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由于测量系统的前端传感器为工业影像测头,不同于常规的接触式测头与激光测头,其输出为被测物体的平面像或平面投影,并且对物体的棱边、尖角等突变部位较为敏感,因而更宜选用具有平面特征的物体来进行回转轴线的位置标定。因此,文中选用了定制的长方体标定块来实现回转轴线原点OR的空间坐标(X0,Y0,Z0)标定。如图2所示,该标定块的形状为长方体,采用特殊合金钢材料制作而成,具有良好的形状精度、尺寸精度和表面质量,并且各条棱边均为锋利直边,没有倒角,也未被倒钝。同时,为了获得较高的标定精度,标定块的厚度L和高度H均采用经过精密测量而得到的实测值。
基于此标定块进行回转轴线的位置标定的步骤如下:
(1)回转工作台旋转到0°位置,将标定块放置在回转工作台的台面上,并借助于千分表或者电感测微仪等对标定块的方位进行机械调整,使标定块的厚度L所在的方向与机器坐标系O-XYZ的X轴平行,高度H所在的方向与Z轴平行,如图3所示。调整好标定块的方位后,为了防止其方位发生变化而影响标定结果,应用粘结剂将标定块暂时固接在回转工作台的台面上。
(2)由三坐标测量机的X、Y和Z轴带动工业影像测头运动,使其对焦于标定块的前表面(通过基于Laplacian算子的对焦评价函数判断),而后锁住X轴和Z轴,使工业影像测头只沿着Y轴移动,直到标定块的左侧棱边出现在工业影像测头的视场中,采集该棱边的图像,并记录此时X、Y轴的光栅尺读数为(X1,Y1),如图4所示;然后通过图像处理提取出该棱边在图像坐标系中的像素坐标,进而计算出该棱边与图像中心之间的像素距离la(单位:pixel),再与像素尺寸当量k(单位:mm/pixel)相乘,从而将像素距离la转化为物理距离a(单位:mm),即
$$a = k \cdot {l_a}$$ (1) (3)回转工作台旋转到180°位置,并由三坐标测量机带动工业影像测头对焦于标定块的后表面,而后锁住X轴和Z轴,使工业影像测头只沿着Y轴移动,直到标定块的右侧棱边出现在工业影像测头的视场中,采集该棱边的图像,并记录此时X、Y轴的光栅尺读数为(X2,Y2),如图5所示;然后通过图像处理提取出该棱边在图像坐标系中的像素坐标,进而计算出该棱边与图像中心之间的像素距离lb,再与像素尺寸当量k相乘,从而将像素距离lb转化为物理距离b,即
$$b = k \cdot {l_b}$$ (2) (4)对L、(X1,Y1)、(X2,Y2)、a和b进行代数运算,从而得到回转轴线的原点OR在机器坐标系O-XYZ中的X0坐标和Y0坐标,计算原理如图6所示。
$${X_0} = \frac{{{X_1} + {X_2} + L}}{2}$$ (3) $${Y_0} = \frac{{{Y_1} + {Y_2} + a - b}}{2}$$ (4) (5)由三坐标测量机带动工业影像测头对焦于标定块的后表面,而后锁住X轴和Y轴,使工业影像测头沿着Z轴向上移动,直到标定块的上侧棱边出现在工业影像测头的视场中,采集该棱边的图像,并记录此时Z轴的光栅尺读数为Z3;然后通过图像处理提取出该棱边在图像坐标系中的像素坐标,进而计算出该棱边与图像中心之间的像素距离lh,再与像素尺寸当量k相乘,从而将像素距离lh转化为物理距离h,即
$$h = k \cdot {l_h}$$ (5) (6)对H、Z3和h进行代数运算,从而得到回转轴线的原点OR在机器坐标系O-XYZ中的Z0坐标,计算原理如图7所示。
$${Z_0} = {Z_3} - h - H$$ (6) 通过以上步骤,即可确定出回转工作台的轴线原点OR在四轴视觉坐标测量系统中的三维空间坐标(X0,Y0,Z0),再结合上文所确定的轴线单位方向向量,从而完成了回转轴线的空间方位标定。这将有助于测量系统中的回转工作台坐标系的建立,并且可以进一步确立测量数据由机器坐标系到回转工作台坐标系的转换关系,从而为实现批量气膜孔特征的孔径、空间位置与轴线角度等形位参数的非接触式四轴联动测量奠定了基础。
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为了验证文中所提出的基于视觉测量的回转轴线标定方法的正确性和有效性,首先按照上文所述的标定方法和步骤,对回转工作台的轴线位置进行了标定。在标定过程中,应用千分表对标定块的方位进行机械调整的过程如图9所示;而控制工业影像测头对焦于标定块表面并采集其锋利棱边图像的过程如图10所示;最终采集到的锋利棱边图像及边缘提取结果如图11所示。
图 10 对焦于长方体标定块的表面并采集其锋利棱边图像
Figure 10. Focusing on the cuboid block surface and capturing the image of its sharp edges
图 11 锋利棱边图像及边缘提取结果:(a)左侧棱边;(b)右侧棱边;(c)上侧棱边
