A method and system for calculating the minimum turning radius of a TBM suitable for ultra-small curve tunnels

Abstract

The application provides a kind of calculation method and system suitable for minimum turning radius of ultra-small curve tunnel TBM, scheme includes: in front shield and support shield, establish dynamic coordinate system and static coordinate system, establish the pose equation of cutter center point M when TBM horizontal steering, calculate the length of each advance hydraulic cylinder, calculate the ball hinge rotation angle of front shield and support shield, calculate the distance from main drive surface to the outer surface of hydraulic cylinder barrel, with the length variation range of hydraulic cylinder, the maximum rotation angle of ball hinge, the non-interference of main drive and hydraulic cylinder as limiting condition, solve the minimum turning radius of ultra-small curve TBM.The application takes the length variation range of hydraulic cylinder, the maximum rotation angle of ball hinge, the non-interference of main drive and hydraulic cylinder as limiting condition, writes Matlab program, can realize the accurate calculation of minimum turning radius of TBM, effectively evaluates its steering ability, provides guidance for compact TBM propulsion system design.

Description

Technical Field

[0001] This invention belongs to the field of engineering machinery technology, and relates to shield tunneling construction and data processing technology, particularly to a method and system for calculating the minimum turning radius of a TBM suitable for ultra-small curved tunnels. Background Technology

[0002] A tunnel boring machine (TBM) is a type of mechanical equipment used for excavating full-face underground tunnels. It encompasses knowledge from multiple disciplines, including mechanics, electronics, materials science, computer science, and control engineering. Its design and manufacturing, to a certain extent, reflect a country's comprehensive scientific and technological level. Ultra-small curve tunnels are often found in pumped-storage power stations, characterized by small turning radii, short distances, and steep gradients. To achieve tunneling with ultra-small turning radii, the propulsion system employs a "V"-shaped design. Figure 2 This is a schematic diagram of the TBM propulsion structure, including cutterhead 1, front shield 2, propulsion cylinder 3, support shield 4, and support shoe 5. The design axis 6 extends along the center of the tunnel wall. During normal TBM tunneling, the support shoe 5 is firmly supported against the tunnel wall, and the friction between the support shoe 5 and the tunnel wall provides the propulsion reaction force. The propulsion cylinder 3 extends, pushing the cutterhead 1 forward. Figure 2 The green outline represents the cutterhead and front shield protruding during the tunneling process. When the TBM turns, the extension length of the propulsion cylinders 3 in each area is adjusted to drive the front shield 2 and the cutterhead system to swing accordingly, changing the attitude of the cutterhead 1 and the shield body, thereby achieving orientation adjustment.

[0003] Ultra-small curve tunnels in energy, coal mining, and metal mining industries, such as pumped storage power stations, have turning sections with very small radii of curvature. Estimating the minimum achievable turning radius based on past design experience is no longer effective for related engineering construction. Summary of the Invention

[0004] To address the aforementioned issues, this invention discloses a method and system for calculating the minimum turning radius of a TBM in ultra-small curved tunnels. This method can accurately calculate the minimum turning radius of a TBM, thereby effectively evaluating its turning capability and providing guidance for the design of compact TBM propulsion systems.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for calculating the minimum turning radius of a TBM (Tunnel Boring Machine) applicable to ultra-small curved tunnels includes the following steps:

[0007] Step 1: Establish a dynamic coordinate system and a static coordinate system on the front shield and the support shield;

[0008] Step 2: Establish the pose equations of the cutterhead center point M and the origin of the moving coordinate system when the TBM is horizontally turning;

[0009] Step 3: Calculate the length of each propulsion hydraulic cylinder;

[0010] Step 4: Calculate the rotation angle of the front shield ball joint and the rotation angle of the support shield ball joint;

[0011] Step 5: Calculate the distance from the main drive surface to the outer surface of the hydraulic cylinder.

[0012] Step 6: Using the range of hydraulic cylinder length variation, the maximum rotation angle of the ball joint, and the absence of interference between the main drive and the hydraulic cylinder as constraints, solve for the minimum turning radius of the ultra-small curve TBM.

[0013] Furthermore, step one specifically includes the following process:

[0014] Moving coordinate system The origin Located at the center of the distribution circle of the front shield ball joint, the hinge point is Corresponding to ball joint 1 # -8 # static coordinate system The origin Located at the center of the distribution circle of the ball joint of the support shield, in the static coordinate system, and The corresponding hinge point is Corresponding to ball joint 9 # -16 # .

