Optimized Sampling Plan Of Free-form Surface Based On CMM Measurement

With the continuous advancement of CNC technology and the development of computer-aided design(CAD)and computer-aided machining(CAM),freeform surfaces are widely used in industry and life.Free-form surfaces can hardly be represented by simple mathematical formulas,so the B-spline theory is commonly used in engineering to express and calculate them.Products with free-form surfaces are often used by designers to achieve certain functional or aesthetic purposes,so it is very important to make sure that the final shape is consistent with the design goals.The coordinate measuring machine(CMM)is a kind of precision instrument which is specially used for surface measurement.Through the contact of the probe with the surface of the measured object,the entity can be digitized into discrete three-dimensional points.Since the CMM can measure almost any surface shape and has high measurement accuracy,it is most frequently used instrument in the measurement of free-form surfaces.Sampling plan is one of the most important factors affecting the accuracy of surface detection,and the core content of the sampling plan is the sampling rules.This paper mainly studies two kinds of adaptive sampling plans: isoparametric line sampling and discrete point sampling.Isoparametric line sampling means that the measuring probe collects points along the isoparametric line of the surface during the measuring process,while discrete point sampling directly acquires discrete data points from the surface according to given rules.The number of lines or points are added as the sampling goes,so the isoparametric lines or measured points need to be reconstructed as substitute surfaces,and the maximum normal deviation between the substitute surface and the original surface is calculated to judge whether the sampling error has achieve the given accuracy.If so,the sampling terminates.Based on the original isoparametric line sampling methods,two optimization algorithms are proposed,i.e.,hybrid sampling method based on normal error and average curvature change and automatic direction finding sampling method.The former is given by the sampling direction,and uses the linear combination of the deviation and the change of the average curvature of the surface to determine the positions of the sample lines.The latter determines the direction of the sample lines according to the change in the curvature of the two parameter directions,and uses the maximum deviation between the substitute surface and the original surface to determine the positions of the sample lines.Then we propose two kinds of discrete point sampling plans based on surface division,i.e.,discrete point sampling method based on normal deviation and discrete point sampling method based on mixed value of normal deviation and Gaussian curvature.The surface is divided based on the rule that points with close normal curvature go the same patch.The first algorithm extracts new sampling points of each surface patch where the deviation is maximum,and the second algorithm extracts new sampling points at each patch where the deviation and Gaussian curvature mixing value is the largest.Each algorithm uses two kinds of point-adding orders: equal point addition and proportional point addition.The former adds the same number of points for each surface patch in the sampling process,while the latter has the number of points proportional to the average curvature of each patch.The proposed algorithms are compared with the existing ones by being applied to several different free-form surfaces.The results show that the sampling plans in this paper can achieve higher sampling accuracy with fewer isoparametric lines or fewer sampling points,and substitute surfaces constructed with sampling lines or sampling points is closer to the original surface both in shape and curvature,and the smoothness is also better.So it is clearly that the sampling plans presented in this paper have higher sampling efficiency and sampling accuracy,which can be applied to more types of free-form surfaces and are able to meet various measurement requirements as well as has a wider application range.