A numerical simulation method for rock breaking by shield tunnel cutterhead based on real wear geometry

Abstract

This invention discloses a numerical simulation method for rock breaking by tunnel boring machine cutterheads based on real wear geometry, relating to the field of tunnel engineering technology. The method acquires point cloud data of the cutterhead edge under different wear conditions through 3D laser scanning. After coordinate correction, section extraction, and quadratic function fitting, its real geometric contour is reconstructed with high fidelity. Based on this, a 3D model of the cutterhead and a near-field dynamic rock model are constructed. Utilizing the rotational symmetry of the cutterhead about the X-axis, the nearest point of intrusion on the cutterhead surface is analytically solved, achieving efficient contact detection. The contact force is calculated by combining penetration depth and the penalty function method, and explicitly coupled to the external force term of the near-field dynamic motion equation. Without pre-setting crack paths, the entire process of crack initiation, propagation, and rock fragmentation is naturally simulated, simultaneously outputting rock breaking load, fragmentation morphology, and energy consumption parameters, significantly improving the realism and computational efficiency of the simulation.

Description

Technical Field

[0001] This invention relates to the field of tunnel engineering technology, and in particular to a numerical simulation method for rock breaking by shield tunnel cutterheads based on real wear geometry. Background Technology

[0002] During shield tunneling, the cutter head is the core component for rock breaking, and its wear condition directly affects tunneling efficiency, cutter life, and construction costs. Traditional cutter head design and performance evaluation are mostly based on idealized geometric models (such as standard circular arc cutters or straight cutters), making it difficult to establish a numerical model of cutter head rock breaking with realistic geometry.

[0003] In existing technologies, three-dimensional measurement techniques can be used to obtain the true cutting edge morphology of a hob at different service stages. Regarding numerical simulation methods, the traditional finite element method (FEM) has limitations such as mesh dependence and pre-defined fracture paths when dealing with large deformation, crack initiation, and propagation problems in quasi-brittle materials like rock. Peridynamics (PD), as a theory of nonlocal continuous media, naturally supports spontaneous crack initiation and arbitrary path propagation through integral equations of motion, making it particularly suitable for simulating the complex fracture behavior of hobs during rock breaking. Among these, bond-based peridynamics is often used in rock fracturing simulation due to its high computational efficiency, but it requires the combination of a reasonable contact algorithm to accurately describe the dynamic interaction between the hob and the rock.

[0004] In existing technologies, cutter-rock contact analysis typically employs simplified geometric assumptions or mesh-based contact detection, which struggles to adapt to the complex curved surfaces of real-world wear edges. Furthermore, contact force calculations often rely on geometric corrections, which can lead to numerical instability when calculating material point motion within a near-field dynamics framework. Additionally, the quantification of rock-breaking energy consumption is frequently based on empirical formulas or macroscopic load integration, lacking a direct correlation with the microscopic fracture process. Summary of the Invention

[0005] The purpose of this invention is to provide a numerical simulation method for rock breaking by tunnel boring machine cutterheads based on real wear geometry, which aims to solve or improve at least one of the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following solution: A numerical simulation method for rock breaking by tunnel boring machine cutterheads based on real wear geometry includes: Three-dimensional laser scanning was used to acquire three-dimensional point cloud data of the cutterhead of the tunnel boring machine under different wear conditions; Coordinate correction and section extraction are performed on point cloud data to construct the true geometric contour of the hobbing cutter edge; A three-dimensional model of the hob is constructed based on the actual geometric contour of the hob's cutting edge, and a rock material model of the near-field dynamics of the bond base is also constructed. The contact relationship between the three-dimensional model of the cutter and the rock material model is determined by the minimum distance criterion, and the nearest point of the intrusion point on the cutter surface is determined. Based on the point of intrusion and the corresponding nearest point, the penetration depth and unit direction vector are calculated, and the position of the rock material model within the 3D model of the intruding cutter is corrected. Calculation of contact force between the cutter and the rock based on the penalty function method; Within the framework of near-field dynamics, the motion equations of points in the rock material are solved to simulate the rock-breaking process of the roller cutter, and the rock-breaking load, fragmentation morphology, and energy consumption parameters are obtained.

