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Error Analysis of a Kind of Binocular Visual Alignment Device

Zhi-Ze Wang, Zhi-Feng Lou, Hong-Xia Song*, Xiao-Dong Wang, Xing-Yuan Wang

Key Laboratory for Micro/Nano Technology and System of Liaoning Province, Dalian University of Technology, Dalian, Liaoning, China

Abstract: Precision assemblies of small interference fitting parts are usually achieved by precision press-fit instrument. As the key module of the precision assembly system, the alignment accuracy of the visual alignment device (VAD) directly affects the assembly quality. In this paper, a precision press-fit instrument was introduced, in which contain a kind of binocular visual alignment device. For this kind of VAD is combined with two cameras and a three-dimensional precision displacement platform, a calibration method was introduced in this paper to measure the tilt angle of the guide rail Z, and the error caused by the tilt of the three guide rails of VAD was analyzed. Finally, the final transfer equation between this two cameras was obtained by taking the error into account. The experimental results show that the analytical method can help the press-fit instrument improve the alignment accuracy effectively, and the alignment accuracy can reach ±10μm, so the instrument can meet the requirement of the assembly work.

Keywords: precision assemblies, visual alignment device, alignment accuracy, transfer equation, tilt angle

Citation: Zhi-Ze Wang, Zhi-Feng Lou, Hong-Xia Song, Xiao-Dong Wang, Xing-Yuan Wang, Error Analysis of a Kind of Binocular Visual Alignment Device. American Journal of Mechanical Engineering, 5 (2). 64-69. January 2017. doi:10.12691/ajme-5-2-5

1. Introduction

The device, which is composed of precision micro driver and sensing device, has been widely used in industry, military and biological fields in recent years because of its small size and reliable performance [1]. In order to improve the assembly quality of micro assembly and the consistency of the product, the manual assembly is gradually replaced by the precision automatic assembly instrument. The vision alignment device (VAD) is indispensable in the automatic precision assembly system, which has the advantages of non-contact, flexibility, high precision, high speed, automation and high intelligent level [2]. Using binocular vision to complete the position detection of circular hole and the alignment work can overcome the disadvantages of the traditional positioning method, which needs locating blocks and has poor flexibility [3,4,5], and the alignment accuracy of the VAD directly affects the assembly quality.

The vision alignment device is generally composed of CCD, optical mirror group, light source and three-dimensional precision displacement platform. An extensive research have been done to reduce the visual alignment error. Xin Ye et al [6] proposed a sub-pixel calibration method to reduce the assembly error, caused by the lens’ distortion of the VAD. Guihua Liu et al [7] put forward a novel camera calibration method of variable focal length, based on the orthogonal rotation matrix. The intrinsic and extrinsic camera parameters in each image linearly can be calculated by this means as long as at least six known points are captured in each image. The experimental results showed that this method has high accuracy and robust. In order to reduce the error caused by the instability of the light source, Zhaobang Pu et al [8] analyzed the intensity, stability and uniformity of the light source in VAD, and designed ring type cold illumination that can automatic adjust intensity of light. Yonglong Tang et al [9]. studied the alignment error which was caused by the prism mounting error in the vision system of the coaxial optical alignment device, and the influence equation of the error was given. Based on the ruled surface theory, Qijing Tang et al [10] established the mathematical model of ruled surfaces. The overall calibration of the visual detective system was realized, and the visual detection error was controlled within ±3%. Daljae Lee et al [11]. proposed a dual imaging system to achieve high alignment accuracy in chip packaging. A vision servoing algorithm had been designed to determine the direction and speed of translation and rotation, the alignment accuracy and the tracking speed had been improved. Y. S. Ihn et al [12]. introduced a fast vision processing algorithm, a modified binary region median filter combined with a labeling based segmentation scheme, for a machine vision system. This method reduced the processing time, and it helped the system become more stable and less noise sensitive even for the light reflections. CY Nian et al [13] designed three-axis motion control mechanism and applied it into an auto-alignment vision system. By analyzing the coordinate relationship, the compensation amount in the 3 axis direction is obtained, and the alignment precision was achieved within 5μm.

