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Mini Milling Cutter Measurement Based on Machine Vision
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1807 – 1811 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
Mini Milling Cutter Measurement Based on Machine Vision Guo Shuxiaa, Zhang Jianchengb, Jiang Xiaofenga, Peng Yina, Wang Leia, a* a
Dept. of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China b Xiamen Tungsten CO., Ltd
Abstract A machine vision based method to measure diameter and maximum swing diameter of mini milling cutter is proposed in this paper. The measure system is made up with a telecentric backlight illuminator, a bilateral-telecentric lens, a CCD camera and a rotate stage. A sub-pixel threshold segmentation algorithm based on gray histogram is used to detect the edges of mini milling cutter. The experiment results show that the resolution and reproducibility of the vision system are 1.0μm and 2.2μm, and the uncertainties are 0.34μm and 2.5μm for diameter and maximum swing diameter separately.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Machine vision; mini milling cutter; diameter; Maximum swing diameter.
1. Structure/Introduction As for the development of the manufacture technology, it is made increasingly needed of on-line, high-precision geometric measurement[1]. Machine vision is to achieve hominine visual function, or realize measurement and judgment by machines instead of eyes[2]. As one of non-contact measurement methods, machine vision measurement doesn't influence the structure and motion characteristics of objects[3], and this technique is widely used in quality detection, electronic semiconductor, medical treatment, etc. [4]. In this article, a machine vision based geometric measurement system for mini milling cutter is designed, which completes an on-line precision measurement of the diameter and maximum swing
* Corresponding author. Tel.: +86-592-218-4852; fax: +86-592-218-5836. E-mail address: [email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.336
1808 2
Shuxia / Procedia Engineering (2011) 1807 – 1811 GuoGuo Shuxia ，etetal/al.Procedia Engineering 0015 (2011) 000–000
diameter, which realize 100% quality control of mini milling cutter manufacture. 2. System Design Usually, a system of machine vision consists of three modules: image capture, image process and analyze, output and display[2]. Firstly, a telecentric back-light illuminator consisted of a telecentric lens and a blue LED is designed, which makes it easy to get clear contour of the mini milling cutter. Besides, this kind of light can successfully avoid the influence of diffraction caused by the thickness of the mini milling cutter [2]. Fig. 1 shows the physical map of the system. By the way, the rotate stage is combined with a rotary encoder, which can trigger the camera, and captures images at a speed of 25 frames per circle while the mini milling cutter rotates.
Fig. 1 Physical map of the system; 1. camera(UI-2250SE-M-GL), 2. bilateral telecentric lens(NAVITAR 1-17797 2/3’’, 1.3 × ), 3. tested milling cutter 4. telecentric back light, 5. high precision rotate stage.
3. Algorithm Design Mini milling cutter to be measured is shown in Fig. 2(a). And as shown in Fig. 2(b), the D1 describes the diameter, which would be considered as height of the minimum enclosing rectangle of the mini milling cutter, and D2 describes the maximum swing diameter, the diameter of the maximum cylinder formed by milling cutter rotation. The tooth would position differently when milling cutter rotates, leading to the change of measure result of the diameter. Fig. 3 shows this change. Thus as rotation finished, the maximum result is preferred as the result of diameter.
Fig. 2 (a)Physical map of the tested drill; (b) Description of tested geometric values —o— sub-pixel threshold —*— sub-pixel edge extraction
key tasks here as aremini edge extraction and diameter calculating. Two methods of edge detection are Fig.The 3 Diameter changes milling cutter rotates; Fig. 4 Stability comparison of two methods
Guo Shuxia et， al.et/ al Procedia Engineering 15 (2011) 1807 – 1811 Guo Shuxia / Procedia Engineering 00 (2011) 000–000
1809 3
compared here, sub-pixel thresholding and sub-pixel edge extraction. Sub-pixel thresholding is based on gray value interpolation, and can achieve a more precise segmentation result[2][5]. And a Gaussian fitting is used to the gray histogram , which describes the grayscale function, and shows the number of pixels right at one grayscale[2], to get a more robust and self-adaptive gray threshold. Normally the edge based segmentation is more robust than threshold based one[2][5], but in our system the sub-pixel threshold shows a better repeatability because the well designed light source, high SNR of the CCD camera and the adaptive threshold. Fig. 4 shows diameter measurement stability using these two methods separately.
