A digital modeling system of a flexible cable motion simulation model

Abstract

The application belongs to the technical field of flexible cable simulation, and particularly relates to a digital modeling system of a flexible cable motion simulation model, which comprises a physical model establishing module and a geometric model establishing module; in the application, the physical model of the flexible cable is modeled by using discrete concentrated mass points and rods, compared with the traditional mass point-spring model, the spring model is replaced by the rod unit, the complexity and modeling difficulty of the cable physical model are reduced, the simulation efficiency of the cable is improved while the physical precision of the cable simulation is ensured, and real-time dynamic simulation of the cable is realized; the geometric model of the cable adopts a discrete "capsule" unit, the matching of the geometric model and the physical model of the cable can be ensured through the mode, so that the display precision of the digital model of the flexible cable is ensured, and the geometric model is driven by the physical model, so that the motion simulation effect of the virtual cable is more realistically presented.

Description

Technical Field

[0001] This invention belongs to the field of flexible cable simulation technology, specifically relating to a digital modeling system for a flexible cable motion simulation model, including a cable physical model modeling method and a geometric model modeling method. Background Technology

[0002] In complex electromechanical products, the laying of flexible cables mainly relies on the designer's experience. This approach can lead to unreasonable cable design, ultimately resulting in cable quality problems and an increased probability of equipment malfunctions. Digital modeling of flexible cables has become an essential tool in cable design. Existing 3D computer-aided design software (Pro / E, CATIA, UG, etc.) already has functional modules for flexible cable laying and can complete the modeling of cable geometry. However, they cannot consider the physical properties of the cable, such as the physical characteristics of the cable under gravity, bending, torsion, and tensile deformation. This results in low simulation accuracy of the digital cable model and an inability to realistically simulate the cable's motion.

[0003] Cables are flexible materials with large deformation characteristics. Existing digital modeling methods for cables can be broadly categorized into two types: geometric modeling and physical modeling, which considers the physical properties of cables. Geometric models typically use methods such as B-spline curves to establish a geometric model of the object to describe its shape. Physical models, on the other hand, establish the kinematic equations of the object based on the principles of mechanics, then obtain the cable's pose information through numerical solutions. Combined with the cable's geometric model, this allows for motion simulation of the cable.

[0004] Common methods for modeling physical cables include the finite element model and the mass-spring model.

[0005] Finite element models, such as common finite element simulation software like Abaqus and Ansys, can perform finite element modeling and simulation of flexible cables. The characteristic is that the digital model of the cable has high simulation accuracy, but low efficiency and cannot guarantee the real-time motion simulation requirements in the field of virtual simulation.

[0006] The mass-spring model discretizes the flexible cable into a series of volumeless mass points, which are connected by massless spring models. The flexible cable is equivalent to a mass-spring system. The pose of the cable motion is obtained by establishing the dynamic equation of the mass-spring system. However, the matching relationship between the mass-spring system and the corresponding cable geometric model is complex, resulting in an incomplete match between the visual geometric model and the physical model of the cable. Summary of the Invention

[0007] (a) Technical problems to be solved

[0008] The technical problem to be solved by this invention is: how to provide a digital modeling system for motion simulation of flexible cables, which can not only realistically express the physical properties of cables, but also generate realistic and visualized cable geometric models. Moreover, this method reduces the modeling difficulty of the physical model of cables, improves the efficiency of motion simulation of cables, and enables real-time motion simulation analysis of cables. This system provides an effective solution for the digital modeling of flexible cables in virtual simulation.

[0009] (II) Technical Solution

[0010] To address the aforementioned technical problems, this invention provides a digital modeling system for a motion simulation model of flexible cables, the modeling system comprising: a physical model modeling module and a geometric model modeling module;

[0011] The physical modeling module is used to establish a physical model of the flexible cable based on the discretized cable model;

[0012] The geometric modeling module is used to establish a geometric model using a discretized geometric modeling method that perfectly matches the physical model.

[0013] In the process of establishing the physical model of the flexible cable by the physical model modeling module, the physical model of the flexible cable is a discretized cable model.

[0014] The physical modeling module includes: a discretization unit, a cable segment model processing unit, a cable segment length confirmation unit, a cable segment quality confirmation unit, a cable segment local coordinate system establishment unit, a world coordinate system establishment unit, a cable segment spatial position determination unit, a cable segment spatial attitude determination unit, a connection point establishment unit, a connection point coordinate determination unit, a connection unit model establishment unit, an angular constraint vector establishment unit, an elastic potential energy expression establishment unit, a cable elastic model establishment unit, and a dynamic equation solving unit.

[0015] The discretization unit is used to discretize the cable model to be created, processing the cable model into a series of discrete cable segment models.

[0016] The cable segment model processing unit is used to process the cable segment model. Each cable segment is established as a rigid rod element, and a concentrated mass element is created at the center of the cable segment so that the mass of the cable segment is concentrated at the center of the rigid rod element.

[0017] The cable segment length confirmation unit is used to confirm the length of the cable segment. When creating the cable segment model, the resolution of the cable discretization is specified. The resolution of the cable refers to the number of cable segments after discretization per unit length of cable.

[0018] The cable segment quality verification unit is used to verify the quality of the cable segments, obtain the equivalent density, cross-sectional shape, cable diameter, and the installation position parameters of the starting and ending points of the cable model to be built, and calculate the concentrated mass of each cable segment through the equivalent parameters of the cable and the length of the cable segment. The sum of the masses of all cable segments represents the mass of the entire cable.

[0019] The cable segment local coordinate system establishment unit is used to establish the local coordinate system of the cable segment. In order to accurately describe the pose of the cable in space, it is necessary to establish a local coordinate system of the cable segment at the center of each cable segment. The center of the cable segment is taken as the origin, the X-axis is the unit vector perpendicular to the axial direction of the cable segment, the Y-axis is the unit vector in the axial direction of the cable segment at that point, and the Z-axis is the unit vector in the binormal direction at that point, which can be obtained by Z = X × Y, thus determining the local coordinate system of the cable segment.

