A method for analyzing the dynamic characteristics of a corrugated baffle belt type lifting system of a ship unloader

Abstract

This invention provides a method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system for a ship unloader. The method includes: constructing a fractional derivative viscoelastic model of the corrugated sidewall conveyor belt and establishing the basic dynamic equations of the corrugated sidewall conveyor belt; establishing discrete dynamic equations for the conveyor belt, the drive device, and the tensioning device, and establishing a discrete dynamic model of the corrugated sidewall belt lifting system; establishing continuous dynamic equations for the conveyor belt, setting boundary conditions and initial conditions, and establishing a continuous dynamic model of the corrugated sidewall belt lifting system; solving the discrete dynamic model or the continuous dynamic model of the corrugated sidewall belt lifting system to obtain the acceleration, velocity, and displacement of the corrugated sidewall belt lifting system, thus obtaining the dynamic response of the corrugated sidewall belt lifting system. The use of a fractional derivative viscoelastic model, and the further establishment of a dynamic model, more realistically reflects the dynamic characteristics of the corrugated sidewall belt lifting system at each stage.

Description

Technical Field

[0001] This invention belongs to the field of conveyor dynamics technology, and in particular relates to a method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system for a ship unloader. Background Technology

[0002] Corrugated sidewall belt conveyor systems are key equipment suitable for transporting bulk materials at steep angles and with large capacities. Their core component, the corrugated sidewall conveyor belt, is typically composed of rubber and a steel cord core, exhibiting significant viscoelastic properties. Under unstable conditions such as starting and braking, the velocity, acceleration, displacement, and dynamic tension at various points on the conveyor belt are all functions of time, resulting in highly significant dynamic phenomena. Accurate analysis of the conveyor belt's dynamic characteristics is crucial for controlling peak dynamic tension, preventing belt breakage accidents, reducing the conveyor belt's safety factor, simplifying the conveyor structure, and saving manufacturing costs.

[0003] Currently, commonly used viscoelastic models for conveyor belts in engineering include classical rheological models such as the Maxwell model, the Kelvin model, and the three-element solid model. These models are composed of spring elements and Newton's sticky pot elements in different combinations, have simple structures, few parameters, and can describe the creep and relaxation behavior of conveyor belts to a certain extent. However, practice shows that these models do not match experimental data well in the early stages of creep and relaxation, and these models are mainly based on constitutive behavior under static loads, making it difficult to accurately reflect the response characteristics of conveyor belts under dynamic conditions, such as the influence of factors like loading frequency, temperature changes, and load history on the stress-strain relationship.

[0004] Fractional derivative models can more accurately describe the frequency correlation and dynamic response of viscoelastic materials with fewer parameters, and these models often contain only a few parameters, making it convenient to predict the dynamic response of viscoelastic materials. Therefore, there is an urgent need in the existing technology for an analytical method that can more accurately describe the dynamic viscoelastic behavior of conveyor belts, establish a dynamic model of the conveyor system, and efficiently solve the dynamic response, in order to overcome the above-mentioned shortcomings of the existing technology. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system for a ship unloader. The corrugated sidewall belt lifting system includes a conveyor belt, a drive unit, and a tensioning device. The method is characterized by the following steps: S1: Construct a fractional derivative viscoelastic model of the corrugated sidewall conveyor belt, and establish the basic dynamic equations of the corrugated sidewall conveyor belt based on the fractional derivative viscoelastic model; S2: Discretize the conveyor belt to establish the discrete dynamic equation of the conveyor belt, and construct the dynamic equations of the drive device and the tensioning device respectively. Based on the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, establish the discrete dynamic model of the corrugated sidewall belt lifting system. S3: Establish the continuous dynamic equation of the conveyor belt, set the boundary conditions and initial conditions of the continuous dynamic model of the conveyor belt, and establish the continuous dynamic model of the corrugated sidewall belt lifting system; S4: Solve the discrete dynamic model or continuous dynamic model of the corrugated sidewall belt hoisting system to obtain the acceleration, velocity and displacement of the corrugated sidewall belt hoisting system, and obtain the dynamic response of the corrugated sidewall belt hoisting system.

[0006] Specifically, step S1 includes: Force analysis was performed on a small segment of the corrugated sidewall conveyor belt, and the equilibrium equation of this small element was obtained: ; in, Let A be the stress, and A be the conveyor belt bearing area. The mass per meter of conveyor belt, Let be the displacement of any point on the conveyor belt. The running resistance per unit length of the conveyor belt; The equations relating the infinitesimal elements of the conveyor belt are rearranged to obtain: ; The fundamental equations of conveyor belt dynamics are obtained by further solving the infinitesimal equilibrium equations and the fractional derivative viscoelastic model.

[0007] Preferably, step S2 is based on the following assumptions: The corrugated sidewall conveyor belt is considered as a geometrically deformed rod; the material is evenly distributed on the corrugated sidewall conveyor belt; the mass of the rotating part of the idler roller is evenly distributed along the longitudinal direction of the corrugated sidewall conveyor belt; the running resistance of the corrugated sidewall conveyor belt is evenly distributed along the direction of the conveyor belt, and the resistance coefficient of the conveyor belt is linearly related to the speed of the conveyor belt; the drive device, tensioning device and drum of the corrugated sidewall belt lifting system are considered as rigid; the mass of the conveyor belt wound on the drum is ignored.

[0008] Based on the above scheme, step S2 includes: S2.1: Considering the influence of conveyor belt sag between idlers, calculate the equivalent elastic modulus of the conveyor belt; S2.2: Using a fractional derivative viscoelastic model, the closed conveyor belt is discretized into multiple elements, and the dynamic equations of each element are obtained based on the mechanical equilibrium equations: , in, For any unit stiffness, Let be the displacement of any element. For the damping of any element, For the operating resistance of any unit, For the mass of any unit, Let the acceleration of any unit be , For the next unit stiffness, For the displacement of the next unit, This represents the displacement of the previous unit. The speed of the previous unit, For the damping of the next unit, For the speed of the next unit, The resistance force experienced by any given element; S2.3: Perform force analysis on the conveyor belt and drive roller to obtain the rotational dynamics equation, and solve for the dynamics equation of the drive device based on the relationship between the linear acceleration and angular acceleration of the roller surface; S2.4: Perform force analysis on the front and rear units of the tensioning device in the corrugated sidewall belt lifting system, decompose the tensioning device into translational and rotational parts, and establish the dynamic equation of the tensioning device; S2.5: Integrating the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, a discrete dynamic model of the corrugated sidewall belt lifting system is obtained: ; in, For the quality matrix, Here is the damping matrix. Here is the stiffness matrix. For the external force matrix, Let be the displacement matrix of the divided elements. The acceleration matrix of the divided unit. This is the velocity matrix of the divided unit.