[0007] Furthermore, constructing the true geometric profile of the hobbing cutter's cutting edge includes: Based on the extracted point cloud of the hob cutting edge centerline region, the least squares method is used to fit the cutting edge cross section to determine the normal vector of the cutting edge cross section. The expression is: In the formula, For unit normal vector, , representing the current orientation of the interface in space; Calculate the axis of rotation of the cutting edge section with respect to the XOY plane. and rotation parameters ,include: Normal vector of the XOY plane ; The normal vector of the cutting edge section Normal vector to the XOY plane Performing the cross product yields the rotation axis vector. The expression is: Based on the normal vector of the cutting edge section Normal vector to the XOY plane Calculate rotation parameters The expression is: Based on the rotation axis vector and rotation parameters A rotation matrix is ​​constructed and the cutting edge section is rotated in coordinates to obtain rotated point cloud data, including: Based on the rotation axis vector Constructing antisymmetric matrices The expression is: According to the antisymmetric matrix Combined with rotation parameters The rotation matrix is ​​constructed using the Rodriguez formula. The expression is: In the formula, It is a 3×3 identity matrix; Each point in the point cloud data of the cutting edge section Rotate the data using the rotation matrix R so that the cutting edge section is parallel to the XOY plane, obtaining the rotated point cloud data, expressed as: In the formula, , , The coordinates of the rotated point cloud data; The centroid coordinates of the rotated point cloud data are translated to the origin to obtain standard point cloud data, including: The expression for calculating the centroid coordinates of a rotated point cloud is: In the formula, , , The coordinates of the centroid point; The spatial area occupied by the rotating point cloud data; The centroid of the rotated point cloud data is translated to the origin by translation. The standard point cloud data is obtained, and the expression is: In the formula, , , Standardize point cloud coordinates; Based on the symmetry of the cutting edge profile, a quadratic function is used for fitting to represent the true geometric profile of the hob cutting edge under different wear conditions, resulting in the following expression: In the formula, The coefficient of the quadratic term reflects the curvature of the cutting edge. The larger the blade, the sharper the cutting edge; This is a constant term.

[0008] Furthermore, the contact relationship between the 3D model of the hob and the rock material model is determined using the minimum distance criterion, and the nearest point of the intrusion point on the hob surface is determined, including: The effective contact radius is obtained by radially expanding the geometric surface of the 3D model of the hobbing cutter by half the distance between rock material points. Based on the Euclidean distance from the rock material point to the cutter axis and the effective contact radius, analyze the rock material points that intrude into the 3D model of the cutter. The expression for the Euclidean distance from a point in the rock material to the axis of the hob is: In the formula, Let be the Euclidean distance from the rock material point to the axis of the hob; Let be the coordinates of the rock material point on the Y-axis of the hob coordinate system; Let be the coordinates of the rock material point on the Z-axis of the hob coordinate system; The expression for the effective contact radius is: In the formula, Effective contact radius; This represents the radius reduction caused by wear. Let X be the coordinates of the rock material point on the X-axis of the hob coordinate system; The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; The spacing between points in the rock material; when At that time, the rock material points that intrude into the 3D model of the cutter are identified and extracted to obtain the set of intrusion material points; Based on the pre-built nearest point optimization model, the nearest point of the intruding material point on the hob surface is solved.

[0009] Furthermore, based on the pre-built nearest point optimization model, the nearest point of the intruding material point on the hob surface is solved, including: The objective function expression is: In the formula, The Euclidean distance from the candidate intrusion point to the hob surface; The coordinates of the point where the material intrudes; Let be the coordinates of the nearest point to be determined on the hob surface; The constraint expression is: In the formula, The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; Optimization is performed using the Lagrange multiplier method, and the expression is: In the formula, This is the Lagrange multiplier method; For Lagrange multipliers; The first-order optimality condition expression for minimum distance is: ; Based on the rotational symmetry of the hob surface about the X-axis, the independent degrees of freedom of y and z are eliminated by radial alignment conditions, and a cubic equation of axial coordinate x is constructed. The closest point is then obtained by solving the equation.