[0020] The world coordinate system establishment unit is used to establish a world coordinate system. The world coordinate system is established with a fixed point in space as the origin and the right-hand rule. The world coordinate system refers to a coordinate system that is fixed relative to the world.

[0021] The cable segment spatial location determination unit is used to determine the spatial location of the cable segment, and determines the spatial location of each cable segment by using the coordinates of the origin of the local coordinate system of the cable segment in the world system.

[0022] The cable segment spatial attitude determination unit is used to determine the spatial attitude of the cable segment. The attitude of the local coordinate system of the cable segment is represented by the rotation of the world system. Here, the rotation of the cable segment is represented in the form of quaternions, and the description of the spatial pose of the cable segment can be obtained.

[0023] The connection point establishment unit is used to establish connection points between cable segments. The connection points between cable segments are established by using the endpoints of the cable segments as the connection points between adjacent cable ends. That is, the end point of the previous cable segment is connected to the beginning point of the next cable segment.

[0024] The connection point coordinate determination unit is used to determine the coordinates of the connection point, specifically its coordinates in the local coordinate system of the cable segment. The coordinates of the connection point and the center coordinates of the cable segment always differ along the axial direction. The distance, l, is the length of the cable segment. By transforming the local coordinate system of the cable segment to the world coordinate system, the coordinates of the cable segment connection point in the world scene are established.

[0025] The connection unit model building unit is used to build the connection unit model of the cable segment. Constraint units, collectively referred to as angular constraint units, are established between the connection points of the cable segment. The angular constraint units constrain the degrees of freedom of the cable's tensile, bending, and torsional directions by limiting the relative displacement, bending angle, and torsional angle between two connection points, and establish the following constraint vectors:

[0026]

[0027] in, This represents the angular constraint vector representation of the entire cable. This is the vector representation of the cable angle constraint between cable segments i and i+1, where T is the transpose of the vector, i is the angle label of the angle constraint element, and N... C The number of angular constraint vectors for the entire cable;

[0028] The angle constraint vector establishment unit is used to establish angle constraint vectors between cable segments, connecting the angle constraint units between two adjacent cable segments, through... This is expressed to limit the displacement, bending angle, and torsional angle of the connecting cable segment. Establish the following expression:

[0029]

[0030] in, For displacement constraints, For bending angle constraints, For the torsional angle constraint, P (i,i+1) P is the connection point between cable segment i and cable segment i+1. (i+1,i) Connect cable segment i+1 to the connection point of cable segment i, via P (i,i+1) P (i+1,i) The relative displacement between connection points limits the amount of cable stretching, θ [i] To limit the bending angle and the amount of bending between cable segments, Ω [i] To limit the twisting angle, the amount of twist in the cable segment is restricted;

[0031] The elastic potential energy expression establishment unit is used to establish the elastic potential energy expression of the cable. Based on the Cosserat theory cable model, it is assumed that the cable diameter is much smaller than the deformed length. Hooke's law is extended to three-dimensional space. The elastic potential energy of the cable includes deformation in three directions: tension, bending, and torsion. By introducing the Young's modulus Y and Poisson's ratio σ of the cable material, the elastic potential energy expression of the cable is constructed: U = U s +U b +U t The meanings of each are as follows:

[0032]

[0033]

[0034]

[0035] Where U represents the elastic potential energy of the cable, U s U represents the potential energy of tensile deformation. b U represents the potential energy of bending deformation. t The potential energy represents torsional deformation, δx represents elongation, κ represents curvature, κ = 1 / R, R is the radius of curvature, Ω is the angle of torsion; the constant c s c b c t These represent the stiffness coefficients of the cable in three directions, obtained from the cable's Young's modulus Y and Poisson's ratio σ.

[0036] The cable elasticity model is established to establish a cable elasticity model with the introduction of angular constraint vectors. A cable is discretized into N cable segment models, and the cable segments are connected by Nc = N-1 angular constraint units. The angular constraint regularization is introduced into the elastic potential energy of the cable system, and the regularized expression of the system potential energy can be obtained, as shown below. The system potential energy with the introduction of angular constraints is highly integrated with the elastic potential energy theory of cables.

[0037]

[0038] Where ε is a diagonal matrix. diag represents the mathematical notation for a diagonal matrix; It is a parameter related to the vector stiffness coefficient, representing the reciprocal of the potential energy stiffness coefficient; The system constraint vector is represented by T, where T is the transpose of the vector, i is the angular constraint element angular label, and q is the generalized coordinate of the cable segment, representing the position and attitude information of the cable segment.

[0039] The dynamic equation solving unit is used to introduce the potential energy of the angularly constrained system into the system dynamic equation. Here, the Lagrange dynamic equation is established, and the dynamic equation is numerically solved to obtain the motion simulation results of the cable physical model.

[0040] At this point, the physical model of the flexible cable has been established.

[0041] The cable segment length confirmation unit is used to confirm the length of the cable segment. The cable resolution refers to the number of cable segments after discretization of a unit length of cable. That is, when the resolution is 100, it means that every 1m of cable is composed of 100 cable segment models, and each cable segment represents 1cm in length.

[0042] The geometric modeling module includes: a geometric model establishment unit and a solution unit;

[0043] The geometric model building unit is used to build the geometric model of the cable. It adopts a modeling method that is completely matched with the physical model—the discretized geometric modeling method. Based on each cable segment in the physical model, the geometric model of the cable segment—the "capsule body" model—is generated according to the position, orientation, and diameter information of the cable segment. The capsule body refers to a cylindrical structure with a hemispherical end, a regular geometric body with a capsule-like shape. The length of the cylinder of the "capsule body" is consistent with the length of the cable segment, and the diameter is consistent with the actual size of the cable. The overall geometric model of the cable is composed of a series of discretized "capsule body" geometric models.