[0009] Further, step S4 is achieved through... Wilson-θ The method for solving the discrete dynamic model of the corrugated sidewall belt lifting system includes: S4.1: Calculate the mass matrix, stiffness matrix, and damping matrix in the discrete dynamic model of the corrugated sidewall belt lifting system; S4.2: Calculate the initial acceleration based on the initial displacement and initial velocity, determine the time step, and calculate the equivalent stiffness matrix; S4.3: Calculate the acceleration, velocity, and displacement of each unit, and obtain the dynamic tension of each unit of the conveyor belt based on the mechanical equilibrium equation between the two units.

[0010] Preferably, step S3 is based on the following assumptions: The corrugated sidewall conveyor belt is simplified as a one-dimensional elastic rod; the deformation of the corrugated sidewall conveyor belt under external force is relatively small compared to the length of the conveyor belt; the mass of the drive part is equivalently converted into the rotational inertia of the drive roller part; the running resistance is calculated as a linear resistance.

[0011] Specifically, step S3 includes: S3.1: Unfold the corrugated sidewall conveyor belt at the tail drive roller so that its carrying section and return section are on the same plane. Take a length of [length missing] at a position x from the origin O. A section of the conveyor belt was subjected to mechanical analysis, and the mechanical equilibrium equation was obtained. S3.2: Simplifying the mechanical equilibrium equations in S3.1 yields the fundamental equations of conveyor belt dynamics: ; in, The mass per unit length of the conveyor belt and materials. The stress is at any cross-section of the conveyor belt; The resistance per unit length of the conveyor belt and materials.

[0012] S3.3: Perform force analysis on the conveyor belt at the drive roller and tension roller to obtain the force balance equation and the boundary conditions of the drive roller and tension roller. S3.4: Considering the preload of the conveyor belt, force analysis is performed by segmenting micro-elements to obtain the initial displacement of the micro-elements of the carrying section and the return section respectively, and the initial speed of the corrugated sidewall belt lifting system in the starting and braking states is obtained based on the initial displacement.

[0013] Based on the above scheme, step S4, solving the continuous dynamics model of the corrugated sidewall belt lifting system, specifically includes: The displacement of the conveyor belt is decomposed into the sum of the initial displacement and the displacement caused by the dynamic load. Substituting this into the continuous dynamics model, it is decomposed into Model 1 and Model 2. For Model 1, the partial differential equations are transformed into a system of ordinary differential equations using the method of separation of variables. The natural frequencies and natural mode shapes are obtained by solving the eigenvalue problem. The displacement is expressed as an infinite series of natural mode shapes. The series coefficients are determined using the initial conditions, thereby obtaining the analytical expressions for the displacement, dynamic load, dynamic load coefficient, velocity, and acceleration of the conveyor belt at any time. Using the same separation of variables method as Model 1, the corresponding analytical expression for Model 2 is obtained.

[0014] Preferably, when the excitation function is an arbitrary continuous function, it is piecewise linearly fitted in the time domain, and the solution is performed separately for the linear segment in each time interval. Within each time period, Model 1 and Model 2 are solved separately according to the slope excitation to obtain the analytical expression of the dynamic response within that time period; By recursively applying the displacement continuity condition and velocity continuity condition at adjacent time points, a piecewise analytical solution for the entire time interval is obtained.

[0015] Preferably, the fractional derivative viscoelastic model is a fractional derivative Maxwell model, a fractional derivative Kelvin model, or a fractional derivative three-element solid viscoelastic model.

[0016] Compared with the prior art, the present invention has the following beneficial effects: This invention employs a fractional derivative viscoelastic model. By introducing a fractional calculus operator, the relationship between stress and strain in the constitutive equation can more accurately reflect the dynamic response characteristics of the conveyor belt over a wide frequency range. This model can more accurately fit the dynamic response performance of the conveyor belt. Furthermore, by establishing a dynamic model based on this model, the dynamic characteristics of the corrugated sidewall belt lifting system at each stage can be more realistically reflected. This invention establishes a discrete dynamic model of a corrugated sidewall belt lifting system. The acceleration, velocity, displacement, and dynamic tension of each discrete element are solved by element division and Wilson-θ method. At the same time, a continuous dynamic model of the corrugated sidewall belt lifting system is also established, which can obtain dynamic parameters such as acceleration, velocity, and displacement at any position and time of the conveyor belt, and realize the dynamic analysis of the corrugated sidewall belt lifting system. This invention first utilizes the principle of model decomposition and superposition to decouple the complex dynamic equations into two models. This not only simplifies the solution process but also enables the accurate determination of the natural frequencies and principal modes of the conveyor belt system using the method of separation of variables, thereby obtaining analytical solutions for displacement, dynamic load, and dynamic load coefficients, providing a precise basis for theoretical analysis. This invention employs piecewise linear fitting and recursive solution to discretize complex continuous excitation into multiple linear segments. Rigid body motion is removed through coordinate transformation within each time segment, and recursive calculation is performed using the continuity condition of time. This overcomes the shortcomings of traditional analytical methods in handling arbitrary function excitations and achieves high-precision numerical simulation of the dynamic response of the conveyor in the entire time domain. Attached Figure Description

[0017] Figure 1 This is a flowchart of the dynamic characteristic analysis method of the present invention; Figure 2 A diagram of the fractional derivative Maxwell model; Figure 3 A diagram of the fractional derivative Kelvin model; Figure 4 A three-element solid viscoelastic model with fractional derivatives; Figure 5 Force analysis diagram of a micro-segment of a corrugated sidewall conveyor belt; Figure 6 A simplified diagram of conveyor belt deflection; Figure 7 This is a force analysis diagram of a micro-segment of the conveyor belt; Figure 8 Force analysis diagram of the driving unit; Figure 9 For the physical model of the tensioning device; Figure 10 System model diagram of a large corrugated sidewall belt lifting system; Figure 11 This is a head-driven, tail-tensioned corrugated sidewall belt lifting system. Figure 12 Boundary force analysis diagram for the drive roller; Figure 13 A boundary force analysis diagram for the tension roller; Figure 14 This is a force analysis diagram of a small segment of a rod. Detailed Implementation

[0018] The invention will be further described below with reference to specific embodiments.

[0019] 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.

[0020] 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.