At present, the method of improving the visual alignment accuracy, which is combined with camera and three-dimensional precision displacement platform, is mostly based on the calibration method, image processing algorithm and visual alignment algorithm. However, the installation error of the guide rail in the device has been not analyzed. For this kind of VAD, even if the two cameras’ alignment accuracy is very high, the final alignment accuracy is still largely affected by the mounting precision of the three guide rails. As a result, it is significant to guarantee the alignment precision by making compensation according to the installation error of the camera guide rail. In this paper, the error caused by the installation error between three camera guide rails was analyzed, based on the developed precision press-fit instrument, and the final alignment error transfer equation was deduced.

2. Accuracy Analysis

2.1. Press-fit Instrument and the Small Interference Fitting Parts

As shown in Figure 1, the main frame of the press-fit instrument is composed of four guide shafts and upper and lower beams. In the assembly process, the assembly components are mounted on the upper and lower fixtures which are fixed on the moving beam and XY precision stage respectively. The relative position of the assembly components are measured by the visual alignment device. The adjustment of part’s posture is realized by the precision turntable and XY precision stage. The force sensor and linear grating scale are used to measure the pressing force and the displacement of moving beam respectively. The moving beam is driven by a ball screw actuator to move along the guide shaft to complete the press-fit work.

Figure 1. Precision press-fit instrument

As shown in Figure 2, the coaxiality, parallelism and perpendicularity of the small interference fitting parts are required. In this paper, the part which was fixed by the upper fixture was defined as part A, and the part which was fixed by the lower fixture was defined as part B. As shown in Figure 3, the assembly process of the small interference fitting parts was as follows:

1) Initialization: Open the press-fit program, initialize the instrument;

2) Feeding: Mounting part A and part B on the upper and lower fixture respectively;

3) Alignment: Moving the camera along three guide rails to the acquisition position to acquire the two parts’ images, then the deviation between two parts can be calculated and the XY precision stage were controlled by the industrial computer to adjust the position of the part B;

4) Press-fitting: The ball screw actuator drives moving beam to move down until the press force, fed back by the force sensor, reaches the threshold value n, and then control the moving beam moves up to the origin position;

5) End: Take out the assembly part, and prepare the next press work.

Figure 2. Assembly process of small interference fitting parts

Figure 3. Flowchart for the assembly process of the precision press-fit instrument

2.2. Visual Alignment Device and Alignment Strategy

The VAD (Figure 4) is mainly composed of the following components: two CCD, two light sources, two telecentric lenses, two mirrors and three precision guide rails. The cameras were moved to the image acquisition position by three-dimensional precision displacement platform (composed of X, Y, Z precision guide rail). In the process of coaxial alignment, the upper camera was moved to the image acquisition position to acquire the image of part A, and the image features were transferred into lower camera through the transfer equation. Then, the lower camera was moved to the acquisition position to acquire the image of part B. During the real-time image processing, the position deviation between part A and part B was calculated by the computer. Meanwhile, the XY precision stage was controlled by the computer to finish the alignment work.

Figure 4. Vision alignment device

The relative position and the coordinate systems of two cameras were shown in Figure 5. The transfer equation between two cameras in this VAD is listed as Equation (1):

[picture] | (1)

In the above equation, , are the physical size per pixel of the camera; a, b are the coordinates of the upper camera’s coordinate origin in the lower camera; is the angle between the two camera coordinate axes; , are the coordinate value of a point in the upper and lower camera system, respectively.

Figure 5. The structure diagram of the upper and lower cameras

2.3. Error Analysis of the Visual Alignment Device

2.3.1. Error Analysis of the Tilt of the Guide Rail Z

The instrument is used to finish the precision assembly work of several kinds of parts. In the assembly and calibration process, due to the height of each part is different, but the camera's focal length is fixed, so the camera’s acquisition position of different part should be different. In the calibrating process of the transfer equation, it is too complex and time-consuming to calibrate all acquisition positions. Therefore, to simplify the calibration process, the calibration result of an arbitrary acquisition position is often used in the assembly process of all kinds of parts. So the image acquisition positions in assembling and calibrating processes are different.

