A method and system for calculating coupled dynamics of a multi-load-carrying freight ropeway

Abstract

A method for calculating coupled dynamics of a multi-load-carrying freight ropeway, comprising: setting calculation parameters based on the freight ropeway; based on the calculation parameters and the resultant force acting on the nodes of the load-carrying rope / traction rope and the resultant rotational torque of the load in the current time step, increasing the time step according to the set time increment step, solving the node motion equation and the load rotation equation, calculating the resultant force acting on the load-carrying rope / traction rope node and the resultant rotational torque of the load, until the preset time period ends. The technical solution provided by the present invention can accurately and efficiently obtain the changes in the force of the load-carrying rope and the traction rope of the freight ropeway during operation and the deflection angle of the load, providing a more accurate calculation basis for the design and selection of the freight ropeway.

Description

Technical Field

[0001] The invention relates to a numerical calculation method in the structural design of a multi-carrying-cable freight ropeway, and in particular to a coupling dynamic calculation method and system for a multi-carrying-cable freight ropeway. Background Art

[0002] The transmission line freight cableway has the advantages of strong applicability and little influence from weather and external environment. It effectively solves the problem of mountain transportation of tower materials, conductors and other materials, while greatly reducing the cost of compensation and road construction. Therefore, it is widely used in the construction of complex terrain projects in mountainous areas.

[0003] Freight ropeway is a mechanized or semi-mechanized transport channel that mainly uses steel wire ropes for load-bearing and transmission. This mechanized transport channel mainly relies on various working structures formed by the related configuration of the working ropes of the ropeway to realize the processes of load-bearing, lifting, conveying and unloading.

[0004] The multi-load-carrying-cable freight ropeway consists of working ropes, including load-carrying ropes and traction ropes, brackets, loads, traction machines, etc. The load-carrying ropes are composed of multiple steel wire ropes arranged side by side; the traction rope is located below the load-carrying ropes and is a closed rope that can be driven by the traction machine to circulate.

[0005] When the cableway is running, the traction machine drum arranged on the starting side rolls, pulling the traction rope to move the load. The traction rope starts from the traction machine, connects each load in series, and runs to the end of the cableway through the roller on the bracket.

[0006] The existing calculation method for multi-loaded cable freight ropeways uses the method of multiplying the load-bearing capacity of a single load-bearing cable by the number of load-bearing cables to obtain the total load-bearing capacity. This method cannot analyze the interaction between the load-bearing cables of the multi-loaded cableway, resulting in inaccurate calculations. In order to meet the calculation accuracy, the existing finite element calculation method needs to divide more units, resulting in low calculation efficiency. Summary of the invention

[0007] In order to solve the problems of inaccurate calculation and low calculation efficiency of load-bearing rope / traction rope and load force in multi-load-bearing rope ropeways in the prior art, the present invention provides a coupled dynamic calculation method and system for multi-load-bearing rope freight ropeways, which can accurately and efficiently obtain the force changes of the load-bearing ropes and traction ropes of the freight ropeway during operation and the deflection angle of the load, providing a more accurate calculation basis for the design and selection of freight ropeways.

[0008] The technical solution provided by the present invention is:

[0009] A method for calculating coupled dynamics of a multi-load-carrying freight ropeway, the improvement of which is that the method comprises:

[0010] Setting calculation parameters based on the freight ropeway;

[0011] Calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters;

[0012] Based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, the time step is increased according to the set time increment step, the node motion equation and the load rotation equation are solved, and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load are calculated until the preset time period ends.

[0013] Preferably, based on the calculation parameters and the resultant force on the nodes of the load-bearing cable / traction cable and the resultant rotational moment on the load at the current time step, the time step is increased according to the set time increment step, the node motion equation and the load rotation equation are solved, and the resultant force on the nodes of the load-bearing cable / traction cable and the resultant rotational moment on the load are calculated at each time step, including:

[0014] Using the central difference method, the calculation parameters and the resultant force are introduced into the node motion equation at the current time step, the node position vector of the load-bearing cable at the next time step is calculated, and the resultant force acting on the node of the load-bearing cable is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the load-bearing cable at each time step in turn;

[0015] Using the central difference method, the calculation parameters and the resultant force are introduced into the node motion equation at the current time step, the node position vector of the traction cable at the next time step is calculated, and the resultant force acting on the traction cable node is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the traction cable at each time step in turn;

[0016] The central difference method is adopted to bring the calculation parameters and the resultant torque into the load rotation equation at the current time step, calculate the deflection angle of the load at the next time step, and calculate the resultant torque of the load at the same time step based on the deflection angle; increase the time step, and calculate the resultant torque of the load at each time step in turn.

[0017] Preferably, the calculation parameters include: cableway span, cableway height difference;

[0018] Elastic modulus of load-bearing cables, cross-sectional area of ​​load-bearing cables, unit properties and node mass, initial position vector of load-bearing cable nodes;

[0019] The elastic modulus of the traction cable, the cross-sectional area of ​​the traction cable, the unit properties and node mass, and the initial position vector of the traction cable node;

[0020] Load mass, load quantity, load initial position and initial deflection angle.

[0021] Preferably, the pre-established motion equations of the load-bearing cable and traction cable nodes are as follows:

[0022]

[0023] Where, m: the mass of the node; The acceleration of the node at the nth time step; The velocity of the nth time step node; F n : The resultant force acting on the nodes of the load-bearing cable / traction cable at the nth time step; ζ: Damping factor.

[0024] Preferably, the load rotation equation is as follows:

[0025]

[0026] In the formula, I c : moment of inertia of the load; The deflection angular acceleration of the load at the nth time step; W n : The resultant moment of the load at the nth time step; Angular velocity of load deflection at the nth time step; ζ: damping factor.

[0027] Preferably, when the node is a load-bearing cable node, the resultant force acting on the load-bearing cable node at the nth time step is calculated as follows:

[0028]

[0029] In the formula, When the node is a load-bearing cable node, the resultant force acts on the load-bearing cable node at the nth time step; The external force on the load-bearing cable node i on the rth load-bearing cable; The force exerted by the load-bearing cable unit on the load-bearing cable node i on the rth load-bearing cable; r: the number of load-bearing cables.

[0030] Preferably, the external force on the load-bearing cable node i of the rth load-bearing cable is Calculate as follows:

[0031]

[0032] In the formula, The mass of the load-bearing cable node i; G: gravitational acceleration vector.

[0033] Preferably, the load-bearing cable unit comprises a conventional load-bearing cable unit and a sliding load-bearing cable unit;

[0034] The conventional load-bearing cable unit is a load-bearing cable unit in which there is no load or support contact point; the sliding load-bearing cable unit is a load-bearing cable unit in which there is a load or support contact point.

[0035] Preferably, when the load-bearing cable unit on the rth load-bearing cable is a conventional load-bearing cable unit, the force acting on the load-bearing cable node by the conventional load-bearing cable unit is Calculate as follows:

[0036]

[0037] Among them, e i : the direction vector from the load-bearing cable node i to i+1 on the rth load-bearing cable; f i r,in : The internal force of the conventional cable unit between the cable nodes i to i+1 on the rth cable.

[0038] Preferably, the conventional load-bearing cable unit internal force f between the load-bearing cable nodes i to i+1 is i r,in Calculate as follows:

[0039]

[0040] Among them, EA l : The product of the elastic modulus of the load-bearing cable and the cross-sectional area; The original length of the unit given by the rth load-bearing cable; The length from node i to node i+1 at the current moment.