[0015] Furthermore, step two specifically includes the following process:

[0016] Establish the pose equation of the cutterhead center point M during TBM horizontal turning:

[0017] Define the front shield pose as , Represents the origin of the moving coordinate system Location coordinates, This represents the rotation angles of the moving coordinate system about the x, y, and z axes of the static coordinate system, namely the offset angle, pitch angle, and roll angle of the front shield. Counterclockwise rotation about the coordinate axes is defined as positive. Point M is the center point of the cutterhead. The moving coordinate system... coordinates of any point in Both can be transformed into a static coordinate system using a rotation transformation matrix. coordinates in It satisfies the following formula:

[0018]

[0019]

[0020] in, This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system;

[0021] During horizontal alignment, the front shield only translates along the y-axis and z-axis and rotates about the x-axis; the front shield attitude is as follows. Origin of the moving coordinate system Location is center point of the cutter head posture as The location is , Center point of the cutter head The offset angle; after the first advance of the TBM curve segment is completed, the center point of the cutter head. The pose change equation is:

[0022]

[0023] in, The turning radius is This represents the change in the front shield angle during a single propulsion process. The deflection angle of the front shield in the initial state of the curve segment;

[0024] Establish a moving coordinate system origin The pose change equation is as follows:

[0025]

[0026] in, Origin of the moving coordinate system To the center point of the cutter head The distance.

[0027] Furthermore, step three specifically includes the following process:

[0028] At any hinge point in the moving coordinate system , Any hinge point corresponding to the static coordinate system , The lengths of each hydraulic cylinder are then expressed as:

[0029] .

[0030] Furthermore, step four specifically includes the following process:

[0031] remember To support the centerline vector of the shield ball hinge, let's denote... The vector of the center line of the front shield ball joint; the vector of the center line of the supporting shield and the front shield ball joint; the direction vector of the hydraulic cylinder when the ball joint rotation angle is zero.

[0032] The expression for the rotation angle of the supporting shield ball joint is:

[0033]

[0034] Define a point on the moving coordinate system , The expression for the centerline vector of the front shield ball joint is:

[0035]

[0036] in, The distance between the static and dynamic coordinate systems;

[0037] The expression for the front shield ball joint rotation angle is:

[0038] .

[0039] Furthermore, step five specifically includes the following process:

[0040] Calculate the main driver Surface to hydraulic cylinder Distance between outer surfaces, hydraulic cylinder The position vector is:

[0041]

[0042] hydraulic cylinder The equation of the axis is expressed as follows:

[0043]

[0044] in, , , ball joint Center coordinates;

[0045] Discretize the main driving surface into coordinate points in a moving coordinate system. The coordinates are transformed into those in the static coordinate system. The expression is:

[0046]

[0047] The expression for the distance d from each coordinate point to the outer surface of the hydraulic cylinder barrel is:

[0048]

[0049] Where r is the outer diameter of the hydraulic cylinder barrel.

[0050] Furthermore, in step six, the limiting condition is:

[0051] The length variation range of the TBM hydraulic cylinder is:

[0052]

[0053] in, These represent the longest and shortest installation distances for each hydraulic cylinder;

[0054] The ball hinge angles of the TBM's support shield and front shield satisfy the following relationship:

[0055]

[0056] in, This is the maximum deflection angle;

[0057] The distance between the main drive and the outer surface of the propulsion cylinder satisfies the following relationship:

[0058] .

[0059] Furthermore, step six specifically includes the following sub-steps:

[0060] (1) Input parameters, including: basic structural parameters of TBM, single propulsion distance, initial value of turning radius and change value of turning radius. ;

[0061] (2) Determine the pose equation of the center point of the tool head and the pose equation of the origin of the moving coordinate system. Based on the parameters in step (1), perform calculations according to the two equations.

[0062] (3) Determine whether the following conditions are met:

[0063]

[0064]

[0065]

[0066] When any condition is not met, calculate Repeat steps (2) and (3). When all these conditions are met, execute step (4) for a second judgment.

[0067] (4) Calculate based on the pose equation of the center point of the cutter head and the pose equation of the origin of the moving coordinate system;

[0068] (5) Determine whether the following conditions are met:

[0069]

[0070]

[0071]

[0072] When all these conditions are met, calculate And repeat steps (4) and (5); when any condition is not met, calculate Output minimum turning radius .

[0073] Furthermore, step six is ​​implemented by writing a Matlab program.