[0044] The calculation unit is used to build a physical model of the cable, consider the actual physical characteristics of the cable, and perform numerical solutions to obtain the cable calculation results. Based on the calculation results, the geometric model of the cable is generated in real time, thus obtaining a realistic cable simulation effect.

[0045] (III) Beneficial Effects

[0046] Compared with existing technologies, the physical model of flexible cables in this invention is composed of discretized concentrated mass points and rods. Compared with the traditional mass-spring model, the rod unit replaces the spring model, which reduces the complexity and modeling difficulty of the cable physical model. While ensuring the physical accuracy of cable simulation, it improves the simulation efficiency of cable and realizes real-time dynamic simulation of cable.

[0047] This invention establishes a novel angular constraint unit between discrete cable segments. The angular constraint unit is used to express the tensile, bending, and torsional deformation characteristics of the flexible cable. At the same time, it establishes the relationship between the angular constraint unit and the physical material of the cable. By setting the physical material parameters of the cable, the physical properties of the flexible cable can be changed.

[0048] This invention adopts a regular "capsule" geometric model, which reduces the complexity of geometric features and effectively improves the efficiency of flexible cables in the collision detection process. At the same time, this form can also more smoothly represent the overall display effect of the cable.

[0049] The geometric model of the cable in this invention adopts a discretized "capsule" unit. This method can ensure the matching between the geometric model and the physical model of the cable, thereby ensuring the display accuracy of the digital model of the flexible cable. At the same time, the physical model drives the geometric model, which more realistically represents the motion simulation effect of the virtual cable. Attached Figure Description

[0050] Figure 1This is a flowchart of the modeling method for the digital model of flexible cables according to the present invention.

[0051] Figure 2 This is a schematic diagram of the physical model of the flexible cable of the present invention.

[0052] Figure 3 This is a schematic diagram of the geometric model of the flexible cable of the present invention. Detailed Implementation

[0053] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0054] To address the aforementioned technical problems, this invention provides a digital modeling system for a motion simulation model of flexible cables, the modeling system comprising: a physical model modeling module and a geometric model modeling module;

[0055] The physical modeling module is used to establish a physical model of the flexible cable based on the discretized cable model;

[0056] The geometric modeling module is used to establish a geometric model using a discretized geometric modeling method that perfectly matches the physical model.

[0057] In the process of establishing the physical model of the flexible cable by the physical model modeling module, the physical model of the flexible cable is a discretized cable model.

[0058] The physical modeling module includes: a discretization unit, a cable segment model processing unit, a cable segment length confirmation unit, a cable segment quality confirmation unit, a cable segment local coordinate system establishment unit, a world coordinate system establishment unit, a cable segment spatial position determination unit, a cable segment spatial attitude determination unit, a connection point establishment unit, a connection point coordinate determination unit, a connection unit model establishment unit, an angular constraint vector establishment unit, an elastic potential energy expression establishment unit, a cable elastic model establishment unit, and a dynamic equation solving unit.

[0059] The discretization unit is used to discretize the cable model to be created, processing the cable model into a series of discrete cable segment models.

[0060] The cable segment model processing unit is used to process the cable segment model. Each cable segment is established as a rigid rod element, and a concentrated mass element is created at the center of the cable segment so that the mass of the cable segment is concentrated at the center of the rigid rod element.

[0061] The cable segment length confirmation unit is used to confirm the length of the cable segment. When creating the cable segment model, the resolution of the cable discretization is specified. The resolution of the cable refers to the number of cable segments after discretization per unit length of cable.

[0062] The cable segment quality verification unit is used to verify the quality of the cable segments, obtain the equivalent density, cross-sectional shape, cable diameter, and the installation position parameters of the starting and ending points of the cable model to be built, and calculate the concentrated mass of each cable segment through the equivalent parameters of the cable and the length of the cable segment. The sum of the masses of all cable segments represents the mass of the entire cable.

[0063] The cable segment local coordinate system establishment unit is used to establish the local coordinate system of the cable segment. In order to accurately describe the pose of the cable in space, it is necessary to establish a local coordinate system of the cable segment at the center of each cable segment. The center of the cable segment is taken as the origin, the X-axis is the unit vector perpendicular to the axial direction of the cable segment, the Y-axis is the unit vector in the axial direction of the cable segment at that point, and the Z-axis is the unit vector in the binormal direction at that point, which can be obtained by Z = X × Y, thus determining the local coordinate system of the cable segment.

[0064] The world coordinate system establishment unit is used to establish a world coordinate system. The world coordinate system is established with a fixed point in space as the origin and the right-hand rule. The world coordinate system refers to a coordinate system that is fixed relative to the world.

[0065] The cable segment spatial location determination unit is used to determine the spatial location of the cable segment, and determines the spatial location of each cable segment by using the coordinates of the origin of the local coordinate system of the cable segment in the world system.

[0066] The cable segment spatial attitude determination unit is used to determine the spatial attitude of the cable segment. The attitude of the local coordinate system of the cable segment is represented by the rotation of the world system. Here, the rotation of the cable segment is represented in the form of quaternions, and the description of the spatial pose of the cable segment can be obtained.

[0067] The connection point establishment unit is used to establish connection points between cable segments. The connection points between cable segments are established by using the endpoints of the cable segments as the connection points between adjacent cable ends. That is, the end point of the previous cable segment is connected to the beginning point of the next cable segment.

[0068] The connection point coordinate determination unit is used to determine the coordinates of the connection point, specifically its coordinates in the local coordinate system of the cable segment. The coordinates of the connection point and the center coordinates of the cable segment always differ along the axial direction. The distance, l, is the length of the cable segment. By transforming the local coordinate system of the cable segment to the world coordinate system, the coordinates of the cable segment connection point in the world scene are established.