As shown in Figure 6, positions 1, 4 are the acquisition positions in the calibrating process. Positions 2, 3 are the acquisition positions in assembly process. If the guide rail Z is tilt relative to the press-fitting direction, the coefficient of transfer equation calculated by the calibration result will be different when the camera is at different heights. Therefore, the tilt of the guide rail Z relative to the press-fitting direction will cause the alignment error.

The coordinate systems of the upper and lower cameras are and , respectively (Figure 5). The press-fitting direction is defined as W axis, and the instrument coordinate system is UVW (Figure 6). There is parallelism error between the guide rail Z and the W axis. The angle between guide rail Z and W axis in the UOW and VOW plane were assumed and respectively. When the upper and lower cameras’ displacements along the guide rail Z were , the errors caused by the tilt of guide rail Z along the U and V directions in the coordinate system of camera can be calculated by Equation (2).

[picture] | (2)

Figure 6. The error analysis diagram of guide rail Z

Since an angle exists between axis and , the angle and are different. These two angles caused by the tilt of guide rail in coordinate system are defined as and . The two angles in coordinate system are defined as and . As shown in Figure 5, the distance along the guide rail between position 1 and position 2 is , and the distance between position 3 and position 4 is . So the alignment error of two cameras caused by the tilt of guide rail Z can be calculated by Equation (2).

In the alignment process, the features of the image obtained by upper camera will be converted into the lower camera using the transfer equation. So the error in the upper camera will change after converting, and the error caused by in lower camera (Equation (5)) can be deduced out according to the Equation (1).

[picture] | (3)

So the alignment error along U, V direction caused by the tilt of guide rail Z can be expressed as Equation (4):

[picture] | (4)

2.3.2. Error Analysis of the Tilt of Guide Rail X and Y

If the deviation of two parts is larger than the camera's view in plane UOV, at this time after capturing image by the upper camera, the lower camera need to be moved along guide rail X, Y, Z to capture the image of part B. So we need to consider the tilt of the guide rail X and Y.

The camera’s depth of field is 270μm, experiments showed that the part is not beyond the camera’s depth of field when the camera moves along the guide rail X and Y. so the error caused by the tilt of guide rail X and Y along W direction could be neglected. In the coordinate system , the projection of the included angle between the camera’s guide rail X and axis in and are and , respectively. The projection of the included angle between the camera’s guide rail Y and axis in and are and , respectively. The movement distance of camera along the guide rail X and Y are and respectively. So the alignment error along U and V direction in lower camera caused by and is listed respectively as follows:

[picture] | (5)

[picture] | (6)

The alignment error caused by the tilt of guide rail X, Y and Z can be expressed as Equation (7):

[picture] | (7)

Combine with transfer equation of the upper and lower cameras, the final transfer equation can be derived as Equation (8):

[picture] | (8)

3. Experiment

3.1. Calibrate the Pixel of Two Cameras and the Coefficient of Transfer Equation

As shown in Table 1, the physical size of per pixel was obtained by the calibration of cameras using the optical standard ruler [14].

Table 1. The Results of Pixel Calibration

As shown in Figure 7, the method of measuring the included angle is described as follows:

1) Fixing the optical standard ruler on the precision turntable;

2) Moving the upper camera to the acquisition position, turning the turntable to make the transverse line parallel with the axis;

3) Setting two points A, B on the standard ruler along the direction of transverse line, the distance between this two points is L. The upper camera was controlled to acquire the image of A. Then, the camera was moved L along the transverse line of the standard ruler to acquire the image of B;

4) Processing images to get the coordinates of A and B ;

5) The angle between the guide rail X and axis can be calculated by Equation (9), and the same method can be used to get the angle between the guide rail X and axis. Then .

[picture] | (9)

Figure 7. The diagram of measuring the inclination of the guide rail X

The images in upper camera were shown in Figure 8, the results were , and .