Fig. 5 (a)Flow chart of algorithm ; (b) extracted edges; (c) minimum enclosing rectangle of edges
Flow chart of algorithm designed is shown in Fig. 5(a). Firstly, threshold is found by gray value histogram. Secondly, the edge (shown in Fig. 5(b)) of the mini milling cutter would be extracted by subpixel threshold. Thirdly, minimum enclosing rectangle (shown in Fig. 5(c)) of the edge would be accessed, of which the height is saved as a “local diameter” at just the moment. Simultaneously, the row coordinates of the up and down edges of the mini milling cutter are saved in two arrays separately. As the rotation completed, the maximum of all these “local diameters” saved before can be considered as the diameter of the cutter. At the same time, the maximum difference between these two arrays of up and down rows is considered as the maximum swing diameter. 4. Experiments and Result Analysis 4.1. Camera calibration Camera calibration is an important part of precise vision measurement, which is used to get the inner and outer parameters of the camera and correct lens distortion[2][6]. Here the calibration is mainly to get the pixel size in vertical direction in order to determine the real size of tested geometric parameters[4]. A precise grid is driven by a X-Y stage(Steinmeyer OFD, KDT 105), 119 images are captured with 100μm steps. A shift of 30.2938 pixel can be detected in image for each 100μm displacement, so the relative pixel size ps would be calculated by formula 1. ps =
actualdistance(100μm) = 3.3010μm/ pixel pixeldistance(30.2938pixel)
(1)
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Shuxia / Procedia Engineering (2011) 1807 – 1811 GuoGuo Shuxia ，etetal/al.Procedia Engineering 0015 (2011) 000–000
A series of polynomials are fitted by data achieved above, which represent the distortion of the lens. The lowest three ones are shown in Formula 2~4, meaning that the coefficients of high-order are almost zero. So the distortion can be ignored. (2)
f ( x ) = 8.551x - 0.01809 f ( x ) = ( − 8 .527 × 10 −6 ) x 2 + 8 .552 x − 0 .03421 f ( x ) = ( − 5 .514 × 10
−6
3
2
) x + 0 .0002993 x + 8 .555 x − 0 .2892
(3) (4)
Where x means the sequence of the images, f(x) is the displacement of the grid image in pixels. 4.2. Resolution and Reproducibility The resolution of the system, saying the minimum distance the system could distinguish, is evaluated with precise grid doing one-way moving driven by the precise mobile stage. The distance is just the resolution when row coordinates of the tested edge change monotonously, which is 1.0μm here. Thus the resolution Res could be calculated by formula 5.
1.0μm = 0.30pixel 3.3010 μm/ pixel Besides, the reproducibility is also evaluated, saying the consistency of the result for the same quantum when measure condition changes[7]. Here it includes two parts. (1). The consistency of the coordinates of the tested edge when moving to the same position at different time; (2). The consistency of diameters when tested cylinder is in different positions. For part one, precise grid moves forward and back once for 2mm. Images are captured just when the tested edge moves to the same position. The repeatability of the coordinates in pixels is shown in Fig. 6(a). Concluding that the maximum difference is 0.68pixel, or 2.2μm, std is 0.12pixel, or 0.4μm. Res=
Fig 6 (a) result of part two about reproducibility; (b) result of part two about reproducibility
For part two, tested cylinder moves along vertical direction of the camera, images are captured for each moving. Then the diameter change is shown in Fig. 6(b), which concluded the maximum change is 0.41pixel, or 1.4μm, std is 0.22pixel, or 0.73μm. 4.3. Uncertainty Analysis For the diameter measurement, the uncertainty results from mainly four parts[7]: (1).the sampling deficiency; (2).the limitation of the system such as the noise of the CCD[8][9], the stability of the light source[10] etc.; (3).the incomplete definition of the diameter because of the possible taper; (4)the verticality approximation and suppose of the mini milling cutter[6]. Besides, for the maximum swing
(5)
Guo Shuxia et， al.et/ al Procedia Engineering 15 (2011) 1807 – 1811 Guo Shuxia / Procedia Engineering 00 (2011) 000–000
diameter, the cylindrical of the mini milling cutter and the concentricity of the rotate stage tremendously impacts the uncertainty of the result. In this paper, the standard deviation of the result is considered as the evaluation of the uncertainty[7]. Fig. 7 shows the results measuring 10 times for the mini milling cutter. The nominal diameter of the milling cutter is 2400μm. The standard deviations are 0.34μm, 2.5μm separately —o— Diameter —*— Maximum Swing Diameter
Fig 7 Measure results of diameter and maximum swing diameter
