New Integrated TBM Disc Cutter Deviation Analysis And Design of The Supporting Cutter-Changing Robot End-Effector

At present, the replacement of disc cutters of the tunnel boring machine (TBM) is a very important and difficult manual operation. Therefore, it is meaningful to study disc cutters of TBM replacement with a robot. In this paper, the machining and assembly deviation of the new integrated disc cutter developed by our research group is modeled and analyzed by using the improved Jacobian-Torsor model, and the analysis results are verified by experiments. On this basis, aiming at the possible radial deviation and angle deviation in the working process of a robot replacing TBM disc cutters, a cutter-changing robot end-effector composed of a guiding mechanism, a flexible connecting mechanism and a universal wrench is designed for the disassembly and assembly of the new integrated disc cutter, and scaled-down models were made for the experiment. The test results show that when there is a radial deviation of 19.21% or an angle deviation of 11° between the fastening bolt and the end-effector of the robot, the robot end-effector can complete the docking with the fastening bolt.


Introduction
The tunnel boring machine (TBM) is the main equipment for tunnel construction at present. The disc cutters installed on the cutter head of TBM are the direct rock-breaking tool, which needs to be replaced frequently. At present, the disc cutters are mainly replaced manually, which is dangerous, inefficient and difficult. The rise of the robot industry provides a new way for replacing TBM disc cutters. Since Bouygues company[1] of France first proposed to use robots to replace disc cutters for TBM in 2007, researchers in Germany, Japan, China, and other countries have successively developed robots to replace disc cutters for TBM in the following ten years [2][3][4]. However, most of them are experimental products, and the working effect of a few products applied in practical engineering can not meet the actual needs [4].
The application of integrated disc cutters is the premise for the robot to replace the disc cutters for TBM. The purpose of this paper is to design the end-* Correspondence: 2538110473@qq.com 1 School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China Full list of author information is available at the end of the article effector of the tool-changing robot for an integrated 1 disc cutter developed by our research team. The main function of the robot is to dock and twist the fastening bolts of the integrated disc cutter.
Docking mechanisms are mostly used in aerospace and underwater technology fields. Common docking mechanisms include rod-cone typed docking mechanism [5], the androgynous peripheral docking mechanism [6], low impact docking system [7], etc. In this paper, the improved rod-cone typed docking mechanism is used to design the docking mechanism of the cutter-changing robot end-effector.
Research on using the robot to assemble and disassemble bolts. Chu, B. [8], etc. designed a bolt connection device for steel beam assembly on the construction site. The robotic bolting device consists of a bolting end-effector, and a gantry-type robotic manipulator, which places the bolts to each bolting position. Zhang, Q. [9], etc. designed a bolt-screwing tool based on a pneumatic slip ring structure, which can realize two-DOF motion of clamping-releasing and rotating. The tool consists of a pneumatic slip ring with a sealed structure and a cylinder-driven gripper.
Li, R.Y. [10], etc. presents a novel spiral search technique developed to improve the rate of successful engagement between the robot end-effector and the screw heads despite uncertainties in the location of the screws. DiFilippo, N. M., and Jouaneh, M. K. [11] introduced a robotic system that combines force and visual sensors to help remove screws from laptops.
Their work focuses on building and testing computer vision modules that automatically find screws. Zhang Q. [12], etc. proposed a novel approach for flexible manipulator conducting screwing task based on robotenvironment contact classification. They used the logistic regression method to classify the contact state according to the force signal, to judge whether the bolt is tightened.
Most of the above studies are aimed at the design of the robot end-effector or the development of the related control strategies and computer vision algorithms, and there is no deviation analysis of the robot's working object. However, the applicability of the robot endeffector is an important factor affecting the performance of the robot. The targeted design of the robot end-effector according to the deviation analysis results of the robot's working object can greatly improve the applicability of the robot.
The Jacobian-Torsor model combines the small displacement spinor theory and the Jacobian matrix in robotics. Through the mathematical representation of the change of geometric elements by the small displacement spinor, the deviation of functional elements is transmitted by the Jacobian matrix, to be transformed into the change of functional requirements.
In 2016, Zeng, W.H. [23] proposed an improved Jacobian-Torsor model, which considers the case with complex transmission paths such as local parallel. On this basis, this paper analyzes the deviation of the new integrated TBM disc cutter system. According to the deviation analysis results of the integrated disc cutter system, the matching cutter-changing robot endeffector is designed.

