基于Voronoi图的圆度误差评定算法及系统
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摘要
在工业生产和制造中,大多数零件的几何形状包含有圆形部分,因此圆度误差的评定具有重要意义。圆度误差评定是检测产品质量、保证加工精度的关键环节之一。目前关于圆度误差评定的方法主要有线性代数法、非线性优化法、随机优化算法、遗传算法、穷举法和基于计算几何的方法等,但均无法快速简捷地求出符合国际标准定义的圆度误差。
本文研究了Voronoi图的性质,分析了Voronoi图在圆度误差评定领域中的应用,通过最近Voronoi图和最远Voronoi图的性质得出了下述结论:对于测量平面上的一组测量点集,当外接圆圆心在其最远Voronoi图上移动时对应的外接圆半径单调收敛,并最终收敛到最小外接圆圆心;当内接圆圆心在其最近Voronoi图上移动时对应的内接圆半径局部单调增大,并最终增大到局部最大内接圆圆心;当区域圆圆心在其最近Voronoi图或最远Voronoi图上移动时对应的区域圆半径差局部单调收敛,并最终收敛到局部最小区域圆圆心。在此基础上提出了一种基于Voronoi图的评定圆度误差的最小外接圆法、最大内接圆法和最小区域圆法,给出了详细的程序流程图,在Windows XP环境中利用Visual C++ 6.0编制了相应的程序,给出了具体的圆度误差评定算例,并与符合定义的穷举法进行了比较。
目前,广泛应用于测量领域的光栅位移传感器通过分立的数显箱实现结果显示,其存在系统灵活性差、不便与其他设备接口和难以实现自动测量等缺点。本文针对此现状,提出了一种基于USB2.0的虚拟光栅数显系统。
研究结果表明利用本文提出的算法求得的结果和理论结果一致,时间复杂度为线性,而且具有简单直观和误差不累积的特点。当用于采样点较多的圆度误差评定时,本文提出的方法具有明显的计算速度优势。基于USB2.0的虚拟光栅数显系统能够满足采集数据的要求。
In industrial production and manufacturing, roundness error evaluation is one of the key measures to detect the product quality and guarantee the machining precision. At present, the existing algorithms for roundness error evaluation mainly include the linear algebra approach, the nonlinear optimization method, the random optimization algorithm, the genetic algorithm, the stochastic optimization approach, the exhaustive approach, and the computational geometry based approachs. However, none of the above mentioned methods can rapidly and simply find the roundness error according to the definition given by the ISO.
In this paper, the characteristics of the Voronoi diagram, as well as the roundness error evaluation utilizing the Voronoi diagram, are studied. According to the analysis, for a given measured point set in a plane, it can be found that (1) the radius of the circumscribed circle decreases monotonously when its center moves from any point on the farthest Voronoi diagram to the minimum circumscribed circle center along the farthest Voronoi edges, (2) the radius of the inscribed circle increases monotonously when its center moves from any point on the nearest Voronoi diagram to the centre of the local maximum inscribed circle along the nearest Voronoi edges, and (3) the radius difference of the zone ring decreases monotonously when its center moves from the minimum circumscribed circle center to the centre of the local minimum zone circle along the nearest or the farthest Voronoi edges. On this basis, an algorithm accessing the minimum circumscribed circle for roundness based on the farthest Voronoi diagram, an algorithm accessing the maximum inscribed circle for roundness based on the nearest Voronoi diagram and an algorithm accessing the minimum zone circle for roundness based on the nearest and the farthest Voronoi diagram are proposed. In addition, the detailed flow charts of the algorithms and the corresponding software with Visual C++ 6.0 in Windows XP environment are presented. Furthermore, the examples to evaluate the roundness error with the developed software based on the algorithms proposed in this paper as well as the comparision with the exhaustive approach are shown.
At present, the grating displacement sensors, widely used in the field of measurement, display the result through separating digital readout. Based on the traditional readout of the grating displacement sensors, not only the system flexibility is poor, but also the interface with other equipments is inconvenient. Keep this in mind, a virtual grating digital readout based on USB 2.0 is presented.