Figure 11. Images of the sharp edges and edge extraction results: (a) Left edge; (b) Right edge; (c) Upper edge
根据公式(1)~(6),即可计算出回转工作台的轴线原点OR在机器坐标系O-XYZ中的三维空间坐标为(X0,Y0,Z0)。为了减小随机误差对标定精度的影响,文中采用多次标定实验的平均值作为最终的回转轴线位置标定结果,即(204.8 328,278.4 686,–10.2 804)。
为了对该标定结果进行验证,文中选用了一个标称尺寸为80 mm的标准量块作为被测物体,应用所搭建的四轴视觉坐标测量系统分别对标准量块的两个被测面进行测量,并基于回转轴线位置的标定结果来获得两个被测面之间的距离,而后再与标称尺寸进行比对,通过测量误差的大小来检验标定方法及标定结果的正确性和有效性。实验现场如图12所示,连续对标准量块进行10次重复性测量,测量结果如表1所示。
表 1 测量结果
Table 1. Measuring results
No. Measuring results/mm Measuring errors/mm 1 80.006 0.006 2 80.008 0.008 3 79.995 −0.005 4 80.006 0.006 5 79.992 −0.008 6 79.993 −0.007 7 79.996 −0.004 8 80.009 0.009 9 80.005 0.005 10 80.006 0.006 从表1可以看出,应用回转轴线位置的标定结果,在对该标准量块的10次测量实验中,所测长度尺寸的平均值为80.001 6 mm,标准差为0.006 4 mm,并且各次测量结果与真实值之间的误差均小于±0.01 mm。影响标准量块测量精度的因素很多,必须进行详细分析,以确保测量结果的准确与可靠。在上述实验过程中,对合成标准不确定度影响显著的因素主要有:(1)测量重复性引起的不确定度分量;(2)三坐标测量机示值误差引起的不确定度分量;(3)对焦评价函数的判别误差引起的不确定度分量。
首先,对标准量块进行了10次重复性测量,则测量重复性引起的不确定度分量u1为:
$${u_1} = \sqrt {\frac{{\sum\limits_{i = 1}^{10} {{{({x_i} - \overline x )}^2}} }}{{10 - 1}}} = 6.4\;{\text{μm}}$$ 其次,PEARL 555型三坐标测量机的示值误差为(2.5+3×L/1 000)μm(L为测量长度),在标准量块的测量过程中,三坐标测量机的最大移动范围为30 mm,则分布区间半宽a为:
$$a = \frac{{(2.5 + 30/1\;000)}}{2} = 1.265\;{\text{μm}}$$ 设示值误差服从均匀分布,取包含因子k=
$\sqrt 3 $ ,则三坐标测量机示值误差引起的不确定度分量u2为:$${u_2} = \frac{a}{{\sqrt 3 }} = 0.73\;{\text{μm}}$$ 再次,文中应用基于Laplacian算子的对焦评价函数来使工业影像测头正确对焦于标准量块的被测表面。经过实验验证,该函数的对焦位置判别误差小于0.005 mm,则分布区间半宽为2.5 μm,设该误差服从均匀分布,取包含因子k=
$\sqrt 3 $ ,则对焦评价函数的判别误差引起的不确定度分量u3为:$${u_3} = \frac{{2.5}}{{\sqrt 3 }} = 1.44\;{\text{μm}}$$ 由于不确定度分量u1、u2和u3相互独立,因而标准量块测量结果的合成标准不确定度uc为:
$${u_c} = \sqrt {u_1^2 + u_2^2 + u_3^2} = 6.60\;{\text{μm}}$$ 实验结果验证了文中所提出的标定方法的正确性和有效性,可以满足了高压涡轮叶片上的气膜孔特征的形位参数检测需求。因此,文中所提出的标定方法,能够准确确定出四轴视觉坐标测量系统中的回转轴线的空间方位,从而为后续不同回转工作台角度位置下的测量数据的坐标转换奠定了基础,使其转换到同一坐标系下,以便于后续的数据处理;同时,回转轴线位置的标定精度也使系统能够满足其他回转体类零件的多轴视觉测量,从而提供了一种四轴视觉坐标测量系统下的回转轴线位置标定方法,解决了回转体零件的多轴视觉测量中的关键问题。
Study on calibration method of rotary axis based on vision measurement