New integrated TBM disc cutter
Traditional disc cutter has many unconnected parts, and it is difficult for robots to disassemble and assemble. To realize rapid cutter change by the robot, an integrated disc cutter suitable for robot operation should be designed first. To this end, an integrated disc cutter was designed. The disc cutter is mainly composed of 1 cutter box, 2 cutter holders, 1 disc cutter, 2 clamping blocks, 2 cushion blocks, 2 shift forks, 2 lifting rods, 2 thread fastening systems, etc., as shown in Fig. 1.
The fastening bolt is installed on the cutter holder through bearings, the fastening bolts and the shift forks are connected by threads, the clamping blocks and the shift forks are hinged, and rotating the fastening bolts can make the clamping blocks swing, as shown in Fig.   2. Rotate the fastening bolts to drive the shift forks to move upward along the fastening bolts, and then push the clamping blocks to swing outwards until they are tightly pressed into the grooves on the cutter holder, and the disc cutter is fixed on the cutter head. Reverse rotation of the fastening bolts can remove the disc cutter from the cutter head.  (1).
The deviation FRb can be expressed as: Where, , , and are the translation vector parameters of the axes , , and respectively. , β, γ are the rotation vectors of the axis , , and respectively. The same goes for the following.
The deviation FRt can be expressed as: The deviation A0 can be expressed as: The deviation FRh can be expressed as: The deviation N can be expressed as: In summary, the position deviation of the fastening bolts is:    According to the accuracy requirements, the tolerance field spinor of T1 is as follows.
According to the accuracy requirements, the tolerance field spinor of T2 is as follows.
Then, the Jacobian-Torsor model of dimension chain 1 is as follows. (2) Dimension chain 2 ① Between bearing 2 and cutter holder There is a clearance fit between the outer ring of bearing 2 and the mounting hole of the cutter base, so it forms a cylindrical to cylindrical connecting pair.
According to the accuracy requirements, its tolerance field spinor is as follows.   (1,1,1,1,1,1) To sum up, variations of torsor models of the thread fastening system are shown in Table 1.

Establish Jacobian-Torsor model
The Jacobian-Torsor model of the

Calculation of assembly deviation between disc cutter and cutter holders
There is a clearance between the disc cutter mounting hole on the cutter holder and the disc cutter  According to the accuracy requirements, the tolerance field spinor of T3 is as follows.
According to the accuracy requirements, the tolerance field spinor of T4 is as follows.
The Jacobian-Torsor model of the local coordinate system 7 of the disc cutter in the local coordinate system 1 of the cutter holder is established. According to the relative position of the two, The Jacobian matrix is as follows.
The Jacobian-Torsor model is as follows.
Then, the assembly deviation between disc cutter and cutter holder is calculated by the extreme value method, and the tolerance is shown in Fig. 6.

Calculation of assembly deviation between cutter holders and cutter box
The tolerance of the cutter holder and cutter box is shown in Fig. 7(a). Clearance fit between cutter holder and cutter box may cause displacement deviation and angle deviation. The geometric model of angle deviation is shown in Fig. 7(b).
According to geometric relations, the maximum deviation between the cutter holder and the cutter box is as follows. Assuming that in the global coordinate system 0, the gap between the cutter box and the mounting hole on the cutter head in the x-axis direction is x, and the gap in the z-axis direction is z. The geometric model is shown in Fig. 8(b).  In the actual situation, the installation gap between the installation hole on the cutter head and the cutter box is about 10mm. In the scaled-down disc cutter model, the installation gap is calculated as 3.3mm, that is, x2max=x3max=3.3mm. So, the calculation of welding deviation between the cutter box and the cutter head is as follows.