[0069] The connection unit model building unit is used to build the connection unit model of the cable segment. Constraint units, collectively referred to as angular constraint units, are established between the connection points of the cable segment. The angular constraint units constrain the degrees of freedom of the cable's tensile, bending, and torsional directions by limiting the relative displacement, bending angle, and torsional angle between two connection points, and establish the following constraint vectors:

[0070]

[0071] in, This represents the angular constraint vector representation of the entire cable. This is the vector representation of the cable angle constraint between cable segments i and i+1, where T is the transpose of the vector, i is the angle label of the angle constraint element, and N is the vector number. C The number of angular constraint vectors for the entire cable;

[0072] The angle constraint vector establishment unit is used to establish angle constraint vectors between cable segments, connecting the angle constraint units between two adjacent cable segments, through... This is expressed to limit the displacement, bending angle, and torsional angle of the connecting cable segment. Establish the following expression:

[0073]

[0074] in, For displacement constraints, For bending angle constraints, For the torsional angle constraint, P (i,i+1) P is the connection point between cable segment i and cable segment i+1. (i+1,i) Connect cable segment i+1 to the connection point of cable segment i, via P (i,i+1) P (i+1,i) The relative displacement between connection points limits the amount of cable stretching, θ [i] To limit the bending angle and the amount of bending between cable segments, Ω [i] To limit the twisting angle, the amount of twist in the cable segment is restricted;

[0075] The elastic potential energy expression establishment unit is used to establish the elastic potential energy expression of the cable. Based on the Cosserat theory cable model, it is assumed that the cable diameter is much smaller than the deformed length. Hooke's law is extended to three-dimensional space. The elastic potential energy of the cable includes deformation in three directions: tension, bending, and torsion. By introducing the Young's modulus Y and Poisson's ratio σ of the cable material, the elastic potential energy expression of the cable is constructed: U = U s +U b +U t The meanings of each are as follows:

[0076]

[0077]

[0078]

[0079] Where U represents the elastic potential energy of the cable, U s U represents the potential energy of tensile deformation. b U represents the potential energy of bending deformation. t The potential energy represents torsional deformation, δx represents elongation, κ represents curvature, κ = 1 / R, R is the radius of curvature, Ω is the angle of torsion; the constant c s c b c t These represent the stiffness coefficients of the cable in three directions, obtained from the cable's Young's modulus Y and Poisson's ratio σ.

[0080] The cable elasticity model is established to establish a cable elasticity model with the introduction of angular constraint vectors. A cable is discretized into N cable segment models, and the cable segments are connected by Nc = N-1 angular constraint units. The angular constraint regularization is introduced into the elastic potential energy of the cable system, and the regularized expression of the system potential energy can be obtained, as shown below. The system potential energy with the introduction of angular constraints is highly integrated with the elastic potential energy theory of cables.

[0081]

[0082] Where ε is a diagonal matrix. diag represents the mathematical notation for a diagonal matrix; It is a parameter related to the vector stiffness coefficient, representing the reciprocal of the potential energy stiffness coefficient; The system constraint vector is represented by T, where T is the transpose of the vector, i is the angular constraint element angular label, and q is the generalized coordinate of the cable segment, representing the position and attitude information of the cable segment.

[0083] The dynamic equation solving unit is used to introduce the potential energy of the angularly constrained system into the system dynamic equation. Here, the Lagrange dynamic equation is established, and the dynamic equation is numerically solved to obtain the motion simulation results of the cable physical model.

[0084] At this point, the physical model of the flexible cable has been established.

[0085] The cable segment length confirmation unit is used to confirm the length of the cable segment. The cable resolution refers to the number of cable segments after discretization of a unit length of cable. That is, when the resolution is 100, it means that every 1m of cable is composed of 100 cable segment models, and each cable segment represents 1cm in length.

[0086] The geometric modeling module includes: a geometric model establishment unit and a solution unit;

[0087] The geometric model building unit is used to build the geometric model of the cable. It adopts a modeling method that is completely matched with the physical model—the discretized geometric modeling method. Based on each cable segment in the physical model, the geometric model of the cable segment—the "capsule body" model—is generated according to the position, orientation, and diameter information of the cable segment. The capsule body refers to a cylindrical structure with a hemispherical end, a regular geometric body with a capsule-like shape. The length of the cylinder of the "capsule body" is consistent with the length of the cable segment, and the diameter is consistent with the actual size of the cable. The overall geometric model of the cable is composed of a series of discretized "capsule body" geometric models.

[0088] The calculation unit is used to build a physical model of the cable, consider the actual physical characteristics of the cable, and perform numerical solutions to obtain the cable calculation results. Based on the calculation results, the geometric model of the cable is generated in real time, thus obtaining a realistic cable simulation effect.

[0089] Furthermore, this invention also provides a digital modeling method for a motion simulation model of a flexible cable, the modeling method comprising:

[0090] Step 1: Establish a physical model of the flexible cable;

[0091] Step 2: Establish the geometric model of the flexible cable;

[0092] In step 1, the physical model of the flexible cable is established, and the physical model of the flexible cable is a discretized cable model; step 1 includes:

[0093] Step 101: Discretize the cable model to be created, and process the cable model into a series of discrete cable segment models;

[0094] Step 102: Processing the cable segment model. Each cable segment is built as a rigid rod element. A concentrated mass element is created at the center of the cable segment so that the mass of the cable segment is concentrated at the center of the rigid rod element.

[0095] Step 103: Confirm the length of the cable segment. When creating the cable segment model, specify the resolution of the cable discretization. The resolution of the cable refers to the number of cable segments after discretization per unit length of cable. That is, when the resolution is 100, it means that every 1m of cable is composed of 100 cable segment models, and each cable segment represents 1cm in length.

[0096] Step 104: Confirm the mass of the cable segment. Before modeling the physical model of the cable, obtain the equivalent density, cross-sectional shape, cable diameter, and installation position parameters of the starting and ending points of the cable model to be built. Calculate the concentrated mass of each cable segment using the equivalent parameters of the cable and the length of the cable segment. The sum of the masses of all cable segments represents the mass of the entire cable.

