Vehicle-tower coupled twinning system based on digital twinning technology

Abstract

A vehicle-tower coupled twinborn system based on a digital twinborn technology is characterized in that a scale model and a software model are arranged, the scale model is in wireless communication connection with the software model, the scale model and the software model form the vehicle-tower coupled twinborn system, and initial parameters are consistent; a variable-amplitude trolley in the reduced scale model is provided with a sensor module, and the sensor module collects acceleration data, speed data and moving length data of the variable-amplitude trolley; the software model acts speed and moving length data on itself to realize twin synchronization with the reduced scale model, and outputs acceleration response data of the trolley unit; and the comparison detection module compares the acceleration response data of the variable amplitude trolley with the acceleration response data of the trolley unit, and adjusts the elastic modulus parameter of the model arm in the software model according to the comparison result. The method has the advantages that a model basis and a new research form are provided for simulation test research of the tower crane, and the research and detection cost is reduced while the accuracy and the reliability of a simulation detection result are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of damage detection of tower cranes, and in particular to a vehicle-tower coupling twin system based on digital twin technology. Background Art

[0002] In modal parameter identification, different-sized and different-precision structures need to select different identification methods according to the actual situation. Generally speaking, for short and simple structures, accurate modal parameters can be obtained by either frequency-domain or time-domain methods. However, for large and complex structures such as flat-top cranes, to ensure the accuracy of the identification results, multiple model experiments or on-site experiments must be carried out.

[0003] For the experimental method of identifying modal parameters of structures, the direct method, i.e., the impact method, is usually used to obtain the frequencies of the model or the real structure. The impact method uses a hammer to strike the same impact point at different speeds and with different forces, and then the vibration response is received by sensors arranged on the structure and the signal is transmitted to the signal processor for numerical transformation in the background, and finally the modal parameters of the entire structure are obtained. This method has been gradually popularized since 1970, and a large number of scholars have studied the identification of modal parameters by this impact method. In the initial stage, scholars only estimated the natural frequency, damping, and mode of the structure through this method and the principle of random vibration, and the mode only included the first three-order vibration modes. To study whether adding different working constraints during the impact work would affect the identification of structural modal parameters, researchers found through self-made model experiments that the constraint conditions have a very obvious impact on the identification of structural modal parameters. In 2023, Liang Peng et al. tried to reveal the change laws of the damping ratio and frequency of the structure in vortex-induced vibration through full-scale structure measurement and numerical simulation. In addition to the impact method for identifying modal parameters, modal parameter identification by external environmental excitation or vibration table is also a commonly used method. Feng Zhouquan et al. proposed a Bayesian method for identifying the damping of a structure through external environmental excitation, improving the simplicity and accuracy of measuring the damping of this kind of structure. Others identified the complex three-dimensional vibration modes of irregular buildings through ambient vibration measurement, and used this method to identify the modal parameters of buildings during storms. By arranging 7 sensors on the tower crane structure, the top of the tower was used as the percussion part. The test shows that the results of the three tests of the two-order frequency change identified by external hammering are basically the same. The greater the degree of damage, the smaller the frequency value. Damage has little effect on the frequency inside the tower surface, and it is difficult to judge whether there is damage directly from the change of modal parameters. The displacement data of the model arm was obtained by using a laser Doppler vibrometer (SLDV) test system, and it was found that the frequency and mode of the structure will change normally with time, traffic flow, and environment. In view of the situation that the structural modal parameters change with the environment, Huo Jing et al. proposed to use the Monte Carlo method to determine the confidence intervals of the mode and damping. In order to improve the accuracy of identifying modal parameters by traditional measurement methods, Chen Yonggao et al. used the neighborhood radius and density threshold in the OPTICS clustering algorithm to achieve density clustering of modal parameters in the stability diagram, achieving an improvement in the accuracy of modal parameter identification. Fang Lu et al. proposed a joint algorithm for time-varying modal parameters of structures based on algorithms such as AMD, ARIMA, and MSSET through the acquisition of the response of the structure changing with time. However, under the research of the above-mentioned researchers, the uncertainty of the percussion method is still very high. The environment where the experimental model or the real structure is located, the arrangement position of the sensor observation points, and the signal processing received by the experimental equipment all have a great impact on the identification accuracy of the traditional method.

[0004] As can be seen from the above, the traditional measurement method has received a lot of attention and research. The reason is the large demand in social production. Although the traditional measurement method can better complete the identification of structural modal parameters, the traditional measurement method lacks a specific and effective simulation tower crane. It is impossible to install sensors with high credibility in a reasonable proportional relationship and position relationship, consuming a large amount of manpower and material resources, and still difficult to meet the simulation needs of tower crane detection; at the same time, the parameters of the traditional software simulation model are difficult to accurately adjust, affecting the accuracy of the model output results. Summary of the Invention

[0005] A vehicle-tower coupled twin system based on digital twin technology provided by the present invention can improve the accuracy and reliability of the simulation detection results of tower cranes by constructing a vehicle-tower coupled twin system.

[0006] To achieve the above object, a vehicle-tower coupled twin system based on digital twin technology provided by the present invention is characterized in that: a scaled model and a software model are provided, the scaled model is wirelessly communicatively connected to the software model, the scaled model and the software model form a vehicle-tower coupled twin system, and their initial parameters are the same;

[0007] A sensor module is provided on the luffing trolley in the scaled model. The sensor module collects the acceleration response data a of the luffing trolley in real time and transmits it to the comparison and detection module. The sensor module also collects the speed data and the moving length data in real time and transmits them to the software model;

[0008] The software model is used to update the speed and moving length data in real time, achieve twin synchronization with the scaled model, and output the acceleration data a' of the trolley unit in the software model to the comparison and detection module;

[0009] The comparison and detection module is used to compare the acceleration response data a with the acceleration data a', and adjust the elastic modulus parameter of the model arm in the software model according to the comparison result, so that the difference is less than 5%, and determine the twin synchronization model with the best coupling effect.