[0021] like Figure 1 As shown, this invention provides a method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system. The corrugated sidewall belt lifting system includes a conveyor belt, idlers, a drive unit, and a tensioning device, etc. The method includes the following steps: S1: Construct a fractional derivative viscoelastic model of the corrugated sidewall conveyor belt, and establish the basic dynamic equations of the corrugated sidewall conveyor belt based on the fractional derivative viscoelastic model; Step S1 includes: S1.1: Combining existing Maxwell models, Kelvin models, or three-element solid viscoelastic models and fractional derivative models, construct a fractional derivative viscoelastic model for corrugated sidewall conveyor belts. The fractional derivative viscoelastic model is a fractional derivative Maxwell model, a fractional derivative Kelvin model, or a fractional derivative three-element solid viscoelastic model.

[0022] In step S1.1, as follows Figures 2-4 As shown, the specific process of establishing the fractional derivative viscoelastic model is as follows: S1.11: The fractional derivative Maxwell model under stress Under the action, the total strain of the model is ,in, , These represent the strains of the spring and the Newton sticky pot that constitute the Maxwell model, respectively. The constitutive equations of the fractional derivative Maxwell model are obtained as follows: (1.1) in, To determine the elastic modulus of the spring in the Maxwell model, The elastic modulus of Newton glue pot, The characteristic time constant, It is the fractional order (0 < <1), where D is a fractional operator.

[0023] Fourier transform of the fractional derivative Maxwell model: (1.2) according to After obtaining the complex modulus of the model, and rearranging and transforming equation (1.2) above, we get: (1.3) in, It is the complex modulus; Furthermore, due to Transform (1.3) into: (1.4) (1.5) (1.6) in, For storing modulus, This is the loss modulus.

[0024] S1.12: The fractional derivative is formed by a linear spring and an Abel sticky pot in parallel, under stress... Under the action, the total stress of the model ,in The constitutive equation of the fractional derivative Kelvin model can be obtained as follows: (1.7) in, , The stresses of the linear spring and the Abel sticky pot are respectively. Let be the elastic modulus of the linear spring. The elastic modulus of Abel's glue pot. For characteristic relaxation time, It is the fractional order (0 < <1), where D is a fractional operator.

[0025] Performing a Fourier transform on the fractional derivative Kelvin model yields the complex modulus: (1.8) (1.9) because , to obtain the storage modulus Loss modulus and loss factor : (1.10) (1.11) (1.12) (1.13) S1.13: The fractional derivative three-element solid viscoelastic model is composed of a linear spring and a fractional Kelvin element connected in series, or a linear spring and a fractional Maxwell element connected in parallel, such as... Figure 4 As shown, this embodiment uses a series configuration, under stress Under the action, the total strain of the model is ,in The constitutive equation for the fractional derivative three-element solid viscoelastic model can be obtained as follows: (1.14) The Fourier transform of the fractional derivative three-element solid viscoelastic model yields: (1.15) (1.16) because , to obtain the storage modulus Loss modulus and loss factor : (1.17) (1.18) (1.19) By constructing the above-mentioned fractional derivative viscoelastic model, this invention can more accurately predict the dynamic response of the corrugated sidewall belt lifting system, and at the same time, it can effectively match the experimental data and more accurately describe the frequency correlation of the conveyor belt.

[0026] Furthermore, such as Figure 5 As shown, step S1.2 is performed: a small segment of the corrugated sidewall conveyor belt is subjected to force analysis, and the equilibrium equation of the small element is obtained: (1.20) Rearranging (1.20) gives: (1.21) in, The stress (N / m) at any point on the cross-section of the corrugated sidewall conveyor belt. 2 A represents the bearing area (m²) of any cross-section of the corrugated sidewall conveyor belt. 2 ), The mass per meter of conveyor belt (kg / m), and the load-bearing branch is The return branch is , The mass of material per unit length (kg / m). The mass of the conveyor belt per unit length (kg / m). Let be the displacement of any point on the conveyor belt. The running resistance per unit length of the conveyor belt; Furthermore, based on (1.21) and the fractional derivative viscoelastic model, the fundamental equations of conveyor belt dynamics are obtained by further solving. Specifically, in this embodiment, the constitutive equation (1.14) of the fractional derivative three-element solid viscoelastic model is adopted. The fundamental equations of the corrugated sidewall conveyor belt dynamics are as follows: (1.22) Where E is the elastic modulus of the conveyor belt, and c is the viscoelastic coefficient of the conveyor belt. Let U0(t) be a unit impulse function, where U(0,t) is the initial displacement of the conveyor belt, U(0,t) is the displacement of the conveyor belt at the starting point of the drive drum at time t, and U(2L,t) is the displacement of the conveyor belt at the ending point of the drive drum at time t. q To drive the rotational inertia of the drum, R q Let S(0,t) be the radius of the driving drum, S(0,t) be the conveyor belt tension at the starting point of the driving drum at time t, S(2L,t) be the conveyor belt tension at the ending point of the driving drum at time t, M(t) be the driving torque, U(L-,t) be the displacement of the conveyor belt at the end of the redirecting drum at time t, U(L+,t) be the displacement of the conveyor belt at the beginning of the redirecting drum return at time t, S(L-,t) be the tension of the conveyor belt at the end of the redirecting drum at time t, S(L+,t) be the tension of the conveyor belt at the beginning of the redirecting drum return at time t, G be the total weight of the conveyor belt and material, m be the total mass of the conveyor belt and material in contact with the redirecting drum, and U(t) be the displacement of the conveyor belt at the redirecting drum.

[0027] make , Then (1.22) transforms into: (1.23) It should be noted that the fundamental equations of dynamics for the corrugated sidewall conveyor belt vary depending on the fractional derivative viscoelastic model of the conveyor belt.

[0028] Because the corrugated sidewall belt hoisting system operates under complex and variable dynamic conditions, there are inevitably many uncertainties. Therefore, a discrete dynamic model of the corrugated sidewall belt hoisting system needs to be established based on the following assumptions: The corrugated sidewall conveyor belt is considered as a geometrically deformed rod; the material is evenly distributed on the corrugated sidewall conveyor belt; the mass of the rotating part of the idler roller is evenly distributed along the longitudinal direction of the corrugated sidewall conveyor belt; the running resistance of the corrugated sidewall conveyor belt is evenly distributed along the direction of the conveyor belt, and the resistance coefficient of the conveyor belt is linearly related to the speed of the conveyor belt; the drive device, tensioning device and drum of the corrugated sidewall belt lifting system are considered as rigid; the mass of the conveyor belt wound on the drum is ignored.