Calculation of comprehensive deviation of fastening bolt
Through the above analysis and calculation, the various Jacobian-Torsor models in Table 2 can be obtained.  The comprehensive deviation envelope circle is shown in Fig. 9. The results show that the angular deviation of the fastening bolt 2 winds around the z-axis is more than 5% of the theoretical calculation range. The rest are within the theoretical range. Therefore, the deviation analysis method is reasonable.

Overall structure design of end effector of tool changing robot
The structure of the cutter-changing robot endeffector is shown in Fig. 11.
1-The guiding mechanism, 2-The universal wrench, 3-The flexible connecting mechanism Fig. 11 The end-effector of the cutter-changing robot Aiming at Deviation 1, a cone-shape guiding mechanism is designed. The guiding mechanism is similar to the horn type. When working, the head of the disc cutter fastening bolt enters from the trumpetshaped big end of the guiding mechanism, and slides along its inner wall to the small end of the guiding mechanism, and reaches the main body of the universal wrench. The guiding mechanism can contain a certain degree of relative position deviation between the axis of the universal wrench and the axis of the fastening bolt through the conical structure.
When the universal wrench at the end of the robot rotates the bolt, the above Deviation 1 will cause the universal wrench rotation eccentrically. Therefore, a flexible terminal connecting mechanism is designed.
The mechanism consists of two universal joints, which can achieve a certain degree of eccentric transmission.

Parametric design of end-effector of supporting cutter-changing robot
According to the assembly deviation analysis results of the new integrated disc cutter system, the parametric design of the universal wrench is carried out.

Parametric design of the guiding mechanism
The basic parameters of the guiding mechanism include the diameter of the big end a, the diameter of the small end b, and the length l, as shown in Fig. 12(a).
(a) Parameters of the guiding mechanism (b) Diameter of the guiding mechanism's small end (2) The diameter of the small end b The diameter of the small end of the guiding mechanism is equal to the diameter of the circumscribed circle of the regular hexagon with the circumscribed circle of the fastening bolt head as the inscribed circle, as shown in Fig. 12(b).
R2 is the circumscribed radius of the fastening bolt head, R2=9.24mm.   The steel bar includes the following three parts, the front part for clamping the bolt head, the back part that is fixed on the sleeve, and the middle part between them. Its lengths are set as g1, g2, and g3 respectively, as shown in Fig. 15.
The g1 should be slightly longer than the working depth of the steel bar, f.
The g2 shall be slightly longer than the working depth of the steel bar, f, and the sum of the installation thickness of the steel bar p.
The g3 shall ensure that the steel bar is stably fixed and less than the working depth of the steel bar f.  (1) Determination of the rotation angle of the universal joint 1 ε

So,
The connecting process of the guiding mechanism and the fastening bolt is shown in Fig. 17, and the geometric relationship of each parameter is shown in Fig. 18. To ensure reliability, take the safety factor of 1.2.
And then, according to the geometry: (2) Determination of the rotation angle of the universal joint 2 μ The process of connecting the end-effector of the cutter-changing robot with the bolt is shown in Fig. 19.
In this process, the universal joint 2 rotates at an angle θ6, and the universal joint 1 rotates at an angle θ5 in a reverse direction so that the axis of the tightening bolt is parallel to the axis of the universal wrench. There are two cases of eccentricity and non-eccentricity, and the eccentric distance k is the radius of the steel bar, that is,  Fig. 20(b).
In the figure, HI

The simulation analysis
The flexible connecting mechanism of the end effector of the cutter-changing robot is a weak component, so it is necessary to carry out finite element analysis on it. The flexible connecting mechanism is made of 20CrMnTi, and the mechanical properties of 20CrMnTi are shown in Table 3. Grade   is 323.49MPa and the maximum strain is 0.238mm, which is less than the required stress of its yield strength 835MPa, which can meet the requirements.

The universal wrench performance test
To verify the designed end-effector of the cutter- which can meet the actual engineering requirements.

Ethics approval and consent to participate
Not applicable.