[0097] Step 105: Establishing the local coordinate system of the cable segment. In order to accurately describe the pose of the cable in space, it is necessary to establish a local coordinate system for each cable segment at the center. The center of the cable segment is taken as the origin, the X-axis is the unit vector perpendicular to the axial direction of the cable segment, the Y-axis is the unit vector in the axial direction of the cable segment at that point, and the Z-axis is the unit vector in the binormal direction at that point. It can be obtained by Z = X × Y, thus determining the local coordinate system of the cable segment.

[0098] Step 106: Establishing the world coordinate system. Using a fixed point in space as the origin, the world coordinate system is established using the right-hand rule. The world coordinate system refers to a coordinate system that is fixed relative to the world.

[0099] Step 107: Determine the spatial location of the cable segment by using the coordinates of the origin of the local coordinate system of the cable segment in the world system.

[0100] Step 108: Determine the spatial pose of the cable segment. The pose of the local coordinate system of the cable segment is represented by the rotation of the world system. Here, the rotation of the cable segment is represented in the form of quaternions, which gives the description of the spatial pose of the cable segment.

[0101] Step 109: Establish connection points between cable segments. Establish connection points between cable segments, using the endpoints of cable segments as connection points between adjacent cable ends. That is, connect the end point of the previous cable segment to the beginning point of the next cable segment.

[0102] Step 110: Determine the coordinates of the connection point. The coordinates of the connection point in the local coordinate system of the cable segment are determined. The coordinates of the connection point and the center coordinates of the cable segment always differ along the axial direction. The distance, l, is the length of the cable segment. By transforming the local coordinate system of the cable segment to the world coordinate system, the coordinates of the cable segment connection point in the world scene are established.

[0103] Step 111: Establish the connection unit model of the cable segment. Constraint elements are established between the connection points of the cable segment. This is a new type of constraint element, uniformly called the angular constraint element. The angular constraint element restricts the relative displacement, bending angle, and torsional angle between two connection points to constrain the degrees of freedom of the cable in the tensile, bending, and torsional directions. The following constraint vector is established:

[0104]

[0105] in, This represents the angular constraint vector representation of the entire cable. This is the vector representation of the cable angle constraint between cable segments i and i+1, where T is the transpose of the vector, i is the angle label of the angle constraint element, and N is the vector number. C The number of angular constraint vectors for the entire cable;

[0106] Step 112: Establish the angular constraint vector between cable segments, connect the angular constraint elements between two adjacent cable segments, and then... This is expressed to limit the displacement, bending angle, and torsional angle of the connecting cable segment. Establish the following expression:

[0107]

[0108] in, For displacement constraints, For bending angle constraints, For the torsional angle constraint, P (i,i+1) P is the connection point between cable segment i and cable segment i+1. (i+1,i) Connect cable segment i+1 to the connection point of cable segment i, via P (i,i+1) P (i+1,i) The relative displacement between connection points limits the amount of cable stretching, θ [i] To limit the bending angle and the amount of bending between cable segments, Ω [i] To limit the twisting angle, the amount of twist in the cable segment is restricted;

[0109] Step 113: Establishing the elastic potential energy expression for the cable. Based on the Cosserat theory cable model, it is assumed that the cable diameter is much smaller than the deformed length. Hooke's law is extended to three-dimensional space. The elastic potential energy of the cable includes deformation in three directions: tension, bending, and torsion. By introducing the Young's modulus Y and Poisson's ratio σ of the cable material, the elastic potential energy expression of the cable is constructed: U = U s +U b +U t The meanings of each are as follows:

[0110]

[0111]

[0112]

[0113] Where U represents the elastic potential energy of the cable, U s U represents the potential energy of tensile deformation. bU represents the potential energy of bending deformation. t The potential energy represents torsional deformation, δx represents elongation, κ represents curvature, κ = 1 / R, R is the radius of curvature, Ω is the angle of torsion; the constant c s c b c t These represent the stiffness coefficients of the cable in three directions, obtained from the cable's Young's modulus Y and Poisson's ratio σ.

[0114] Step 114: Establish the cable elasticity model by introducing angular constraint vectors. A cable is discretized into N cable segment models, and the cable segments are connected by Nc = N-1 angular constraint units. The angular constraint regularization is introduced into the elastic potential energy of the cable system, and the regularized expression of the system potential energy can be obtained, as shown below. The system potential energy with angular constraints is highly integrated with the elastic potential energy theory of cables.

[0115]

[0116] Where ε is a diagonal matrix. diag represents the mathematical notation for a diagonal matrix; It is a parameter related to the vector stiffness coefficient, representing the reciprocal of the potential energy stiffness coefficient; The system constraint vector is represented by T, where T is the transpose of the vector, i is the angular constraint element angular label, and q is the generalized coordinate of the cable segment, representing the position and attitude information of the cable segment.

[0117] Step 115: Introduce the potential energy of the angularly constrained system into the system dynamic equations. Here, establish the Lagrange dynamic equations and solve them numerically to obtain the motion simulation results of the cable physical model.

[0118] This concludes the physical model establishment for the flexible cable in step 1.

[0119] Step 2 includes:

[0120] Step 201: Establish the geometric model of the cable, using a modeling method that perfectly matches the physical model—the discretized geometric modeling method; based on each cable segment in the physical model, generate the geometric model of the cable segment—the "capsule" model—according to the position, orientation, and diameter information of the cable segment. The capsule refers to a cylindrical structure with a hemispherical end, a regular geometric body resembling a capsule. The length of the cylinder of the "capsule" is consistent with the length of the cable segment, and the diameter is consistent with the actual size of the cable. The overall geometric model of the cable is composed of a series of discretized "capsule" geometric models.

[0121] Step 202: By building a physical model of the cable, considering the actual physical characteristics of the cable, and performing numerical solutions, the cable calculation results are obtained. Based on the calculation results, the geometric model of the cable is generated in real time, thus obtaining a realistic cable simulation effect.