[0041] Preferably, when the load-bearing cable unit on the r-th load-bearing cable is a sliding load-bearing cable unit, the force acting on the load-bearing cable node i by the sliding load-bearing cable unit is calculated as follows:

[0042]

[0043] In the formula, e i1 : unit direction vector from the load-bearing cable node i to the adjacent first contact point B; f i r,in ': Internal force of the sliding cable unit between the cable nodes i to i+1 on the rth cable;

[0044] The force exerted by the sliding load-bearing cable unit on the load-bearing cable node i+1 is calculated as follows:

[0045]

[0046] In the formula, e i2 : The unit direction vector from the load-bearing cable node i+1 to the adjacent first contact point B.

[0047] Preferably, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 on the rth load-bearing cable is i r,in'Includes: the internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1 and the internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1.

[0048] Preferably, when there is only one contact point in the sliding load-bearing cable unit, the internal force of the sliding load-bearing cable unit between nodes i to i+1 of the rth load-bearing cable is calculated as follows:

[0049]

[0050] In the formula, f i r,in ': Internal force of the sliding load-bearing cable unit with one contact point between nodes i and i+1 of the rth load-bearing cable; B: The first contact point; The length from node i to the first contact point B; The length from the first contact point B to the node i+1;

[0051] When there are two contact points in the sliding load-bearing cable unit, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 is i r,in ” Calculate according to the following formula:

[0052]

[0053] In the formula, f i r,in ”: Internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1; B: first contact point; P: second contact point; The length from node i to the second contact point P; The length from the second contact point P to the first contact point B; The length from the first contact point B to the node i+1.

[0054] Preferably, when the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step is calculated as follows:

[0055]

[0056] In the formula, F Tj n : When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step; External force on the traction cable node j; The force exerted by the traction cable unit on the traction cable node j.

[0057] Preferably, the external force on the traction cable node j is It includes the external forces on the traction cable nodes at non-load points and the external forces on the traction cable nodes where the loads are located.

[0058] Preferably, the external force on the traction cable node at the non-load point is calculated as follows:

[0059]

[0060] In the formula, External force on the traction cable node at the non-load point; M Tj : The mass of the traction cable node j; G: The gravity acceleration vector of the load-bearing cable node.

[0061] Preferably, the external force at the traction cable node where the load is located is calculated as follows:

[0062]

[0063] In the formula, External forces at the dragline nodes where the loads are located; The mass of the traction cable node j where the load is located; The force exerted by the load-bearing cable unit on the rth load-bearing cable on the sth load node.

[0064] Preferably, the load cable unit on the rth load cable is s The force The load cable unit with 1 contact point is subjected to the sth load P s The force The load cable unit with two contact points is subjected to the sth load P s The force

[0065] Preferably, the load cable unit with one contact point on the rth load cable is s The force Calculate as follows:

[0066]

[0067] In the formula, e i1 :Load P s The unit vector from the contact point of the load-bearing cable unit to the adjacent load-bearing cable node or bracket contact point on one side; e i2 :Load P s The unit vector from the contact point of the load-bearing cable unit to the contact point of the adjacent load-bearing cable node or bracket on the other side; f i in ': Internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1;

[0068] The load cable element with two contact points is subjected to the sth load P s The force Calculate as follows:

[0069]

[0070] f i r,in ”: Internal force of the sliding cable unit with two contact points between the cable nodes i to i+1.

[0071] Preferably, the traction cable unit comprises a conventional traction cable unit and a sliding traction cable unit;

[0072] The conventional traction cable unit is a traction cable unit in which there is no load or support contact point in the unit; the slip traction cable unit is a traction cable unit in which there is a support contact point in the unit.

[0073] Preferably, when the traction cable unit is a conventional traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0074]

[0075] In the formula, e j is the direction vector from the traction cable node i to i+1; Conventional traction cable unit internal forces between traction cable nodes j to j+1.

[0076] Preferably, the conventional traction cable unit internal force between the traction cable nodes j to j+1 is Calculate as follows:

[0077]

[0078] In the formula, The original length of the traction rope unit; l j : The length of the traction cable between the jth node and the j+1th node in the current time step; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0079] Preferably, when the traction cable unit is a sliding traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0080]

[0081] In the formula, e j : The unit vector from cable node j to j+1; Internal force of the sliding cable unit between cable nodes j to j+1.

[0082] Preferably, when the traction cable unit is a sliding traction cable unit, the internal force of the sliding traction cable unit between the traction cable nodes j to j+1 is Calculate as follows:

[0083]

[0084] In the formula, Internal force of the sliding cable unit with one contact point between cable nodes j and j+1; B': the third contact point; l j,B' : The length from the traction cable node to the third contact point; l B',j+1 : The length from the third contact point to the traction cable node j+1; Given the initial length of the traction cable unit; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0085] Preferably, the acceleration of the nth time step node Calculate as follows:

[0086]

[0087] In the formula, x n+1 : The position vector of the node at the n+1th time step; x n : The position vector of the node at the nth time step; x n -1 : The position vector of the node at the n-1th time step;

[0088] The velocity of the node at the nth time step Calculate as follows:

[0089]

[0090] Preferably, the node position vector at the n+1th time step is calculated as follows:

[0091]

[0092] Where, c1: first damping correlation coefficient; c2: second damping correlation coefficient;

[0093] Among them, the first damping correlation coefficient c1 is calculated according to the following formula:

[0094]

[0095] The second damping correlation coefficient c2 is calculated as follows:

[0096]

[0097] Preferably, the resultant moment of the load at the nth time step is calculated as follows:

[0098]

[0099] Where W n : The resultant moment of the load at the nth time step; The moment of the load-bearing cable at the nth time step; The moment of the traction cable on the load at the nth time step; The moment caused by the load gravity at the nth time step.

[0100] Preferably, the deflection angle of the load at the n+1th time step is calculated as follows:

[0101]

[0102] In the formula, ω n+1 : deflection angle of the load at the n+1th time step; ω n : deflection angle of the load at the nth time step; ω n-1 : deflection angle of the load at the n-1th time step; I c : Moment of inertia of the load, W n : The torque of the load at the nth time step; c1: The first damping correlation coefficient; c2: The second damping correlation coefficient; h: The time increment step;

[0103] Among them, the first damping correlation coefficient c1 is calculated according to the following formula:

[0104]

[0105] The second damping correlation coefficient c2 is calculated as follows:

[0106]

[0107] A coupled power calculation system for a multi-carrying cableway freight ropeway includes a parameter module, a first calculation module, and a second calculation module;

[0108] Parameter module: used for setting calculation parameters based on the freight ropeway;

[0109] The first calculation module is used to calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters;

[0110] The second calculation module is used to increase the time step according to the set time increment step size based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational torque of the load in the current time step, solve the node motion equation and the load rotation equation, calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational torque of the load, until the preset time period ends.

[0111] Compared with the prior art, the present invention has the following beneficial effects:

[0112] The technical solution provided by the present invention adopts a coupled dynamic calculation method to analyze the stress conditions of the load-bearing rope and the traction rope of the single-load-bearing-rope freight ropeway during the working process, which conforms to the actual operating conditions of the single-load-bearing-rope freight ropeway, and can more accurately and efficiently obtain the tension change results of the load-bearing rope and the traction rope of the freight ropeway during the working process, providing a more accurate calculation basis for the design and selection of the freight ropeway.