5. Conclusion An on-line vision based measure system for milling cutter is presented in this paper. The system is calibrated, the solution and reproducibility are evaluated, and an algorithm for precise measurement of diameter of the milling cutter based on gray value histogram and sub-pixel thresholding is proposed. As the results show, the measurement uncertainties are 0.34μm and 2.5μm for diameter and maximum swing diameter separately. References [1] Anders Ryberg, Anna-Karin Christiansson, Kenneth Eriksson. Accuracy Investigation of a Vision Based System for Pose Measurements. J Control, Automation, Robotics and Vision; 2006. p.1-6 [2] Carsten Steger, Markus Ulrich. Machine Vision Algorithms and Application. M Hsinghua University Publishing,BeiJing; 2009. [3] Meilian Liu, Kejie Li, Huimin Cai, and Ping Song. Vision Measurement Method for Impact Point in Large PlanarRegion. J Intelligent Control and Information Processing (ICICIP); 2010. p.379-83 [4] Yuan Jiangtao, Yang Li, Wang Xiaochuan, Zhang Jian, Jin Renxi. Measurement and Analysis of Water Mist Droplet Size Based on Machine Vision. J ACTA OPTICA SINICA 2009; p.2842-7 [5] Xu Guo-Sheng. System of Measuring the Sub-pixel Edge of Linear CCD Based on Auto Focusing. J Information and Computing; 2010. p.78-81 [6] Rafael C.Conzalez, Richard E. Woods. Digital Image Processing Second Edition. M Publishing House of Electronics Industry, BeiJing; 2009. [7] Liu Zhimin, Liu Feng. Evaluation and Expression of Uncertainty in Measurement. J China Academic Journal Electronic Publishing House; 1996. p.96-9 [8] G. Hausler, P, Ettl, M. Schenk et al. Limits of Optical Range Sensors and How to Exploit Them. J In Trends in Optics and Photonics, ICO IV, Springer Series in Optical Sciences; 1999. p.328-42 [9] Kim A. Winick. Cramér-Rao lower bounds on the performance of charge-coupled-device optical position estimators. J Journal of the Optical Society of America; 1986. p. 1809-15 [10] Dainty, J. C.(1970) Some Statistical Properties of Random Speckle Patterns in Coherent and Partially Coherent Illumination. J Journal of Modern Optics; 1970. p.761-72
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Procedia Engineering
Procedia Engineering 00 (2011) 000–000 Procedia Engineering 15 (2011) 1807 – 1811 www.elsevier.com/locate/procedia
Advanced in Control Engineeringand Information Science
Mini Milling Cutter Measurement Based on Machine Vision Guo Shuxiaa, Zhang Jianchengb, Jiang Xiaofenga, Peng Yina, Wang Leia, a* a
Dept. of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005, China b Xiamen Tungsten CO., Ltd
Abstract A machine vision based method to measure diameter and maximum swing diameter of mini milling cutter is proposed in this paper. The measure system is made up with a telecentric backlight illuminator, a bilateral-telecentric lens, a CCD camera and a rotate stage. A sub-pixel threshold segmentation algorithm based on gray histogram is used to detect the edges of mini milling cutter. The experiment results show that the resolution and reproducibility of the vision system are 1.0μm and 2.2μm, and the uncertainties are 0.34μm and 2.5μm for diameter and maximum swing diameter separately.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [CEIS 2011] Keywords: Machine vision; mini milling cutter; diameter; Maximum swing diameter.
1. Structure/Introduction As for the development of the manufacture technology, it is made increasingly needed of on-line, high-precision geometric measurement[1]. Machine vision is to achieve hominine visual function, or realize measurement and judgment by machines instead of eyes[2]. As one of non-contact measurement methods, machine vision measurement doesn't influence the structure and motion characteristics of objects[3], and this technique is widely used in quality detection, electronic semiconductor, medical treatment, etc. [4]. In this article, a machine vision based geometric measurement system for mini milling cutter is designed, which completes an on-line precision measurement of the diameter and maximum swing
* Corresponding author. Tel.: +86-592-218-4852; fax: +86-592-218-5836. E-mail address: [email protected]
1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.08.336
1808 2
Shuxia / Procedia Engineering (2011) 1807 – 1811 GuoGuo Shuxia ，etetal/al.Procedia Engineering 0015 (2011) 000–000
diameter, which realize 100% quality control of mini milling cutter manufacture. 2. System Design Usually, a system of machine vision consists of three modules: image capture, image process and analyze, output and display[2]. Firstly, a telecentric back-light illuminator consisted of a telecentric lens and a blue LED is designed, which makes it easy to get clear contour of the mini milling cutter. Besides, this kind of light can successfully avoid the influence of diffraction caused by the thickness of the mini milling cutter [2]. Fig. 1 shows the physical map of the system. By the way, the rotate stage is combined with a rotary encoder, which can trigger the camera, and captures images at a speed of 25 frames per circle while the mini milling cutter rotates.