Figure 8. The images of measuring the included angle between guide rail X and axis U₁

The coefficients in the Equation (1) can be calculated by the imprint method which is introduced in the reference [15]. The measurement steps are as follows:

1) Fixing the aluminum block on the upper fixture;

2) Moving the beam down until the positioning semi-circle press a pattern on the aluminum block;

3) Moving the beam up to the original position, control the upper and lower cameras acquire the images of the positioning semi-circle and the pattern respectively;

4) Processing images to get the center coordinates, and calibrating the coefficients a and b by substituting these two coordinates into Equation (1).

The images are shown in Figure 9. The two coordinate points are (878.94, 626.66) and (866.71, 688.95) respectively, and the two coefficients are a=89.1µm and b=-538.1µm.

Figure 9. The calibration images of the conversion equation’s coefficient

3.2. Measure the Tilt Angle of Guide Rail Z

The procedure to measure the tilt angle (, ) in U₁V₁W is illustrated as below:

1) Moving the beam up to the original position, open the upper camera and move the camera to the image acquisition position to acquire the image of part A, and save this image;

2) Moving the beam and camera down 10mm, and save the image. Repeat this procedure to get a group of images;

3) Deal with the above images in the image processing software to get the coordinates of the circles’ centre. Combine these coordinates with the displacement of the part A along W direction, the movement track of the centre point of part A can be obtained;

4) Fitting space linear equation with the above three-dimensional coordinate points, then the angle (, ) can be calculated.

By means of the above method, a group of coordinates in was acquired and is shown in Table 2:

Table 2. The path of the camera in U₁V₁W coordinate system

The coordinates in can be derived based on the Equation (1), and the results are shown in Table 3:

Table 3. The path of the camera in U₂V₂W coordinate system

The , , and can be calculated by fitting the space linear equation with the above values. The results are , ;, .

The tilt angle of guide rail X and Y in can use the method which was introduced in Figure 7. In the alignment process, since the two parts can’t go beyond the cameras’ view, the cameras don’t need to move along guide rail X and Y. So the tilt of guide rail X and Y cannot bring the alignment error in. That can be expressed as Equation 10:

[picture] | (10)

3.3. Alignment Experiment

In order to verify the feasibility of the error analysis, the imprint method was used again. Firstly, these two cameras were controlled to acquire the images of positioning semi-circle and its pattern after pressing. Then, the upper camera was controlled to move to 40000µm and 60000µm respectively along the guide rail Z. Meanwhile, control the upper camera to acquire the images at these two positions. The images were shown in Figure 10. Processing the images to get the center coordinates. Then, the process results of the upper camera’s images were substituted into the transfer equations (Equation (1) and Equation (10)). The results are shown in the Table 4. Finally, the alignment error were calculated. As is shown in Table 5.

Figure 10. Images after alignment

Table 4. The results of the image processing and vision alignment conversion

Table 5. The alignment error of the instrument

As shown in Table 5, the alignment error caused by the tilt of guide rail is large, and it will directly lead to the failure of assembly work. But, the alignment error is greatly reduced after adding compensation, the alignment accuracy affected by is not obvious, and the alignment accuracy of the press-fit instrument can achieve the requirement of assembly work.

4. Conclusion

In this paper, based on the developed precision press-fit instrument, the visual alignment device which is composed of camera and three-dimensional precision displacement platform was introduced. For this kind of VAD, the alignment error caused by the tilt of camera guide rail Z had been analyzed, and the error influence equation was derived. Combined with the analysis results, the final transfer equation between two cameras was given. Experimental results demonstrated that final transfer equation can help the press-fit instrument improve the alignment accuracy effectively. The alignment accuracy can reach ±10μm, and the instrument becomes more flexible, and it can accomplish the assembly work of the small interference fitting parts with different sizes.

Acknowledgements

The authors gratefully acknowledge the Financial Support by the National Science and Technology Major Project (Project no. 2013ZX04001091), the National Science-technology Support Plan Project (Project no. 2014BAF08B02), and the Fundamental Research Fund for the Central Universities (Project no. DUT16RC(3)034).

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