A long-distance belt conveyor space coupling dynamics model modeling and simulation method

Abstract

This invention relates to the field of belt conveyor dynamics simulation, and in particular to a modeling and simulation method for a spatially coupled dynamics model of a long-distance belt conveyor. The modeling method includes discretizing the conveyor belt and wire rope into segments, establishing a three-dimensional coupled dynamics model of the trailer system, conveyor belt, and wire rope, establishing a global spatial internal force model of the long-distance belt conveyor, and establishing an external load vector dynamics model, including track irregularity excitation force, wheel-rail tangential nonlinear friction force, conical wheel excitation force, and material gravity; and establishing a global spatial dynamics model of the long-distance belt conveyor. This invention proposes and implements a vertical-longitudinal-lateral joint modeling framework: simultaneously considering three-dimensional contact dynamics and tangential friction, as well as the coupling of the supporting belt segment-frame-wheel-track within a single model, which can more realistically describe the coupled vibration behavior of the trailer-type belt conveyor in actual operation.

Description

Technical Field

[0001] This invention relates to the field of dynamic simulation of belt conveyors, and in particular to a modeling and simulation method for spatially coupled dynamics of long-distance belt conveyors. Background Technology

[0002] Belt conveyors are core equipment in the continuous transportation of bulk materials. With the continuous expansion of industrial scale, the length of conveyor lines, carrying capacity, and operating speed are constantly increasing. Traditional idler roller conveyors are gradually showing their shortcomings in terms of high energy consumption, high vibration, rapid component wear, and heavy maintenance workload. The industry's demand for new conveying structures that are energy-efficient, have high carrying capacity, low resistance, and stable operation is becoming increasingly urgent.

[0003] Against this backdrop, the trailer-type belt conveyor has attracted attention as a new structural system composed of "track-trailer-conveyor belt-wire rope". This structure uses trailers to replace idlers to support the conveyor belt, which can significantly reduce running resistance, improve overall transmission efficiency, and have better running stability. The introduction of the trailer structure makes the system exhibit dynamic characteristics different from traditional conveyors, including (1) the system is a chain-type multi-car structure: the whole is composed of multiple trailers running in series, and the system's degrees of freedom are highly distributed; (2) the flexible coupling relationship between the conveyor belt and the trailer is significant: the conveyor belt, as a flexible body, has its tension, deflection and trailer dynamic response mutually affecting each other; (3) wheel-rail contact introduces trailer dynamic factors: the trailer runs along the track, introducing wheel-rail contact, friction, impact and other trailer dynamic characteristics; (4) the flexible connection between workshops cannot be ignored: the trailers are connected by wire ropes or other flexible components, which significantly affects the system stability and vibration transmission path.

[0004] Due to the aforementioned characteristics, the dynamic complexity of idler belt conveyors is much higher than that of traditional idler roller conveyors, and simplified one-dimensional or local models are no longer applicable.

[0005] In existing studies, most studies only analyze the vertical vibration, local collision or single working point of the motorcycle, which has the following technical limitations: (1) lack of a unified dynamic framework that covers longitudinal / lateral / vertical motion at the same time; (2) failure to incorporate the flexibility of the conveyor belt and the flexibility of the wire rope into the system-level coupling modeling; (3) difficulty in supporting numerical solutions for the coordinated operation of multiple motorcycles and inability to handle workshop coupling effects; (4) inability to simulate the effect of conical wheel effect on system dynamics. Summary of the Invention

[0006] This invention aims to solve the above problems and provides a method for modeling and simulating the spatial coupling dynamics of long-distance belt conveyors. The technical solution adopted is as follows: A method for modeling a spatially coupled dynamic model of a long-distance belt conveyor includes the following steps: S1. Define the direction perpendicular to the conveyor belt surface downwards as the vertical direction, the direction of the trolley's movement along the track as the longitudinal direction, and the direction perpendicular to both the vertical and longitudinal directions in space as the transverse direction; discretize the conveyor belt into segments, and divide the discretized segments into supporting belt segments supported by the trolley and suspended belt segments connecting adjacent supporting belt segments; discretize the wire rope into segments; establish a three-dimensional coupled dynamic model of the trolley system, the conveyor belt, and the wire rope, wherein the trolley system includes a single trolley, supporting belt segments, and track segments below the trolley; S2. Establish a global spatial internal force model for a long-distance belt conveyor; S3. Establish an external load vector dynamic model, wherein the external load includes track irregularity excitation force, wheel-rail tangential nonlinear friction force, and material gravity; S4. Establish a global spatial dynamics model for long-distance belt conveyors.

[0007] Based on the above scheme, the following assumptions are made: Long-distance belt conveyor consists of It consists of 10 trailers, each of which includes a frame and wheels; For each trolley system, the supporting belt segment, frame, wheels, and track are defined as key nodes. Each key node has translational degrees of freedom in the vertical z, longitudinal x, and lateral y directions. Therefore, each trolley system has a total of 12 displacement degrees of freedom. Let the displacement vector of the i-th trolley be denoted as... (1-1) Subscript p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; For each flexible belt segment, namely the conveyor belt segment and the wire rope segment, each segment is defined with nodes at both ends. Each node has translational degrees of freedom in the vertical z, longitudinal x, and transverse y directions. Thus, each flexible belt segment has a total of 6 degrees of freedom.

[0008] Based on the above scheme, step S1 includes, S1-1. The mass matrix of the conveyor belt segment is: (1-2) in , is a three-directional identity matrix. For the quality of the conveyor belt segment; The mass matrix of the wire rope segment is (1-3) in For the quality of the wire rope segment; The mass matrix of a single trailer unit is formed by assembling the supporting belt segment, frame, wheels, and track segment according to nodes. (1-4) in, To support the quality of the belt segment, take ; For the quality of the frame; The mass of the wheel; The mass of the equivalent track segment; S1-2. Define each discrete segment of the conveyor belt and wire rope as having two endpoints, Left and Right, respectively, and the displacement vector of each flexible segment is: Define a 6×6 local stiffness matrix. Under the conditions of independent linear elastic coupling in all directions and no transverse coupling between nodes, the stiffness matrix of the conveyor belt segment is: (1-5) any m-th sub-block Take diagonal form In the formula, For the vertical stiffness of the conveyor belt segment, For the longitudinal stiffness of the conveyor belt segment, Let be the lateral stiffness of the conveyor belt segment; then (1-6) The stiffness matrix of the wire rope segment is (1-7) The nth sub-block Take diagonal form In the formula, For the vertical stiffness of the wire rope segment, For the longitudinal stiffness of the wire rope segment, Let be the lateral stiffness of the wire rope segment; then (1-8) The stiffness matrix of a single trailer unit under three-dimensional coupling is:

[0009] (1-9) Each sub-block and All are 3×3 matrices. This represents the structure's own stiffness matrix. Represents the stiffness matrix between adjacent structures, where the subscripts are... p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; ,in For the stiffness matrix of the supporting belt segment, The frame elastic support stiffness matrix, Here is the wheel-rail contact stiffness matrix. This is the equivalent track segment stiffness matrix; (1-10) (1-11) (1-12) (1-13) in These represent the vertical, longitudinal, and lateral stiffness of the supporting strip segment, respectively. These represent the vertical, longitudinal, and lateral stiffness of the frame's elastic supports, respectively. These represent the vertical, longitudinal, and lateral stiffness of the wheel and rail, respectively. These represent the vertical, longitudinal, and lateral stiffness of the track, respectively. Supporting strip - frame stiffness matrix: ; Frame-wheel stiffness matrix: ; Wheel-track stiffness matrix: ; S1-3. Conveyor belt segment damping matrix (1-14) (1-15) in These are the vertical, longitudinal, and transverse damping coefficients of the conveyor belt segment, respectively. Wire rope segment damping matrix (1-16) (1-17) in These are the vertical, longitudinal, and lateral damping coefficients of the wire rope segment, respectively. Motorcycle unit damping matrix Same as the stiffness matrix structure of the motorcycle unit (1-18) Each sub-block and All are 3×3 matrices. This represents the structure's own damping matrix. Represents the damping matrix between adjacent structures, where the subscripts are... p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and track.

[0010] Based on the above scheme, step S2 includes: S2-1. Sort the degrees of freedom of the multiple trailer unit-conveyor belt-wire rope spatial dynamics models to form a global displacement vector: (2-1) in Let be the displacement vector of the i-th trailer unit; Let be the displacement vector of the e-th segment of the conveyor belt supporting the belt segment. This represents the total number of suspended sections. Let be the displacement vector of the e-th wire rope segment. This represents the total number of wire rope segments; The displacement vector of the i-th trailer unit is (2-2) in Let be the vertical displacement of the support segment of the i-th trailer unit. Let be the longitudinal displacement of the support segment of the i-th trailer unit. Let be the lateral displacement of the support segment of the i-th trailer unit. Let be the vertical displacement of the i-th trailer unit frame. Let be the longitudinal displacement of the i-th trailer unit frame. Let represent the lateral displacement of the i-th trailer unit frame. Let be the vertical displacement of the wheel of the i-th trailer unit. Let be the longitudinal displacement of the wheel of the i-th trailer unit. Let be the lateral displacement of the wheel of the i-th trailer unit. Let be the vertical displacement of the track segment of the i-th trailer unit. Let be the longitudinal displacement of the track segment of the i-th trailer unit. Let be the lateral displacement of the track segment of the i-th trailer unit; The displacement vector of the e-th conveyor belt supporting the belt segment is (2-3) in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th conveyor belt support segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th conveyor belt support segment, respectively. The displacement vector of the e-th segment of the wire rope is (2-4) in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th wire rope segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th wire rope segment, respectively. S2-2. Establish a global stiffness matrix based on the coupling stiffness between the flexible segment and the trailer unit, and the stiffness between the flexible segments. (2-5) in The stiffness matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; Let be the stiffness matrix of the aforementioned coupled subsystem – the non-directly connected suspended strip segment; The stiffness matrix of the above-mentioned coupled subsystem - non-directly connected wire rope segment; Here is the stiffness matrix of the conveyor belt; Here is the stiffness matrix of the wire rope; (2-6) in The connection stiffness between trailer units is affected by both the conveyor belt section and the wire rope section. (2-7) in This is the set of all suspended strip segments connecting the i-th trailer unit and the (i+1)-th trailer unit; This is the set of all wire rope segments connecting the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral stiffness of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral stiffness of the nth wire rope segment, respectively. ; Let be the coupling selection vectors of the m-th suspended strip segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the m-th suspended strip segment is a suspended strip segment directly connected to the supporting strip segment in the trailer unit, then (2-8) (2-9) (2-10) These are the right-end coupling selection vectors for the m-th suspended strip segment and the i-th trailer unit, respectively. These are the coupling selection vectors for the left end of the nth wire rope segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the nth wire rope segment is directly connected to the trailer unit, then... (2-11) (2-12) (2-13) If the nth wire rope segment is not directly connected to the trailer unit, then the vector is selected as 0; These are the coupling selection vectors for the right end of the nth wire rope segment and the ith trailer unit, respectively. Furthermore, (2-14) in (2-15) (2-16) (2-17) (2-18) (2-19) in Let be the stiffness matrix of the m-th conveyor belt segment; This is the selection matrix used to align the degrees of freedom at the end points of the suspended belt segment with the degrees of freedom of the support belt segment of the trailer unit; (2-20) in Let be the stiffness matrix of n steel wire rope segments; This is the selection matrix used to align the degrees of freedom at the ends of the wire rope segments with the degrees of freedom of the trailer unit frame; All suspended belt segments other than those not directly connected to the support segment of the trailer unit constitute the conveyor belt stiffness matrix. (2-21) All wire rope segments other than those not directly connected to the trailer unit frame constitute the wire rope stiffness matrix. (2-22); S2-3. Establish the global damping matrix. (2-23) in The damping matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; The damping matrix of the aforementioned coupled subsystem - the non-directly connected suspended strip segment; The damping matrix for the non-directly connected wire rope segment of the aforementioned coupled subsystem; The damping matrix of the conveyor belt; The damping matrix of the wire rope; (2-24) in The connection damping between trailer units is affected by both the conveyor belt section and the wire rope section. (2-25) in This is the set of all suspended strip segments connecting the i-th trailer unit and the (i+1)-th trailer unit; This is the set of all wire rope segments connecting the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral damping of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral damping of the nth wire rope segment, respectively. ; Furthermore, (2-26) in (2-27) (2-28) (2-29) in Let be the damping matrix of the m-th conveyor belt segment; (2-30) in Let n be the damping matrix of the nth conveyor belt segment; All suspended belt segments other than those not directly connected to the support segment of the trailer unit constitute the conveyor belt damping matrix. (2-31) All wire rope segments other than those not directly connected to the trailer unit frame constitute the wire rope damping matrix. (2-32); S2-4. Establish the global quality matrix (2-33) in The mass matrix of the trailer unit group includes all trailer units, as well as the suspension belt segment and wire rope segment directly connected to the aforementioned trailer units. (2-34) in Let i be the mass matrix of the i-th trailer unit; The conveyor belt mass matrix includes all conveyor belt segments except for the supporting belt segment of the trailer unit and the suspended belt segment directly connected to the trailer unit. (2-35) The wire rope mass matrix includes all wire rope segments except those directly connected to the trailer unit frame. (2-36).