[0122] Example 1

[0123] The technical solution of this embodiment includes: establishing a modeling method for a digital model of flexible cables, which can achieve complete matching between the physical model and the geometric model of flexible cables; and, based on the modeling method for the digital model of flexible cables, proposing a method for rapidly generating flexible cable models from rigid cable models, thereby achieving rapid generation of flexible cables. The modeling method flow of this invention is as follows: Figure 1 As shown, the specific implementation of the present invention is illustrated using digital modeling of a single flexible cable as an example.

[0124] The first step is to create a physical model of the flexible cable.

[0125] like Figure 2 The diagram shows a schematic of the physical model of a flexible cable. The flexible cable consists of discretized cable segment models, each segment being constructed as a rigid rod element structure. Each cable segment includes points with concentrated mass and connection points between segments. In the diagram, i represents the rigid rod element of the i-th cable segment, and XiYiZ... i XiYiZ represents the local coordinates of the i-th cable segment. i The centroid and concentrated mass point of the i-th cable segment are located at the position of the segment centroid and the position of the concentrated mass point. The total concentrated mass of all cable segments is the total mass of the entire cable. The cable segments are connected by points P. A new type of constraint unit is established between the connection points of adjacent cable segments. This constraint unit is used to represent the tensile, bending, and torsional characteristics of the cable.

[0126] By assembling cable segments into a cable model, describing the spatial position and orientation of the cable is to determine the spatial position description of each cable segment. Therefore, it is necessary to construct the relationship between a local coordinate system fixed at the center of the cable segment and a world coordinate system fixed in space, so as to obtain the spatial position and orientation description of the cable.

[0127] Establish local coordinates at the centroid of the cable segment, creating a spatial local coordinate system (P-XYZ) for the cable segment. Here, X is a unit vector perpendicular to the cable segment's axial direction, Y is a unit vector along the cable segment's axial direction at that point, and Z is a unit vector along the binormal direction at that point, which can be obtained by Z = X × Y. Establish a world coordinate system (O-uvw) with a fixed point O in space, and let r be the vector from point O to a point in space. By establishing the transformation relationship between the cable segment's local coordinate system and the world coordinate system, the spatial pose of the cable segment is described.

[0128] Description of the spatial location of the cable segment: The position transformation between the local coordinate system and the world coordinate system of the cable segment can be directly accomplished by vector translation.

[0129] Cable segment spatial attitude description: The attitude of the cable segment's local coordinate system is represented by the rotation amount of the world coordinate system. This scheme uses the quaternion λ to represent the rotation.

[0130] λ=(λ0λ1λ2λ3) T ,

[0131] Where λ0 is the real part parameter of the quaternion, and λ1, λ2, and λ3 are the imaginary part parameters corresponding to the three coordinate axes; the quaternion satisfies the constraints. And the quaternion parameter λ k (0≤k≤3) are all real numbers.

[0132] Define the basis vectors of the world coordinate system as in These are the vector bases corresponding to the three directions of the world coordinate system. The vector bases are expressed as:

[0133]

[0134]

[0135]

[0136] Define the basis vectors of the local coordinate system of the cable segment as d1, d2, and d3, where d1, d2, and d3 are the vector bases for the three directions of the local coordinate system of the cable segment, respectively. The rotation matrix R can be obtained from the attitude quaternion λ of the local coordinate system of the cable segment in the world coordinate system. The basis vectors of the local coordinate system of the cable segment are obtained through rotation transformation using a rotation matrix, as expressed below:

[0137]

[0138] Through the above coordinate transformation, a spatial pose description of the cable segment's local coordinate system can be established.

[0139] The next step is to establish a constraint model for cable tension, bending, and torsion.

[0140] Figure 2 As shown in the schematic diagram of the physical model of the flexible cable, the flexible cable is discretized into cable segments, which are connected by angular constraint elements. The angular constraint elements established between the connection points of the cable segments can represent the physical properties of the cable, such as bending, twisting, and stretching. The relative positions, bending angles, and twisting angles between adjacent cable segments are described below:

[0141] The angular constraint vector of the flexible cable segment is:

[0142]

[0143] Each corner constraint Connecting cable segments i and i+1. To handle large deformations in flexible cables, bending and twisting angles are directly expressed as angles.

[0144] like Figure 2 The local coordinate representation of the cable segment is introduced here by using a fixed vector d. (i) =Y (i) , represents the local axial direction vector of cable segment i, and introduces the vector. sum vector And vector X (i) and Z (i+1) Perpendicular to d (i) and d (i+1) The angular constraint expression for the cable is as follows:

[0145]

[0146] The first three-dimensional component of the angular constraint element corresponds to a spherical constraint. The spherical constraint restricts the cable's stretch. Each cable segment has two connection points with its adjacent segment, namely P... (i，1) and P (i，2) P (i，1) P is the connection point between the previous cable segment and the previous cable segment. (i，2) This is the connection point between one cable segment and the next; for example, P. (i，2) and P (i+1，1) An angular constraint element is established between the connection points of cable segment i and cable segment i+1.

[0147] Represented in the world coordinate system:

[0148] P (i，2) =X (i) +r (i，2)

[0149] Among them, X (i) Let r be the centroid location of the cable segment. (i，2) This refers to the position of the connection point relative to the centroid of the cable.

[0150] The second three-dimensional component of the angular constraint element corresponds to the constraint φ. b =θ can limit the amount of bending between cable segments, thus representing the bending characteristics of the cable;

[0151] The third three-dimensional component of the angular constraint element corresponds to the constraint φ. t=Ω can restrict the rotation of the cable segment around the axis, exhibiting the torsional characteristics of the cable and generating torsional force.

[0152] The methods for calculating the angles of bending and torsion are as follows:

[0153] θ [i] =arctan[|d (i) ×d (i+1) | / (d (i) ·d (i+1) )]

[0154]

[0155] Here, the angle is calculated using the arctangent, and the angle ranges from -π to π. η represents the number of twists, and i represents the label of the angle constraint.