[0010] Through the above design, the scaled model and the software model form a vehicle-tower coupling twin system. The two realize real-time data transmission through wireless or wired communication methods. The software model dynamically updates the model parameters according to the speed and moving length data of the luffing trolley, and outputs the acceleration response data of the trolley unit in the software model;

[0011] By comparing the directly measured acceleration response data a with the acceleration data a' calculated by the software model, the elastic modulus parameter in the software model is finely adjusted according to the comparison result to ensure the accuracy of the acceleration data a' output by the software model.

[0012] When the difference between the acceleration response data a and the acceleration data a' is less than 5% after the adjustment of the elastic modulus parameter, a vehicle-tower coupling twin system with the best coupling effect is determined, effectively solving the problem that it is difficult to accurately detect the actual elastic modulus of the scaled tower crane model, and thus there is a deviation between the elastic modulus parameter set in the software model and the actual elastic modulus, resulting in inaccurate acceleration data a' output by the software model.

[0013] The acceleration response data a and the acceleration data a' can also be used for the simulation detection of the modal parameters of the tower crane model and the subsequent damage identification simulation detection of the tower crane model.

[0014] Preferably: The scaled model is provided with a tower crane model, a luffing trolley and a motor module. The tower crane model includes a tower body model and a model arm. The bottom of the tower body model is fixed to the ground. The top of the tower body model is welded to the fixed end of the model arm. The free end of the model arm faces the motor module. The motor module includes a motor, and the motor is fixed on the motor base;

[0015] A fixed pulley is installed at the upper end of the tower body. A luffing trolley is slidably installed on the model arm. The fixed pulley, the luffing trolley and the driving wheel of the motor are on the same horizontal straight line, and the three are connected by a belt to form a horizontal sliding system for the luffing trolley.

[0016] Through the above design, the tower crane and the luffing trolley form a vehicle-tower coupling system, realizing the externalization of driving power, simplifying the unnecessary installation structure of the trolley, and fully ensuring the technical effect of non-interference detection of the trolley. The fixed pulley, the belt and the motor are used to drive the luffing trolley to move horizontally and uniformly on the model arm. Furthermore, the acceleration response and the moving length data generated by the luffing trolley during the movement are detected in real time through a sensor. The detection module is used to identify the modal parameters of the tower crane model according to the acceleration response and the moving length data.

[0017] Preferably, a tower crane base is provided at the bottom of the tower body model. The lower surface of the tower crane base fits the ground and is fixed to the ground by tower crane base bolts. Four vertical columns perpendicular to the ground are welded on the upper surface of the tower crane base, and a cross column is welded between two adjacent columns;

[0018] The tower crane base cooperates with the tower crane base bolts to fix the tower crane to the ground.

[0019] The top of the column is welded with a tower crane top seat. An assembly plate is fixed on the upper surface of the tower crane top seat by assembly bolts. The fixed pulley is fixed on the lower surface of the tower crane top seat; the assembly plate is welded to the fixed end of the model arm;

[0020] The assembly plate is used to realize the assembly of the model arm and the tower crane.

[0021] The model arm is provided with two lower cross bars and one upper cross bar, which are arranged in a triangular shape to form a triangular frame, and connecting rods are welded between any two cross bars;

[0022] Pulley tracks are arranged on the outer sides of the two lower cross bars;

[0023] The connecting rods are used to improve the firmness of the model arm, and the pulley tracks are used to ensure that the luffing trolley can run normally on the model arm. Ensure the reliability of the whole model data detection.

[0024] The luffing trolley is provided with a square car plate. Vertical limiting hanging arms are welded at the four corners of the square car plate. Wheels are installed on the inner sides of the four limiting hanging arms. The four wheels are opposite to each other in pairs, and two wheels are matched to roll on each pulley track;

[0025] A belt hole is provided at each of the front and rear ends of the square vehicle board. One end of the belt is fixed to one belt hole, and the other end of the belt is fixed to the other belt hole after passing around the fixed pulley and the driving wheel.

[0026] The belt passes around the fixed pulley and the driving wheel to form a smooth driving system. Then, a motor is used to control the driving wheel to drive the luffing trolley to move smoothly, and external force is used for driving, eliminating the vibration interference of the trolley's own motor or the tower crane model motor.

[0027] Preferably: The software model is provided with a beam part and a trolley unit. The beam part corresponds to the model arm, and the trolley unit corresponds to the luffing trolley;

[0028] The beam part is composed of n beam units, and one beam unit and the trolley unit form a vehicle-tower coupling unit.

[0029] The vehicle-tower coupling unit well simulates the coupling effect between the vehicle and the tower.

[0030] The vehicle-tower coupling unit has 5 degrees of freedom, and the 5 degrees of freedom are respectively the vertical displacement u A and the rotational displacement θ A of the left end node of the beam unit, the vertical displacement u B and the rotational displacement θ B of the right end node of the beam unit, and the vertical displacement q v of the luffing trolley.

[0031] Preferably: The sensor module includes an acceleration sensor, a speed sensor and a displacement sensor. The acceleration sensor is arranged on the luffing trolley, and the acceleration sensor collects the acceleration response data a of the longitudinal jump of the luffing trolley in real time. The speed sensor is installed on the fixed pulley or the driving wheel, and the speed sensor collects the speed data of the luffing trolley walking horizontally along the beam in real time;

[0032] The displacement sensor is arranged on the wheels of the luffing trolley, and the displacement sensor collects the moving length data of the luffing trolley in real time. This displacement sensor is a rotary encoder wheel.

[0033] By using the sensor module to collect various parameters of the scaled model in real time, the real acquisition of simulation data is realized, meeting the requirements of the simulation twin system for reliable twin data, and effectively improving the accuracy and reliability of the simulation detection results.