[0113] The technical solution provided by the present invention establishes a coupling relationship between the load-bearing cable and the traction cable through the load, calculates the impact dynamic response generated during the continuous operation of the load and through the bracket, thereby obtaining more accurate calculation results of the tension of the load-bearing cable and the traction cable.

[0114] The technical solution provided by the present invention regards the load and the support node as the contact point that slides in the load-bearing cable and the traction cable unit, realizes the contact slip calculation of the load-bearing cable and the traction cable of the single-load-bearing cable freight ropeway, and improves the efficiency of the dynamic analysis calculation of the freight ropeway.

[0115] The technical solution provided by the present invention can freely set the nodes of the load-bearing cables and the traction cables according to the calculation requirements, and can obtain good calculation accuracy with fewer nodes, thereby greatly improving the analysis and calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 It is a schematic diagram of a method for calculating coupling power of a multi-carrying cableway freight ropeway according to the present invention;

[0117] Figure 2 It is a schematic diagram of a double-carrying-cable freight ropeway;

[0118] Figure 3 It is a schematic diagram of the structure of a double-carrying-cable freight ropeway;

[0119] Figure 4 It is a schematic diagram of a four-carrying-cable freight ropeway;

[0120] Figure 5 It is a schematic diagram of the structure of a four-carrying-cable freight ropeway;

[0121] Figure 6 It is a schematic diagram of the type of the load-bearing cable and the traction cable unit of the present invention;

[0122] Figure 7 It is a schematic diagram of the unit internal force of the conventional load-bearing cable unit on the rth load-bearing cable of the present invention to the load-bearing cable node;

[0123] Figure 8 It is a schematic diagram of the unit internal force of the sliding load-bearing cable unit on the load-bearing cable node when there is one contact point on the rth load-bearing cable of the present invention;

[0124] Fig. 9 It is a schematic diagram of the unit internal force of the sliding load-bearing cable unit on the load-bearing cable node when there are two contact points on the rth load-bearing cable of the present invention;

[0125] Fig.10 It is a schematic diagram of the load acting on the load by the load-bearing cable unit of the present invention;

[0126] Fig.11 It is a schematic diagram of a closed-loop traction rope of the present invention;

[0127] Fig.12 It is a schematic diagram of load force analysis of the present invention;

[0128] Fig.13 It is a schematic diagram of the property transformation of the sliding load-bearing cable unit of the present invention;

[0129] Fig.14 The coupled dynamic analysis process of the multi-carrying cableway freight ropeway of the present invention;

[0130] Fig.15 It is a schematic diagram of the coupled dynamic analysis system of the single-carrying-cable freight ropeway of the present invention. DETAILED DESCRIPTION

[0131] In order to better understand the present invention, the content of the present invention is further described below in conjunction with the accompanying drawings and examples.

[0132] Embodiment 1:

[0133] A method for calculating the coupled dynamics of a multi-loaded freight ropeway, such as Figure 1 As shown, the method includes:

[0134] Step 1: setting calculation parameters based on the freight ropeway;

[0135] Step 2: Calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters;

[0136] Step 3: Based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, increase the time step according to the set time increment step, solve the node motion equation and the load rotation equation, and calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load until the preset time period ends.

[0137] Step 1: setting calculation parameters based on the freight ropeway;

[0138] Multi-cable ropeways usually include double-cable ropeways such as Figure 2 and Figure 3 As shown, and the four-cable ropeway, as Figure 4 and Figure 5 shown.

[0139] Taking a two-stage cableway as an example, the span of the first stage of the cableway is L1, and the height difference is h1, while the span of the second stage is L2, and the height difference is h2.

[0140] Each load-bearing cable is divided into m units, with a total of m+1 nodes. The mass of each node is M li r (i=1,…,m+1), node position vector x r li (i=1,2,…,m+1), where r represents the load-bearing cable number, r=1,2,4.

[0141] The closed traction cable is divided into p units, with a total of p+1 nodes. The mass of each node is M Ti (i=1,…,p+1), node position vector x Tj (j=1,2,…,p+1). There are g loads in total, which are fixedly connected to the traction rope and are located at the jth s On nodes (i=1,…,g).

[0142] There are k support nodes in total, and the position vector is x Be (e=1,2,…,k), where x B1 、x Bk is the position vector of the starting end A and the end end B of the cableway support.

[0143] The mass of the load-carrying and traction cable nodes can be evenly distributed according to the initial length of the divided element.

[0144] Unit mass of the load-bearing cable q l , the initial length of the i-th unit of the r-th load-bearing cable (r=1,2) is l r0 i , then the quality of node i is:

[0145]

[0146] The mass of the nodes at the head and tail of the rth load-bearing cable is defined as follows:

[0147]

[0148] The unit mass of the traction cable is q T , the initial length of the i-th unit is Then the quality of node i is:

[0149]

[0150] Since the traction cable is a closed cable with cyclic motion, the mass of all nodes of the traction cable is the same, without distinguishing between the beginning and the end.

[0151] Since the load is set to be attached to the node of the traction cable, the node mass of the traction cable where the load is located is the sum of the node unit mass and the load mass:

[0152]

[0153] Where M Ps is the mass of the sth load.

[0154] During the movement, relative slip will occur between the contact point and the load-bearing cable, causing the sliding load-bearing cable unit to change. Therefore, the stress comparison method is used to judge the contact state of the load-bearing cable unit.

[0155] like Fig.13 As shown, when the distance between the load-bearing cable node i and the first contact point B is less than ξ (a given small quantity), the first contact point B may be in contact with the load-bearing cable unit i-1 or the load-bearing cable unit i, and therefore the internal forces of each load-bearing cable unit when the first contact point B is in contact with the load-bearing cable unit i-1 and the load-bearing cable unit i are calculated respectively.

[0156] The contact point tends to slide toward the unit with smaller internal force of the load-bearing cable unit, that is, the first contact point B contacts the load-bearing cable unit with smaller internal force of the load-bearing cable unit, and the load-bearing cable unit is a sliding load-bearing cable unit.

[0157] Step 2: Calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters;

[0158] Specifically, when the node is a load-bearing cable node, the resultant force acting on the load-bearing cable node at the nth time step is calculated as follows:

[0159]

[0160] In the formula, When the node is a load-bearing cable node, the resultant force acts on the load-bearing cable node at the nth time step; The external force on the cable node i of the rth cable; The force exerted by the load-bearing cable unit on the load-bearing cable node i on the rth load-bearing cable; r: the number of load-bearing cables;

[0161] Among them, the external force on the node i of the rth load-bearing cable is Calculate as follows:

[0162]

[0163] In the formula, The mass of the load-bearing cable node i; G: gravity acceleration vector; d: the number of load-bearing cable nodes;

[0164] like Figure 6 As shown in the figure, according to whether there is a load or a support contact slip node in the rth load-bearing cable unit, it is divided into a conventional load-bearing cable unit and a sliding load-bearing cable unit. A conventional load-bearing cable unit refers to a load-bearing cable node in which there is no load or support contact slip; a sliding load-bearing cable unit refers to a node in which there is a load or support contact slip in the load-bearing cable unit. The traction cable unit is the same as the load-bearing cable unit, and is also divided into a conventional traction cable unit and a sliding load-bearing cable unit.

[0165] The force exerted by the load-bearing cable unit on the rth load-bearing cable on the load-bearing cable node i It includes the force on the load-bearing cable node when the load-bearing cable unit is a conventional load-bearing cable unit and the force on the load-bearing cable node when the load-bearing cable unit is a sliding load-bearing cable unit.