[0011] Preferably, step S3 includes: S3-1. Track irregularity excitation force: Establish the formula for the vertical irregularity spectral density of the orbit. (3-1) in For the orbital vertical irregularity spectral density, Spatial frequency, unit 1 / m. The vertical amplitude coefficient, The vertical decay exponent; The inverse Fourier transform is used to convert the frequency domain signal into the vertical spatial domain signal. (3-2) in This represents the spatial domain signal for vertical irregularities in the orbit. For the complex spectrum of vertical irregularities in the orbit, , To be a random phase angle that follows a uniform distribution, , This represents the number of sampling points; The vertical irregularity excitation force between the wheel and rail is then... (3-3) in , which is the difference in track profile displacement; Establish the formula for longitudinal irregularity spectral density of orbit (3-4) in The longitudinal irregularity spectral density of the orbit. For vertical amplitude coefficient, The longitudinal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the longitudinal spatial domain signal (3-5) in This refers to longitudinal unevenness in the track. The complex spectrum represents the longitudinal irregularities of the track. ; The longitudinal irregularity excitation force between the wheel and rail is (3-6) in ; Establish the formula for the transverse irregularity spectral density of the track. (3-7) in This represents the spectral density of transverse irregularities in the orbit. This is the horizontal amplitude coefficient. It is the horizontal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the transverse spatial domain signal (3-8) in This refers to lateral unevenness in the track. This represents the complex spectrum of the orbit's lateral irregularities. ; The excitation force of lateral irregularity between wheel and rail is (3-9) in ; S3-2. Wheel-rail tangential nonlinear friction force: Probe longitudinal / lateral tangential force vectors (3-10) Wheel rail positive pressure Friction saturates and smooths into (3-11) in The tangential force between the wheel and rail, including longitudinal tangential force. and lateral tangential force ,and , ; Preload includes the weight of the material, the weight of the conveyor belt segment, and the weight of the trolley itself; The coefficient of friction between the wheel and the rail. This is a very small positive number used to avoid a denominator of 0 and to reduce gradient abrupt changes at saturation.

[0012] Based on the above scheme, the external load also includes the excitation force of the conical wheel, which includes vertical contact force and lateral contact force. The process of establishing its dynamic model includes: S3-3-1. Let the wheel width be w and the cone angle be... The radius of the contact point at the wheel flange is ; When the lateral offset of the wheel reaches half of the wheel width, the contact radius will decrease linearly to a minimum value, and the geometric relationship is as follows: (3-12) Mapping the vertical displacement to a local effective radius, and then performing normalization and smoothing, then... (3-13) in A normalized scale used to adjust sensitivity and smoothness; using a sine map to... Mapped to ,but (3-14) Vertical offset h is (3-15) In vertical relative displacement As a response to vertical irregularities in the track Additional deformation (3-16) in The vertical irregular displacement after adding the conical wheel effect; The vertical relative displacement after adding the conical wheel effect is: (3-17) The vertical contact force between the wheel and rail after adding the conical wheel effect is: (3-18) S3-3-2. Define the lateral offset s of the conical wheel, then (3-19) In the lateral relative displacement, s is taken as the lateral irregularity of the track. Additional deformation (3-20) in This refers to the lateral irregularity displacement after adding the conical wheel effect; The lateral relative displacement after adding the conical wheel effect is: (3-21) The wheel-rail lateral contact force after adding the conical wheel effect is: (3-22).

[0013] Based on the above scheme, step S4 includes Establish the overall dynamic equations of the space-coupled system (4-1) Where F is the external load of the system.

[0014] (4-2) in, This represents the total mass of the materials.

[0015] A simulation method for a spatially coupled dynamic model of a long-distance belt conveyor, based on the aforementioned spatially coupled dynamic model of a long-distance belt conveyor, includes: The implicit solver MATLAB ode15s is used for stepwise integration to output the time-domain response results of the dynamic model, and frequency-domain analysis is performed.

[0016] The beneficial effects of this invention are as follows: A combined vertical-longitudinal-lateral modeling framework was proposed and implemented: it simultaneously considers triaxial contact dynamics, tangential friction, and the coupling of the support belt segment-frame-wheel-track within a single model, which can more realistically describe the coupled vibration behavior of the trailer belt conveyor in actual operation. A multi-layered rigid-flexible coupling assembly method for multi-vehicle systems is proposed, which forms a global system matrix through three layers of coupling: the first layer: the coupling between the support belt segment, the frame, the wheel, and the track; the second layer: the coupling between the support belt segment and the suspended belt segment directly connected to the support belt segment, and the coupling between the frame and the rope segment directly connected to the frame; the third layer: the coupling between non-directly connected suspended belt segments and between non-directly connected rope segments. A hybrid strategy of segmented discretization of conveyor belts and wire ropes and equivalent track parameters is adopted to capture the dynamic characteristics of key flexible connection positions of conveyor belts and wire ropes while maintaining computational efficiency. Introducing the conical wheel effect in both the radial and axial directions of the wheel improves the model's versatility in handling complex working conditions; It can be directly input into numerical computing environments such as MATLAB, supports sensitivity analysis of parameters such as number of segments, stiffness, equivalent track stiffness, and velocity, and outputs engineering evaluation indicators such as root mean square error, peak value, and spectrum, which facilitates engineering design and optimization. Attached Figure Description