[0034] Preferably: The initial parameters include the model arm length l, the mass per unit length m q , the elastic modulus E and the cross-sectional moment of inertia I, as well as the mass m v , the stiffness k v and the speed v of the luffing trolley.

[0035] Preferably, the expression of the vehicle-tower coupling unit is as follows:

[0036]

[0037] Rewrite formula (26) as:

[0038]

[0039]

[0040] where formula (28) represents the beam element expression, {u b} is the displacement array of the beam element, {u b} = {u A θ A u B θ B}, u A and θ A represent the degrees of freedom of the left end node of the beam element, and u B and θ B represent the degrees of freedom of the right end node of the beam element; is the first derivative of {u b}, is the second derivative of {u b}, m b is the mass matrix of the beam element, k b is the stiffness matrix of the beam element, and c b is the damping matrix of the beam element;

[0041] Formula (29) represents the trolley element expression, q v is the vertical displacement generated by the luffing trolley during its own operation, m v is the mass of the luffing trolley, k v is the stiffness of the luffing trolley, c v is the damping of the luffing trolley, v is the speed of the luffing trolley, is the first derivative of q v and is the second derivative of q v . {N} is the distribution coefficient of the forces on the wheels in the vertical displacements and rotational displacements at both end nodes, g is the acceleration due to gravity, {N'} is the first derivative of {N}, and the superscript "T" represents the matrix transpose.

[0042] Preferably, the value of {N} is the Hermite interpolation polynomial, and the result after cubic interpolation is:

[0043]

[0044] The mass matrix m of the beam elementb The expression is as follows:

[0045]

[0046] The stiffness matrix k of the beam element b The expression is as follows:

[0047]

[0048] The damping matrix c of the beam element b The expression is as follows:

[0049] c b = a0m b + a1k b (14)

[0050] Wherein, represents the length mass of the vehicle-tower coupling unit, EI is the elastic stiffness of the beam element, α0 and α1 represent the damping ratio constants, the unit of α0 is s, and the unit of α1 is s -1 .

[0051] Preferably: The process of assembling n beam elements and a trolley element into the software model is as follows:

[0052] According to the formula (28), n beam elements are assembled to obtain the beam part; on the basis of the formula (28), the formula (29) is added to assemble the luffing trolley and the beam part;

[0053] The software model consists of two parts, one part is the beam part and the other part is the luffing trolley. Therefore, when assembling the software model, the two parts are assembled first, and then the luffing trolley is assembled on the beam part to complete the overall assembly.

[0054] The assembly of the beam part includes the assembly of the mass matrix, the stiffness matrix and the damping matrix, and the assembly methods of the mass matrix, the stiffness matrix and the damping matrix are the same;

[0055] Among them, the assembly method of the stiffness matrix is as follows:

[0056] First, according to the degree-of-freedom coding order, the stiffness coefficients of the right node of the s-th beam element and the left node of the s+1-th beam element are superimposed and calculated, that is, the stiffness coefficients at the intersection nodes of the two connected beam elements are superimposed and assembled to complete the process of converting from the element stiffness matrix to the global stiffness matrix;

[0057] Secondly, in order to facilitate the assembly of the stiffness matrix of the luffing trolley, the luffing trolley degree of freedom q in the formula (29) v and the beam degree of freedom {u bSwap the order of {}, and the following formula is obtained after adjustment:

[0058]

[0059] Among them, the vertical displacement of the luffing trolley is differentiated twice to obtain the acceleration response of the luffing trolley

[0060] According to the moving position of the luffing trolley on the beam part over time, add the stiffness matrix of the luffing trolley to the element stiffness matrix of the beam element corresponding to the position where it is located, and update the element stiffness matrix of the beam element on the overall stiffness matrix, thereby completing the update of the overall stiffness matrix.

[0061] The beneficial effects of the present invention are: by constructing a vehicle-tower coupled twin system, realizing the twin mapping of the scaled model on the simulation system, it is possible to accurately detect and identify the modal parameters of the tower crane model by installing only a small number of sensors, providing a model basis and a new research form for the simulation test research of tower cranes. While effectively improving the accuracy and reliability of the simulation test results, it also reduces the research and detection costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is the structural block diagram of the present invention;

[0063] Figure 2 is the schematic diagram of the vehicle-tower coupling unit structure in the embodiment;

[0064] Figure 3 is the schematic diagram of the rigid wheel in the embodiment;

[0065] Figure 4 is the schematic diagram of the degree-of-freedom coding of the first part of the software model in the embodiment;

[0066] Figure 5 is the schematic diagram of the degree-of-freedom coding of the second part of the software model in the embodiment;

[0067] Figure 6 is the schematic diagram of the ordinary beam assembly in the first stage of the embodiment;

[0068] Figure 7 is the schematic diagram of the luffing trolley assembly in the second stage of the embodiment;

[0069] Figure 8 is the comparison diagram of the acceleration response of the luffing trolley in the embodiment;

[0070] Figure 9 is the comparison diagram of the acceleration response of the flat-top tower crane in the embodiment;

[0071] Figure 10 is the three-dimensional structure schematic diagram of the scaled model in the embodiment;

[0072] Figure 11 The front view of the scale model in the embodiment;

[0073] Figure 12 The schematic structural diagram of the luffing trolley in the embodiment. Specific implementation manners

[0074] The present invention will be further described in detail below with reference to the accompanying drawings and specific examples. The following embodiments or drawings are used to illustrate the present invention, but not to limit the scope of the present invention.