[0156] The next step is to study the energy expression of flexible cables.

[0157] The deformation conditions that flexible cables need to meet in motion simulation are as follows, including the bending characteristic (R), torsional characteristic (Ω), and tensile characteristic (δx). Generally, cable deformation is a combination of tensile, bending, and torsional deformation. The resulting stress depends on the cable's material parameters, including Young's modulus and Poisson's ratio. The deformation energy of a cable of length L can be expressed as:

[0158]

[0159]

[0160]

[0161] Where δx represents elongation, κ represents curvature (κ = 1 / R), R is the radius of curvature, and Ω is the angle of twist. The constant c... s c b c t These represent the stiffness coefficient values ​​of the cable in three directions:

[0162] c s =YA / L,

[0163] c b =YI A / L,

[0164] c t =YI A / 2(1+σ)L

[0165] Where A is the cross-sectional area of ​​the cable, and I... A Y is the moment of inertia of this cable segment along the central axis, σ is the Young's modulus of the material, L is the Poisson's ratio, and L is the length of the cable.

[0166] The next step is to introduce the expression of the elasticity model of the flexible cable under constraints.

[0167] The physical model of a flexible cable consists of N rigid bodies bounded by Nc = N-1 constraints. By introducing a special angular constraint, the geometric tension, bending, and torsion between the object pairs can be parameterized. When this output is regularized, properties representing physical elasticity are introduced into the cable model; the regularization parameters correspond to the tensile, bending, and torsional stiffness. Introducing constraint regularization into the flexible cable physical model system establishes the relationship between the flexible cable's elastic model and the system constraints, thereby enabling the representation of the flexible cable's physical characteristics through the system's angular constraints.

[0168] By introducing the potential energy of the system through constraint regularization, the system expression can be obtained as follows:

[0169]

[0170] Where ε is a diagonal matrix. diag represents the mathematical notation for a diagonal matrix. It is a parameter related to the vector stiffness coefficient, representing the reciprocal of the potential energy stiffness coefficient, T is the transpose sign of the vector, i is the angular constraint element angular label, and q is the generalized coordinate of the cable segment, representing the position and attitude information of the cable segment.

[0171] For a length of L a and L b The angular constraint between two adjacent cable segments a and b has the following coefficients. Typically, the discretized cable segments of the same cable have the same length:

[0172]

[0173]

[0174]

[0175] By transforming the cable bending potential energy expressed as curvature into a measurement of bending radius θ, when assuming a small local bending angle, κ≈θ / (L) a +L b The transformed bending deformation energy is:

[0176]

[0177] At this point, the physical model of the cable is complete. The potential energy of the angular constraint system is introduced into the system dynamic equations, the Lagrange dynamic equations are established, and the dynamic equations are solved numerically to obtain the motion simulation results of the cable physical model.

[0178] The next step is to build the cable geometric model based on the cable physical model.

[0179] Flexible cable geometric model, such as Figure 3 As shown, the geometric model employs a modeling method that perfectly matches the physical model—the discretized geometric modeling method. Based on each cable segment in the physical model, a geometric model of the cable segment—a "capsule" model—is generated according to the segment's position, orientation, and diameter information. A capsule is a cylindrical structure with hemispherical ends, resembling a capsule in shape, and is a regular geometric form. Figure 3 In this model, i represents the i-th "capsule" model. The length of the cylinder of the i-th "capsule" is the same as the length of the i-th cable segment, and the diameter is the same as the actual diameter of the cable. The overall geometric model of the cable is composed of discrete "capsule" geometric models. This method of generating the geometric model of flexible cable based on the physical model can achieve a high degree of matching between the geometric model and the physical model.

[0180] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A digital modeling system for simulating the motion of flexible cables, characterized in that, The modeling system includes: a physical model modeling module and a geometric model modeling module; The physical modeling module is used to establish a physical model of the flexible cable based on the discretized cable model; The geometric modeling module is used to establish a geometric model using a discretized geometric modeling method that perfectly matches the physical model; The physical modeling module includes: a discretization unit, a cable segment model processing unit, a cable segment length confirmation unit, a cable segment quality confirmation unit, a cable segment local coordinate system establishment unit, a world coordinate system establishment unit, a cable segment spatial position determination unit, a cable segment spatial attitude determination unit, a connection point establishment unit, a connection point coordinate determination unit, a connection unit model establishment unit, an angular constraint vector establishment unit, an elastic potential energy expression establishment unit, a cable elastic model establishment unit, and a dynamic equation solving unit. The cable segment model processing unit is used to process the cable segment model. Each cable segment is established as a rigid rod element, and a concentrated mass element is created at the center of the cable segment so that the mass of the cable segment is concentrated at the center of the rigid rod element. The connection unit model building unit is used to build the connection unit model of the cable segment. Constraint units, collectively referred to as angular constraint units, are established between the connection points of the cable segment. The angular constraint units constrain the degrees of freedom of the cable's tensile, bending, and torsional directions by limiting the relative displacement, bending angle, and torsional angle between two connection points, and establish the following constraint vectors: in, This represents the angular constraint vector representation of the entire cable. Let T be the vector representation of the cable angle constraint between cable segments i and i+1, where T is the transpose of the vector and i is the label of the angle constraint element. The number of angular constraint vectors for the entire cable; The angle constraint vector establishment unit is used to establish angle constraint vectors between cable segments, connecting the angle constraint units between two adjacent cable segments, through... This is expressed to limit the displacement, bending angle, and torsional angle of the connecting cable segment. Establish the following expression: in, For displacement constraints, For bending angle constraints, To constrain the torsional angle, Connect cable segment i to the connection point of cable segment i+1. Connect cable segment i+1 to the connection point of cable segment i, via The relative displacement between connection points limits the amount of cable stretching. To limit the bending angle, the amount of bending between cable segments is restricted. To limit the twisting angle, the amount of twist in the cable segment is restricted; The elastic potential energy expression establishment unit is used to establish the elastic potential energy expression of the cable. Based on the Cosserat theory cable model, it is assumed that the cable diameter is much smaller than the deformed length. Hooke's law is extended to three-dimensional space. The elastic potential energy of the cable includes deformation in three directions: tension, bending, and torsion. This is achieved by introducing Young's modulus Y and Poisson's ratio of the cable material. The elastic potential energy expression for constructing the cable is U=U s + U b +U t The meanings of each are as follows: Where U represents the elastic potential energy of the cable, U s U represents the potential energy of tensile deformation. b U represents the potential energy of bending deformation. t This represents the potential energy for torsional deformation. Indicates elongation. Indicates curvature, R is the radius of curvature. For the angle of twist; constant , , These represent the stiffness coefficients of the cable in three directions, derived from the cable's Young's modulus Y and Poisson's ratio. Parameters obtained; The cable elasticity model building unit is used to build a cable elasticity model with the introduction of angular constraint vectors. A cable is discretized into N cable segment models, and the cable segments are connected by Nc=N-1 angular constraint units. The angular constraint regularization is introduced into the elastic potential energy of the cable system, and the regularized expression of the system potential energy can be obtained, as shown below. The system potential energy with the introduction of angular constraints is highly integrated with the theory of cable elastic potential energy. in, It is a diagonal matrix. , Mathematical notation for diagonal matrices; , is a parameter related to the vector stiffness coefficient, representing the reciprocal of the potential energy stiffness coefficient; The system constraint vector is represented by T, where T is the transpose of the vector, i is the angular constraint element label, and q is the generalized coordinate of the cable segment, representing the position and attitude information of the cable segment.