[0166] Specifically, when the load-bearing cable unit on the rth load-bearing cable is a conventional load-bearing cable unit, the force acting on the load-bearing cable node is Calculate as follows:

[0167]

[0168] Among them, e i : the unit vector of the load-bearing cable nodes i to i+1 on the rth load-bearing cable; f i r,in : The internal force of the conventional cable unit between the cable nodes i to i+1 on the rth cable.

[0169] If f i r,in <0, then let f i r,in =0.

[0170] Specifically, when the load-bearing cable unit is a sliding load-bearing cable unit, the force acting on the load-bearing cable node is:

[0171] The force exerted by the sliding load-bearing cable unit on the load-bearing cable node i is calculated as follows:

[0172]

[0173] In the formula, e i1 : unit vector from the load-bearing cable node i to the adjacent first contact point B; f i r,in ': Internal force of the sliding cable unit between the cable nodes i to i+1 on the rth cable;

[0174] in, In the formula, The position vector of node i on the r-th root load cable; Position vector of the first contact point B on the rth load-bearing cable;

[0175] The force exerted by the sliding load-bearing cable unit on the load-bearing cable node i+1 is calculated as follows:

[0176]

[0177] In the formula, e i2 : The unit vector from the cable node i+1 to the adjacent first contact point B;

[0178] in, In the formula, The position vector of node i+1 on the rth root carrier cable.

[0179] Specifically, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 on the rth load-bearing cable is i r,in 'Includes: Internal force f of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1 i r,in ' and the internal force f of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1 i r,in ”.

[0180] Specifically, Figure 7 As shown, the conventional load-bearing cable unit internal force f between the load-bearing cable nodes i to i+1 is i r,in Calculate as follows:

[0181]

[0182] Among them, EA l : The product of the elastic modulus of the load-bearing cable and the cross-sectional area; The original length of the unit given by the rth load-bearing cable; The length from node i to node i+1 at the current moment;

[0183] in, The position vector of node i on the r-th root load cable; The position vector of node i+1 on the rth root carrier cable.

[0184] like Figure 8 As shown in the figure, when there is only one contact point in the sliding load-bearing cable unit, the internal force f of the sliding load-bearing cable unit between the nodes i to i+1 of the rth load-bearing cable is i r,in 'Calculate according to the following formula:

[0185]

[0186] Where, B: first contact point; The length from node i to the first contact point B; The length from the first contact point B to the node i+1;

[0187] in,

[0188]

[0189] In the formula, The position vector of node i on the r-th root load cable; The position vector of node i+1 on the r-th root load cable; The position vector of the first contact point B on the rth load-bearing cable.

[0190] If f i r,in '<0, then let f i r,in '=0.

[0191] like Fig. 9 As shown in the figure, when there are two contact points in the sliding load-bearing cable unit, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 is i r,in ” Calculate according to the following formula:

[0192]

[0193] In the formula, The length from node i to the second contact point P; The length from the second contact point P to the first contact point B; The length from the first contact point B to the node i+1;

[0194] in:

[0195]

[0196] In the formula, The position vector of the second contact point P on the rth load-bearing cable.

[0197] If f i r,in ”<0, then let f i r,in ”=0.

[0198] Specifically, when the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step is calculated as follows:

[0199]

[0200] In the formula, F Tj n : When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step; External force on the traction cable node j; The force exerted by the traction cable unit on the traction cable node j.

[0201] Among them, the external force on the traction cable node j is Calculate separately according to the dragline nodes at non-load points and the dragline nodes at load points:

[0202] The external force on the traction cable node at the non-load point is calculated as follows:

[0203]

[0204] Where M Tj : The mass of the traction cable node j; G: The gravity acceleration vector of the load-bearing cable node;

[0205] The external force at the traction cable node where the load is located is calculated as follows:

[0206]

[0207] In the formula, The mass of the traction cable node j where the load is located; The force exerted by the rth load-bearing cable on the sth load node;

[0208] Among them, Fig.10 As shown in the figure, the force exerted by the i-th load-bearing cable unit of the r-th load-bearing cable on the s-th load is Calculate as follows:

[0209]

[0210] In the formula, e i1 :Load P s The unit vector from the contact point of the load-bearing cable unit to the adjacent load-bearing cable node or bracket contact point on one side; ei2 :Load P s The unit vector from the contact point of the load-bearing cable unit to the contact point of the adjacent load-bearing cable node or bracket on the other side; f i in ': Internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1;

[0211] The load cable element with two contact points is subjected to the sth load P s The force Calculate as follows:

[0212]

[0213] f i r,in ”: Internal force of the sliding cable unit with two contact points between the cable nodes i to i+1.

[0214] Specifically, the traction cable unit includes a conventional traction cable unit and a sliding traction cable unit; the conventional traction cable unit is a traction cable unit in which there is no load or support contact point; the sliding traction cable unit is a traction cable unit in which there is a support contact point.

[0215] Specifically, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0216] When the traction cable unit is a conventional traction cable unit, the force exerted by the traction cable unit on the traction cable node j is Calculate as follows:

[0217]

[0218] In the formula, e j is the direction vector from the traction cable node i to i+1; Conventional traction cable unit internal forces between traction cable nodes j to j+1.

[0219] The calculation method of the internal force of the conventional traction cable unit is the same as the calculation method of the internal force of the conventional load-bearing cable unit. Calculate as follows:

[0220]

[0221] In the formula, The original length of the traction rope unit; l j : The length of the traction cable between the jth node and the j+1th node in the current time step; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0222] When the traction cable unit is a sliding load cable unit, the force of the traction cable unit on the traction cable node j is The method for calculating the internal force of the sliding traction cable unit is the same as the method for calculating the force of the sliding load-bearing cable unit on the load-bearing cable node. When the traction cable unit is a sliding load-bearing cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0223]

[0224] In the formula, e j : The unit vector from cable node j to j+1; Internal force of the sliding cable unit between cable nodes j to j+1.

[0225] When the traction cable unit is a sliding traction cable unit, the internal force of the sliding traction cable unit between the traction cable nodes j to j+1 is Calculate as follows:

[0226]

[0227] In the formula, Internal force of the sliding cable unit with one contact point between cable nodes j and j+1; B': the third contact point; l j,B' : The length from the traction cable node to the third contact point; l B',j+1 : The length from the third contact point to the traction cable node j+1; Given the initial length of the traction cable unit; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0228] The cyclic motion of the traction rope is as follows Fig.11 As shown. The closed traction cable is divided into g units, with a total of g nodes. The mass of each traction cable node is M Tj (j=1,…,g+1), at the initial time t0, node 1 coincides with the starting point A, such as Fig.11 As shown in (a) in .

[0229] At the next moment t1, after the closed cable circulates, the positions of each point are as follows Fig.11 As shown in (b) in . When node j moves to the starting point A, Fig.11 In (c), the numbers are adjusted, and j→1, 1→2, 2→3, …, g-1→g are recorded, and the next cycle can be carried out.

[0230] The change in the distance between A and g is used as the movement sign of the traction rope.

[0231] According to Newton's second law, motion equations are established for the working cables (load-bearing cables / traction cables), brackets, and loads involved in the cableway working cable coupling analysis.

[0232] Specifically, the resultant moment W of the load s at the nth time step is s n Calculate as follows:

[0233]

[0234] In the formula, The moment of the load cable with respect to the load s at the nth time step; The moment of the traction cable on the load s at the nth time step; The moment due to gravity of load s at the nth time step.