[0075] As Figure 1 shown: A scale model and a software model are provided. The scale model is wirelessly communicatively connected to the software model. The scale model and the software model form a vehicle-tower coupled twin system, and their initial parameters are the same;

[0076] A sensor module is provided on the luffing trolley in the scale model. The sensor module collects the acceleration response data a of the luffing trolley in real time and transmits it to the comparison and detection module. The sensor module also collects the speed data and the moving length data in real time and transmits them to the software model;

[0077] The software model is used to update the speed and moving length data in real time, realize twin synchronization with the scale model, and output the acceleration data a' of the trolley unit in the software model to the comparison and detection module;

[0078] The comparison and detection module is used to compare the acceleration response data a with the acceleration data a', and adjust the elastic modulus parameter of the model arm in the software model according to the comparison result.

[0079] The software model is provided with a beam part and a trolley unit. The beam part corresponds to the model arm 12, and the trolley unit corresponds to the luffing trolley;

[0080] The beam part is composed of n beam units. One beam unit and the trolley unit form a vehicle-tower coupling unit.

[0081] The sensor module includes an acceleration sensor, a speed sensor, and a displacement sensor. The acceleration sensor is provided on the luffing trolley. The acceleration sensor collects the acceleration response data a of the longitudinal jump of the luffing trolley in real time. The speed sensor is installed on the fixed pulley. The speed sensor collects the speed data of the luffing trolley walking transversely along the beam in real time;

[0082] The displacement sensor is provided on the wheel of the luffing trolley. The displacement sensor collects the moving length data of the luffing trolley in real time. The speed sensor and the displacement sensor are rotary encoding wheels.

[0083] The initial parameters include the length l of the model arm, the mass m per unit length q , the elastic modulus E, the moment of inertia I of the cross-section, and the mass m of the luffing trolley v , the stiffness k v , and the speed v.

[0084] As Figure 10 , Figure 11 shown: The scaled model is provided with a tower crane model 1, a luffing trolley 2, and a motor module 3. The tower crane model 1 includes a tower body model 11 and a model arm 12. The bottom of the tower body model 11 is fixed to the ground, and the top of the tower body model 11 is welded to the fixed end of the model arm 12. The free end of the model arm 12 faces the motor module 3. The motor module 3 includes a motor, and the motor is fixed on a motor base 31;

[0085] A fixed pulley 5 is installed at the upper end of the tower body 11. A luffing trolley 2 is slidably installed on the model arm 12. The fixed pulley 5, the luffing trolley 2, and the driving wheel of the motor are on the same horizontal straight line, and the three are connected by a belt 4 to form a horizontal sliding system for the luffing trolley 2.

[0086] The bottom of the tower body model 11 is provided with a tower crane base 13. The lower surface of the tower crane base 13 fits the ground and is fixed to the ground by tower crane base bolts. Four vertical columns perpendicular to the ground are welded on the upper surface of the tower crane base 13, and a cross column is welded between adjacent two vertical columns.

[0087] The top of the vertical column is welded with a tower crane top base 14. An assembly plate is fixed on the upper surface of the tower crane top base 14 by assembly bolts. The fixed pulley 5 is fixed on the lower surface of the tower crane top base 14; the assembly plate is welded to the fixed end of the model arm 12.

[0088] The model arm 12 is provided with two lower cross bars 15 and an upper cross bar 16, and the three are arranged in a triangular frame. Connecting rods are welded between any two cross bars;

[0089] Pulley tracks are arranged on the outer sides of the two lower cross bars 15.

[0090] The motor module 3 is provided with a motor base 31 and a motor 6. The bottom of the motor base 31 is provided with a motor base 32. The lower surface of the motor base 32 fits the ground and is fixed to the ground by motor base 32 bolts. Four circular vertical columns perpendicular to the ground are welded on the upper surface of the motor base 32, and the top of the circular vertical columns is welded with a motor top base 33.

[0091] A jacking plate 34 is provided on the motor top seat 33. One end of the jacking plate 34 close to the model arm 12 is hinged to the motor top seat 33. A threaded jacking hole is provided at the other end of the jacking plate 34 away from the model arm 12. A jacking screw 35 is inserted into the threaded jacking hole. The nut end of the jacking screw 35 is located on the upper surface of the jacking plate 34, and the lower end of the jacking screw 35 abuts against the upper surface of the motor top seat 33.

[0092] The jacking plate and the jacking screw cooperate to slightly adjust the position of the motor up and down to ensure that the belt remains horizontal.

[0093] As Figure 10 、 Figure 12 shown: The luffing trolley 2 is provided with a square car plate 21. Vertical limiting hanging arms 22 are welded at the four corners of the square car plate 21. Wheels 23 are installed inside the four limiting hanging arms 22. The four wheels 23 are pairwise opposite, and two wheels 23 roll on each pulley track.

[0094] One belt hole 24 is provided at the front and rear ends of the square car plate 21 respectively. One end of the belt 4 is fixed to one belt hole 24. After the other end of the belt 4 bypasses the fixed pulley and the driving wheel, it is fixed to the other belt hole 24.

[0095] In order to more accurately analyze the modal parameters of the overall tower crane, the tower crane is discretized into multiple units, and it is assumed that the luffing trolley only acts on one unit. In order to more realistically simulate the coupling situation between the tower crane and the luffing trolley in reality, the stiffness and damping of the luffing trolley will be considered. Since the luffing trolley and the model arm are in contact through steel wheels in real life, the stiffness of the luffing trolley will be taken as approaching infinity.

[0096] The car-tower coupling unit well reflects the coupling relationship between the luffing trolley and the model arm. In order to facilitate subsequent finite element simulation, the beam part of the car-tower coupling unit is assumed to be a beam element. The degrees of freedom of the entire car-tower coupling unit can be seen from Figure 2 to be 5 degrees of freedom. This is because the lateral displacement degrees of freedom at the nodes are not considered in this embodiment, so there are 4 degrees of freedom for the two nodes. At the same time, the luffing trolley also belongs to a separate structural part, and its uniform motion will also cause vertical displacement of itself and the model arm, which is the 5th degree of freedom.

