采样点数对圆柱体计算尺寸评定结果的影响

Influence of sampling points on evaluation results of calculated sizes of cylinder

针对在进行圆柱体计算尺寸评定时采样点数选取的问题,对基于折线和弧线表征的圆周轮廓的计算尺寸进行了研究,提出了一种基于折线和弧线的圆周轮廓表征方法,建立了其周长和面积评定模型,分析了采样点数对圆柱体计算尺寸的影响。首先,对圆柱体轮廓要素的提取进行了阐述,确定了圆柱体径向尺寸的系统误差,并提出了基于折线和弧线表征的圆周轮廓周长、面积和体积的计算方法,建立了圆周轮廓的周长直径、面积直径和体积直径的评定模型;然后,对不同采样点数时,基于折(或弧)线的圆周轮廓周长计算值与(椭)圆周长之差、折(或弧)线的圆周轮廓面积计算值,与(椭)圆面积之差分别进行了理论计算;最后,采用7种采样点数分别对试样的圆周轮廓进行了采样,基于所建立的计算尺寸评定模型,对试样的周长直径、面积直径和体积直径进行了评定;并依据理论计算和实验,研究了采样点数对圆柱体计算尺寸的影响。研究结果表明:采用折线表征圆周轮廓时,采样点数对其周长直径、体积直径的评定结果影响较大,对其面积直径的评定结果影响相对较小;采用弧线表征圆周轮廓时,采样点数对其周长直径、面积直径和体积直径的评定结果影响均非常小。

Aiming at the problem of selecting sampling points when evaluating the calculation size of cylinder,a calculation size of roundness profiles was studied based on broken lines and arcs.A method based on broken lines and arcs to characterize the contour of a circle was proposed,its perimeter and area evaluation models were established,and the influence of the number of sampling points on the calculated size of the cylinder was analyzed.Firstly,the extraction of cylinder contour elements was explained,the systematic error of their radial sizes of the cylinder was determined,and a calculation method of perimeter,area and volume of roundness profiles was proposed based on broken lines and arcs,the corresponding evaluation models for perimeter diameters,area diameters and volume diameters of roundness profiles were established.Then,for the different sampling points of each roundness profile,the theoretical calculation of the differences between the calculation values of perimeters of the broken-line(arcs)based profiles and the perimeters of the corresponding circles or ellipses and between the calculation values of areas of the broken-line(arcs)based profiles and the areas of the corresponding circles or ellipses were carried out.Finally,the roundness profiles of sample were extracted based on seven different sampling points,the perimeter diameters,area diameters and volume diameters of the sample were evaluated on the basis of the established models of calculation sizes.According to the theoretical calculations and experiments,the influence of the number of sampling points on the cylindrical calculation sizes was researched.The research results show that when the roundness profiles are characterized by the broken-lines,the number of the sampling points has larger influence on the evaluation results of perimeter diameters and volume diameters and has relative less influence on the evaluation results of area diameters,and that when the roundness profiles are characterized by the arcs,the number of the sampling points has very small influence on the evaluation results of perimeter diameters,area diameters and volume diameters.