Fig. 1 Physical map of the system; 1. camera(UI-2250SE-M-GL), 2. bilateral telecentric lens(NAVITAR 1-17797 2/3’’, 1.3 × ), 3. tested milling cutter 4. telecentric back light, 5. high precision rotate stage.
3. Algorithm Design Mini milling cutter to be measured is shown in Fig. 2(a). And as shown in Fig. 2(b), the D1 describes the diameter, which would be considered as height of the minimum enclosing rectangle of the mini milling cutter, and D2 describes the maximum swing diameter, the diameter of the maximum cylinder formed by milling cutter rotation. The tooth would position differently when milling cutter rotates, leading to the change of measure result of the diameter. Fig. 3 shows this change. Thus as rotation finished, the maximum result is preferred as the result of diameter.
Fig. 2 (a)Physical map of the tested drill; (b) Description of tested geometric values —o— sub-pixel threshold —*— sub-pixel edge extraction
key tasks here as aremini edge extraction and diameter calculating. Two methods of edge detection are Fig.The 3 Diameter changes milling cutter rotates; Fig. 4 Stability comparison of two methods
Guo Shuxia et， al.et/ al Procedia Engineering 15 (2011) 1807 – 1811 Guo Shuxia / Procedia Engineering 00 (2011) 000–000
1809 3
compared here, sub-pixel thresholding and sub-pixel edge extraction. Sub-pixel thresholding is based on gray value interpolation, and can achieve a more precise segmentation result[2][5]. And a Gaussian fitting is used to the gray histogram , which describes the grayscale function, and shows the number of pixels right at one grayscale[2], to get a more robust and self-adaptive gray threshold. Normally the edge based segmentation is more robust than threshold based one[2][5], but in our system the sub-pixel threshold shows a better repeatability because the well designed light source, high SNR of the CCD camera and the adaptive threshold. Fig. 4 shows diameter measurement stability using these two methods separately.
Fig. 5 (a)Flow chart of algorithm ; (b) extracted edges; (c) minimum enclosing rectangle of edges
Flow chart of algorithm designed is shown in Fig. 5(a). Firstly, threshold is found by gray value histogram. Secondly, the edge (shown in Fig. 5(b)) of the mini milling cutter would be extracted by subpixel threshold. Thirdly, minimum enclosing rectangle (shown in Fig. 5(c)) of the edge would be accessed, of which the height is saved as a “local diameter” at just the moment. Simultaneously, the row coordinates of the up and down edges of the mini milling cutter are saved in two arrays separately. As the rotation completed, the maximum of all these “local diameters” saved before can be considered as the diameter of the cutter. At the same time, the maximum difference between these two arrays of up and down rows is considered as the maximum swing diameter. 4. Experiments and Result Analysis 4.1. Camera calibration Camera calibration is an important part of precise vision measurement, which is used to get the inner and outer parameters of the camera and correct lens distortion[2][6]. Here the calibration is mainly to get the pixel size in vertical direction in order to determine the real size of tested geometric parameters[4]. A precise grid is driven by a X-Y stage(Steinmeyer OFD, KDT 105), 119 images are captured with 100μm steps. A shift of 30.2938 pixel can be detected in image for each 100μm displacement, so the relative pixel size ps would be calculated by formula 1. ps =
actualdistance(100μm) = 3.3010μm/ pixel pixeldistance(30.2938pixel)
(1)
1810 4
Shuxia / Procedia Engineering (2011) 1807 – 1811 GuoGuo Shuxia ，etetal/al.Procedia Engineering 0015 (2011) 000–000
A series of polynomials are fitted by data achieved above, which represent the distortion of the lens. The lowest three ones are shown in Formula 2~4, meaning that the coefficients of high-order are almost zero. So the distortion can be ignored. (2)
f ( x ) = 8.551x - 0.01809 f ( x ) = ( − 8 .527 × 10 −6 ) x 2 + 8 .552 x − 0 .03421 f ( x ) = ( − 5 .514 × 10
−6
3
2
) x + 0 .0002993 x + 8 .555 x − 0 .2892
(3) (4)
Where x means the sequence of the images, f(x) is the displacement of the grid image in pixels. 4.2. Resolution and Reproducibility The resolution of the system, saying the minimum distance the system could distinguish, is evaluated with precise grid doing one-way moving driven by the precise mobile stage. The distance is just the resolution when row coordinates of the tested edge change monotonously, which is 1.0μm here. Thus the resolution Res could be calculated by formula 5.