[0029] S2: Discretize the conveyor belt to establish the discrete dynamic equation of the conveyor belt, and construct the dynamic equations of the drive device and the tensioning device respectively. Based on the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, establish the discrete dynamic model of the corrugated sidewall belt lifting system. In this embodiment, step S2 includes: S2.1: Considering the influence of conveyor belt sag between idlers, calculate the equivalent elastic modulus of the conveyor belt; like Figure 6 As shown, the corrugated sidewall conveyor belt is laid flat on the idler rollers. Due to its own weight, the conveyor belt will sag, resulting in sag. Therefore, the sag is analyzed to obtain the equivalent elastic modulus of the conveyor belt: S2.11: Assuming the tension of the conveyor belt remains constant within the OA section, decompose the conveyor belt tension F at point O into... and Remove section OB. Since the conveyor belt experiences no bending moment at any cross-section, the moment acting on the cross-section at point B is zero. (2.1) Among them, M k Let f be the moment at the cross section at point B. x This refers to the frictional resistance experienced by section OB during operation. β The angle of inclination; Taking moments about point A, we get: (2.2) Among them, M A Let A be the torque at point A. l To increase the segment length.

[0030] Eliminate by combining (2.1) and (2.2). ,get: (2.3) S2.12: For Taking the derivative, we get: (2.4) when At that time, the position of maximum sag of the conveyor belt is obtained: Substituting this value into (2.3), we obtain the maximum verticality: (2.5) S2.13: In equation (2.5) It is the horizontal component of the conveyor belt tension, when taken x When = 0, the turning angle at point O can be obtained: (2.6) Combining equations (2.5) and (2.6), we get: (2.7) S2.14: The sag of the conveyor belt is as specified in ISO standards. ,and Substituting the maximum sag h=0.02 into the equation, we get... Therefore there is The length of the conveyor belt is calculated using the arc length formula: (2.8) When the conveyor belt tension is Increase to At that time, the length of the conveyor belt arc changes as follows: (2.9) The elastic strain of the conveyor belt caused by the change in arc length between the two idlers is: (2.10) S2.15: According to the Taylor series expansion: (2.11) Take the first two terms of the Taylor series expansion: Substitute (2.10) and take We can obtain: (2.12) It can be known for Increase to The elastic strain of the conveyor belt caused by time.

[0031] When the tension of the conveyor belt is from Increase to The viscoelastic strain of the conveyor belt is: (2.13) in, The elastic modulus per unit width of the conveyor belt under ideal conditions (unit: ); The width of the conveyor belt is (mm). S2.16: Considering an ideal state, neglecting the weight of the conveyor belt itself, and placing it flat on the two idlers, this is the equivalent state without sag. The equivalent effect of the conveyor belt then becomes: (2.14) Where E is the equivalent elastic modulus of the conveyor belt when sag exists; according to ,get: (2.15) Further simplification yields the equivalent elastic modulus of the conveyor belt as follows: (2.16) According to the expression for the equivalent elastic modulus, the equivalent elastic modulus of the conveyor belt is independent of the type of conveyor belt selected, and it is also applicable to the fractional derivative Maxwell model, the fractional derivative Kelvin model, and the fractional derivative three-element solid viscoelastic model.

[0032] S2.2: Using a fractional derivative viscoelastic model, the closed conveyor belt is discretized into multiple elements, and the dynamic equation of each element is obtained based on the mechanical equilibrium equation. S2.21: As Figure 7 As shown, u is the displacement at point x on the cross-section of the conveyor belt. Here, u and U have the same meaning. Taking a small segment of the conveyor belt at point x, the forces acting on the small segment include the elastic force of the conveyor belt, the inertial force between the material and the conveyor belt, and the running resistance of the material and the conveyor belt, and assuming that the conveyor belt is an equivalent case with no sag; Based on the equilibrium conditions of the forces acting on the infinitesimal segments of the conveyor belt, the following equilibrium equations are derived: (2.17) Take the distance from the origin O as The infinitesimal element at the location , To be applied to The tension value at that point, and its displacement is The resistance on its infinitesimal segment is ; S2.22: Using a fractional derivative three-element solid viscoelastic model, the entire closed conveyor belt is discretized into several elements. The dynamic equation of any element i is taken as follows: (2.18) in, For any unit stiffness, Let be the displacement of any element. For the damping of any element, For the operating resistance of any unit, The mass of any unit; Further simplification of (2.18) yields: (2.19) S2.3: Perform force analysis on the conveyor belt and drive roller to obtain the rotational dynamics equation, and solve for the dynamics equation of the drive device (which includes the drive roller, motor and other complete drive systems) based on the relationship between the linear acceleration and angular acceleration of the roller surface. This invention considers the drive roller and the corrugated sidewall conveyor belt as a single unit, without considering overall relative sliding, such as Figure 8 As shown, a force analysis is performed on the drive roller, and the mechanical equations are established: (2.20) in, and For tension, For driving torque, For the resistance torque, To drive the roller radius, Let J be the angular acceleration and J be the moment of inertia of the driving drum. Based on the linear acceleration of the outermost edge of the roller ,get: (2.21) set up (2.21) can be further transformed into: (2.22) S n S1 is: (2.23) (2.24) Substituting (2.23) and (2.24) into (2.22) yields the dynamic equations of the drive device: (2.25) S2.4: Perform force analysis on the front and rear units of the tensioning device in the corrugated sidewall belt lifting system, decompose the tensioning device into translational and rotational parts, and establish the dynamic equation of the tensioning device; Step S2.4 of the present invention incorporates the tensioning device into the entire system, such as... Figure 9 As shown; S2.41: First, perform a force analysis on the preceding unit k of the tensioning device: (2.26) in: (2.27) (2.28) in, This refers to the displacement at the point where the conveyor belt separates from the tension roller. This refers to the displacement at the point where the conveyor belt meets the tension roller. Because the displacement generated at the point where the conveyor belt meets the tensioning device is affected by the tension roller, based on the relative motion relationship... , ,set up , , Let k+2 be the displacement of the conveyor belt unit. Let the displacement generated by the (k+1)th conveyor belt unit be: (2.29) (2.30) Substituting (2.29) into (2.28) gives: (2.31) have: (2.32) Substituting (2.27), (2.31), and (2.32) into (2.26), we get: (2.33) After sorting, we can obtain: (2.34) Establish the dynamic equations for the translational and rotational parts of the tensioning device: (2.35) (2.36) S2.42: Force analysis of the unit k+3 following the tensioning device yields the following results: (2.37) according to: (2.38) (2.39) (2.40) (2.41) The dynamic equations of this unit are obtained as follows: (2.42) S2.5: Integrating the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, a discrete dynamic model of the corrugated sidewall belt lifting system is obtained: ; in, For the quality matrix, Here is the damping matrix. Here is the stiffness matrix. For the external force matrix, Let be the displacement matrix of the divided elements. The acceleration matrix of the divided unit. This is the velocity matrix of the divided unit.