[0097] As Figure 2 shown: The car-tower coupling unit is composed of a luffing trolley and a beam element. The luffing trolley is simplified into a mass of m v , stiffness of k v , damping of c v , wheel mass of m wThe calculation model, the position where the luffing trolley contacts the beam element is at x from the left end of the beam element c At this point, this position changes with the moving speed and time of the luffing trolley. Then, the motion equation of the luffing trolley can be expressed as:

[0098]

[0099] Among them, q v is the vertical displacement generated when the luffing trolley works by itself. Since there is no spring in the simplified calculation model of the luffing trolley, the vertical displacement q w and q v are the same;

[0100] In reality, the luffing trolley and the tower crane are connected and move through steel wheels, and the contact surface is a point contact. It is simulated as a schematic diagram of a rigid wheel as Figure 3 shown. Since the wheel is rigid, there is no elastic restoring force between the top of the wheel and the luffing trolley, and it is only affected by the damping force F1; at the same time, due to the interaction relationship between the model arm and the luffing trolley, the wheel will also be subjected to the reaction force p1 from the model arm; then, the expression of the motion equation of the wheel of the luffing trolley is:

[0101]

[0102] Among them, F1 can be expressed as:

[0103] The motion equation of the car-tower coupling unit is as follows:

[0104]

[0105] Among them, mb represents the consistent mass matrix of the beam element, cb represents the damping matrix of the beam element, k b represents the stiffness matrix of the beam element, {u b} represents the displacement column array of the ordinary unit beam, and its value is:

[0106] {u b} = {u A θ A u B θ B} (5)

[0107] Among them, u A and θ A represent the left node degrees of freedom of the ordinary unit beam, and u B and θ B represent the right node degrees of freedom of the ordinary unit beam, the right endpoint degrees of freedom.

[0108] The value of {N} is the Hermite interpolation polynomial, and the result after cubic interpolation is as follows:

[0109]

[0110] Here, {N} is the distribution coefficient of the vertical displacement and rotational displacement at both ends of the force on the wheel, which is related to the position x of the wheel c and the length L of the beam element;

[0111] For the vehicle-tower coupling element, its consistent mass matrix can be obtained in the following way:

[0112] Assume that the left end of the ordinary beam is subjected to a unit angular acceleration The acceleration distribution along the beam length is:

[0113]

[0114] Among them, ψ(x) is the displacement shape function at the nodes of the ordinary beam. According to D'Alembert's principle, the calculation result of the inertial force resisting this acceleration is:

[0115]

[0116] The nodal inertial force generated by this acceleration is calculated from the distributed inertial force in formula (8) through the virtual displacement principle, which is called the mass influence coefficient associated with the acceleration. Introduce a vertical virtual displacement, and when the external nodal force pa does work equal to the distributed inertial force fI(x) does work, that is, use the following formula:

[0117]

[0118] Then represent the internal virtual displacement with the interpolation function and substitute it into formula (8), and finally derive the mass influence coefficient formula as:

[0119]

[0120] Among them, mij is any mass influence coefficient of any beam segment, i is the number of the beam segment, and j represents the type of displacement degree of freedom at the beam end node.

[0121] Since the vehicle-tower coupling element is a homogeneous ordinary beam structure, its consistent mass matrix is:

[0122]

[0123] Among them, m represents the mass per unit length of the vehicle-tower coupling element;

[0124] The stiffness matrix of the beam elementkb Calculated by a method similar to the mass coefficient of the analysis unit, any stiffness coefficient corresponding to the beam bending can be expressed by the following formula:

[0125]

[0126] where, ψ ″(x) represents the virtual curvature, EI is the elastic stiffness of the beam element, and through the interpolation function, the stiffness matrix of the vehicle-tower coupling element is obtained:

[0127]

[0128] Assuming that the damping is proportional to the combination of the consistent mass matrix and the stiffness matrix, then a simple damping matrix formula can be obtained. This method is called Rayleigh damping, and this method is used to calculate the damping matrix of the beam element cb :

[0129] c b = a0m b + a1k b (14)

[0130] The two coefficients in the above formula are obtained by solving a pair of simultaneous equations:

[0131]

[0132] where, ω m and ω n are two specific frequencies of the known tower crane, ξ m and ξ n are the damping ratios corresponding to the first two frequency values. The relationship between the damping ratio and the frequency is obtained from formula (15) as:

[0133]

[0134] Since it is rarely possible to obtain detailed information on the variation of the damping ratio with frequency, it is usually assumed that the damping ratios applied to the control frequencies of the two tower cranes are the same, i.e., ξ m = ξ n = ξ, and formula (15) is simplified to the following expression:

[0135]

[0136] In the vehicle-tower coupling unit, the luffing trolley will not accidentally fall outside the model arm slide rail, and at the same time, it will not rush out of the slide rail or jump off the slide rail due to excessive speed. Then, for the luffing trolley, there is the following formula:

[0137] q w = u c={N} T {u b}(18)

[0138] Taking the first derivative of the above formula gives:

[0139]

[0140] Taking the second derivative gives:

[0141]

[0142] The following relationships are used in the differentiation of the above two equations:

[0143]

[0144] Substituting equations (19) and (20) into equation (1), the motion equation of the car body can be obtained and expressed as follows:

[0145]

[0146] Then, substituting equations (3), (19), (20), and (22) into equation (2), the contact force between the luffing trolley and the tower crane can be obtained as:

[0147]

[0148] Next, substituting equation (23) into equation (4), the motion equation of the car-tower coupling unit can be expressed as:

[0149]

[0150] Combining equations (22) and (24) into a matrix, the expression of the car-tower coupling unit is as follows:

[0151]

[0152] The above car-tower coupling unit can be used for subsequent damage mode research of tower cranes, and can also be used for luffing trolleys with different structures to identify the frequencies and vibration modes of tower cranes. In most cases, the wheel mass is much smaller than the overall mass of the tower crane, so it can be ignored. Then the above expression of the car-tower coupling unit can be simplified to:

[0153]

[0154] It can be seen from the above formula (26) that the expression of the vehicle-tower coupling unit contains two parts, and all five degrees of freedom of the vehicle-tower coupling unit are taken into account. The five degrees of freedom are the vertical displacement, rotational displacement of the beam end node, and the vertical displacement of the luffing trolley. The vehicle-tower coupling unit well simulates the coupling effect between the vehicle and the tower.

