A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision
Abstract
:1. Introduction
2. Principle for Contouring Error Detection Using a Single Camera
2.1. Measurement System and Principle
2.2. Camera Calibration Method Considering the Distortion Partition of DOF
3. High Precision 3D Positioning of Machine Tool Movement
3.1. High-Quality Image Acquisition for Machine Tool Movement
3.2. Accurate Encoding and Identification Method for Coded Targets
- A)
- Case 1: only one encoding region around the central pointAs shown in Figure 10a, suppose that this encoding region consists of “1”, then the number of “0” with respect to the non-encoding region is , and we get the binary sequence .
- B)
- Case 2: more than one encoding region around the central pointThe numbers of “0” in the non-encoding region between two adjacent encoding regions (Figure 10b) can be deduced by . Where describes the angle formed by adjacent two vectors (e.g., ), ; and are the numbers of “1” in two adjacent encoding regions. By traversing the entire ring pattern, we get the binary sequence of..
- A)
- Case 1: if orAs shown in Figure 12, Let , and assume the first encoding region consists of number of “1”, where . First, numbers of “1” from the back to the front of this sequence are read and then connected with the following sequence to get the ; while the remain number of “1” in the first encoding region is denoted by . Finally, the new segment is obtained by connecting to .
- B)
- Case 2:binary numbers from the back of the entire binary sequence to the front are read to form (Figure 13), and the remain binary sequence is denoted by . Then, the new segment is obtained by connecting to .
4. 3D High Spatial-Temporal Measurement of Large-Scale and Relatively High-Dynamic Contouring Error
4.1. Pose Estimation Algorithms Comparison
4.2. Wide Range Contouring Error Detection
5. Contouring Error Detection Test and Vision Measurement Accuracy Verification
5.1. Experimental Equipment and Tested Trajectories
5.2. Experiment for Verifying the Proposed Calibration Method
- (1)
- Accuracy verification of equal-radius partition modelAs shown in Figure 21b,c, distortion curve of each subregion is different from that of calculated by all the lines in the image. Firstly, the performance of in-plane distortion partition model is judged by the straightness error after distortion correction. As illustrated in Table 3, the maximum and average straightness errors of each subregion are smaller than that are calculated by all the lines in the image, which indicate the accuracy of the proposed partition method. The optimal distortion curve for each subregion can be seen in the enlarged view of Figure 21c.
- (2)
- Accuracy verification of the 3D distortion partition modelThen, based on the front and rear object planes with known depths and the calibrated distortion parameters, the distortion coefficients on each partition of the two middle object planes are estimated by the method in Section 2.2. Thereafter, the derived distortions of the two middle planes are compared with that calculated directly by the plumb-line method to verify the accuracy of the proposed DOF distortion partition model.Table 4 illustrates the difference |C − O| between the distortion calculated with or without DOF distortion partition model and the observed one. The results indicate that the maximum and average differences are 1.75 μm and 0.86 μm, while the distortion differences calculated without the partition model are more than twice the corresponding difference calculated with the partition distortion, which show the high accuracy of the proposed partition method.
5.3. Case Study for Illustrating Advantages in 3D High Temporal-Spatial Measurement
5.4. Case Study for Highlighting 3D Detection of Contouring Error of a Space Trajectory
5.5. Remarks on Major Contributors for Measurement Uncertainties
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
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Index | Parameter Values |
---|---|
Camera and resolution | Camera: EoSens® 25 CXP; Full resolution: 5120 × 5120 pixels |
Lens | Nikon 24–70 mm |
Lens mount | F-Mount |
Exposure time | 3000 μs |
Spatial resolution (without subpixel accuracy) | 0.0195 mm/pixel |
Size of the measurement basis | 231 mm × 231 mm |
FOV | 60 mm × 60 mm |
Light source | Flat backlight |
Light-emitting area | 250 mm × 250 mm |
Number of coding primitives | 1024 (see Figure 6a for detail) |
Geometrical accuracy of single coded targets | <1 μm |
Calibration accuracy of spatial geometric information | 0.5 μm |
Camera Resolution | 5120 × 5120 pixels | 3072 × 3072 pixels | 1024 × 1024 pixels |
---|---|---|---|
The collected static image | | | |
Allowable maximum FPS | 33 FPS | 208 FPS | 308 FPS |
FPS used in tests | 25 FPS | 100 FPS | 150 FPS |
Subregion 1 | Subregion 2 | Subregion 3 | Subregion 4 | Entire Image | |
---|---|---|---|---|---|
Maximum distance error/pixel | 0.12 | 0.19 | 0.45 | 0.81 | 3.53 |
Mean distance error/pixel | 0.07 | 0.06 | 0.11 | 0.24 | 0.27 |
Object Plane /mm | Subregion | Distortion | ||||
---|---|---|---|---|---|---|
Observed (μm) | With Partition Model | Without Partition Model | ||||
Calculated (μm) | Difference |C − O| (μm) | Calculated (μm) | Difference |C − O| (μm) | |||
428 mm | Subregion 1 (Radial distance = 13 mm) | − 0.31 | − 0.3 | 0.01 | − 0.34 | 0.03 |
Subregion 2 (Radial distance = 26 mm) | − 20.25 | − 20.09 | 0.16 | − 17.63 | 2.62 | |
Subregion 3 (Radial distance = 39 mm) | − 31.95 | − 30.85 | 1.1 | − 28.94 | 3.01 | |
Subregion 4 (Radial distance = 52 mm) | − 37.35 | − 36.05 | 1.3 | − 32.67 | 4.68 | |
448 mm | Subregion 1 (Radial distance = 14 mm) | − 0.23 | − 0.22 | 0.01 | − 0.21 | 0.02 |
Subregion 2 (Radial distance = 28 mm) | − 14.42 | − 13.78 | 0.64 | − 12.9 | 1.52 | |
Subregion 3 (Radial distance = 42 mm) | − 24.31 | − 3.23 | 1.08 | − 21.83 | 2.48 | |
Subregion 4 (Radial distance = 56 mm) | − 27.97 | − 26.22 | 1.75 | − 24.76 | 3.21 |
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Li, X.; Liu, W.; Pan, Y.; Ma, J.; Wang, F. A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision. Sensors 2019, 19, 744. https://doi.org/10.3390/s19030744
Li X, Liu W, Pan Y, Ma J, Wang F. A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision. Sensors. 2019; 19(3):744. https://doi.org/10.3390/s19030744
Chicago/Turabian StyleLi, Xiao, Wei Liu, Yi Pan, Jianwei Ma, and Fuji Wang. 2019. "A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision" Sensors 19, no. 3: 744. https://doi.org/10.3390/s19030744
APA StyleLi, X., Liu, W., Pan, Y., Ma, J., & Wang, F. (2019). A Knowledge-Driven Approach for 3D High Temporal-Spatial Measurement of an Arbitrary Contouring Error of CNC Machine Tools Using Monocular Vision. Sensors, 19(3), 744. https://doi.org/10.3390/s19030744