[0017] Figure 1 Flowchart of the dynamic model establishment for this invention; Figure 2 : Structural diagram of the belt conveyor test bench to which this invention applies; Figure 3 : A schematic diagram of the rotating mechanism of the belt conveyor test bench to which this invention applies; Figure 4 The present invention provides a dynamic model of the motorcycle unit. Figure 5 This invention provides a multibody dynamics model for a belt conveyor. Figure 6 The model of this invention solves for the final lateral relative displacement curve; Figure 7 The model of this invention solves for the lateral offset curve caused by the conical wheel; Figure 8 The relative relationship between conical offset and vertical displacement in the solution results of the model of this invention. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments: In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0019] In the description of this invention, it should be understood that the terms "center," "length," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," and "inner," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0020] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0021] The spatially coupled dynamic model of a long-distance belt conveyor is established based on a belt conveyor simulation test bench, such as... Figures 2 to 3 As shown, the test bench includes a trolley 1, a track, a wire rope 3, a slewing mechanism 4, a conveyor belt 5, idlers 6, rollers 7, and a tensioning device 8. The track includes a progress section track 21 and a return section track 22. The slewing mechanism 4 connects the first and second ends of the progress section track 21 and the return section track 22, forming a closed-loop structure. The slewing mechanism includes a tilting track 41, a slewing wheel 42, a tensioning carriage 43, and a counterweight 44. The counterweight 44 pulls the tensioning carriage 42, thereby enabling the slewing mechanism 4 to perform a tensioning function. The trolleys 1 are spaced apart on the progress section track 22 and slide along the track. Each trolley includes a frame 11 and wheels 12. The wheels 12 contact the track, and the frame 11 supports the conveyor belt 5. Wire ropes 3 connect adjacent frames 11. The conveyor belt 5 is wound around the track and the rollers 7 at both ends. The portion of the conveyor belt 5 outside the track is supported by idlers 6. The test bench also includes a vibration monitoring module 9, which is installed on the track, specifically on the process section track 21, and is used to detect the real-time vibration signal and vibration state of the track 21.

[0022] like Figure 1 , Figure 4 and Figure 5 As shown, a modeling method for a spatially coupled dynamic model of a long-distance belt conveyor includes the following steps: S1. Define the direction perpendicular to the conveyor belt surface downwards as the vertical direction, the direction of the trolley's movement along the track as the longitudinal direction, and the direction perpendicular to both the vertical and longitudinal directions in space as the transverse direction; discretize the conveyor belt into segments, and divide the discretized segments into supporting belt segments supported by the trolley and suspended belt segments connecting adjacent supporting belt segments; discretize the wire rope into segments; establish a three-dimensional coupled dynamic model of the trolley system, the conveyor belt, and the wire rope, wherein the trolley system includes a single trolley, supporting belt segments, and track segments below the trolley; S2. Establish a global spatial internal force model for a long-distance belt conveyor; S3. Establish an external load vector dynamic model, wherein the external load includes track irregularity excitation force, wheel-rail tangential nonlinear friction force, and material gravity; S4. Establish a global spatial dynamics model for long-distance belt conveyors.

[0023] Assumptions are made regarding the test bench and dynamic model: Long-distance belt conveyor consists of It consists of 10 trailers, each of which includes a frame and wheels; For each trolley system, the supporting belt segment, frame, wheels, and track are defined as key nodes. Each key node has translational degrees of freedom in the vertical z, longitudinal x, and lateral y directions. Therefore, each trolley system has a total of 12 displacement degrees of freedom. Let the displacement vector of the i-th trolley be denoted as... (1-1) Subscript p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; For each flexible belt segment, namely the conveyor belt segment and the wire rope segment, each segment is defined with nodes at both ends. Each node has translational degrees of freedom in the vertical z, longitudinal x, and transverse y directions. Thus, each flexible belt segment has a total of 6 degrees of freedom.

[0024] Step S1 includes, S1-1. The mass matrix of the conveyor belt segment is: (1-2) in , is a three-directional identity matrix. For the quality of the conveyor belt segment; The mass matrix of the wire rope segment is (1-3) in For the quality of the wire rope segment; The mass matrix of a single trailer unit is formed by assembling the supporting belt segment, frame, wheels, and track segment according to nodes. (1-4) in, To support the quality of the belt segment, take ; For the quality of the frame; The mass of the wheel; The mass of the equivalent track segment; S1-2. Define each discrete segment of the conveyor belt and wire rope as having two endpoints, Left and Right, respectively, and the displacement vector of each flexible segment is: Define a 6×6 local stiffness matrix. Under the conditions of independent linear elastic coupling in all directions and no transverse coupling between nodes, the stiffness matrix of the conveyor belt segment is: (1-5) any m-th sub-block Take diagonal form In the formula, For the vertical stiffness of the conveyor belt segment, For the longitudinal stiffness of the conveyor belt segment, Let be the lateral stiffness of the conveyor belt segment; then (1-6) The stiffness matrix of the wire rope segment is (1-7) The nth sub-block Take diagonal form In the formula, For the vertical stiffness of the wire rope segment, For the longitudinal stiffness of the wire rope segment, Let be the lateral stiffness of the wire rope segment; then (1-8) The stiffness matrix of a single trailer unit under three-dimensional coupling is:

[0025] (1-9) Each sub-block and All are 3×3 matrices. This represents the structure's own stiffness matrix. Represents the stiffness matrix between adjacent structures, where the subscripts are... p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; ,in For the stiffness matrix of the supporting belt segment, The frame elastic support stiffness matrix, Here is the wheel-rail contact stiffness matrix. This is the equivalent track segment stiffness matrix; (1-10) (1-11) (1-12) (1-13) in These represent the vertical, longitudinal, and lateral stiffness of the supporting strip segment, respectively. These represent the vertical, longitudinal, and lateral stiffness of the frame's elastic supports, respectively. These represent the vertical, longitudinal, and lateral stiffness of the wheel and rail, respectively. These represent the vertical, longitudinal, and lateral stiffness of the track, respectively. Supporting strip - frame stiffness matrix: ; Frame-wheel stiffness matrix: ; Wheel-track stiffness matrix: ; S1-3. Conveyor belt segment damping matrix (1-14) (1-15) in These are the vertical, longitudinal, and transverse damping coefficients of the conveyor belt segment, respectively. Wire rope segment damping matrix (1-16) (1-17) in These are the vertical, longitudinal, and lateral damping coefficients of the wire rope segment, respectively. Motorcycle unit damping matrix Same as the stiffness matrix structure of the motorcycle unit (1-18) Each sub-block and All are 3×3 matrices. This represents the structure's own damping matrix. Represents the damping matrix between adjacent structures, where the subscripts are... p , e , w , r These respectively represent the supporting belt segment, frame, wheels, and track.