[0155] The expression of the vehicle-tower coupling unit has been derived above. Next, the MATLAB software will be used to simulate the overall software model by combining multiple vehicle-tower coupling units, so as to identify the modal parameters of the tower crane.

[0156] Since a series of programming is required for the MATLAB software, in order to more simply implement the simulation of the software model, especially the simulation of the uniform motion of the luffing trolley, the expression of the vehicle-tower coupling unit is decomposed in this embodiment. According to formula (26), the general formula of the vehicle-tower coupling unit can be rewritten as:

[0157]

[0158] Or the expression of the vehicle-tower coupling unit can also be directly rewritten into two units:

[0159]

[0160] Formulas (28) and (29) are the expressions of the two parts of the vehicle-tower coupling unit respectively. It can be clearly seen that the expression of the luffing trolley is relatively complex because the coupling effect between the luffing trolley and the model arm is expressed through the expression of the luffing trolley in this embodiment.

[0161] The result of the expression of a single vehicle-tower coupling unit has been derived above. Next, the overall model assembly of the software model will be carried out. But before the assembly, the degree-of-freedom coding of the entire model needs to be listed as a whole. The degree-of-freedom coding required in this article is divided into two major parts. The first part is to first consider the software model as composed of countless ordinary beams. At this time, the boundary conditions of the structure are the boundary conditions of a simply supported beam, ignoring the lateral displacement degree of freedom at the node. Then the number of degrees of freedom of the entire software model is 2N + 3, and the (2N + 3)-th degree of freedom is the vertical displacement degree of freedom generated by the luffing trolley itself, as Figure 4 shown. The reason for placing the degree of freedom of the luffing trolley in the degree-of-freedom coding is that, firstly, it can be better divided into two major parts, namely the ordinary beam part and the moving mass block part, and secondly, it is to better realize the coupling effect between the vehicle and the tower and can more quickly and accurately perform the coding of the overall structure.

[0162] As Figure 5As shown, it is a schematic diagram of the change in the overall degrees of freedom after considering the boundary conditions of the software model. This is the second part of the degrees-of-freedom encoding. Since it is a cantilever beam structure, the two ends are respectively a fixed end and a free end. The degrees of freedom of the fixed end are 0, and the degrees of freedom of the free end are 3. Also, because the lateral displacement degrees of freedom are not considered, the degrees of freedom of the free end are 2. The degrees of freedom of each intermediate node have not changed and remain 2. Then the total number of degrees of freedom of the beam element is 2N. Adding the one degree of freedom carried by the luffing trolley, the total number of degrees of freedom of the overall VTI system is 2N + 1. The difference between the two is very important and is an important prerequisite for the subsequent assembly of the vehicle-tower coupling system through MATLAB.

[0163] Next, it is the most important step in implementing vehicle-tower coupling in MATLAB programming, that is, how to assemble the two major units mentioned above. The significance of this step is to form the stiffness matrix, mass matrix, and damping matrix of the vehicle-tower coupling system. However, due to the relatively complex assembly process, in order not to cause confusion in understanding, the entire assembly process will be divided into two stages to gradually complete the assembly of the software model. First, similar to the degrees-of-freedom encoding, the assembly of the ordinary beam structure is carried out first, and the formula used in this part is (28); then, considering the luffing trolley on the structure of the ordinary beam, formula (29) is added.

[0164] Next, the specific processes of the two major assembly stages will be described in detail in combination with the diagrams. First, the first assembly stage is relatively simple, which is to assemble N individual identical beam elements. For the beam element, the same assembly method is used for the overall mass matrix, overall stiffness matrix, and overall damping matrix. In order not to repeat the description, only the assembly method of the overall stiffness matrix will be listed in this article. When the luffing trolley moves uniformly to the (n = 2) beam element, the degrees-of-freedom stiffness coefficients of the left and right nodes of this beam element are shown in Table 1:

[0165] Table 1

[0166]

[0167] As Figure 6As shown, it is a simplified schematic diagram of the first stage of assembly. The horizontal and vertical coordinates of the entire figure are the number of degrees of freedom encoding of the first block. Square blocks are used to represent ordinary beam structures. Since the number of degrees of freedom of an ordinary beam is 4, the side length of this block is also 4×4. That is, the degrees of freedom encoding of the ordinary unit beam with n = 1 are 1, 2, 3, and 4. 1 and 2 are the degrees of freedom at the left end, and 3 and 4 are the degrees of freedom at the right end. It can be clearly seen from the figure that there is an overlap between the first block and the second block, which means that the stiffness coefficients of the right node of the first block and the left node of the second block need to be superimposed. For the first stage, it is actually to superimpose and assemble the stiffness coefficients at the intersecting nodes of ordinary beams in pairs, completing the process of converting from the element stiffness matrix to the global stiffness matrix. Through Figure 6 It can be seen that the number of rows and columns of the global stiffness matrix formed after the completion of the entire first stage of assembly is 2N + 2. The assembly of the luffing trolley will be carried out in the second stage.