[0010] Furthermore, based on the rotational symmetry of the hob surface about the X-axis, the independent degrees of freedom of y and z are eliminated through the radial alignment condition, and a cubic equation in univariate form for the axial coordinate x is constructed. Solving this equation yields the closest point, including: according to ,get ,in ; Substitution After simplification, we obtain a cubic algebraic equation: Transform the cubic algebraic equation into its standard form: When the discriminant When there are three real roots, they can be explicitly solved using Cardano's trigonometric formula: For each candidate solution Calculate the coordinates of the corresponding surface points using the following expression: The distance to all candidate intrusion material points is calculated using the following expression: choose The smallest point As the nearest point.

[0011] Furthermore, based on the intrusion point and its corresponding nearest point, the penetration depth and unit direction vector are calculated to correct the position of the rock material model within the 3D model of the intruding cutter, including: The penetration depth is determined based on the coordinates of the point of intrusion into the material and the corresponding nearest point, expressed as: In the formula, Penetration depth; For the point of intrusion into the material; The nearest point to the intruding material point; The unit direction vector is expressed as: In the formula, It is a unit direction vector; Total displacement correction distance of the intrusion material point The expression is: In the formula, The initial spacing of the rock material points; Total displacement correction vector The expression is: The correction is applied to the intruding material point based on the total displacement correction vector, expressed as: In the formula, These are the corrected coordinates of the rock material points.

[0012] Furthermore, the contact force between the cutter and the rock is calculated based on the penalty function method, including: Introducing equivalent normal penalty stiffness The expression is: In the formula, This is the normal penalty coefficient; The elastic modulus of the rock material; This represents the equivalent contact area of ​​the rock material point; Based on equivalent normal penalty stiffness The contact force is calculated by combining the penetration depth of the intruding material point and the unit direction vector, and the expression is: In the formula, For contact force; Penetration depth; It is a unit direction vector.

[0013] Furthermore, the motion equations of points in the rock material are solved within the near-field dynamics framework to simulate the rock-breaking process of the roller cutter, obtaining rock-breaking loads, fragmentation morphology, and energy consumption parameters, including: In the formula, , and They are matter points Mass density, acceleration, and volumetric force density; For along the material point and Force density at the connection points; For matter points The ethnic region.

