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激光照射到深孔内壁后[13],由于内壁不是平面,所以反射光变成了受内壁曲率及反射率影响的漫反射光,但可以看出,只有和入射光角度相近的角度范围才能直接通过反射镜反射至振镜,从而被CCD1和CCD2采集得到,而角度超过该阈值时必然会在管内形成多次漫反射,即使能够最终达到振镜面,其达到时间也明显慢于测试位置的光信号,所以采用谐波调制的方式可以通过回波信号相位信息将不再时间窗函数中的数据剔除,从而提升检测信噪比。
设CCD1的坐标系O1(x1, y1, z1),CCD2的坐标系O2(x2, y2, z2),与之对应的像面可表示为OL1(xL1, yL1)和OL2(xL2, yL2)。则深孔内壁上测试区域中任意点P(xP, yP, zP)可以通过两个CCD的测试数据进行联合求解。
$$ \left[ {\begin{array}{*{20}{c}} {{x_1}} \\ {{y_1}} \\ {{\textit{z}_1}} \\ 1 \end{array}} \right]{\text{ = }}\left[ {\begin{array}{*{20}{c}} {{r_{11}}}&{{r_{12}}}&{{r_{13}}}&{{t_1}} \\ {{r_{21}}}&{{r_{22}}}&{{r_{23}}}&{{t_2}} \\ {{r_{31}}}&{{r_{32}}}&{{r_{33}}}&{{t_3}} \\ 0&0&0&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_2}} \\ {{y_2}} \\ {{\textit{z}_2}} \\ 1 \end{array}} \right] $$ (1) $$ R = \left[ {\begin{array}{*{20}{c}} {{r_{11}}}&{{r_{12}}}&{{r_{13}}} \\ {{r_{21}}}&{{r_{22}}}&{{r_{23}}} \\ {{r_{31}}}&{{r_{32}}}&{{r_{33}}} \end{array}} \right]\text{,}T = \left[ {\begin{array}{*{20}{c}} {{t_1}} \\ {{t_2}} \\ {{t_3}} \end{array}} \right] $$ (2) 式中:R为两个CCD的旋转矩阵;T为两个CCD的平移矩阵。在R和T中,参数r11~r33和t1、t2、t3是根据两个CCD的预设位置和两个CCD空间坐标系的关系计算得到的。由此可见,将CCD1中的数据统一到CCD2中后,就能将目标位置的点数据进行解算。对于待测点P而言,对于CCD1可表示为:
$$ \left[ {\begin{array}{*{20}{c}} {{x_1}} \\ {{y_1}} \\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{c_1}}&0&0&0 \\ 0&{{c_1}}&0&0 \\ 0&0&1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_P}} \\ {{y_P}} \\ {{\textit{z}_P}} \\ 1 \end{array}} \right] $$ (3) CCD2可表示为:
$$ \left[ {\begin{array}{*{20}{c}} {{x_2}} \\ {{y_2}} \\ 1 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{c_2}}&0&0&0 \\ 0&{{c_2}}&0&0 \\ 0&0&1&0 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{x_P}} \\ {{y_P}} \\ {{\textit{z}_P}} \\ 1 \end{array}} \right] $$ (4) 式中:c1和c2表示坐标转换系数。
将公式(2)代入公式(3)和公式(4)可以得到P点的坐标表达式为:
$$ \left\{ \begin{gathered} {X_P}\left| {_1} \right. = \frac{{{x_1}}}{{{c_1}}}{Z_P} \hfill \\ {Y_P}\left| {_1} \right. = \frac{{{y_1}}}{{{c_1}}}{Z_P} \hfill \\ {Z_P}\left| {_1} \right. = \frac{{{c_1}\left( {{c_2}{t_1} - {x_2}{t_3}} \right)}}{{{x_2}{k_1} - {c_2}{k_2}}} \hfill \\ \end{gathered} \right. $$ (5) 其中,c1和c2表示坐标转换系数,k1和k2为解算系数,则:
$$ \left\{ \begin{gathered} {k_1} = {r_{31}}{x_1} + {r_{32}}{y_1} + {c_1}{r_{33}} \hfill \\ {k_2} = {r_{11}}{x_1} + {r_{12}}{y_1} + {c_1}{r_{13}} \hfill \\ \end{gathered} \right. $$ (6) 由于测试深孔内壁前,系统可以通过标定获取旋转矩阵和平移矩阵的参数值,故P点的坐标值变成通过两组已知测量量求解一组未知量的计算。
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为了对比不同深孔的光学检测效果,分别选用了三种深孔类型:(1) 孔深5 cm,孔径5 cm;(2) 孔深15 cm,孔径9 cm;(3) 孔深50 cm,孔径15 cm。通过该系统获取孔内壁点云信息,然后将重建的内壁三维面型与理想深孔数模点云位置进行对比,分析深孔加工偏差程度。
插入深孔的反射镜直径为4 cm,对光轴近轴范围的线激光反射并成像于两个固定位置CCD上,振镜扫描速度为10次/s,采集得到的点云通过MATLAB进行滤波。滤波函数与谐波信号匹配,对光程不符合测试范围的测试点进行剔除,然后对剩余有效点云进行三维重建,一个谐振调制周期的重建结果见图3。
由图3 (a)和(b)可以看出,在采用谐波匹配点云优化算法前,点云总量大,但有很多点的位置偏差明显较大,分析认为这些点很多是由于在深孔内壁进行一次或多次反射叠加产生的,所以已经无法反映真实的深孔内壁位置信息。而通过与谐波频率匹配的闸门信号对CCD采集信号进行滤波,就能将非一次反射的回波信号屏蔽,从而仅获取扫描线激光近轴条件的回波信号。平均偏差从0.53 mm降低至0.12 mm。可见,采用优化算法对于提升深孔内壁点云获取速度和抑制杂散点具有很好的效果。
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为了验证该系统计算的内壁点坐标位置精确程度,采用切割机将深孔从中间切开,从而获得一个内半圆柱表面,该表面就是深孔内壁的一次。若该表面测试结果符合设计要求,则可认为在反射镜测试区域对称的深孔中,三维面型的获取是一致的。采用Handyscan对相同测试区域的内壁面进行扫描,然后对比两组数据之间位置偏差,从而分析系统的位置计算精度。位置偏差如图4所示。