[0235] in,

[0236]

[0237] In the formula, The rth load-bearing cable exerts force on load s; The vertical component of the load s by the rth load-bearing cable; D lr : The distance from the rth load-bearing cable to the center of load s;

[0238]

[0239] In the formula, The vertical component of the force acting on the load node s by the traction cable; D T : The distance from the traction cable to the center of the load s.

[0240]

[0241] In the formula, G Ps : load s gravity; D G : The distance from the load s to the center of the trolley.

[0242] The load-bearing cables are always in contact, and the displacement constraint relationship between the contact points of each load-bearing cable and the load can be obtained:

[0243]

[0244] In the formula, The spatial displacement vector of the contact point between the rth load-bearing cable and the load s; x Ps : spatial displacement vector of the sth load; ω s : Deflection angle of load s.

[0245] The force that causes the deflection of the sth running trolley includes the force of the load-bearing cable on the trolley in the surface Ω2 Traction force Tj and load G Ps , its action position is as follows Fig.12 As shown, the deflection angle of the load in the surface Ω2 is ω s , counterclockwise is positive and clockwise is negative.

[0246] Step 3: Based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, increase the time step according to the set time increment step, solve the node motion equation and the load rotation equation, and calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load until the preset time period ends.

[0247] Specifically, the central difference method is adopted to bring the calculation parameters and the resultant force into the node motion equation at the current time step, calculate the node position vector of the load-bearing cable at the next time step, and calculate the resultant force of the load-bearing cable node according to the position vector; increase the time step, and calculate the node position vector and the resultant force of the load-bearing cable at each time step in turn;

[0248] Using the central difference method, the calculation parameters and the resultant force are introduced into the node motion equation at the current time step, the node position vector of the traction cable at the next time step is calculated, and the resultant force acting on the traction cable node is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the traction cable at each time step in turn;

[0249] Using the central difference method, the calculation parameters and the resultant moment are introduced into the load rotation equation at the current time step, the deflection angle of the load at the next time step is calculated, and the resultant moment of the load at the same time step is calculated according to the deflection angle; the time step is increased, and the resultant moment of the load at each time step is calculated in sequence;

[0250] According to Newton's second law, when the damping force is not considered, the motion equation of the rth load-bearing cable node is:

[0251]

[0252] Similarly, the motion equation of the traction cable node is:

[0253]

[0254] In the formula, are the acceleration and the resultant force of the r-th load-bearing cable node i (r=1, 2, 4); F Tj are the acceleration and the resultant force of the traction cable node i respectively.

[0255] The bracket is always at rest during the analysis, so its motion equation is:

[0256]

[0257] In the formula, is the bracket node acceleration.

[0258] The rotation equation of the load under the action of multiple load cables is:

[0259]

[0260] In the formula, I c : moment of inertia of the load; The rotational acceleration of the load s; W s : The torque acting on the load s.

[0261] According to Newton's second law, an energy dissipation mechanism is introduced into the motion equation and the virtual damping force is increased so that the structure can reach static equilibrium.

[0262] Specifically, the pre-established motion equations of the load-bearing cable and traction cable nodes are as follows:

[0263]

[0264] Where, m: the mass of the node; The acceleration of the node at the nth time step; The velocity of the nth time step node; F n : The resultant force acting on the node of the load-bearing cable or traction cable at the nth time step; ζ>0 is the damping factor;

[0265] The load rotation equation is as follows:

[0266]

[0267] In the formula, I c : moment of inertia of the load; Deflection angular acceleration of load s; The resultant moment of the load s at the nth time step; Load s is the angular velocity of deflection.

[0268] Specifically, the acceleration of the node at the nth time step is Calculate as follows:

[0269]

[0270] Where h is the time increment step; x n+1 : The position vector of the node at the n+1th time step; x n: The position vector of the node at the nth time step; x n-1 : The position vector of the node at the n-1th time step;

[0271] The velocity of the node at the nth time step Calculate as follows:

[0272]

[0273] Specifically, the time increment step length traction cable parameter is determined and calculated as follows:

[0274]

[0275] Where h is the time increment step.

[0276] Specifically, the acceleration of the node at the nth time step is Calculate as follows:

[0277]

[0278] Where h is the time increment step; x n+1 : The position vector of the node at the n+1th time step; x n : The position vector of the node at the nth time step; x n-1 : The position vector of the node at the n-1th time step;

[0279] The velocity of the node at the nth time step Calculate as follows:

[0280]

[0281] Specifically, solving the motion equations of the load-bearing cable and the traction cable nodes includes:

[0282] The acceleration of the nth time step and speed Substitute into the load-bearing cable and traction cable node motion equations, solve the load-bearing cable and traction cable node motion equations, and obtain the load-bearing cable and traction cable node position vectors at the n+1th time step.

[0283] Specifically, the node position vector at the n+1th time step is calculated as follows:

[0284]

[0285] Where, c1, c2: coefficients related to damping;

[0286] Among them, c1 is calculated as follows:

[0287]

[0288] c2 is calculated as follows:

[0289]

[0290] Specifically, the deflection angle of the load at the n+1th time step is calculated as follows:

[0291]

[0292] In the formula, The deflection angle of load s at the n+1th time step; The deflection angle of load s at the nth time step; The deflection angle of the load s at the n-1th time step; I cs : moment of inertia of load s, The torque to which the load s is subjected at the nth time step; c1, c2: coefficients related to damping;

[0293] Among them, c1 is calculated as follows:

[0294]

[0295] c2 is calculated as follows:

[0296]

[0297] During the operation of the multi-load-carrying freight ropeway, it is necessary to determine whether there are support nodes and load nodes in the load-carrying and traction cable units, and to perform traction cable cycle operations, and record the unit number, node number, unit property and other information of the load-carrying and traction cables, and update them in real time according to the movement. That is, during the operation of the ropeway, the sliding unit in the load-carrying / traction cable needs to be judged at each time step, and the unit property information needs to be updated. The detailed process of coupled dynamic calculation of multi-load-carrying freight ropeway is as follows Fig.14 shown.

[0298] Embodiment 2:

[0299] Based on the same inventive concept, the present invention also provides a coupled dynamic analysis system for a multi-carrying freight ropeway, such as Fig.15 As shown, it includes a parameter module, a first calculation module and a second calculation module;

[0300] Parameter module: used for setting calculation parameters based on the freight ropeway;

[0301] The first calculation module is used to calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters;

[0302] The second calculation module: based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, the time step is increased according to the set time increment step, the node motion equation and the load rotation equation are solved, and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load are calculated until the preset time period ends.

[0303] Specifically, in the parameter module, the calculation parameters include: cableway span, cableway height difference;

[0304] The properties of the load-bearing cable unit and the mass of the node, the initial position vector of the load-bearing cable node;

[0305] Drag cable unit properties and node mass, drag cable node initial position vector;

[0306] Initial deflection angle of the load.

[0307] Specifically, in the first calculation module, the resultant force of the load-bearing cable node at the load-bearing cable node in the nth time step is calculated according to the following formula:

[0308]

[0309] In the formula, When the node is a load-bearing cable node, the resultant force acts on the load-bearing cable node at the nth time step; The external force on the cable node i of the rth cable; The force exerted by the load-bearing cable unit on the load-bearing cable node i on the rth load-bearing cable; r: the number of load-bearing cables;

[0310] Specifically, the external force on the load-bearing cable node i on the rth load-bearing cable is Calculate as follows:

[0311]

[0312] In the formula, The mass of the load-bearing cable node i; G: gravitational acceleration vector.