[0026] Step S2 includes: S2-1. Sort the degrees of freedom of the multiple trailer unit-conveyor belt-wire rope spatial dynamics models to form a global displacement vector: (2-1) in Let be the displacement vector of the i-th trailer unit; Let be the displacement vector of the e-th segment of the conveyor belt supporting the belt segment. This represents the total number of suspended sections. Let be the displacement vector of the e-th wire rope segment. This represents the total number of wire rope segments; The displacement vector of the i-th trailer unit is (2-2) in Let be the vertical displacement of the support segment of the i-th trailer unit. Let be the longitudinal displacement of the support segment of the i-th trailer unit. Let be the lateral displacement of the support segment of the i-th trailer unit. Let be the vertical displacement of the i-th trailer unit frame. Let be the longitudinal displacement of the i-th trailer unit frame. Let represent the lateral displacement of the i-th trailer unit frame. Let be the vertical displacement of the wheel of the i-th trailer unit. Let be the longitudinal displacement of the wheel of the i-th trailer unit. Let be the lateral displacement of the wheel of the i-th trailer unit. Let be the vertical displacement of the track segment of the i-th trailer unit. Let be the longitudinal displacement of the track segment of the i-th trailer unit. Let be the lateral displacement of the track segment of the i-th trailer unit; The displacement vector of the e-th conveyor belt supporting the belt segment is (2-3) in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th conveyor belt support segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th conveyor belt support segment, respectively. The displacement vector of the e-th segment of the wire rope is (2-4) in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th wire rope segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th wire rope segment, respectively. S2-2. Establish a global stiffness matrix based on the coupling stiffness between the flexible segment and the trailer unit, and the stiffness between the flexible segments. (2-5) in The stiffness matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; Let be the stiffness matrix of the aforementioned coupled subsystem – the non-directly connected suspended strip segment; The stiffness matrix of the above-mentioned coupled subsystem - non-directly connected wire rope segment; Here is the stiffness matrix of the conveyor belt; Here is the stiffness matrix of the wire rope; (2-6) in The connection stiffness between trailer units is affected by both the conveyor belt section and the wire rope section. (2-7) in This is the set of all suspended strip segments connecting the i-th trailer unit and the (i+1)-th trailer unit; This is the set of all wire rope segments connecting the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral stiffness of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral stiffness of the nth wire rope segment, respectively. ; Let be the coupling selection vectors of the m-th suspended strip segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the m-th suspended strip segment is a suspended strip segment directly connected to the supporting strip segment in the trailer unit, then (2-8) (2-9) (2-10) These are the right-end coupling selection vectors for the m-th suspended strip segment and the i-th trailer unit, respectively. These are the coupling selection vectors for the left end of the nth wire rope segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the nth wire rope segment is directly connected to the trailer unit, then... (2-11) (2-12) (2-13) If the nth wire rope segment is not directly connected to the trailer unit, then the vector is selected as 0; These are the coupling selection vectors for the right end of the nth wire rope segment and the ith trailer unit, respectively. Furthermore, (2-14) in (2-15) (2-16) (2-17) (2-18) (2-19) in Let be the stiffness matrix of the m-th conveyor belt segment; This is the selection matrix used to align the degrees of freedom at the end points of the suspended belt segment with the degrees of freedom of the support belt segment of the trailer unit; (2-20) in Let be the stiffness matrix of n steel wire rope segments; This is the selection matrix used to align the degrees of freedom at the ends of the wire rope segments with the degrees of freedom of the trailer unit frame; All suspended belt segments other than those not directly connected to the support segment of the trailer unit constitute the conveyor belt stiffness matrix. (2-21) All wire rope segments other than those not directly connected to the trailer unit frame constitute the wire rope stiffness matrix. (2-22); S2-3. Establish the global damping matrix. (2-23) in The damping matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; The damping matrix of the aforementioned coupled subsystem - the non-directly connected suspended strip segment; The damping matrix for the non-directly connected wire rope segment of the aforementioned coupled subsystem; The damping matrix of the conveyor belt; The damping matrix of the wire rope; (2-24) in The connection damping between trailer units is affected by both the conveyor belt section and the wire rope section. (2-25) in This is the set of all suspended strip segments connecting the i-th trailer unit and the (i+1)-th trailer unit; This is the set of all wire rope segments connecting the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral damping of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral damping of the nth wire rope segment, respectively. ; Furthermore, (2-26) in (2-27) (2-28) (2-29) in Let be the damping matrix of the m-th conveyor belt segment; (2-30) in Let n be the damping matrix of the nth conveyor belt segment; All suspended belt segments other than those not directly connected to the support segment of the trailer unit constitute the conveyor belt damping matrix. (2-31) All wire rope segments other than those not directly connected to the trailer unit frame constitute the wire rope damping matrix. (2-32); S2-4. Establish the global quality matrix (2-33) in The mass matrix of the trailer unit group includes all trailer units, as well as the suspension belt segment and wire rope segment directly connected to the aforementioned trailer units. (2-34) in Let i be the mass matrix of the i-th trailer unit; The conveyor belt mass matrix includes all conveyor belt segments except for the supporting belt segment of the trailer unit and the suspended belt segment directly connected to the trailer unit. (2-35) The wire rope mass matrix includes all wire rope segments except those directly connected to the trailer unit frame. (2-36).

[0027] Step S3 includes: S3-1. Track irregularity excitation force: the shape of the track This will generate forced terms in the contact expression, which manifest as forced displacement excitation and are reflected in the local contact force. In the expression.

[0028] Establish the formula for the vertical irregularity spectral density of the orbit. (3-1) in For the orbital vertical irregularity spectral density, Spatial frequency, unit 1 / m. The vertical amplitude coefficient, The vertical decay exponent; The inverse Fourier transform is used to convert the frequency domain signal into the vertical spatial domain signal. (3-2) in This represents the spatial domain signal for vertical irregularities in the orbit. For the complex spectrum of vertical irregularities in the orbit, , To be a random phase angle that follows a uniform distribution, , This represents the number of sampling points; The vertical irregularity excitation force between the wheel and rail is then... (3-3) in , which is the difference in track profile displacement; Establish the formula for longitudinal irregularity spectral density of orbit (3-4) in The longitudinal irregularity spectral density of the orbit. For vertical amplitude coefficient, The longitudinal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the longitudinal spatial domain signal (3-5) in This refers to longitudinal unevenness in the track. The complex spectrum represents the longitudinal irregularities of the track. ; The longitudinal irregularity excitation force between the wheel and rail is (3-6) in ; Establish the formula for the transverse irregularity spectral density of the track. (3-7) in This represents the spectral density of transverse irregularities in the orbit. This is the horizontal amplitude coefficient. It is the horizontal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the transverse spatial domain signal (3-8) in This refers to lateral unevenness in the track. This represents the complex spectrum of the orbit's lateral irregularities. ; The excitation force of lateral irregularity between wheel and rail is (3-9) in ; S3-2. Wheel-rail tangential nonlinear friction force: Probe longitudinal / lateral tangential force vectors (3-10) Wheel rail positive pressure Friction saturates and smooths into (3-11) in The tangential force between the wheel and rail, including longitudinal tangential force. and lateral tangential force ,and , ; Preload includes the weight of the material, the weight of the conveyor belt segment, and the weight of the trolley itself; The coefficient of friction between the wheel and the rail. This is a very small positive number used to avoid a denominator of 0 and to reduce gradient abrupt changes at saturation.