[0033] like Figure 10As shown, the corrugated sidewall belt lifting system is simplified. A single-drum drive is installed at both the head and tail, and a counterweight tensioning device is installed at the head. The carrying section of the conveyor is divided into n units. Starting from the left drive drum, the first unit to start in the carrying section is numbered sequentially as 1, 2, 3...n. The tail drive drum is unit n+1. The return section is numbered sequentially from the tail drive drum as n+2, n+3,..., n+m-1. The tensioning device is divided into rotating units and translational units, numbered n+m. There is a certain distance between the tensioning units and the head drive drum, which are defined as units n+m+1 and n+m+2. The head drive drum is defined as unit n+m+3.

[0034] S2.51: In the corrugated sidewall belt lifting system, the tail drive roller (n+1th unit), the n+m-1 and n+m+1 units on both sides of the tensioning device, the rotation unit and translation unit of the tensioning device, and the head drive roller (n+m+3th unit) are different from other units. The other units adopt Equation (2.19) as the dynamic equation of any unit.

[0035] The displacements of the meeting and separation points of the tensioning device are respectively ,available: ,in, and Consistent definition and Consistent definition and With consistent definition, it refers to the longitudinal displacement of the conveyor belt unit generated by the tensioning device. This refers to the radial displacement offset of the conveyor belt at the tension roller. It is a directional coefficient used to distinguish between the "inflow end" and "outflow end" of the conveyor belt contacting the tension roller.

[0036] The dynamic equation for the tail drive roller is: (2.43) No. The dynamic equations of the unit: (2.44) No. The dynamic equations of the unit: (2.45) The dynamic equations of the translational unit of the tensioning device: (2.46) No. The dynamic equation of the unit is: (2.47) No. The dynamic equation of the unit, namely the head drive roller, is: (2.48) S2.52: Based on the above dynamic equations, the discrete dynamic model of the corrugated sidewall belt lifting system is obtained as follows: (2.49) in, For displacement vectors, and These are the velocity vector and the acceleration vector, respectively. S2.53: Mass Matrix The mass unit is the sum of the mass of the material, the conveyor belt, and the idler. The conveyor belt and the material move in translational motion, while the idler rotates. Therefore, the mass of the idler needs to be converted into the moment of inertia or equivalent mass. The mass of the load-bearing section mainly consists of three parts: the mass of the material, the conveyor belt, and the idlers. (2.50) in, For the bearing section The quality of the segment For the linear quality of the material, For the quality of the conveyor belt line, Linear mass of the rotating part of the load-bearing section idler roller assembly. For the bearing section Segment length; The return section mass includes the mass of the conveyor belt and the mass of the idler rollers equivalent to that on the conveyor belt: (2.51) in, For the return segment The quality of the segment The linear mass of the rotating section of the return section idler roller assembly. For the return segment Segment length; The (n+1)th unit is the tail drive section, whose mass consists of two parts: the drive roller and the drive unit. (2.52) in, The equivalent mass of the tail drive unit (drive unit is the name after discretization of the drive roller) is given. The moment of inertia of the tail drive roller. The moment of inertia of the tail drive motor is equivalent to that on the drive drum. The moment of inertia of the tail drive unit reducer is equivalent to that on the drive drum. The rotational inertia of the tail drive unit coupling is equivalent to that on the drive drum. The diameter of the tail drive roller is denoted as ; the (n+m+3)th unit is the head drive part, which is calculated in the same way as the (n+1)th unit and will not be described in detail here. No. The unit is a tensioning unit (tensioning device), consisting of a tensioning roller and a counterweight block. The tensioning roller involves both translation and rotation, therefore the mass of the tensioning unit is divided into two parts: the mass of the rotating part and the mass of the translational part. The mass of the rotating part is: (2.53) The mass of the translational part is: (2.54) in, The rotational inertia of the guide roller is equivalent to that of the tension roller. The moment of inertia of the clamping roller, To tighten the diameter of the roller, For the quality of the guiding device, The mass of the hammer.

[0037] S2.54: The external force matrix is: The external force on any segment i is ,in, ; The dynamic drag coefficient of the external force matrix is: ,in, The coefficient of static friction between the material and the conveyor belt. A coefficient independent of conveyor belt speed. A coefficient related to the conveyor belt speed; Bearing section: (2.55) (2.56) (2.57) Return trip: (2.58) (2.59) (2.60) in, For the conveying tilt angle of the corrugated sidewall belt lifting system, The trough angle coefficient of the idler roller group. The coefficient of friction between the conveyor belt and the idler rollers. This refers to the distance between the forward-tilting idler rollers of the load-bearing section. This refers to the distance between the forward-tilting idler rollers on the return section. The forward tilt angle of the idler roller assembly. For the roller trough angle, The main resistance of the conveyor belt For the resistance of the conveyor belt inclination, This adds resistance; Tensioning unit (first) unit): Rotating part: (2.61) Translational part: (2.62) And there are , It provides the driving force for the operation of the corrugated sidewall belt lifting system.

[0038] S2.55: Stiffness matrix: ; Damping matrix: ; in, ; The stiffness and damping of each element are: (2.63) in, For the equivalent elastic modulus, is the viscoelastic hysteresis time constant.

[0039] This invention considers a corrugated sidewall belt lifting system with helical tensioning. A continuous dynamic model of the corrugated sidewall belt lifting system is established based on the following assumptions: the corrugated sidewall conveyor belt is simplified as a one-dimensional elastic rod; the deformation of the corrugated sidewall conveyor belt under external force is relatively small compared to the length of the conveyor belt; the mass of the drive device is equivalently converted into the rotational inertia of the drive drum; and the running resistance is calculated as a linear resistance.

[0040] S3: Establish the continuous dynamic equation of the conveyor belt, set the boundary conditions and initial conditions of the continuous dynamic model of the conveyor belt, and establish the continuous dynamic model of the corrugated sidewall belt lifting system; Step S3 includes: S3.1: Disconnect the corrugated sidewall conveyor belt from the meeting point, which is regarded as the origin of the coordinate system O. Unfold the conveyor belt from the tail drive roller, with the carrying section and return section placed in the same plane. The total length is 2L, with the redirecting roller as the midpoint. Consider the unfolded conveyor belt as an elastic support with one end fixed and the other end free. Consider the head drive as the fixed end.