[0074] The present invention also provides a calculation system for the minimum turning radius of a TBM in an ultra-small curved tunnel, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the calculation method for the minimum turning radius of a TBM in an ultra-small curved tunnel.

[0075] The beneficial effects of this invention are as follows:

[0076] The present invention establishes a dynamic coordinate system and a static coordinate system on the front shield and the support shield, and establishes the pose equation of the cutterhead center point M and the pose equation of the origin of the dynamic coordinate system when the TBM is turning horizontally. The calculation is performed with the hydraulic cylinder length variation range, the maximum rotation angle of the ball joint, and the absence of interference between the main drive and the hydraulic cylinder as constraints. This enables the accurate calculation of the minimum turning radius of the TBM, effectively evaluates the TBM's turning capability, and provides guidance for the design of compact TBM propulsion systems. Attached Figure Description

[0077] Figure 1 A flowchart illustrating the implementation of a method for calculating the minimum turning radius of a TBM (Tunnel Boring Machine) in an ultra-small curved tunnel, provided by this invention.

[0078] Figure 2 This is a schematic diagram of the TBM propulsion structure.

[0079] Figure 3 A schematic diagram of the dynamic and static coordinate system of the TBM propulsion system;

[0080] Figure 4 This is a schematic diagram of a TBM turning and tunneling.

[0081] Figure 5 This is a schematic diagram of the TBM ball joint structure;

[0082] Figure 6 This is a schematic diagram showing the interference between the TBM main drive and the hydraulic cylinder.

[0083] List of identifiers in attached diagrams:

[0084] 1. Cutterhead; 2. Front shield; 3. Propulsion cylinder; 4. Support shield; 5. Support shoe; 6. Design axis; 7. Static coordinate system; 8. Dynamic coordinate system; 9. Ball joint; 10. Ball joint cover; 11. Ball joint seat; 12. Propulsion cylinder 2 #13. Main Drive 1 # 14. Interference location. Detailed Implementation

[0085] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In the description of the present invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation.

[0086] This invention provides a method for calculating the minimum turning radius of a TBM (Tunnel Boring Machine) applicable to ultra-small curved tunnels, comprising the following steps:

[0087] Step 1: Simplify the front shield 2 and the support shield 4 into a moving coordinate system 8 and a stationary coordinate system 7. Simplify the propulsion cylinder 3 into a branch connecting the moving and stationary coordinate systems, and establish the moving coordinate system 8 and the stationary coordinate system 7 on the front shield 2 and the support shield 4 respectively, as follows: Figure 3 As shown. Moving coordinate system The origin Located at the center of the distribution circle of the front shield ball joint 9, the hinge point is Corresponding to ball joint 1 # -8 # static coordinate system The origin Located at the center of the distribution circle of the ball joint of the support shield, in the static coordinate system, and The corresponding hinge point is Corresponding to ball joint 9 # -16 # .

[0088] Step 2: Establish the pose equations for the cutterhead center point M and the origin of the moving coordinate system during TBM horizontal turning; specifically including:

[0089] Define the front shield pose as , Represents the origin of the moving coordinate system Location coordinates, These represent the rotation angles of the moving coordinate system about the x, y, and z axes of the static coordinate system, i.e., the offset angle, pitch angle, and roll angle of the front shield 2. Counterclockwise rotation about the coordinate axes is defined as positive. Point M is the center point of the cutterhead. (Moving coordinate system) coordinates of any point in Both can be transformed into a static coordinate system using a rotation transformation matrix. coordinates in It satisfies the following formula:

[0090]

[0091]

[0092] in, This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system.

[0093] When the front shield is horizontally adjusted, it only translates along the y-axis and z-axis and rotates about the x-axis. Therefore, the attitude of the front shield is: Origin of the moving coordinate system Location is center point of the cutter head posture as The location is , Center point of the cutter head The offset angle, after the first advance of the TBM curve segment is completed, the center point of the cutter head. The pose change equation is:

[0094]

[0095] in, The turning radius is This represents the change in the front shield angle during a single propulsion process. The angle of deflection of the front shield in the initial state of the curve segment.

[0096] Moving coordinate system origin The pose change equation is:

[0097]

[0098] in, , The center points of the cutter head are respectively Location coordinates, Origin of the moving coordinate system To the center point of the cutter head The distance.

[0099] The relationship between the single deflection angle and the single advance distance after the first advance of the TBM on the curved segment is determined by the following expression:

[0100]

[0101] The distance traveled in a single thrust. This represents the maximum deflection angle of the front shield during a single propulsion process.