[0014] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: This invention discloses a numerical simulation method for rock breaking of tunnel boring machine (TBM) cutterheads based on real wear geometry. The method acquires the real wear geometry of the cutterheads through 3D laser scanning, and reconstructs the cutting edge profile with high fidelity by combining point cloud processing and quadratic function fitting. It uses the rotational symmetry of the cutterheads to analytically solve for the nearest point, achieving efficient contact detection. It calculates the contact force based on the penetration depth and penalty function method, and explicitly couples it to the peri-field dynamic external force term. Under the bond-based peri-field dynamics framework, it naturally simulates crack initiation, propagation, and rock block separation without the need for pre-setting the fracture path. Finally, it synchronously outputs the rock breaking load, fragmentation morphology, and energy consumption parameters, improving the realism and efficiency of TBM cutterhead rock breaking simulation. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a schematic flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the actual new cutting tool of the hobbing cutter in this embodiment; Figure 3 This is a schematic diagram of the actual object where the uniform wear of the hob reaches its limit in this embodiment; Figure 4 This is a schematic diagram of the point cloud data obtained by the hobbing cutter using a 3D scanner in this embodiment; Figure 5 This is a schematic diagram of the 3D point cloud data after the hobbing cutter calibration in this embodiment; Figure 6 This is a schematic diagram of the XOZ plane profile of the hobbing cutter in this embodiment; Figure 7 This is a schematic diagram of the profile curves of different radial wear of the hob in this embodiment; Figure 8 This is a schematic diagram of the particle point motion equation of the hob's entry dynamics in this embodiment; Figure 9 This is a schematic diagram showing the situation in this embodiment when the particle points have not invaded the cutter. Figure 10 This is a schematic diagram of particle intrusion into the hobbing cutter in this embodiment; Figure 11 This is a schematic diagram of the rock-breaking and cutting effect in the numerical simulation of this embodiment; Figure 12 This is a schematic diagram illustrating the actual rock-breaking and cutting effect in the experiment of this embodiment; Figure 13This is a schematic diagram illustrating the impact of hob penetration and radial wear on energy consumption in this embodiment. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] The purpose of this invention is to provide a numerical simulation method for rock breaking by tunnel boring machine cutterheads based on real wear geometry, which aims to solve or improve at least one of the above-mentioned technical problems.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, this invention provides a numerical simulation method for rock breaking by shield tunnel cutterheads based on real wear geometry, including: Step 1: Use 3D laser scanning to acquire 3D point cloud data of the shield tunnel cutterhead under different wear conditions; Step 2, as follows Figure 2 , 3 The diagram illustrates the process of a hob going from new to fully worn. Figure 4 The diagram shows point cloud data acquired using a 3D scanner, and the realistic geometric contour of the hobbing cutter's cutting edge constructed based on this point cloud data, including: Step 21: Based on the extracted point cloud of the hob cutting edge centerline region, fit the cutting edge cross-section using the least squares method to determine the normal vector of the cutting edge cross-section. The expression is: In the formula, For unit normal vector, , representing the current orientation of the interface in space; Step 22, calculate the axis of rotation of the cutting edge section with respect to the XOY plane. and rotation parameters ,include: Normal vector of the XOY plane ; The normal vector of the cutting edge section Normal vector to the XOY plane Performing the cross product yields the rotation axis vector. The expression is: Based on the normal vector of the cutting edge section Normal vector to the XOY plane Calculate rotation parameters The expression is: Step 23, based on the rotation axis vector and rotation parameters A rotation matrix is ​​constructed and the cutting edge section is rotated in coordinates to obtain rotated point cloud data, including: Based on the rotation axis vector Constructing antisymmetric matrices The expression is: According to the antisymmetric matrix Combined with rotation parameters The rotation matrix is ​​constructed using the Rodriguez formula. The expression is: In the formula, It is a 3×3 identity matrix; Each point in the point cloud data of the cutting edge section Rotate the data using the rotation matrix R so that the cutting edge section is parallel to the XOY plane, obtaining the rotated point cloud data, expressed as: In the formula, , , The coordinates of the rotated point cloud data; Step 2.4: Translate the centroid coordinates of the rotated point cloud data to the origin to obtain standard point cloud data, including: The expression for calculating the centroid coordinates of a rotated point cloud is: In the formula, , , The coordinates of the centroid point; The spatial area occupied by the rotating point cloud data; The centroid of the rotated point cloud data is translated to the origin by translation. To obtain standard point cloud data, such as Figure 5 As shown, the expression is: In the formula, , , Standardize point cloud coordinates; Step 2.5, according to Figure 5 From the three-dimensional data, obtain the planar data of the XOZ section, such as... Figure 6 As shown, based on the symmetry of the cutting edge cross-sectional profile, a quadratic function is used for fitting to represent the true geometric profile of the hob cutting edge under different wear conditions, such as... Figure 7 As shown, the expression is: In the formula, The coefficient of the quadratic term reflects the curvature of the cutting edge. The larger the blade, the sharper the cutting edge; This is a constant term.

[0021] Step 3: Based on the processed point cloud data of the hobbing cutter blade, construct a three-dimensional model of the hobbing cutter by rotation, and at the same time construct a rock material model of bond-base near-field dynamics, as shown in Table 1 and Table 2. Table 1

[0022] Table 2

[0023] Among them, the bond-based peri-field dynamics model describes the fracture behavior of bonds between points in rock materials through the critical tensile failure criterion.

[0024] Step 4: Use the minimum distance criterion to determine the contact relationship between the 3D model of the hob and the rock material model, and determine the nearest point of the intrusion point on the hob surface, such as... Figure 9 As shown, point Q represents a particle in the rock mass, such as... Figure 10 As shown, the particle at point Q enters the hob and needs to be moved to point W on the hob surface, including: To simulate the contact between a rigid disc cutting tool and PD material points, a penalty-based contact algorithm was employed. During the tool-rock interaction, only material points directly in contact with the tool surface were considered, such as... Figure 9 The Q point in the diagram. As the tool advances and rotates, the Q point may penetrate the tool body in the next time step t+Δt, as... Figure 10 As shown. To maintain physical consistency, any intruding material point will move outward along the shortest distance to the tool surface.