[0029] This scheme incorporates the conical wheel effect into the contact geometry mapping. The radius of the conical wheel changes gradually with the normal direction, while simultaneously generating a lateral axial offset. That is, the external load also includes the conical wheel excitation force, which comprises both vertical and lateral contact forces. The dynamic model establishment process includes: S3-3-1. Let the wheel width be w and the cone angle be... The radius of the contact point at the wheel flange is ; When the lateral offset of the wheel reaches half of the wheel width, the contact radius will decrease linearly to a minimum value, and the geometric relationship is as follows: (3-12) Mapping the vertical displacement to a local effective radius, and then performing normalization and smoothing, then... (3-13) in A normalized scale used to adjust sensitivity and smoothness; using a sine map to... Mapped to ,but (3-14) Vertical offset h is (3-15) In vertical relative displacement As a response to vertical irregularities in the track Additional deformation (3-16) in The vertical irregular displacement after adding the conical wheel effect; The vertical relative displacement after adding the conical wheel effect is: (3-17) The vertical contact force between the wheel and rail after adding the conical wheel effect is: (3-18) S3-3-2. Define the lateral offset s of the conical wheel, then (3-19) In the lateral relative displacement, s is taken as the lateral irregularity of the track. Additional deformation (3-20) in This refers to the lateral irregularity displacement after adding the conical wheel effect; The lateral relative displacement after adding the conical wheel effect is: (3-21) The wheel-rail lateral contact force after adding the conical wheel effect is: (3-22).

[0030] Step S4 includes Establish the overall dynamic equations of the space-coupled system (4-1) Where F is the external load of the system.

[0031] (4-2) in, This represents the total mass of the materials.

[0032] A simulation method for a spatially coupled dynamic model of a long-distance belt conveyor, based on the aforementioned spatially coupled dynamic model of a long-distance belt conveyor, includes: The implicit solver MATLAB ode15s is used for stepwise integration to output the time-domain response results of the dynamic model, and frequency-domain analysis is performed.

[0033] Frequency domain analysis includes, but is not limited to, (1) Dominant frequency: The peak energy corresponds to the most significant vibration mode of the system, which can be used to judge the stability of the operating state; (2) Frequency band energy distribution: The energy ratio of different frequency bands (low frequency 0–50Hz, mid frequency 50–500Hz, high frequency 500–5000Hz), which is used to evaluate the structural flexibility, impact component and friction excitation effect; (3) Resonance peak identification: Identify the natural frequencies caused by the coupling of the trailer-track, trailer-belt segment and belt segment-rope segment; (4) Frequency rotation and harmonic characteristics (1×, 2×, 3× jumping frequency): Detect key dynamic phenomena such as wheel-rail excitation and the self-stability of the conical wheel lateral movement.

[0034] Figure 6 and Figure 7 The time-domain analysis results obtained from the simulation, Figure 6 The curve shows the change in lateral displacement of the vehicle body, which is caused by the combined effects of track irregularities and conical wheels. Figure 7 The lateral displacement curve generated by the action of the conical wheel. Figure 8 This represents the relative relationship between the lateral offset and longitudinal displacement caused by the conical wheel.

[0035] The present invention has been described above by way of example, but the present invention is not limited to the specific embodiments described above. Any modifications or variations made based on the present invention shall fall within the scope of protection claimed by the present invention.

Claims

1. A method of modeling long distance belt conveyor space coupled dynamics model, characterized in that, Includes the following steps: S1. Define the direction perpendicular to the conveyor belt surface downwards as the vertical direction, the direction of the trolley's movement along the track as the longitudinal direction, and the direction perpendicular to both the vertical and longitudinal directions in space as the transverse direction; discretize the conveyor belt into segments, and divide the discretized segments into supporting belt segments supported by the trolley and suspended belt segments connecting adjacent supporting belt segments; discretize the wire rope into segments; establish a three-dimensional coupled dynamic model of the trolley system, the conveyor belt, and the wire rope, wherein the trolley system includes a single trolley, supporting belt segments, and track segments below the trolley; The following assumptions are made: The long distance belt conveyor is composed of vehicles, each vehicle comprising a vehicle frame and wheels; For each trolley system, the supporting belt segment, frame, wheels, and track are defined as key nodes. Each key node has translational degrees of freedom in the vertical z, longitudinal x, and lateral y directions. Therefore, each trolley system has a total of 12 displacement degrees of freedom. Let the displacement vector of the i-th trolley be denoted as... （1-1） Subscript p , f , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; For each flexible belt segment, namely the conveyor belt segment and the wire rope segment, each segment is defined with nodes at both ends. Each node has translational degrees of freedom in the vertical z, longitudinal x, and transverse y directions. Thus, each flexible belt segment has a total of 6 degrees of freedom. S2. Establish a global spatial internal force model for a long-distance belt conveyor; S2-1. Sort the degrees of freedom of multiple trailer unit-conveyor belt-wire rope spatial dynamics models to form a global displacement vector; S2-2. Based on the stiffness coupling sub-matrix between the vehicle coupling subsystem and the conveyor belt segment and the wire rope segment, as well as the stiffness matrix between adjacent segments of the discrete segments of the conveyor belt and the wire rope, establish the global stiffness matrix; S2-3. Establish the global damping matrix; S2-4. Establish the global quality matrix; S3. Establish an external load vector dynamic model, wherein the external load includes track irregularity excitation force, wheel-rail tangential nonlinear friction force, material gravity and conical wheel excitation force, wherein the conical wheel excitation force includes vertical contact force and lateral contact force; S4. Establish a global spatial dynamics model for long-distance belt conveyors; Establish the overall dynamic equations of the space-coupled system （4-1） （4-2） in, This represents the total mass of the materials.