[0313] Specifically, the load-bearing cable unit includes a conventional load-bearing cable unit and a sliding load-bearing cable unit;

[0314] The conventional load-bearing cable unit is a load-bearing cable unit in which there is no load or support contact point; the sliding load-bearing cable unit is a load-bearing cable unit in which there is a load or support contact point.

[0315] Specifically, when the load-bearing cable unit on the rth load-bearing cable is a conventional load-bearing cable unit, the force acting on the load-bearing cable node by the conventional load-bearing cable unit is Calculate as follows:

[0316]

[0317] Among them, e i : the direction vector from the load-bearing cable node i to i+1 on the rth load-bearing cable; f i r,in : The internal force of the conventional cable unit between the cable nodes i to i+1 on the rth cable.

[0318] Specifically, the conventional load-bearing cable unit internal force f between the load-bearing cable nodes i to i+1 is i r,in Calculate as follows:

[0319]

[0320] Among them, EA l : The product of the elastic modulus of the load-bearing cable and the cross-sectional area; The original length of the unit given by the rth load-bearing cable; The length from node i to node i+1 at the current moment.

[0321] Specifically, when the load-bearing cable unit on the rth load-bearing cable is a sliding load-bearing cable unit, the force acting on the load-bearing cable node i by the sliding load-bearing cable unit is calculated as follows:

[0322]

[0323] In the formula, e i1 : unit direction vector from the load-bearing cable node i to the adjacent first contact point B; f i r,in ': Internal force of the sliding cable unit between the cable nodes i to i+1 on the rth cable;

[0324] The force exerted by the sliding load-bearing cable unit on the load-bearing cable node i+1 is calculated as follows:

[0325]

[0326] In the formula, e i2 : The unit direction vector from the load-bearing cable node i+1 to the adjacent first contact point B.

[0327] Specifically, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 on the rth load-bearing cable is i r,in 'Includes: the internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1 and the internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1.

[0328] Specifically, when there is only one contact point in the sliding load-bearing cable unit, the internal force of the sliding load-bearing cable unit between nodes i to i+1 of the rth load-bearing cable is calculated as follows:

[0329]

[0330] In the formula, f i r,in ': Internal force of the sliding load-bearing cable unit with one contact point between nodes i and i+1 of the rth load-bearing cable; B: The first contact point; The length from node i to the first contact point B; The length from the first contact point B to the node i+1;

[0331] When there are two contact points in the sliding load-bearing cable unit, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 is i r,in ” Calculate according to the following formula:

[0332]

[0333] In the formula, f i r,in ”: Internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1; B: first contact point; P: second contact point; The length from node i to the second contact point P; The length from the second contact point P to the first contact point B; The length from the first contact point B to the node i+1.

[0334] Specifically, when the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step is calculated as follows:

[0335]

[0336] In the formula, F Tj n : When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step; External force on the traction cable node j; The force exerted by the traction cable unit on the traction cable node j.

[0337] Specifically, the external force on the traction cable node j is It includes the external forces on the traction cable nodes at non-load points and the external forces on the traction cable nodes where the loads are located.

[0338] Specifically, the external force on the traction cable node at the non-load point is calculated as follows:

[0339]

[0340] In the formula, External force on the traction cable node at the non-load point; M Tj : The mass of the traction cable node j; G: The gravity acceleration vector of the load-bearing cable node.

[0341] Specifically, the external force at the traction cable node where the load is located is calculated as follows:

[0342]

[0343] In the formula, External forces at the dragline nodes where the loads are located; The mass of the traction cable node j where the load is located; The force exerted by the load-bearing cable unit on the rth load-bearing cable on the sth load node.

[0344] Specifically, the load cable unit on the rth load cable is subjected to the sth load P s The force The load cable unit with 1 contact point is subjected to the sth load P s The force The load cable unit with two contact points is subjected to the sth load P s The force

[0345] Specifically, the load cable unit with one contact point on the rth load cable is subjected to the sth load P s The force Calculate as follows:

[0346]

[0347] In the formula, e i1 :Load P s The unit vector from the contact point of the load-bearing cable unit to the adjacent load-bearing cable node or bracket contact point on one side; e i2 :Load P s The unit vector from the contact point of the load-bearing cable unit to the contact point of the adjacent load-bearing cable node or bracket on the other side; f i in ': Internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1;

[0348] The load cable element with two contact points is subjected to the sth load P s The force Calculate as follows:

[0349]

[0350] fi r,in ”: Internal force of the sliding cable unit with two contact points between the cable nodes i to i+1.

[0351] Specifically, the traction rope unit includes a conventional traction rope unit and a sliding traction rope unit;

[0352] The conventional traction cable unit is a traction cable unit in which there is no load or support contact point in the unit; the slip traction cable unit is a traction cable unit in which there is a support contact point in the unit.

[0353] Specifically, when the traction cable unit is a conventional traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0354]

[0355] In the formula, e j is the direction vector from traction cable node i to i+1; Conventional traction cable unit internal forces between traction cable nodes j to j+1.

[0356] Specifically, the conventional traction cable unit internal force between the traction cable nodes j to j+1 is Calculate as follows:

[0357]

[0358] In the formula, The original length of the traction rope unit; l j : The length of the traction cable between the jth node and the j+1th node in the current time step; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0359] Specifically, when the traction cable unit is a sliding traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows:

[0360]

[0361] In the formula, e j : The unit vector from cable node j to j+1; Internal force of the sliding cable unit between cable nodes j to j+1.

[0362] Specifically, when the traction cable unit is a sliding traction cable unit, the internal force of the sliding traction cable unit between the traction cable nodes j to j+1 is Calculate as follows:

[0363]

[0364] In the formula, Internal force of the sliding cable unit with one contact point between cable nodes j and j+1; B': the third contact point; l j,B' : The length from the traction cable node to the third contact point; l B',j+1 : The length from the third contact point to the traction cable node j+1; Given the initial length of the traction cable unit; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

[0365] Specifically, the resultant moment of the load at the nth time step is calculated as follows:

[0366]

[0367] Where W n : The resultant moment of the load at the nth time step; The moment of the load-bearing cable at the nth time step; The moment of the traction cable on the load at the nth time step; The moment caused by the load gravity at the nth time step.

[0368] Specifically, in the second calculation module, the node motion equation includes:

[0369] The motion equations of the load-bearing cable and traction cable nodes are shown below:

[0370]

[0371] Where, m: the mass of the node; The acceleration of the node at the nth time step; F n : The resultant force acting on the node of the load-bearing cable or traction cable at the nth time step; f dmp : The first virtual damping force;

[0372] The load rotation equation is as follows:

[0373]

[0374] In the formula, I c : moment of inertia of the load; Deflection angular acceleration of load s; W s n : The resultant moment of the load s at the nth time step; f dmp ': The second virtual damping force;

[0375] Among them, the first virtual damping force f dmp Calculate as follows:

[0376]

[0377] In the formula, ζ>0 is the damping factor;

[0378] The second virtual damping force f dmp 'Calculate according to the following formula:

[0379]

[0380] In the formula, Angular velocity of load deflection.

