parameters. The sampling strategy is usually selected based on experience of the operator, so the discrepancy of estimated result is unavoidable, and it is necessary to study on a unified sampling strategy.Besides the accuracy of instrument and required uncertainty of estimated parameters, the geometric features of a workpiece should be considered in determining the proper sampling strategy. After modeling the geometric features, the rationality of sampling strategy can be judged by the rationality of the model, and the estimation of geometric parameters can be evaluated by identification of the model.In this paper, some models of typical geometric contours are discussed in detail, for example, Fourier Harmonics for a circle, Legendre/Fourier Harmonics(LF) for a cylinder, Sphere Harmonics(SH) for a sphere and B-spline, Parametric Spline and Non-Uniform B-spline for a free-form curve or surface, etc.In this paper, a method called" Bi-measurement Evaluation Method" (BMET) is proposed for the first time, then the rationality of the model and the number of sampling points can be judged, and the parameters of noise in the sampling sequence and the uncertainty of contour parameters estimated can be evaluated.Based on the BMET proposed, the modelings and identifications for some typical contours are discussed as follows:(1) Circle: based on BEMT, the circularity is decomposed into two parts: oneis the circularity caused by the dominating harmonics, the other is the circularity by the noise in the sampling sequence. Composing two parts of the circularities, the estimated value of circularity and its uncertainty can be calculated. It is proved by simulation experiments and real measurements that the standard deviations and the bias of the estimated values of circularities are lower by this method than that by the least square method. Meanwhile, the results affected by the non-uniform sampling from eccentricity in measuring a circle are discussed, and a method to decrease this effect is proposed.(2) Circular arc: The harmonic characteristics of a circle can be estimated by Discrete Fourier Transform, which, however, cannot be used in the case of a circular arc because the sampling points around the whole circle cannot be obtained in this way. By means of interpolation and iteration proposed in this paper, the harmonic characteristics of a circular arc are estimated satisfactorily.(3) Free-form curve and surface: BEMT is applied for measuring a free-form curve and surface, for example, the profile of train-wheel, to estimate the variance of noise in sampling sequence and to judge the rationality of the number of sampling points. In addition, the principle error of accumulated chord parametric cubic spline is discussed in detail.(4) Cylinder: Non-uniform sampling is needed in essence when modeling a cylinder with LF. In this paper, a method based on Gauss-integral is applied to identify the parameters of LF model. It is proposed for the first time that the estimated values of LF parameters are non-equivale...