[0025] Step 41: Considering the finite volume effect of rock material points, in the contact detection, the geometric surface of the 3D model of the hob is radially extended by half the rock material point spacing to obtain the effective contact radius; Step 42: Analyze the rock material points that intrude into the 3D model of the cutter based on the Euclidean distance from the rock material points to the cutter axis and the effective contact radius. The expression for the Euclidean distance from a point in the rock material to the axis of the hob is: In the formula, Let be the Euclidean distance from the rock material point to the axis of the hob; Let be the coordinates of the rock material point on the Y-axis of the hob coordinate system; Let be the coordinates of the rock material point on the Z-axis of the hob coordinate system; The expression for the effective contact radius is: In the formula, Effective contact radius; This represents the radius reduction caused by wear. Let X be the coordinates of the rock material point on the X-axis of the hob coordinate system; The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; The spacing between points in the rock material; when At that time, the rock material points that intrude into the 3D model of the cutter are identified and extracted to obtain the set of intrusion material points.

[0026] Step 43: Based on the pre-built nearest point optimization model, solve for the nearest point of the intruding material point on the hob surface, including: The nearest point optimization model includes: The objective function expression is: In the formula, The Euclidean distance from the candidate intrusion point to the hob surface; The coordinates of the point where the material intrudes; Let be the coordinates of the nearest point to be determined on the hob surface; The goal of the above optimization is to minimize D by finding the nearest point on the hob surface.

[0027] The constraint expression is: In the formula, The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; Optimization is performed using the Lagrange multiplier method, and the expression is: In the formula, This is the Lagrange multiplier method; For Lagrange multipliers; The first-order optimality condition expression for minimum distance is: ; Based on the rotational symmetry of the hob surface about the X-axis, the independent degrees of freedom of y and z are eliminated through radial alignment conditions, and a cubic equation in univariate form for the axial coordinate x is constructed. Solving for the closest point yields the following: S1, according to ,get ,in ; indicates that the nearest point and the point of material intrusion are located in the same radial plane; S2, substitute the relation from S1 into After simplification, we obtain a cubic algebraic equation: S3, transforming the cubic algebraic equation into its standard form: S4, when the discriminant When there are three real roots, they can be explicitly solved using Cardano's trigonometric formula: S5, for each candidate solution Calculate the coordinates of the corresponding surface points using the following expression: S6, calculate the distance to all candidate intrusion material points, the expression is: choose The smallest point As the nearest point.

[0028] Step 5: Based on the intrusion point and its corresponding nearest point, calculate the penetration depth and unit direction vector, and perform position correction on the rock material model within the 3D model of the intruding cutter, including: The penetration depth is determined based on the coordinates of the point of intrusion into the material and the corresponding nearest point, expressed as: In the formula, Penetration depth; For the point of intrusion into the material; The nearest point to the intruding material point; The unit direction vector is expressed as: In the formula, It is a unit direction vector; Ignoring the influence of rock mass deformation on the volume of material points, the rock mass material points are still considered to have a side length of... For cubic elements, to avoid geometric overlap in numerical contact, the intrusion material points are located in the direction vector. A further displacement correction of dx / 2 is applied.

[0029] Total displacement correction distance of the intrusion material point The expression is: In the formula, The initial spacing of the rock material points; Total displacement correction vector The expression is: The correction is applied to the intruding material point based on the total displacement correction vector, expressed as: In the formula, These are the corrected coordinates of the rock material points.

[0030] Step 6, calculate the contact force between the cutter and the rock based on the penalty function method, including: Introducing equivalent normal penalty stiffness The expression is: In the formula, This is the normal penalty coefficient; The elastic modulus of the rock material; This represents the equivalent contact area of ​​the rock material point; Based on equivalent normal penalty stiffness The contact force is calculated by combining the penetration depth of the intruding material point and the unit direction vector, and the expression is: In the formula, For contact force; Penetration depth; It is a unit direction vector.

[0031] Step 7: Solve the equations of motion for points in the rock material within the peri-field dynamics framework, such as... Figure 8 As shown, the rock-breaking process of a roller cutter is simulated to obtain rock-breaking load, fragmentation morphology, and energy consumption parameters, including: In the formula, , and They are matter points Mass density, acceleration, and volumetric force density; For along the material point and Force density at the connection points; For matter points The ethnic region.

[0032] After the calculation is completed, the result is as follows: Figure 11 As shown, with Figure 12 The experimental results are similar.