2. The method for modeling a spatially coupled dynamic model of a long-distance belt conveyor according to claim 1, characterized in that, Step S1 includes, S1-1. The mass matrix of the conveyor belt segment is: （1-2） in , is a three-directional identity matrix. For the quality of the conveyor belt segment; The mass matrix of the wire rope segment is （1-3） in For the quality of the wire rope segment; The mass matrix of a single trailer unit is formed by assembling the supporting belt segment, frame, wheels, and track segment according to nodes. （1-4） in, To support the quality of the belt segment, take ; For the quality of the frame; The mass of the wheel; The mass of the equivalent track segment; S1-2. Define each discrete segment of the conveyor belt and wire rope as having two endpoints, Left and Right, respectively, and the displacement vector of each flexible segment is: Define a 6×6 local stiffness matrix. Under the conditions of independent linear elastic coupling in all directions and no transverse coupling between nodes, the stiffness matrix of the conveyor belt segment is: （1-5） any m-th sub-block Take diagonal form In the formula, For the vertical stiffness of the conveyor belt segment, For the longitudinal stiffness of the conveyor belt segment, Let be the lateral stiffness of the conveyor belt segment; then （1-6） The stiffness matrix of the wire rope segment is （1-7） The nth sub-block Take diagonal form In the formula, For the vertical stiffness of the wire rope segment, For the longitudinal stiffness of the wire rope segment, Let be the lateral stiffness of the wire rope segment; then （1-8） The stiffness matrix of a single trailer unit under three-dimensional coupling is: （1-9） Each sub-block and All are 3×3 matrices, where the subscripts are... p , f , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; ,in For the stiffness matrix of the supporting belt segment, The frame elastic support stiffness matrix, Here is the wheel-rail contact stiffness matrix. This is the equivalent track segment stiffness matrix; （1-10） （1-11） （1-12） （1-13） in These represent the vertical, longitudinal, and lateral stiffness of the supporting strip segment, respectively. These represent the vertical, longitudinal, and lateral stiffness of the frame's elastic supports, respectively. These represent the vertical, longitudinal, and lateral stiffness of the wheel and rail, respectively. These represent the vertical, longitudinal, and lateral stiffness of the track, respectively. Supporting strip - frame stiffness matrix: ; Frame-wheel stiffness matrix: ; Wheel-track stiffness matrix: ; S1-3. Conveyor belt segment damping matrix （1-14） （1-15） in These are the vertical, longitudinal, and transverse damping coefficients of the conveyor belt segment, respectively. Wire rope segment damping matrix （1-16） （1-17） in These are the vertical, longitudinal, and lateral damping coefficients of the wire rope segment, respectively. Motorcycle unit damping matrix Same as the stiffness matrix structure of the motorcycle unit （1-18） Each sub-block and All are 3×3 matrices, where the subscripts are... p , f , w , r These respectively represent the supporting belt segment, frame, wheels, and rails; ,in To support the damping matrix of the belt segment, For the frame elastic support damping matrix, Here is the wheel-rail contact damping matrix. This is the damping matrix for the equivalent track segment.