1.0μm = 0.30pixel 3.3010 μm/ pixel Besides, the reproducibility is also evaluated, saying the consistency of the result for the same quantum when measure condition changes[7]. Here it includes two parts. (1). The consistency of the coordinates of the tested edge when moving to the same position at different time; (2). The consistency of diameters when tested cylinder is in different positions. For part one, precise grid moves forward and back once for 2mm. Images are captured just when the tested edge moves to the same position. The repeatability of the coordinates in pixels is shown in Fig. 6(a). Concluding that the maximum difference is 0.68pixel, or 2.2μm, std is 0.12pixel, or 0.4μm. Res=
Fig 6 (a) result of part two about reproducibility; (b) result of part two about reproducibility
For part two, tested cylinder moves along vertical direction of the camera, images are captured for each moving. Then the diameter change is shown in Fig. 6(b), which concluded the maximum change is 0.41pixel, or 1.4μm, std is 0.22pixel, or 0.73μm. 4.3. Uncertainty Analysis For the diameter measurement, the uncertainty results from mainly four parts[7]: (1).the sampling deficiency; (2).the limitation of the system such as the noise of the CCD[8][9], the stability of the light source[10] etc.; (3).the incomplete definition of the diameter because of the possible taper; (4)the verticality approximation and suppose of the mini milling cutter[6]. Besides, for the maximum swing
(5)
Guo Shuxia et， al.et/ al Procedia Engineering 15 (2011) 1807 – 1811 Guo Shuxia / Procedia Engineering 00 (2011) 000–000
diameter, the cylindrical of the mini milling cutter and the concentricity of the rotate stage tremendously impacts the uncertainty of the result. In this paper, the standard deviation of the result is considered as the evaluation of the uncertainty[7]. Fig. 7 shows the results measuring 10 times for the mini milling cutter. The nominal diameter of the milling cutter is 2400μm. The standard deviations are 0.34μm, 2.5μm separately —o— Diameter —*— Maximum Swing Diameter
Fig 7 Measure results of diameter and maximum swing diameter
5. Conclusion An on-line vision based measure system for milling cutter is presented in this paper. The system is calibrated, the solution and reproducibility are evaluated, and an algorithm for precise measurement of diameter of the milling cutter based on gray value histogram and sub-pixel thresholding is proposed. As the results show, the measurement uncertainties are 0.34μm and 2.5μm for diameter and maximum swing diameter separately. References [1] Anders Ryberg, Anna-Karin Christiansson, Kenneth Eriksson. Accuracy Investigation of a Vision Based System for Pose Measurements. J Control, Automation, Robotics and Vision; 2006. p.1-6 [2] Carsten Steger, Markus Ulrich. Machine Vision Algorithms and Application. M Hsinghua University Publishing,BeiJing; 2009. [3] Meilian Liu, Kejie Li, Huimin Cai, and Ping Song. Vision Measurement Method for Impact Point in Large PlanarRegion. J Intelligent Control and Information Processing (ICICIP); 2010. p.379-83 [4] Yuan Jiangtao, Yang Li, Wang Xiaochuan, Zhang Jian, Jin Renxi. Measurement and Analysis of Water Mist Droplet Size Based on Machine Vision. J ACTA OPTICA SINICA 2009; p.2842-7 [5] Xu Guo-Sheng. System of Measuring the Sub-pixel Edge of Linear CCD Based on Auto Focusing. J Information and Computing; 2010. p.78-81 [6] Rafael C.Conzalez, Richard E. Woods. Digital Image Processing Second Edition. M Publishing House of Electronics Industry, BeiJing; 2009. [7] Liu Zhimin, Liu Feng. Evaluation and Expression of Uncertainty in Measurement. J China Academic Journal Electronic Publishing House; 1996. p.96-9 [8] G. Hausler, P, Ettl, M. Schenk et al. Limits of Optical Range Sensors and How to Exploit Them. J In Trends in Optics and Photonics, ICO IV, Springer Series in Optical Sciences; 1999. p.328-42 [9] Kim A. Winick. Cramér-Rao lower bounds on the performance of charge-coupled-device optical position estimators. J Journal of the Optical Society of America; 1986. p. 1809-15 [10] Dainty, J. C.(1970) Some Statistical Properties of Random Speckle Patterns in Coherent and Partially Coherent Illumination. J Journal of Modern Optics; 1970. p.761-72
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