The research results show that not only the algorithms proposed in this thesis can access the roundness error according with the definition, but also the time complexity is linear without error accumulation. The larger the scale of the sampling points of the measured point set is, the more apparent the predominance of the computing speed of the algorithm proposed in this thesis is. The virtual grating digital readout system based on USB 2.0 can meet the need of data acquisition.
本文研究了Voronoi图的性质,分析了Voronoi图在圆度误差评定领域中的应用,通过最近Voronoi图和最远Voronoi图的性质得出了下述结论:对于测量平面上的一组测量点集,当外接圆圆心在其最远Voronoi图上移动时对应的外接圆半径单调收敛,并最终收敛到最小外接圆圆心;当内接圆圆心在其最近Voronoi图上移动时对应的内接圆半径局部单调增大,并最终增大到局部最大内接圆圆心;当区域圆圆心在其最近Voronoi图或最远Voronoi图上移动时对应的区域圆半径差局部单调收敛,并最终收敛到局部最小区域圆圆心。在此基础上提出了一种基于Voronoi图的评定圆度误差的最小外接圆法、最大内接圆法和最小区域圆法,给出了详细的程序流程图,在Windows XP环境中利用Visual C++ 6.0编制了相应的程序,给出了具体的圆度误差评定算例,并与符合定义的穷举法进行了比较。
目前,广泛应用于测量领域的光栅位移传感器通过分立的数显箱实现结果显示,其存在系统灵活性差、不便与其他设备接口和难以实现自动测量等缺点。本文针对此现状,提出了一种基于USB2.0的虚拟光栅数显系统。
研究结果表明利用本文提出的算法求得的结果和理论结果一致,时间复杂度为线性,而且具有简单直观和误差不累积的特点。当用于采样点较多的圆度误差评定时,本文提出的方法具有明显的计算速度优势。基于USB2.0的虚拟光栅数显系统能够满足采集数据的要求。
In industrial production and manufacturing, roundness error evaluation is one of the key measures to detect the product quality and guarantee the machining precision. At present, the existing algorithms for roundness error evaluation mainly include the linear algebra approach, the nonlinear optimization method, the random optimization algorithm, the genetic algorithm, the stochastic optimization approach, the exhaustive approach, and the computational geometry based approachs. However, none of the above mentioned methods can rapidly and simply find the roundness error according to the definition given by the ISO.
In this paper, the characteristics of the Voronoi diagram, as well as the roundness error evaluation utilizing the Voronoi diagram, are studied. According to the analysis, for a given measured point set in a plane, it can be found that (1) the radius of the circumscribed circle decreases monotonously when its center moves from any point on the farthest Voronoi diagram to the minimum circumscribed circle center along the farthest Voronoi edges, (2) the radius of the inscribed circle increases monotonously when its center moves from any point on the nearest Voronoi diagram to the centre of the local maximum inscribed circle along the nearest Voronoi edges, and (3) the radius difference of the zone ring decreases monotonously when its center moves from the minimum circumscribed circle center to the centre of the local minimum zone circle along the nearest or the farthest Voronoi edges. On this basis, an algorithm accessing the minimum circumscribed circle for roundness based on the farthest Voronoi diagram, an algorithm accessing the maximum inscribed circle for roundness based on the nearest Voronoi diagram and an algorithm accessing the minimum zone circle for roundness based on the nearest and the farthest Voronoi diagram are proposed. In addition, the detailed flow charts of the algorithms and the corresponding software with Visual C++ 6.0 in Windows XP environment are presented. Furthermore, the examples to evaluate the roundness error with the developed software based on the algorithms proposed in this paper as well as the comparision with the exhaustive approach are shown.
At present, the grating displacement sensors, widely used in the field of measurement, display the result through separating digital readout. Based on the traditional readout of the grating displacement sensors, not only the system flexibility is poor, but also the interface with other equipments is inconvenient. Keep this in mind, a virtual grating digital readout based on USB 2.0 is presented.
The research results show that not only the algorithms proposed in this thesis can access the roundness error according with the definition, but also the time complexity is linear without error accumulation. The larger the scale of the sampling points of the measured point set is, the more apparent the predominance of the computing speed of the algorithm proposed in this thesis is. The virtual grating digital readout system based on USB 2.0 can meet the need of data acquisition.
引文
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