3. The method for modeling a spatially coupled dynamic model of a long-distance belt conveyor according to claim 2, characterized in that, In step S2: S2-1. The global displacement vector is as follows: （2-1） in Let be the displacement vector of the i-th trailer unit; Let be the displacement vector of the e-th segment of the conveyor belt supporting the belt segment. This represents the total number of suspended sections. Let be the displacement vector of the e-th wire rope segment. This represents the total number of wire rope segments; The displacement vector of the i-th trailer unit is （2-2） in Let be the vertical displacement of the support segment of the i-th trailer unit. Let be the longitudinal displacement of the support segment of the i-th trailer unit. Let be the lateral displacement of the support segment of the i-th trailer unit. Let be the vertical displacement of the i-th trailer unit frame. Let be the longitudinal displacement of the i-th trailer unit frame. Let represent the lateral displacement of the i-th trailer unit frame. Let be the vertical displacement of the wheel of the i-th trailer unit. Let be the longitudinal displacement of the wheel of the i-th trailer unit. Let be the lateral displacement of the wheel of the i-th trailer unit. Let be the vertical displacement of the track segment of the i-th trailer unit. Let be the longitudinal displacement of the track segment of the i-th trailer unit. Let be the lateral displacement of the track segment of the i-th trailer unit; The displacement vector of the e-th conveyor belt supporting the belt segment is （2-3） in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th conveyor belt support segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th conveyor belt support segment, respectively. The displacement vector of the e-th segment of the wire rope is （2-4） in , , These represent the vertical, longitudinal, and lateral displacements of the left end node of the e-th wire rope segment, respectively. , These represent the vertical, longitudinal, and lateral displacements of the right end node of the e-th wire rope segment, respectively. S2-2. The global stiffness matrix is ​​as follows: （2-5） in This is the global stiffness matrix; The stiffness matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; The stiffness matrix of the aforementioned coupled subsystem—the non-directly connected suspended strip segment—is... for The transposed coupling block is used to describe the effect of the non-directly connected suspended strip segment on the stiffness of the above-mentioned coupled subsystem. The stiffness matrix of the aforementioned coupled subsystem – the non-directly connected wire rope segment – ​​is given. for The transposed coupling block is used to describe the effect of the non-directly connected wire rope segment on the stiffness of the above-mentioned coupling subsystem. Here is the stiffness matrix of the conveyor belt; Here is the stiffness matrix of the wire rope; （2-6） （2-7） in It is the set of all suspended belt segments that are directly connected to the supporting belt segment between the i-th trailer unit and the (i+1)-th trailer unit; It is the set of all wire rope segments that are directly connected to the frame between the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral stiffness of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral stiffness of the nth wire rope segment, respectively. ; Let be the coupling selection vectors of the m-th suspended strip segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the m-th suspended strip segment is a suspended strip segment directly connected to the supporting strip segment in the trailer unit, then （2-8） （2-9） （2-10） These are the right-end coupling selection vectors for the m-th suspended strip segment and the i-th trailer unit, respectively. These are the coupling selection vectors for the left end of the nth wire rope segment and the i-th trailer unit, respectively, and correspond to the displacement vector of the i-th trailer unit; if the nth wire rope segment is directly connected to the trailer unit, then... （2-11） （2-12） （2-13） If the nth wire rope segment is not directly connected to the trailer unit, then the vector is selected as 0; These are the coupling selection vectors for the right end of the nth wire rope segment and the ith trailer unit, respectively. Furthermore, combining equations (2-7) to (2-13), equation (2-7) can be more conveniently expressed as follows: （2-14） in （2-15） （2-16） （2-17） （2-18） （2-19） in Let be the stiffness matrix of the m-th conveyor belt segment; This is the selection matrix used to align the degrees of freedom at the end points of the suspended belt segment with the degrees of freedom of the support belt segment of the trailer unit; （2-20） in Let be the stiffness matrix of n steel wire rope segments; This is the selection matrix used to align the degrees of freedom at the ends of the wire rope segments with the degrees of freedom of the trailer unit frame; All suspended belt segments not directly connected to the supporting belt segments of the trailer unit constitute the conveyor belt stiffness matrix. （2-21） All wire rope segments not directly connected to the trailer unit frame constitute the wire rope stiffness matrix. （2-22）； S2-3. The global damping matrix is ​​as follows: （2-23） in Represents the global damping matrix; The damping matrix of the coupled subsystem of a single trailer unit - the suspended belt segment directly connected to its supporting belt segment + the wire rope segment directly connected to its frame; The damping matrix of the aforementioned coupled subsystem—the non-directly connected suspended strip segment—is... express The transposed coupling block is used to describe the damping effect of the non-directly connected suspended belt segment on the trailer coupling subsystem. The damping matrix for the non-directly connected wire rope segment of the aforementioned coupled subsystem is... express The transposed coupling block is used to describe the damping effect of the non-directly connected wire rope segment on the trailer coupling subsystem. The damping matrix of the conveyor belt; The damping matrix of the wire rope; （2-24） in （2-25） in It is the set of all suspended belt segments that are directly connected to the supporting belt segment between the i-th trailer unit and the (i+1)-th trailer unit; It is the set of all wire rope segments that are directly connected to the frame between the i-th trailer unit and the (i+1)-th trailer unit; These represent the vertical, longitudinal, and lateral damping of the m-th suspended segment, respectively. ; These represent the vertical, longitudinal, and lateral damping of the nth wire rope segment, respectively. ; Furthermore, equation (2-25) can be more conveniently expressed as follows: （2-26） in （2-27） （2-28） （2-29） in Let be the damping matrix of the m-th conveyor belt segment; （2-30） in Let n be the damping matrix of the nth conveyor belt segment; All suspended belt segments not directly connected to the supporting belt segments of the trailer unit constitute the conveyor belt damping matrix. (2-31) All wire rope segments not directly connected to the trailer unit frame constitute the wire rope damping matrix. （2-32）； S2-4. Establish the global quality matrix （2-33） in The mass matrix of the trailer unit group includes all trailer units as well as the suspension belt segment and wire rope segment directly connected to the aforementioned trailer units. （2-34） in Let i be the mass matrix of the i-th trailer unit; The conveyor belt mass matrix includes all conveyor belt segments except for the supporting belt segment of the trailer unit and the suspended belt segment directly connected to the trailer unit. （2-35） The wire rope mass matrix includes all wire rope segments except those directly connected to the trailer unit frame. （2-36）。 4. The method for modeling a spatially coupled dynamic model of a long-distance belt conveyor according to claim 1, characterized in that, Step S3 includes: S3-1. Track irregularity excitation force: Establish the formula for the vertical irregularity spectral density of the orbit. （3-1） in For the orbital vertical irregularity spectral density, Spatial frequency, unit 1 / m. The vertical amplitude coefficient, The vertical decay exponent; The inverse Fourier transform is used to convert the frequency domain signal into the vertical spatial domain signal. （3-2） in This represents the spatial domain signal for vertical irregularities in the orbit. For the complex spectrum of vertical irregularities in the orbit, , To be a random phase angle that follows a uniform distribution, , This represents the number of sampling points; The vertical irregularity excitation force between the wheel and rail is then... （3-3） in , which is the difference in track profile displacement; Establish the formula for longitudinal irregularity spectral density of orbit （3-4） in The longitudinal irregularity spectral density of the orbit. For vertical amplitude coefficient, The longitudinal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the longitudinal spatial domain signal （3-5） in This refers to longitudinal unevenness in the track. The complex spectrum represents the longitudinal irregularities of the track. ; The longitudinal irregularity excitation force between the wheel and rail is （3-6） in ; Establish the formula for the transverse irregularity spectral density of the track. （3-7） in This represents the spectral density of transverse irregularities in the orbit. This is the horizontal amplitude coefficient. It is the horizontal decay index; Applying the inverse Fourier transform to convert the frequency domain signal into the transverse spatial domain signal （3-8） in This refers to lateral unevenness in the track. This represents the complex spectrum of the orbit's lateral irregularities. ; The excitation force of lateral irregularity between wheel and rail is （3-9） in ; S3-2. Wheel-rail tangential nonlinear friction force: Probe longitudinal / lateral tangential force vectors （3-10） in This represents the probe tangential force vector at the wheel-rail contact point; Wheel rail positive pressure ,in Indicates static preload. This indicates that only the positive pressure increment generated by the compression contact is taken; Friction saturation and smoothing （3-11） in The tangential force between the wheel and rail, including longitudinal tangential force. and lateral tangential force ,and , ; Preload includes the weight of the material, the weight of the conveyor belt segment, and the weight of the trolley itself; The coefficient of friction between the wheel and the rail. This is a very small positive number used to avoid a denominator of 0 and to reduce gradient abrupt changes at saturation.

5. The method for modeling a spatially coupled dynamic model of a long-distance belt conveyor according to claim 1, characterized in that, The dynamic model establishment process for the vertical and lateral contact forces included in the excitation force of the conical wheel includes: S3-3-1. Let the wheel width be w and the cone angle be... The radius of the contact point at the wheel flange is ; When the lateral offset of the wheel reaches half of the wheel width, the contact radius will decrease linearly to a minimum value, and the geometric relationship is as follows: （3-12） Mapping the vertical displacement to a local effective radius, and then performing normalization and smoothing, then... （3-13） in A normalized scale used to adjust sensitivity and smoothness; using a sine map to... Mapped to ,but （3-14） Vertical offset h is （3-15） In vertical relative displacement As a response to vertical irregularities in the track Additional deformation （3-16） in The vertical irregular displacement after adding the conical wheel effect; The vertical relative displacement after adding the conical wheel effect is: （3-17） The vertical contact force between the wheel and rail after adding the conical wheel effect is: （3-18） S3-3-2. Define the lateral offset s of the conical wheel, then （3-19） In the lateral relative displacement, s is taken as the lateral irregularity of the track. Additional deformation （3-20） in This refers to the lateral irregularity displacement after adding the conical wheel effect; The lateral relative displacement after adding the conical wheel effect is: （3-21） The wheel-rail lateral contact force after adding the conical wheel effect is: （3-22）。 6. A simulation method for a spatially coupled dynamic model of a long-distance belt conveyor, characterized in that, Based on the spatial coupling dynamics model of the long-distance belt conveyor according to any one of claims 1 to 5, it includes: The implicit solver MATLAB ode15s is used for stepwise integration to output the time-domain response results of the dynamic model, and frequency-domain analysis is performed.

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