由图4 (a)和(b)可以看出,系统计算得到的点位置在x轴和y轴上与Handyscan的测试数据相近。x轴上绝大多数测试点位置偏差在0.1~0.4 mm之间,均值为0.240 mm;y轴上绝大多数测试点位置偏差在0.1~0.4 mm之间,均值为0.228 mm。其截面距离关系有:
$$ d = \sqrt {{x^2} + {y^2}} $$ (7) 故两个方向上的综合测试精度均值为0.234 mm。总体上看,系统对深孔内壁三维面型检测的精度优于引言中较通用的内壁面型检测方法。
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通过对比相同范围深孔内壁的三维面型数据获取时间,分析讨论了算法优化前后的用时,并对5 cm×5 cm范围的三维重建进行分析,以在固定范围内递增采样点数的方式对比算法的收敛速度,测试结果如图5所示。
根据不同采样点数对应的计算时间可以看出,当总采样点数较小的时候,优化前后的差异不大,基本都是在2.4 s左右完成三维点云数据的重建。但是当固定测试区域中的采样点逐渐增加时,优化算法的效果就逐渐明显了,当采样点超过2000个时,两种算法的用时曲线发生分离,当达到3500点左右时,优化后算法基本保持在12.4 s,而优化后仅为7.9 s。由于测试限定范围区间,所以采样点数设定在5000个以下,由此可以看出采用谐波匹配滤波算法进行优化可以有效降低系统的运算时间成本。
Three-dimensional surface profile analysis system of deep hole inner wall based on laser harmonic modulation
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摘要: 为了快速精确地获取深孔结构内壁三维面型,从而分析深孔加工质量,提出了一种基于激光谐波调制的线型扫描系统,设计了可深入深孔结构的反射式光学系统。研究了通过时间窗滤波的谐波匹配点云优化算法,该算法利用谐波调制相位范围对近轴线扫描区域进行阈值分离,从而完成点云数据的滤波。实验针对三种不同类型的深孔进行了测试,并采用Handyscan三维成像仪进行了点云数据对比。文中对5 cm×5 cm的内壁区域进行了量化分析, 对比了优化前后的三维点云图像。优化前的点云中明显包含很多杂散点,综合平均偏差为0.53 mm,而采用优化后,噪声被有效抑制,综合平均偏差降为0.12 mm。在x轴方向上,系统位置偏差均值为0.240 mm,在y轴方向上,系统位置偏差均值为0.228 mm。由于优化后降低了需要计算的点云总量,故其收敛速度也有一定的改善,在3000点以上趋于稳定,约为优化前用时的65.8%。可见该系统适用于深孔内壁三维面型检测,为深孔测试与数据降噪提供了新的思路。Abstract: In order to quickly and accurately obtain the three-dimensional surface profile of the inner wall of the deep hole structure and analyze the quality of the deep hole processing, a line scanning system based on laser harmonic modulation was proposed, and a reflective optical system that can penetrate deep into the deep hole structure was designed. The point cloud optimization algorithm for harmonic matching through time window filtering was studied. The algorithm used the harmonic modulation phase range to threshold the near-axis scanning area, thereby completing the point cloud data filtering. Experiments were conducted on three different types of deep holes, and the point cloud data was compared with the Handyscan three-dimensional imager. In this paper, the inner wall area of 5 cm×5 cm was quantitatively analyzed, and the three-dimensional point cloud images before and after optimization were compared. The point cloud before optimization obviously contained many stray points, and the comprehensive average deviation was 0.53 mm. After optimization, the noise was effectively suppressed, and the comprehensive average deviation was reduced to 0.12 mm. In the x-axis direction, the average value of the system position deviation was 0.240 mm, and in the y-axis direction, the average value of the system position deviation was 0.228 mm. Since the total amount of point cloud that needs to be calculated was reduced after optimization, the convergence speed had also been improved to a certain extent, and it stabilized above 3000 points, which was about 65.8% of the time before optimization. It can be seen that the system is suitable for the three-dimensional surface inspection of the inner wall of deep holes, and it provided a new idea for deep hole testing and data noise reduction.
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Key words:
- laser imaging /
- deep hole testing /
- harmonic modulation /
- threshold noise reduction
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