2. The digital modeling system for the motion simulation model of flexible cables as described in claim 1, characterized in that, In the process of establishing the physical model of the flexible cable by the physical model modeling module, the physical model of the flexible cable is a discretized cable model. The discretization unit is used to discretize the cable model to be created, processing the cable model into a series of discrete cable segment models. The cable segment length confirmation unit is used to confirm the length of the cable segment. When creating the cable segment model, the resolution of the cable discretization is specified. The resolution of the cable refers to the number of cable segments after discretization per unit length of cable. The cable segment quality verification unit is used to verify the quality of the cable segments, obtain the equivalent density, cross-sectional shape, cable diameter, and the installation position parameters of the starting and ending points of the cable model to be built, and calculate the concentrated mass of each cable segment through the equivalent parameters of the cable and the length of the cable segment. The sum of the masses of all cable segments represents the mass of the entire cable. The cable segment local coordinate system establishment unit is used to establish the local coordinate system of the cable segment. In order to accurately describe the pose of the cable in space, it is necessary to establish a local coordinate system of the cable segment at the center of each cable segment. The center of the cable segment is taken as the origin, the X-axis is the unit vector perpendicular to the axial direction of the cable segment, the Y-axis is the unit vector in the axial direction of the cable segment at that point, and the Z-axis is the unit vector in the binormal direction at that point, which can be obtained by Z=X×Y, thus determining the local coordinate system of the cable segment. The world coordinate system establishment unit is used to establish a world coordinate system. The world coordinate system is established with a fixed point in space as the origin and the right-hand rule. The world coordinate system refers to a coordinate system that is fixed relative to the world. The cable segment spatial location determination unit is used to determine the spatial location of the cable segment, and determines the spatial location of each cable segment by using the coordinates of the origin of the local coordinate system of the cable segment in the world system. The cable segment spatial attitude determination unit is used to determine the spatial attitude of the cable segment. The attitude of the local coordinate system of the cable segment is represented by the rotation of the world system. Here, the rotation of the cable segment is represented in the form of quaternions, and the description of the spatial pose of the cable segment can be obtained. The connection point establishment unit is used to establish connection points between cable segments. The connection points between cable segments are established by using the endpoints of the cable segments as the connection points between adjacent cable ends. That is, the end point of the previous cable segment is connected to the beginning point of the next cable segment. The connection point coordinate determination unit is used to determine the coordinates of the connection point, specifically its coordinates in the local coordinate system of the cable segment. The coordinates of the connection point and the center coordinates of the cable segment always differ along the axial direction. distance, Given the length of the cable segment, and by using the transformation relationship between the local coordinate system and the world coordinate system of the cable segment, the coordinates of the cable segment connection point in the world scene are established; The dynamic equation solving unit is used to introduce the potential energy of the angularly constrained system into the system dynamic equation. Here, the Lagrange dynamic equation is established, and the dynamic equation is numerically solved to obtain the motion simulation results of the cable physical model. At this point, the physical model of the flexible cable has been established. The cable segment length confirmation unit is used to confirm the length of the cable segment. The cable resolution refers to the number of cable segments after discretization of a unit length of cable. That is, when the resolution is 100, it means that every 1m of cable is composed of 100 cable segment models, and each cable segment represents 1cm in length.

3. The digital modeling system for the motion simulation model of flexible cables as described in claim 2, characterized in that, The geometric modeling module includes: a geometric model building unit and a solution unit; The geometric model building unit is used to build the geometric model of the cable, employing a modeling method that perfectly matches the physical model—the discretized geometric modeling method. Based on each cable segment in the physical model, and according to the position, orientation, and diameter information of the cable segment, a geometric model of the cable segment—a "capsule" model—is generated. A capsule is a cylindrical structure with a hemispherical end, resembling a capsule in shape. The length of the "capsule" cylinder is consistent with the length of the cable segment, and its diameter is consistent with the actual size of the cable. The overall geometric model of the cable is composed of discrete "capsule" geometric models. The calculation unit is used to build a physical model of the cable, consider the actual physical characteristics of the cable, perform numerical solutions, obtain the cable calculation results, and generate the geometric model of the cable in real time based on the calculation results.

Images