[0033] Next, the number of particles after rock mass fragmentation is calculated and converted into mass. Based on the normal load in the numerical simulation results, the normal load is multiplied by the penetration depth to obtain the work done by the cutter in rock breaking. Then, the work done by the cutter is divided by the rock mass to obtain the energy consumption of the cutter in rock breaking. Figure 13 As shown.

[0034] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0035] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A numerical simulation method for rock breaking by shield tunnel cutterheads based on real wear geometry, characterized in that, include: Three-dimensional laser scanning was used to acquire three-dimensional point cloud data of the cutterhead of the tunnel boring machine under different wear conditions; Coordinate correction and section extraction are performed on point cloud data to construct the true geometric contour of the hobbing cutter edge; A three-dimensional model of the hob is constructed based on the actual geometric contour of the hob's cutting edge, and a rock material model of the near-field dynamics of the bond base is also constructed. The contact relationship between the three-dimensional model of the cutter and the rock material model is determined by the minimum distance criterion, and the nearest point of the intrusion point on the cutter surface is determined. Based on the point of intrusion and the corresponding nearest point, the penetration depth and unit direction vector are calculated, and the position of the rock material model within the 3D model of the intruding cutter is corrected. Calculation of contact force between the cutter and the rock based on the penalty function method; Within the framework of near-field dynamics, the motion equations of points in the rock material are solved to simulate the rock-breaking process of the roller cutter, and the rock-breaking load, fragmentation morphology, and energy consumption parameters are obtained.

2. The numerical simulation method for shield tunnel cutter rock breaking based on real wear geometry according to claim 1, characterized in that, The construction of the true geometric contour of the hobbing cutter's cutting edge includes: Based on the extracted point cloud of the hob cutting edge centerline region, the least squares method is used to fit the cutting edge cross section to determine the normal vector of the cutting edge cross section. The expression is: In the formula, For unit normal vector, , representing the current orientation of the interface in space; Calculate the axis of rotation of the cutting edge section with respect to the XOY plane. and rotation parameters ,include: Normal vector of the XOY plane ; The normal vector of the cutting edge section Normal vector to the XOY plane Performing the cross product yields the rotation axis vector. The expression is: Based on the normal vector of the cutting edge section Normal vector to the XOY plane Calculate rotation parameters The expression is: Based on the rotation axis vector and rotation parameters A rotation matrix is ​​constructed and the cutting edge section is rotated in coordinates to obtain rotated point cloud data, including: Based on the rotation axis vector Constructing antisymmetric matrices The expression is: According to the antisymmetric matrix Combined with rotation parameters The rotation matrix is ​​constructed using the Rodriguez formula. The expression is: In the formula, It is a 3×3 identity matrix; Each point in the point cloud data of the cutting edge section Rotate the data using the rotation matrix R so that the cutting edge section is parallel to the XOY plane, obtaining the rotated point cloud data, expressed as: In the formula, , , The coordinates of the rotated point cloud data; The centroid coordinates of the rotated point cloud data are translated to the origin to obtain standard point cloud data, including: The expression for calculating the centroid coordinates of a rotated point cloud is: In the formula, , , The coordinates of the centroid point; The spatial area occupied by the rotating point cloud data; The centroid of the rotated point cloud data is translated to the origin by translation. The standard point cloud data is obtained, and the expression is: In the formula, , , Standardize point cloud coordinates; Based on the symmetry of the cutting edge profile, a quadratic function is used for fitting to represent the true geometric profile of the hob cutting edge under different wear conditions, resulting in the following expression: In the formula, The coefficient of the quadratic term reflects the curvature of the cutting edge. The larger the blade, the sharper the cutting edge; This is a constant term.

3. The numerical simulation method for shield tunnel cutter rock breaking based on real wear geometry according to claim 1, characterized in that, The process of determining the contact relationship between the 3D model of the hob and the rock material model using the minimum distance criterion, and determining the nearest point of the intrusion point on the hob surface, includes: The effective contact radius is obtained by radially expanding the geometric surface of the 3D model of the hobbing cutter by half the distance between rock material points. Based on the Euclidean distance from the rock material point to the cutter axis and the effective contact radius, analyze the rock material points that intrude into the 3D model of the cutter. The expression for the Euclidean distance from a point in the rock material to the axis of the hob is: In the formula, Let be the Euclidean distance from the rock material point to the axis of the hob; Let be the coordinates of the rock material point on the Y-axis of the hob coordinate system; Let be the coordinates of the rock material point on the Z-axis of the hob coordinate system; The expression for the effective contact radius is: In the formula, Effective contact radius; This represents the radius reduction caused by wear. Let X be the coordinates of the rock material point on the X-axis of the hob coordinate system; The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; The spacing between points in the rock material; when At that time, the rock material points that intrude into the 3D model of the cutter are identified and extracted to obtain the set of intrusion material points; Based on the pre-built nearest point optimization model, the nearest point of the intruding material point on the hob surface is solved.