[0102] The relationship between the front shield deflection angle and the turning radius of the TBM at the initial moment of the curve segment is determined by the following expression:

[0103]

[0104] in, This refers to the distance from the support shield to the center point of the cutterhead.

[0105] Step 3: Calculate the length of each propulsion hydraulic cylinder. For example... Figure 4 As shown, during TBM turning and tunneling, the support shoe 5 tightens the tunnel wall to fix the support shield 4, and the turning is achieved by controlling the extension of each hydraulic cylinder. When the maximum advance distance is reached, the hydraulic cylinders no longer provide thrust, and the shield is fixed by the compression of the rock. At this time, the support shoe retracts, the hydraulic cylinders reset, and the support shield moves forward under the restoring force of the hydraulic cylinders, completing one cycle of tunneling. During the turning process, the TBM cannot exceed the capacity limit of the propulsion cylinders; that is, the range of change in the propulsion cylinder length is limited by the longest and shortest installation distances. Each time a tunneling operation is completed, the moving coordinate system... mid hinge point The pose can be transformed into a static coordinate system using a rotation transformation matrix. The pose in the system is determined by the hinge point in the moving coordinate system. Corresponding static coordinate system mid hinge point Based on the position and orientation, the length of each propulsion cylinder 3 can be calculated. Specifically:

[0106] At any hinge point in the moving coordinate system , Any hinge point in the static coordinate system , Then the length of each hydraulic cylinder can be expressed as:

[0107]

[0108] During TBM cornering, the length of the propulsion hydraulic cylinder changes. Due to the limitations of the longest and shortest installation distances, the TBM cannot exceed the capacity limit of the propulsion cylinder during cornering. The range of change in the hydraulic cylinder length is as follows:

[0109]

[0110] in, These represent the longest and shortest installation distances for each hydraulic cylinder.

[0111] Step 4: Calculate the rotation angle of the front shield ball joint and the rotation angle of the support shield ball joint.

[0112] like Figure 5As shown, the ball joint structure includes a ball joint 9, a ball joint cover 10, and a ball joint seat 11. During the turning process, the position of the front shield 2 changes, and the direction vector of the hydraulic cylinder also changes accordingly, causing the ball joint rotation angle to rotate accordingly. However, the deflection angle of the ball joint cannot exceed its maximum deflection angle. The center vector of the front shield ball joint needs to be defined at a point in the moving coordinate system. , , The distance between the static and dynamic coordinate systems is, after coordinate transformation, expressed as: Based on the formula for calculating the angle between two vectors, the deflection angles of the supporting shield and the front shield are determined, and the spherical hinge angles of the supporting shield and the front shield are calculated. The specific calculation process is as follows:

[0113] During the turn, the pose of the front shield 2 changes, and the direction vector of the hydraulic cylinder changes. And it changes accordingly, record To support the centerline vector of the shield ball hinge, let's denote... The vector of the centerline of the front shield ball joint, the vector of the centerline of the supporting shield and the front shield ball joint, and the direction vector of the hydraulic cylinder when the ball joint rotation angle is zero:

[0114]

[0115] The expression for the rotation angle of the supporting shield ball joint is:

[0116]

[0117] Define a point on the moving coordinate system , The expression for the centerline vector of the front shield ball joint is:

[0118]

[0119] in, This represents the distance between the static and dynamic coordinate systems.

[0120] The expression for the front shield ball joint rotation angle is:

[0121]

[0122] During the turning process, the ball joint of the TBM must rotate within the maximum allowable deflection angle. The ball joint angles of the supporting shield and the front shield must satisfy the following relationship:

[0123]

[0124] This is the maximum deflection angle;

[0125] Step 5: Calculate the distance from the main drive surface to the outer surface of the hydraulic cylinder.

[0126] The main drive is rigidly connected to the front shield, and the main drive moves synchronously with the front shield. The smaller the turning radius, the larger the deflection angle of the front shield, and the greater the possibility of interference between the main drive and the hydraulic cylinder. The location where the main drive and the hydraulic cylinder interfere during the TBM's steering process is shown in Figure 14. Figure 6 As shown in the red circle, the main drive arrangement is symmetrical, therefore, as long as the main drive is guaranteed during turning... 13 and hydraulic cylinder Minimum gap between 12 There will be no interference during the TBM's steering process. Knowing the position vector of the hydraulic cylinder axis, the equation of the hydraulic cylinder axis can be obtained. The main drive surface is discretized into coordinate points in a moving coordinate system, which are then transformed into coordinates in a static coordinate system using a coordinate transformation method. The main drive surface is then calculated using the point-to-line distance formula. 13 and hydraulic cylinder The minimum gap between 1 and 2.