[0041] like Figure 11 As shown, L is the horizontal length of the conveyor. Let the meeting point O be the origin. The corrugated sidewall conveyor belt is unfolded at the tail drive roller, ensuring that its carrying section and return section are on the same plane. At a position x from the origin O, we take a length of... A section of the belt was subjected to mechanical analysis, and the mechanical equilibrium equations were obtained: (3.1) in, Let x be the tension of the conveyor belt at a distance x from the origin. Let x be the elastic displacement of the conveyor belt at a distance x from the origin. The mass per unit length of the conveyor belt and materials, the bearing section Return trip ; The mass per unit length of the material. Mass per unit length of conveyor belt The resistance per unit length of the conveyor belt during operation; Conveyor belt tension Substituting this into (3.1), we get: (3.2) in, Let the area of ​​any cross-section of the conveyor belt be . The stress is at any cross-section of the conveyor belt; Further details: (3.3) S3.2: Order Simplifying (3.3) yields the fundamental equations of conveyor belt dynamics: (3.4) The kinematic relationship is: (3.5) The constitutive equation of the viscous body in the corrugated sidewall conveyor belt is: (3.6) in, and For differential operators, , .

[0042] Furthermore, based on the fundamental dynamic equation of the corrugated sidewall conveyor belt obtained in step S1 (1.23): , , ; It should be noted that equation (1.23) is a general equation of motion for a one-dimensional continuum based on Newton's second law, and has universality; equation (3.4) is a closed partial differential equation of wave motion after substituting a specific constitutive relation; equation (3.4) is an open system of equations, and a single equation cannot simultaneously solve for displacement and stress, making the solution complex, while equation (1.23) is a standard second-order linear partial differential equation (wave equation), which is mathematically closed and relatively simple to solve. Therefore, equation (1.23) is used as the final basic equation of dynamics for the corrugated sidewall conveyor belt for subsequent calculations.

[0043] In the bearing section ( When ), the resistance is ,in, ; on the return trip ( When ), the resistance is In the formula ;in, The resistance per unit length of the load-bearing section during conveyor belt operation. The resistance per unit length of the return section during conveyor belt operation. This refers to the tilt angle during transport.

[0044] S3.3: Perform force analysis on the conveyor belt at the drive roller and tension roller to obtain the force balance equation and the boundary conditions of the drive roller and tension roller. S3.31: As Figure 12 As shown, the drive roller of the conveyor is at the origin. The drive roller is balanced by the driving force and inertial force and the tension of the conveyor belt. Assuming there is no relative slippage of the conveyor belt at the drive roller, the upper part of the conveyor belt is considered rigid, meaning that the displacement at the meeting point and the separation point of the drive roller are equal. Thus, the force balance equation is derived: (3.7) in, For the equivalent mass of the drive unit, The tension at the separation point, The tension at the point of encounter; S3.32: As Figure 13 As shown, the force balance equation between the conveyor belt tension and the tail drive roller is: (3.8) The displacement condition is: (3.9) S3.33: The corrugated sidewall conveyor belt and the drive roller are considered to have no relative sliding, and the drive roller is considered to be a rigid body. Therefore, the displacements at the meeting point and the separation point of the drive roller and the corrugated sidewall conveyor belt are equal. Boundary conditions at the drive drum of the corrugated sidewall belt lifting system: : (3.10) : (3.11) Boundary conditions at the tension roller of the corrugated sidewall belt lifting system: (3.12) S3.4: Considering the preload of the conveyor belt, force analysis is performed by segmenting micro-elements to obtain the initial displacement of the micro-elements of the carrying section and the return section respectively, and the initial speed of the corrugated sidewall belt lifting system in the starting and braking states is obtained based on the initial displacement.

[0045] S3.41: As Figure 14 As shown, the mechanical analysis of the rod is as follows: When in the bearing section hour: (3.13) Bearing segment micro-element segment rod The elongation is: (3.14) Bearing segment micro-element segment rod The absolute displacement is: (3.15) On the return trip hour: (3.16) Return segment micro-element member The elongation is: (3.17) Return segment micro-element member The absolute displacement is: (3.18) Therefore, considering the preload, the initial displacement of the corrugated sidewall belt lifting system with head and tail driving and head tensioning is obtained by combining formulas (3.15) and (3.18), as follows: (3.19) S3.42: When the corrugated sidewall belt lifting system is in the starting state: (3.20) When the corrugated sidewall belt lifting system is in braking condition: (3.21) Based on the above steps, the continuous dynamic model of the corrugated sidewall belt lifting system is as follows: (3.22) The discrete dynamic model and the continuous dynamic model of the corrugated sidewall belt hoisting system were established in steps S2 and S3, respectively. The established dynamic models were solved in step S4 to obtain the dynamic response of the corrugated sidewall belt hoisting system.

[0046] S4: Solve the discrete dynamic model or continuous dynamic model of the corrugated sidewall belt hoisting system to obtain the acceleration, velocity and displacement of the corrugated sidewall belt hoisting system, and obtain the dynamic response of the corrugated sidewall belt hoisting system.

[0047] The discrete dynamic model of the corrugated sidewall belt lifting system is a nonlinear matrix differential equation with variable elastic modulus, variable stiffness, variable damping, and variable external force input. Therefore, step S4 is performed through... Wilson-θ The discrete dynamic model of the corrugated sidewall belt lifting system is solved by the method.

[0048] Wilson-θ The formula for calculating and solving the method is: (4.1) (4.2) pass Wilson-θ The specific steps for solving this problem include: S4.1: Combine equations (2.19) to (2.48) to calculate the mass matrix, stiffness matrix, damping matrix and coefficient matrix in the discrete dynamic model of the corrugated sidewall belt lifting system; S4.2: Calculate the initial acceleration based on the initial displacement and initial velocity, determine the time step, and calculate the equivalent stiffness matrix; S4.21: Given initial displacement and speed And calculate the initial acceleration; (4.3) S4.22: Determine the time step And calculate the integration constant, and take... ; , , , , , , , , (4.4) S4.23 Calculate the equivalent stiffness matrix: .

[0049] S4.3: Calculate the acceleration, velocity, and displacement of each unit, and obtain the dynamic tension of each unit of the conveyor belt based on the mechanical equilibrium equation between the two units, specifically: Calculations are performed for each time step: S4.31: Equivalent load at time: (4.5) S4.32: Displacement at time: ; S4.33: Acceleration, velocity, and displacement at time: (4.6) (4.7) (4.8) The acceleration, velocity, and displacement of each unit of the conveyor belt are obtained using the above formulas. Furthermore, the dynamic tension of each unit of the conveyor belt is obtained through the mechanical equilibrium equations between two adjacent viscoelastic units. (4.9) Step S4 involves solving the continuous dynamics model of the corrugated sidewall belt hoisting system, specifically including: S4.4: According to equation (3.22), the initial displacement caused by the initial tension is: = (4.10) The displacement at any point is the sum of the initial displacement and the displacement caused by the dynamic load applied to the corrugated sidewall conveyor belt: (4.11) in, Let be the displacement of any point. This is the initial displacement. The displacement of any point caused by a dynamic load.