[0168] First, before the second stage of assembly, in order to more conveniently assemble the stiffness matrix of the luffing trolley, formula (29) needs to swap the order of the degrees of freedom q of the luffing trolley v and the degrees of freedom {u b} of the beam. After adjustment, the following formula can be obtained:

[0169]

[0170] For the example given in the first stage, the luffing trolley element needs to be added to the beam element with n = 2, which means that the stiffness matrix of the luffing trolley needs to be added to the original element matrix of the ordinary beam, and the stiffness matrix of the overall structure of the software model is complete. It should be noted that N and N′ in formula (30) change with the position xc of the luffing trolley. For the vehicle-tower coupling element proposed in the present invention, how to realize the movement of the luffing trolley element on the beam element is the most crucial step, as Figure 7 shown. First, the position where the luffing trolley element is located needs to be obtained. Then, the element matrix of this beam element will be superimposed with the element matrix of the luffing trolley. Due to the external force of the luffing trolley acting on this beam element, the {N} of this beam element is different from that in the first stage. The latest element matrix is recalculated, and finally the element matrix is superimposed on the global matrix obtained in the first stage.

[0171] The above text described how to stack the luffing trolley unit onto the beam unit. Next, it will explain how to achieve real-time luffing trolley stacking. Assume that the luffing trolley is moving at a constant speed. Therefore, the {N} of the ordinary beam also changes continuously over time, and it is necessary to update {N} in real time according to the time transformation. Assume that the update rate is the same as the trolley moving speed, with a value of Δt. Next, the description of the second-stage luffing trolley matrix assembly path will continue with the example in the above text. When the luffing trolley runs to the beam unit with n = 2, at this time, it is necessary to update the element matrices of the degrees of freedom numbered 3, 4, 5, and 6 of this beam unit. At the same time, the degree of freedom 2N + 3 of the luffing trolley is added to the element matrix of the original beam unit along with the corresponding element matrix, and the result is shown in Table 2. At the same time, the degrees of freedom of all other beam units do not change. When the luffing trolley moves to the next unit, such as n = 3, the corresponding degrees of freedom at this time are 5, 6, 7, 8, and 2N + 3, and then the matrix state at this moment can be updated.

[0172] Table 2

[0173]

[0174]

[0175] Finally, the matrix of the software model is obtained by using each step of the assembly, and then the system matrix within the entire time range can be obtained completely. At this time, the boundary conditions of the cantilever beam are not considered in the software model matrix. Next, as shown in Figure 5 , the boundary conditions are considered. That is, the degrees of freedom of the beam unit when n = 1 are only the vertical and rotational degrees of freedom of the right-end node, and the degrees of freedom of the beam unit when n = N have 4 degrees of freedom. Therefore, the degrees of freedom of the entire software model are 2N + 1. Through accurate boundary conditions, the correct VTI system matrix is extracted from the total matrix. Up to this step, the overall mass matrix, overall stiffness matrix, and overall damping matrix of the final VTI system are calculated. Finally, the response of any degree of freedom of the entire system at any time can be obtained by solving through an appropriate numerical solution method. Commonly used numerical solution methods include the central difference method, fourth-order R - k method, and newmark-β. In this article, the commonly used newmark-β method is adopted to solve the VTI system. In the newmark-β method, it is necessary to calculate the integral constants, as shown below:

[0176] a0 = 1 / (β×dt 2 ) (31)

[0177] a1 = γ / (β×dt) (32)

[0178] a2 = 1 / (β×dt) (33)

[0179] a3 = 1 / (2×β) - 1 (34)

[0180] a4 = γ / β - 1 (35)

[0181] a5 = dt / 2(γ / β - 2) (36)

[0182] a6 = dt×(1 - γ) (37)

[0183] a7 = γ×dt (38)

[0184] Among them, γ represents the coefficient of the weight of the linear change between the initial and final accelerations' influence on the velocity change, γ = 0.25; β represents the coefficient of the weight of the contribution of these initial and final accelerations to the displacement change, β = 0.5; a0 - a7 represent the calculated integral constants, and dt represents the time variation.

[0185] Next, the various parameters of different parts of the adopted software model are as shown in Table 1 below:

[0186] Table 1

[0187]

[0188] According to the above parameter settings, two schemes of theoretical derivation and numerical simulation are used to verify the acceleration response of the luffing trolley for obtaining the modal parameters of the tower crane.

[0189] In the numerical simulation, the software model assembly is realized by using the MATLAB programming software. The frequency of the tower crane is successfully identified by using the response of the luffing trolley, and the body acceleration response values obtained from the theoretical derivation and numerical simulation and the acceleration response values of the flat-top tower crane are compared, as Figure 8 、 Figure 9 shown.

[0190] As Figure 8 shown, it includes the acceleration response value of the luffing trolley obtained from the theoretical derivation and the acceleration response value of the luffing trolley obtained through numerical simulation. It can be clearly seen from Figure 8 that there are small differences between the theoretical value and the numerical simulation value: the peak values of the response values are roughly equal, the overall vibration period and vibration waveform are relatively consistent, but there are slight deviations in the response values at the underestimated parts of the vibration waveform. The main reason for the above-described deviation may be that many real external factors are ignored in the theoretical derivation process, including the damping of the luffing trolley itself. At the same time, in the theoretical derivation, the stiffness of the luffing trolley is considered to be 0 in this paper, while in the numerical simulation, the stiffness of the luffing trolley is considered to be close to infinity, and the numerical simulation is closer to the coupling effect between the tower crane and the luffing trolley in reality.

[0191] As Figure 9As shown, it includes the acceleration response values of the tower crane obtained from theoretical derivation and the response values of the tower crane obtained through numerical simulation. It can be clearly seen from Figure 9 that the vibration modes and periods between the two are roughly the same. However, compared with the comparison diagram of the acceleration response of the luffing trolley, there is a deviation in the response value between the simulation value and the theoretical value. Whether at the trough or peak of the vibration waveform of the response value, there is a certain difference in the response value, and moreover, the difference between the two is continuously increasing with the passage of time.