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摘要: 为了实现高压涡轮叶片上的气膜孔特征的高精高效测量,设计并搭建了一套非接触式的四轴视觉坐标测量系统。针对其中的回转轴线的空间位置标定难题,结合工业影像测头的成像特点,提出了一种基于视觉测量的回转轴线标定方法。在标定过程中,采用了定制的长方体标定块,并通过回转工作台与三坐标测量机之间的配合,使工业影像测头对焦于标定块的表面并采集到其锋利棱边的图像,而后再通过边缘提取、像素距离计算、物理距离转化和代数运算等步骤,最终确定了回转工作台的轴线在机器坐标系中的空间方位。最后,选用一个标称尺寸为80 mm的标准量块作为被测物体,以对标定方法及标定结果进行验证,各次测量结果的误差均小于±0.01 mm,并进行了合成标准不确定度的分析。实验结果表明:文中所提出的回转轴线标定方法能够达到较高的标定精度和较好的重复性,能够满足气膜孔形位参数的检测要求。Abstract: For the purpose of inspecting the film cooling holes on high-pressure turbine blade in a rapid and accurate manner, a non-contact four-axis vision coordinate measuring system was designed and established in the paper. With regard to the determination difficulty of the spatial location of the rotary axis, a calibration method based on vision measurement was proposed in the paper, which fully considered the imaging characteristics of industrial CCD used in the system. In the calibrating procedure, a specially designed cuboid mental block was applied as the target. Through the coordination between the turntable and the coordinate measuring machine, the industrial CCD focused on the block surface and then captured the sharp edges of the block. And then, the spatial orientation of the rotary axis in the machine coordinate system could be determined by edge extraction, pixel distance calculation, physical distance conversion and algebraic operation etc. Finally, a gauge block was selected to be inspected by the measuring system to verify the calibration method and results, whose nominal size was 80 mm. As the experimental results showed, the measuring errors were all smaller than ±0.01 mm. Therefore, the calibration method of rotary axis proposed in the paper showed higher calibration precision and repeatability, which could meet the inspecting requirements of the shape and position parameters of film cooling holes.
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Key words:
- vision measurement /
- coordinate measuring machine /
- rotary table /
- film cooling hole
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表 1 测量结果
Table 1. Measuring results
No. Measuring results/mm Measuring errors/mm 1 80.006 0.006 2 80.008 0.008 3 79.995 −0.005 4 80.006 0.006 5 79.992 −0.008 6 79.993 −0.007 7 79.996 −0.004 8 80.009 0.009 9 80.005 0.005 10 80.006 0.006 -
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