[0050] Substituting (4.10) and (4.11) into formula (3.22) and simplifying, we get: (4.12) S4.5: Decompose the continuous dynamics model into Model 1 (4.13) and Model 2 (4.14): They are respectively: (4.13) (4.14) S4.6: Solve for Model 1: set up First, simplify the boundary conditions, let:

[0051] (4.15) From equation (4.13), we obtain the system of equations (4.16): (4.16) make Substituting this into the first equation of the above system of equations, we get: (4.17) Divide both sides by get: (4.18) The two sides of the equation are independent functions of x and t, and the equation holds true. Therefore, both sides must be constants. Let this constant be... Substituting into the above equation, we get:

[0052] (4.19) Solving (4.19) yields: (4.20) Boundary conditions , Substituting into (4.20), we get: , ; make ,get ; This yields a particular solution to the system of equations (4.19): (4.21) Simultaneously, the initial conditions of the model must be met, and the intrinsic function (in mathematical and physical vibration analysis, the intrinsic function refers to the function describing the spatial deformation of the system, that is, the spatial characteristic shape of the object vibrating at the natural frequency of the system; the intrinsic function is...) Overlay:

[0053] (4.22) The inherent characteristics of conveyor belts are: (4.23) If the infinite series in (4.22) is convergent and can be differentiated twice, then (4.21) and (4.22) can satisfy the initial displacement and boundary conditions; choosing an appropriate and ,make To satisfy the initial conditions of the system of equations (4.16), let: (4.24) and It is a function defined on the interval [0, 2L], therefore we choose... and The coefficients of the expansion are respectively , That's all; (4.25) (4.26) (4.27) (4.28) in, , The nth-order modal coefficients corresponding to the initial displacement contribution , The coefficients represent the nth-order modal coefficients corresponding to the initial velocity contribution. In the subscript, z refers to the coefficients under standard conditions or low altitude, with an integration range of [0, L]. h refers to the coefficients under high altitude conditions, with an integration range of [L, 2L]. This reflects static deformation. It reflects the conversion of the initial velocity into the vibration amplitude in the later stage.

[0054] The above formulas can be used to determine the displacement, dynamic load, dynamic load coefficient, velocity, and acceleration of the corrugated sidewall belt lifting system at any given time in the carrying section and return section. The displacement is: (4.29) (4.30) The dynamic load is: (4.31) (4.32) The dynamic load factor is: (4.33) (4.34) The speed is: (4.35) (4.36) The acceleration is: (4.37) (4.38) S4.7: Solve for Model 2 (4.14): set up To homogenize the boundary conditions of the system of equations, let... (4.39) Further, we obtain the following system of equations: (4.40) The last two items are initial conditions, which can be obtained according to the solution logic of Model 1: (4.41) (4.42) The inherent characteristics of corrugated sidewall conveyor belts are: (4.43) (4.44) (4.45) (4.46) (4.47) The displacement is: (4.48) (4.49) The dynamic load is: (4.50) (4.51) The dynamic load factor is: (4.52) (4.53) The speed is: (4.54) (4.55) The acceleration is: (4.56) (4.57) When an arbitrary continuous acceleration function is used for excitation, it cannot be solved by the above method. Therefore, the continuous acceleration function is fitted with straight lines with different slopes, and then solved piece by piece.

[0055] S4.8: Solve for any continuous function in Model 1: Pick ; in, For time intervals, , The start-up time of the corrugated sidewall belt lifting system. The number of segments that divide the space equally; when hour, , ;

[0056] in: (4.58) (4.59) (4.60) (4.61) when hour, ,

[0057] make The time point is zero, and the time coordinate is... After performing coordinate transformation, we obtain: , (4.62) (4.63) Removing the rigid body translation part from the above equation, we get: (4.64) when The continuity condition of time is known ,have to: (4.65) (4.66) (4.67) (4.68) (4.69) when hour, (4.70) (4.71) Based on the previous calculations: (4.72) in: (4.73) (4.74) (4.75) (4.76) when hour: The dynamic loads of the carrying section and the return section are as follows: (4.77) (4.78) The dynamic load factors are as follows: (4.79) (4.80) The speeds are respectively: (4.81) (4.82) The accelerations are respectively: (4.83) (4.84) when hour: The dynamic loads of the carrying section and the return section are as follows: (4.85) (4.86) The dynamic load factors are as follows: (4.87) (4.88) The speeds are respectively: (4.89) (4.90) The accelerations are respectively: (4.91) (4.92) S4.9: Solve for any continuous function in Model 2: Pick In the formula, For time intervals, , The start-up time of the corrugated sidewall belt lifting system. The number of segments that divide the space equally; when hour, , ; (4.93) when At that time, using the same method as Model 1, we can obtain: (4.94) in: (4.95) (4.96) (4.97) (4.98) when hour: The dynamic loads of the carrying section and the return section are as follows: (4.99) (4.100) The dynamic load factors are as follows: (4.101) (4.102) The speeds are respectively: (4.103) (4.104) The accelerations are respectively: (4.105) (4.106) when At that time, the dynamic loads of the bearing section and the return section are respectively: (4.107) (4.108) The dynamic load factors are as follows: (4.109) (4.110) The speeds are respectively: (4.111) (4.112) The accelerations are respectively: (4.113) (4.114) Through the above steps, the solution formulas for the dynamic load, dynamic load coefficient, velocity and acceleration of the two models decomposed from the corrugated sidewall belt lifting system under arbitrary continuous acceleration function excitation were obtained respectively. The dynamic response of the corrugated sidewall belt lifting system with head and tail drive and tail tension is the result of superimposing the solutions of model one and model two.

[0058] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0059] While the specific embodiments of the present invention have been described above, they are not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system, wherein the corrugated sidewall belt lifting system comprises a conveyor belt, a drive device, and a tensioning device, characterized in that, Includes the following steps: S1: Construct a fractional derivative viscoelastic model of the corrugated sidewall conveyor belt, and establish the basic dynamic equations of the corrugated sidewall conveyor belt based on the fractional derivative viscoelastic model; S2: Discretize the conveyor belt to establish the discrete dynamic equation of the conveyor belt, and construct the dynamic equations of the drive device and the tensioning device respectively. Based on the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, establish the discrete dynamic model of the corrugated sidewall belt lifting system. S3: Establish the continuous dynamic equation of the conveyor belt, set the boundary conditions and initial conditions of the continuous dynamic model of the conveyor belt, and establish the continuous dynamic model of the corrugated sidewall belt lifting system; S4: Solve the discrete dynamic model or continuous dynamic model of the corrugated sidewall belt hoisting system to obtain the acceleration, velocity and displacement of the corrugated sidewall belt hoisting system, and obtain the dynamic response of the corrugated sidewall belt hoisting system.

2. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 1, characterized in that, Step S1 includes: Force analysis was performed on a small segment of the corrugated sidewall conveyor belt, and the equilibrium equation of this small element was obtained: ； in, Let A be the stress, and A be the conveyor belt bearing area. The mass per meter of conveyor belt, Let be the displacement of any point on the conveyor belt. The running resistance per unit length of the conveyor belt; The equations relating the infinitesimal elements of the conveyor belt are rearranged to obtain: ; The fundamental equations of conveyor belt dynamics are obtained by further solving the infinitesimal equilibrium equations and the fractional derivative viscoelastic model.

3. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 1, characterized in that, Step S2 is based on the following assumptions: The corrugated sidewall conveyor belt is considered as a geometrically deformed rod; the material is evenly distributed on the corrugated sidewall conveyor belt; the mass of the rotating part of the idler roller is evenly distributed along the longitudinal direction of the corrugated sidewall conveyor belt; the running resistance of the corrugated sidewall conveyor belt is evenly distributed along the direction of the conveyor belt, and the resistance coefficient of the conveyor belt is linearly related to the speed of the conveyor belt; the drive device, tensioning device and roller of the corrugated sidewall belt lifting system are considered rigid; the mass of the conveyor belt wound on the roller is ignored.

4. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 3, characterized in that, Step S2 includes: S2.1: Considering the influence of conveyor belt sag between idlers, calculate the equivalent elastic modulus of the conveyor belt; S2.2: Using a fractional derivative viscoelastic model, the closed conveyor belt is discretized into multiple elements, and the dynamic equations of each element are obtained based on the mechanical equilibrium equations: ， in, For any unit stiffness, Let be the displacement of any element. For the damping of any element, For the operating resistance of any unit, For the mass of any unit, Let the acceleration of any unit be... For the next unit stiffness, For the displacement of the next unit, This represents the displacement of the previous unit. The speed of the previous unit, For the damping of the next unit, For the speed of the next unit, The resistance force experienced by any unit; S2.3: Perform force analysis on the conveyor belt and drive roller to obtain the rotational dynamics equation, and solve for the dynamics equation of the drive device based on the relationship between the linear acceleration and angular acceleration of the roller surface; S2.4: Perform force analysis on the front and rear units of the tensioning device in the corrugated sidewall belt lifting system, decompose the tensioning device into translational and rotational parts, and establish the dynamic equation of the tensioning device; S2.5: Integrating the discrete dynamic equations of the conveyor belt, the drive device, and the tensioning device, a discrete dynamic model of the corrugated sidewall belt lifting system is obtained: ； in, For the quality matrix, Here is the damping matrix. Here is the stiffness matrix. For the external force matrix, Let be the displacement matrix of the divided elements. The acceleration matrix of the divided unit. This is the velocity matrix of the divided unit.

5. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 4, characterized in that, The step S4 is through Wilson-θ The method for solving the discrete dynamic model of the corrugated sidewall belt lifting system includes: S4.1: Calculate the mass matrix, stiffness matrix, and damping matrix in the discrete dynamic model of the corrugated sidewall belt lifting system; S4.2: Calculate the initial acceleration based on the initial displacement and initial velocity, determine the time step, and calculate the equivalent stiffness matrix; S4.3: Calculate the acceleration, velocity, and displacement of each unit, and obtain the dynamic tension of each unit of the conveyor belt based on the mechanical equilibrium equation between the two units.

6. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 1, characterized in that, Step S3 is based on the following assumptions: The corrugated sidewall conveyor belt is simplified as a one-dimensional elastic rod; the deformation of the corrugated sidewall conveyor belt under external force is relatively small compared to the length of the conveyor belt; the mass of the drive part is equivalently converted into the rotational inertia of the drive roller part; the running resistance is calculated as a linear resistance.

7. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 6, characterized in that, Step S3 includes: S3.1: Unfold the corrugated sidewall conveyor belt at the tail drive roller so that its carrying section and return section are on the same plane. Take a length of [length missing] at a position x from the origin O. A section of the conveyor belt was subjected to mechanical analysis, and the mechanical equilibrium equation was obtained. S3.2: Simplifying the mechanical equilibrium equations in S3.1 yields the fundamental equations of conveyor belt dynamics: ； in, The mass per unit length of the conveyor belt and materials. The stress is at any cross-section of the conveyor belt; The resistance per unit length of the conveyor belt and materials. S3.3: Perform force analysis on the conveyor belt at the drive roller and tension roller to obtain the force balance equation and the boundary conditions of the drive roller and tension roller. S3.4: Considering the preload of the conveyor belt, force analysis is performed by segmenting micro-elements to obtain the initial displacement of the micro-elements of the carrying section and the return section respectively, and the initial speed of the corrugated sidewall belt lifting system in the starting and braking states is obtained based on the initial displacement.

8. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 1, characterized in that, Step S4, solving the continuous dynamics model of the corrugated sidewall belt lifting system, specifically includes: The displacement of the conveyor belt is decomposed into the sum of the initial displacement and the displacement caused by the dynamic load. Substituting this into the continuous dynamics model, it is decomposed into Model 1 and Model 2. For Model 1, the partial differential equations are transformed into a system of ordinary differential equations using the method of separation of variables. The natural frequencies and natural mode shapes are obtained by solving the eigenvalue problem. The displacement is expressed as an infinite series of natural mode shapes. The series coefficients are determined using the initial conditions, thereby obtaining the analytical expressions for the displacement, dynamic load, dynamic load coefficient, velocity, and acceleration of the conveyor belt at any time. Using the same separation of variables method as Model 1, the corresponding analytical expression for Model 2 is obtained.

9. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 8, characterized in that, When the activation function is an arbitrary continuous function, it is piecewise linearly fitted in the time domain, and the solution is obtained for each linear segment in each time interval. Within each time period, Model 1 and Model 2 are solved separately according to the slope excitation to obtain the analytical expression of the dynamic response within that time period; By recursively applying the displacement continuity condition and velocity continuity condition at adjacent time points, a piecewise analytical solution for the entire time interval is obtained.

10. The method for analyzing the dynamic characteristics of a corrugated sidewall belt lifting system according to claim 1, characterized in that, The fractional derivative viscoelastic model is either the fractional derivative Maxwell model, the fractional derivative Kelvin model, or the fractional derivative three-element solid viscoelastic model.

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