4. The numerical simulation method for rock breaking by shield tunnel cutterhead based on real wear geometry according to claim 3, characterized in that, The step of solving for the nearest point of the intruding material on the hob surface based on the pre-constructed nearest point optimization model includes: The objective function expression is: In the formula, The Euclidean distance from the candidate intrusion point to the hob surface; The coordinates of the point where the material intrudes; Let be the coordinates of the nearest point to be determined on the hob surface; The constraint expression is: In the formula, The curvature coefficients are the result of a quadratic fitting of the cutting edge profile. This is the reference radius when the hob is not worn; Optimization is performed using the Lagrange multiplier method, and the expression is: In the formula, This is the Lagrange multiplier method; For Lagrange multipliers; The first-order optimality condition expression for minimum distance is: ； Based on the rotational symmetry of the hob surface about the X-axis, the independent degrees of freedom of y and z are eliminated by radial alignment conditions, and a cubic equation of axial coordinate x is constructed. The closest point is then obtained by solving the equation.

5. The numerical simulation method for rock breaking by shield tunnel cutterheads based on real wear geometry according to claim 4, characterized in that, Based on the rotational symmetry of the hob surface about the X-axis, the independent degrees of freedom of y and z are eliminated through radial alignment conditions, and a cubic equation in univariate form for the axial coordinate x is constructed. Solving for the closest point includes: according to ,get ,in ; Substitution After simplification, we obtain a cubic algebraic equation: Transform the cubic algebraic equation into its standard form: When the discriminant When there are three real roots, they can be explicitly solved using Cardano's trigonometric formula: For each candidate solution Calculate the coordinates of the corresponding surface points using the following expression: The distance to all candidate intrusion material points is calculated using the following expression: choose The smallest point As the nearest point.

6. The numerical simulation method for rock breaking by shield tunnel cutterhead based on real wear geometry according to claim 1, characterized in that, The step of calculating the penetration depth and unit direction vector based on the intrusion point and the corresponding nearest point, and correcting the position of the rock material model within the 3D model of the intruding cutter, includes: The penetration depth is determined based on the coordinates of the point of intrusion into the material and the corresponding nearest point, expressed as: In the formula, Penetration depth; For the point of intrusion into the material; The nearest point to the intruding material point; The unit direction vector is expressed as: In the formula, It is a unit direction vector; Total displacement correction distance of the intrusion material point The expression is: In the formula, The initial spacing of the rock material points; Total displacement correction vector The expression is: The correction is applied to the intruding material point based on the total displacement correction vector, expressed as: In the formula, These are the corrected coordinates of the rock material points.

7. The numerical simulation method for rock breaking by shield tunnel cutterhead based on real wear geometry according to claim 1, characterized in that, The calculation of the contact force between the cutter and the rock based on the penalty function method includes: Introducing equivalent normal penalty stiffness The expression is: In the formula, This is the normal penalty coefficient; The elastic modulus of the rock material; This represents the equivalent contact area of ​​the rock material point; Based on equivalent normal penalty stiffness The contact force is calculated by combining the penetration depth of the intruding material point and the unit direction vector, and the expression is: In the formula, For contact force; Penetration depth; It is a unit direction vector.

8. The numerical simulation method for rock breaking by shield tunnel cutterhead based on real wear geometry according to claim 1, characterized in that, The method involves solving the motion equations of rock material points within a near-field dynamics framework to simulate the rock-breaking process using a roller cutter, obtaining rock-breaking loads, fragmentation patterns, and energy consumption parameters, including: In the formula, , and They are matter points Mass density, acceleration, and volumetric force density; For along the material point and Force density at the connection points; For matter points The ethnic region.

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