[0381] Specifically, the acceleration of the node at the nth time step is Calculate as follows:

[0382]

[0383] Where h is the time increment step; x n+1 : The position vector of the node at the n+1th time step; x n : The position vector of the node at the nth time step; x n-1 : The position vector of the node at the n-1th time step;

[0384] The velocity of the node at the nth time step Calculate as follows:

[0385]

[0386] Specifically, solving the motion equations of the load-bearing cable and the traction cable nodes includes:

[0387] The acceleration of the nth time step and speed Substituted into the equation of motion of the load-bearing cable and traction cable nodes,

[0388] Solve the motion equations of the load-bearing cable and traction cable nodes to obtain the position vectors of the load-bearing cable and traction cable nodes at the n+1th time step.

[0389] Specifically, the node position vector at the n+1th time step is calculated as follows:

[0390]

[0391] Where, c1: first damping coefficient; c2: second damping coefficient;

[0392] Among them, the first damping coefficient c1 is calculated according to the following formula:

[0393]

[0394] The second damping coefficient c2 is calculated as follows:

[0395]

[0396] Specifically, the deflection angle of the load at the n+1th time step is calculated as follows:

[0397]

[0398] In the formula, ω n+1 : deflection angle of the load at the n+1th time step; ω n : deflection angle of the load at the nth time step; ω n-1 : deflection angle of the load at the n-1th time step; I c : Moment of inertia of the load, W n : The torque of the load at the nth time step; c1: The first damping correlation coefficient; c2: The second damping correlation coefficient; h: The time increment step;

[0399] Among them, the first damping coefficient c1 is calculated according to the following formula:

[0400]

[0401] The second damping coefficient c2 is calculated as follows:

[0402]

[0403] The above facts indicate that the technical solution provided by the present invention can realize the overall analysis of the load-bearing cables and traction cables of a multi-load-bearing freight cableway. The cyclic motion of the traction cables drives the load to run on the load-bearing cables. The load-bearing cables and the traction cables establish a coupling relationship through the load, which conforms to the actual operating conditions of the freight cableway. The impact dynamic response generated by the continuous operation of the load and the support can be calculated, providing an accurate and reasonable theoretical basis and calculation method for the coupled dynamic analysis of the working cables of the freight cableway.

[0404] The technical solution provided by the present invention realizes the traveling motion of the traction rope by shortening the length between the end node of the traction rope and the starting fixed point under the premise that the initial length of the traction rope remains unchanged, thereby realizing the cyclic motion analysis and calculation efficiency of the traction rope.

[0405] Obviously, the described embodiments are only some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0406] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0407] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0408] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0409] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0410] The above are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are included in the scope of the claims of the present invention to be approved.

Claims

1. A method for calculating coupled dynamics of a multi-carrying freight ropeway, characterized in that: The method comprises: Setting calculation parameters based on the freight ropeway; Calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters; Based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load at the current time step, the time step is increased according to the preset time increment step length, and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load are calculated until the preset time period ends; The method of increasing the time step according to a preset time increment step based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, and calculating the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in each time step includes: Using the central difference method, in the current time step, the calculation parameters and the resultant force are introduced into the pre-established node motion equation, the node position vector of the load-bearing cable in the next time step is calculated, and the resultant force acting on the node of the load-bearing cable is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the load-bearing cable in each time step in turn; Using the central difference method, the calculation parameters and the resultant force are introduced into the node motion equation at the current time step, the node position vector of the traction cable at the next time step is calculated, and the resultant force acting on the traction cable node is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the traction cable at each time step in turn; Using the central difference method, the calculation parameters and the resultant torque are introduced into the pre-established load rotation equation at the current time step, the deflection angle of the load at the next time step is calculated, and the resultant torque of the load at the same time step is calculated according to the deflection angle; the time step is increased, and the resultant torque of the load at each time step is calculated in sequence; When the node is a load-bearing cable node, the resultant force acting on the load-bearing cable node at the nth time step is calculated as follows: In the formula, When the node is a load-bearing cable node, the resultant force acts on the load-bearing cable node at the nth time step; The external force on the load-bearing cable node i on the rth load-bearing cable; The force exerted by the load-bearing cable unit on the load-bearing cable node i on the rth load-bearing cable; r: the number of load-bearing cables; When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step is calculated as follows: In the formula, F Tj n : When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step; External force on the traction cable node j; The force of the traction cable unit on the traction cable node j; The resultant moment of the load at the nth time step is calculated as follows: Where W n : The resultant moment of the load at the nth time step; The moment of the load-bearing cable at the nth time step; The moment of the traction cable on the load at the nth time step; The moment caused by the load gravity at the nth time step.

2. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The calculation parameters include: cableway span and cableway height difference; Elastic modulus of load-bearing cables, cross-sectional area of ​​load-bearing cables, unit properties and node mass, initial position vector of load-bearing cable nodes; The elastic modulus of the traction cable, the cross-sectional area of ​​the traction cable, the unit properties and node mass, and the initial position vector of the traction cable node; Load mass, load quantity, load initial position and initial deflection angle.

3. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The pre-established node motion equation is shown in the following formula: Where, m: the mass of the node; The acceleration of the node at the nth time step; The velocity of the nth time step node; F n : The resultant force acting on the nodes of the load-bearing cable / traction cable at the nth time step; ζ: Damping factor.

4. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The pre-established load rotation equation is shown below: In the formula, I c : moment of inertia of the load; The deflection angular acceleration of the load at the nth time step; W n : The resultant moment of the load at the nth time step; Angular velocity of load deflection at the nth time step; ζ: damping factor.

5. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The external force on the node i of the rth load-bearing cable is Calculate as follows: In the formula, The mass of the load-bearing cable node i; G: gravitational acceleration vector.

6. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The load-bearing cable unit comprises a conventional load-bearing cable unit and a sliding load-bearing cable unit; The conventional load-bearing cable unit is a load-bearing cable unit in which there is no load or support contact point; the sliding load-bearing cable unit is a load-bearing cable unit in which there is a load or support contact point.

7. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 6, characterized in that: When the load-bearing cable unit on the rth load-bearing cable is a conventional load-bearing cable unit, the conventional load-bearing cable unit Forces acting on the cable nodes Calculate as follows: Among them, e i : the direction vector from the load-bearing cable node i to i+1 on the rth load-bearing cable; f i r,in : The internal force of the conventional cable unit between the cable nodes i to i+1 on the rth cable.

8. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 7, characterized in that: The conventional load-bearing cable unit internal force f between the load-bearing cable nodes i to i+1 i r,in Calculate as follows: Among them, EA l : The product of the elastic modulus of the load-bearing cable and the cross-sectional area; The original length of the unit given by the rth load-bearing cable; The length from node i to node i+1 at the current moment.

9. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 6, characterized in that: When the load-bearing cable unit on the rth load-bearing cable is a sliding load-bearing cable unit, the force acting on the load-bearing cable node i by the sliding load-bearing cable unit is calculated as follows: In the formula, e i1 : unit direction vector from the load-bearing cable node i to the adjacent first contact point B; f i r,in ': Internal force of the sliding cable unit between the cable nodes i to i+1 on the rth cable; The force exerted by the sliding load-bearing cable unit on the load-bearing cable node i+1 is calculated as follows: In the formula, e i2 : The unit vector from the load-bearing cable node i+1 to the adjacent first contact point B.

10. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 9, characterized in that: The internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 on the rth load-bearing cable i r,in 'include: The internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1 and the internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1.

11. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 10, characterized in that: When there is only one contact point in the sliding load-bearing cable unit, the internal force of the sliding load-bearing cable unit between nodes i to i+1 of the rth load-bearing cable is calculated as follows: In the formula, EA l : product of elastic modulus and cross-sectional area of ​​load-bearing cable; f i r,in ': Internal force of the sliding load-bearing cable unit with one contact point between nodes i and i+1 of the rth load-bearing cable; B: first contact point; The length from node i to the first contact point B; The length from the first contact point B to the node i+1; When there are two contact points in the sliding load-bearing cable unit, the internal force f of the sliding load-bearing cable unit between the load-bearing cable nodes i to i+1 is i r,in ” Calculate according to the following formula: In the formula, f i r,in ”: Internal force of the sliding load-bearing cable unit with two contact points between the load-bearing cable nodes i to i+1; B: first contact point; P: second contact point; The length from node i to the second contact point P; The length from the second contact point P to the first contact point B; The length from the first contact point B to the node i+1.

12. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: External force on traction cable node j It includes the external forces on the traction cable nodes at non-load points and the external forces on the traction cable nodes where the loads are located.

13. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 12, characterized in that: The external force on the traction cable node at the non-load point is calculated as follows: In the formula, External force on the traction cable node at the non-load point; M Tj : The mass of the traction cable node j; G: gravity acceleration vector of the load-bearing cable node.

14. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 12, characterized in that: The external force at the traction cable node where the load is located is calculated as follows: In the formula, External forces at the dragline nodes where the loads are located; The mass of the traction cable node j where the load is located; The force exerted by the load-bearing cable unit on the rth load-bearing cable on the sth load node.

15. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 14, characterized in that: The load cable unit on the rth load cable is subjected to the sth load P s The force The load cable unit with 1 contact point is subjected to the sth load P s The force The force exerted by the load cable unit with two contact points on the sth load Ps 16. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 15, characterized in that: The load cable unit with one contact point on the rth load cable is subjected to the sth load P s The force Calculate as follows: In the formula, e i1 :Load P s The unit vector from the contact point of the load-bearing cable unit to the adjacent load-bearing cable node or bracket contact point on one side; e i2 :Load P s The unit vector from the contact point of the load-bearing cable unit to the contact point of the adjacent load-bearing cable node or bracket on the other side; f i r，in ′: internal force of the sliding load-bearing cable unit with one contact point between the load-bearing cable nodes i to i+1; The load cable element with two contact points is subjected to the sth load P s The force Calculate as follows: f i r,in ”: Internal force of the sliding cable unit with two contact points between the cable nodes i to i+1.

17. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 1, characterized in that: The traction rope unit includes a conventional traction rope unit and a sliding traction rope unit; The conventional traction cable unit is a traction cable unit in which there is no load or support contact point in the unit; the slip traction cable unit is a traction cable unit in which there is a support contact point in the unit.

18. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 17, characterized in that: When the traction cable unit is a conventional traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows: In the formula, e j is the direction vector from traction cable node i to i+1; Conventional traction cable unit internal forces between traction cable nodes j to j+1.

19. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 18, characterized in that: The conventional traction cable unit internal force between traction cable nodes j to j+1 Calculate as follows: In the formula, The original length of the traction rope unit; l j : The length of the traction cable between the jth node and the j+1th node in the current time step; EA t : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

20. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 17, wherein: When the traction cable unit is a sliding traction cable unit, the force of the traction cable unit on the traction cable node j is The calculation method is as follows: In the formula, e j : The unit vector from cable node j to j+1; Internal force of the sliding cable unit between cable nodes j to j+1.

21. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 20, characterized in that: When the traction cable unit is a sliding traction cable unit, the internal force of the sliding traction cable unit between the traction cable nodes j to j+1 Calculate as follows: In the formula, Internal force of the sliding traction cable unit with one contact point between traction cable nodes j to j+1; B': the third contact point; l j,B' : The length from the traction cable node to the third contact point; l B',j+1 : The length from the third contact point to the traction cable node j+1; Given the initial length of the traction cable unit; EA l : The product of the elastic modulus and the cross-sectional area of ​​the traction cable.

22. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 3, characterized in that: The acceleration of the node at the nth time step Calculate as follows: In the formula, x n+1 : The position vector of the node at the n+1th time step; x n : The position vector of the node at the nth time step; x n-1 : The position vector of the node at the n-1th time step; The velocity of the node at the nth time step Calculate as follows:

23. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 22, characterized in that: The node position vector at the n+1th time step is calculated as follows: Where, c1: first damping correlation coefficient; c2: second damping correlation coefficient; Among them, the first damping correlation coefficient c1 is calculated according to the following formula: The second damping correlation coefficient c2 is calculated as follows:

24. The method for calculating coupled dynamics of a multi-carrying freight ropeway according to claim 4, characterized in that: The deflection angle of the load at the n+1th time step is calculated as follows: In the formula, ω n+1 : deflection angle of the load at the n+1th time step; ω n : deflection angle of the load at the nth time step; ω n-1 : deflection angle of the load at the n-1th time step; I c : Moment of inertia of the load, W n : The torque of the load at the nth time step; c1: The first damping correlation coefficient; c2: The second damping correlation coefficient; h: The time increment step; Among them, the first damping correlation coefficient c1 is calculated according to the following formula: The second damping correlation coefficient c2 is calculated as follows:

25. A coupled power calculation system for a multi-carrying freight ropeway, characterized in that: It includes a parameter module, a first calculation module and a second calculation module; Parameter module: used for setting calculation parameters based on the freight ropeway; The first calculation module is used to calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment acting on the load at the current time step according to the calculation parameters; The second calculation module is used to increase the time step according to the preset time increment step length based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load at the current time step, and calculate the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load until the preset time period ends; The method of increasing the time step according to a preset time increment step based on the calculation parameters and the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in the current time step, and calculating the resultant force acting on the nodes of the load-bearing cable / traction cable and the resultant rotational moment of the load in each time step includes: Using the central difference method, in the current time step, the calculation parameters and the resultant force are introduced into the pre-established node motion equation, the node position vector of the load-bearing cable in the next time step is calculated, and the resultant force acting on the node of the load-bearing cable is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the load-bearing cable in each time step in turn; Using the central difference method, the calculation parameters and the resultant force are introduced into the node motion equation at the current time step, the node position vector of the traction cable at the next time step is calculated, and the resultant force acting on the traction cable node is calculated according to the position vector; increasing the time step, and calculating the node position vector and the resultant force acting on the traction cable at each time step in turn; Using the central difference method, the calculation parameters and the resultant torque are introduced into the pre-established load rotation equation at the current time step, the deflection angle of the load at the next time step is calculated, and the resultant torque of the load at the same time step is calculated according to the deflection angle; the time step is increased, and the resultant torque of the load at each time step is calculated in sequence; When the node is a load-bearing cable node, the resultant force acting on the load-bearing cable node at the nth time step is calculated as follows: In the formula, When the node is a load-bearing cable node, the resultant force acts on the load-bearing cable node at the nth time step; The external force on the load-bearing cable node i on the rth load-bearing cable; The force exerted by the load-bearing cable unit on the load-bearing cable node i on the rth load-bearing cable; r: the number of load-bearing cables; When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step is calculated as follows: In the formula, F Tj n : When the node is a traction cable node, the resultant force acting on the traction cable node at the nth time step; External force on the traction cable node j; The force of the traction cable unit on the traction cable node j; The resultant moment of the load at the nth time step is calculated as follows: Where W n : The resultant moment of the load at the nth time step; The moment of the load-bearing cable at the nth time step; The moment of the traction cable on the load at the nth time step; The moment caused by the load gravity at the nth time step.

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