[0127] Calculate the distance from the main drive surface to the outer surface of the hydraulic cylinder. Since the main drive arrangement is symmetrical, only the main drive surface needs to be calculated. Surface to hydraulic cylinder Distance between outer surfaces, hydraulic cylinder The position vector is:

[0128]

[0129] hydraulic cylinder The equation of the axis is expressed as follows:

[0130]

[0131] in, , , ball joint Center coordinates;

[0132] Discretize the main driving surface into coordinate points in a moving coordinate system. Transform the coordinates into a static coordinate system. The expression is:

[0133]

[0134] The expression for the distance d from each coordinate point to the outer surface of the hydraulic cylinder barrel is:

[0135]

[0136] Where r is the outer diameter of the hydraulic cylinder barrel.

[0137] Step 6: Using the range of hydraulic cylinder length variation, the maximum rotation angle of the ball joint, and the absence of interference between the main drive and the hydraulic cylinder as constraints, write a Matlab program to solve for the minimum turning radius of the ultra-small curve TBM.

[0138] During the turning process, the front shield of the TBM deflects at a large angle, and the main unit has a compact structure. It is necessary to ensure that there is no interference between the main drive and the propulsion cylinder. The distance between the main drive and the outer surface of the propulsion cylinder needs to satisfy the following relationship:

[0139]

[0140] When a TBM is tunneling around a curve, it must simultaneously meet the constraints of the hydraulic cylinder length variation range, the maximum rotation angle of the ball joint, and the absence of interference between the main drive and the hydraulic cylinder. A Matlab program should be written to solve for the minimum turning radius of the TBM on the ultra-small curve.

[0141] like Figure 1 As shown, the specific flow of the Matlab program is as follows:

[0142] (1) Input parameters, including: basic structural parameters of TBM, single propulsion distance, initial value of turning radius and change value of turning radius. ;

[0143] (2) Determine the pose equation of the center point of the tool head and the pose equation of the origin of the moving coordinate system. Based on the parameters in step (1), perform calculations according to the two equations.

[0144] (3) Determine whether the following conditions are met:

[0145]

[0146]

[0147]

[0148] When any condition is not met, calculate Repeat steps (2) and (3). When all these conditions are met, execute step (4) for a second judgment.

[0149] (4) Calculate based on the pose equation of the center point of the cutter head and the pose equation of the origin of the moving coordinate system;

[0150] (5) Determine whether the following conditions are met:

[0151]

[0152]

[0153]

[0154] When all these conditions are met, calculate And repeat steps (4) and (5); when any condition is not met, calculate Output minimum turning radius .

[0155] The present invention also provides a calculation system for the minimum turning radius of a TBM in an ultra-small curved tunnel, including a memory, a processor, and a computer program stored in the memory. The processor executes the computer program to implement the steps of the calculation method for the minimum turning radius of a TBM in an ultra-small curved tunnel.

[0156] Taking a compact TBM as an example, its shortest installation distance for hydraulic cylinders is... The longest installation distance is The maximum deflection angle of the ball joint is The front shield ball joint distribution angle is The support shield ball hinge distribution angle is Using the calculation method of this patent, the minimum turning radius of this TBM is calculated as follows: The design of the tunnel construction for a certain pumped storage power station The minimum turning radius is consistent, thus verifying the effectiveness of the calculation method of this patent.

[0157] It should be noted that the above content merely illustrates the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. For those skilled in the art, various improvements and modifications can be made without departing from the principle of the present invention, and all such improvements and modifications fall within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating the minimum turning radius of a TBM (Tunnel Boring Machine) applicable to ultra-small curved tunnels, characterized in that, Includes the following steps: Step 1: Establish a dynamic coordinate system and a static coordinate system on the front shield and the support shield; Step 2: Establish the pose equations of the cutterhead center point M and the origin of the moving coordinate system when the TBM is horizontally turning; Step 3: Calculate the length of each propulsion hydraulic cylinder; Step 4: Calculate the rotation angle of the front shield ball joint and the rotation angle of the support shield ball joint; Step 5: Calculate the distance from the main drive surface to the outer surface of the hydraulic cylinder. Step Six: Using the constraints of the hydraulic cylinder length variation range, the maximum rotation angle of the ball joint, and the absence of interference between the main drive and the hydraulic cylinder, solve for the minimum turning radius of the ultra-small curve TBM; this includes the following sub-steps: (1) Input parameters, including: basic structural parameters of TBM, single propulsion distance, initial value of turning radius and change value of turning radius. ; (2) Determine the pose equation of the center point of the tool head and the pose equation of the origin of the moving coordinate system. Based on the parameters in step (1), perform calculations according to the two equations. (3) Determine whether the following conditions are met: When any condition is not met, calculate Repeat steps (2) and (3). When all these conditions are met, execute step (4) for a second judgment. (4) Calculate based on the pose equation of the center point of the cutter head and the pose equation of the origin of the moving coordinate system; (5) Determine whether the following conditions are met: When all these conditions are met, calculate And repeat steps (4) and (5); when any condition is not met, calculate Output minimum turning radius .

2. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step one specifically includes the following process: Moving coordinate system The origin Located at the center of the distribution circle of the front shield ball joint, the hinge point is Corresponding to ball joint 1 # -8 # static coordinate system The origin Located at the center of the distribution circle of the ball joint of the support shield, in the static coordinate system, and The corresponding hinge point is Corresponding to ball joint 9 # -16 # .

3. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step two specifically includes the following process: Establish the pose equation of the cutterhead center point M during TBM horizontal turning: Define the front shield pose as , Represents the origin of the moving coordinate system Location coordinates, This represents the rotation angles of the moving coordinate system about the x, y, and z axes of the static coordinate system, namely the offset angle, pitch angle, and roll angle of the front shield. Counterclockwise rotation about the coordinate axes is defined as positive. Point M is the center point of the cutterhead. The moving coordinate system... coordinates of any point in Both can be transformed into a static coordinate system using a rotation transformation matrix. coordinates in It satisfies the following formula: in, This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system; During horizontal alignment, the front shield only translates along the y-axis and z-axis and rotates about the x-axis; the front shield attitude is as follows. Origin of the moving coordinate system Location is center point of the cutter head posture as The location is , Center point of the cutter head The offset angle; after the first advance of the TBM curve segment is completed, the center point of the cutter head. The pose change equation is: in, The turning radius, This represents the change in the front shield angle during a single propulsion process. The deflection angle of the front shield in the initial state of the curve segment; Establish a moving coordinate system origin The pose change equation is as follows: in, Origin of the moving coordinate system To the center point of the cutter head The distance.

4. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step three specifically includes the following process: At any hinge point in the moving coordinate system , Any hinge point in the static coordinate system , The lengths of each hydraulic cylinder are then expressed as: in, This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system.

5. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step four specifically includes the following process: remember To support the centerline vector of the shield ball hinge, let's denote... The vector of the centerline of the front shield ball joint. The direction vector of the hydraulic cylinder; The expression for the rotation angle of the supporting shield ball joint is: Define a point on the moving coordinate system , The expression for the centerline vector of the front shield ball joint is: in, This represents the distance between the static and dynamic coordinate systems. This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system; The expression for the front shield ball joint rotation angle is: 。 6. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step five specifically includes the following process: Calculate the main driver Surface to hydraulic cylinder Distance between outer surfaces, hydraulic cylinder The position vector is: hydraulic cylinder The equation of the axis is expressed as follows: in, , , ball joint ; Discretize the main driving surface into coordinate points in a moving coordinate system. Transform the coordinates into a static coordinate system. The expression is: This is the rotation transformation matrix between the static and dynamic coordinate systems. For moving coordinate system Coordinates in a static coordinate system; The expression for the distance d from each coordinate point to the outer surface of the hydraulic cylinder barrel is: Where r is the outer diameter of the hydraulic cylinder barrel.

7. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, In step six, the following constraints apply: The length variation range of the TBM hydraulic cylinder is: in, The length of the hydraulic cylinder. These represent the longest and shortest installation distances for each hydraulic cylinder; The ball hinge angles of the support shield and the front shield of the TBM satisfy the following relationship: in, This is the maximum deflection angle; Distance between the main drive and the outer surface of the propulsion cylinder The following relationship must be satisfied: 。 8. The method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels according to claim 1, characterized in that, Step six is ​​implemented by writing a Matlab program.

9. A calculation system for the minimum turning radius of a TBM (Tunnel Boring Machine) in ultra-small curved tunnels, comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method for calculating the minimum turning radius of a TBM applicable to ultra-small curved tunnels as described in any one of claims 1-8.

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