[0192] Figure 8 and Figure 9 both verify the accuracy between the theoretical derivation and the numerical simulation through the comparison of the simulation value and the theoretical value. In addition to the difference in the stiffness value of the luffing trolley, another reason for the above difference is the difference in the methods used. During theoretical derivation, the modal superposition method was used to represent the displacement response value, while in numerical simulation, the Hermite interpolation method was used to obtain the distribution coefficient of the displacement response value at the node of the unit beam. Thus, it can be seen that it is inevitable to have a difference between the theoretical value and the simulation value, and the difference is small and can be ignored. By comparing Figure 8 and Figure 9 it can be seen that the acceleration response of the luffing trolley oscillates more obviously than that of the flat-top tower crane. This is because the luffing trolley directly absorbs energy to generate vibration, and secondly, it is affected by the vibration wave, which makes the amplitude of the high-frequency components in the acceleration of the luffing trolley larger.

[0193] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A vehicle-tower coupled twin system based on digital twin technology, characterized in that: A scaled model and a software model are provided. The scaled model is wirelessly communicatively connected to the software model. The scaled model and the software model form a vehicle-tower coupled twin system, and their initial parameters are the same; A sensor module is provided on the luffing trolley in the scaled model. The sensor module collects the acceleration response data a of the luffing trolley in real time and transmits it to the comparison and detection module. The sensor module also collects the speed data and the moving length data in real time and transmits them to the software model; The software model is used to update the speed and moving length data in real time, achieve twin synchronization with the scaled model, and output the acceleration data a' of the trolley unit in the software model to the comparison and detection module; The comparison and detection module is used to compare the acceleration response data a with the acceleration data a', and adjust the elastic modulus parameter of the model arm in the software model according to the comparison result.

2. The vehicle-tower coupled twin system based on digital twin technology according to claim 1, wherein: The scaled model is provided with a tower crane model (1), a luffing trolley (2) and a motor module (3). The tower crane model (1) includes a tower body model (11) and a model arm (12). The bottom of the tower body model (11) is fixed to the ground. The top of the tower body model (11) is welded to the fixed end of the model arm (12). The free end of the model arm (12) faces the motor module (3). The motor module (3) includes a motor, and the motor is fixed on a motor base (31); A fixed pulley (5) is installed at the upper end of the tower body (11). A luffing trolley (2) is slidably installed on the model arm (12). The fixed pulley (5), the luffing trolley (2) and the driving wheel of the motor are on the same horizontal straight line, and the three are connected by a belt (4) to form a horizontal sliding system of the luffing trolley (2).

3. The vehicle-tower coupled twin system based on digital twin technology according to claim 2, wherein: The bottom of the tower body model (11) is provided with a tower crane base (13). The lower surface of the tower crane base (13) fits the ground and is fixed to the ground by tower crane base bolts. Four vertical columns perpendicular to the ground are welded on the upper surface of the tower crane base (13), and a cross column is welded between adjacent two columns; The top of the column is welded with a tower crane top seat (14). An assembly plate is fixed on the upper surface of the tower crane top seat (14) by assembly bolts. The fixed pulley (5) is fixed on the lower surface of the tower crane top seat (14); The assembly plate is welded to the fixed end of the model arm (12); The model arm (12) is provided with two lower cross bars (15) and an upper cross bar (16), and the three are arranged in a pin shape to form a triangular frame. Connecting rods are welded between any two cross bars; Pulley tracks are provided on the outer sides of the two lower cross bars (15); The luffing trolley (2) is provided with a square car plate (21). Vertical limiting hanging arms (22) are welded at the four corners of the square car plate (21). Wheels (23) are installed on the inner sides of the four limiting hanging arms (22). The four wheels (23) are pairwise opposite, and two wheels (23) are matched with each pulley track to roll; A belt hole (24) is provided at each of the front and rear ends of the square vehicle plate (21). One end of the belt (4) is fixed to one belt hole (24). After the other end of the belt (4) bypasses the fixed pulley and the driving wheel, it is fixed to the other belt hole (24).

4. The vehicle-tower coupled twin system based on digital twin technology according to claim 2, characterized in that: The software model is provided with a beam part and a trolley unit. The beam part corresponds to the model arm (12), and the trolley unit corresponds to the luffing trolley; The beam part is composed of n beam units. One beam unit and the trolley unit form a vehicle-tower coupling unit.

5. The vehicle-tower coupled twin system based on digital twin technology according to claim 2, wherein: The sensor module includes an acceleration sensor, a speed sensor, and a displacement sensor. The acceleration sensor is arranged on the luffing trolley. The acceleration sensor collects the acceleration response data a of the longitudinal jump of the luffing trolley in real time. The speed sensor is installed on the fixed pulley or the driving wheel. The speed sensor collects the speed data of the luffing trolley walking transversely along the beam in real time; The displacement sensor is arranged on the wheel of the luffing trolley. The displacement sensor collects the moving length data of the luffing trolley in real time. This displacement sensor is a rotary encoder wheel.

6. The vehicle-tower coupled twin system based on digital twin technology according to claim 2, wherein: The initial parameters include the length l of the model arm, the mass m per unit length, q the elastic modulus E, the moment of inertia I of the cross-section, and the mass m of the luffing trolley, v the stiffness k, v and the speed v.

7. The vehicle-tower coupled twin system based on digital twin technology according to claim 4, characterized in that: The expression of the vehicle-tower coupling unit is as follows: Rewrite formula (26) as: Among them, formula (28) represents the beam element expression, {u b} is the displacement array of the beam element, {u b} = {u A θ A u B θ B}, u A and θ A represent the degrees of freedom of the left node of the beam element, u B and θ B represent the degrees of freedom of the right node of the beam element; is the first derivative of {u b}, is the second derivative of {u b}, m b is the mass matrix of the beam element, k b is the stiffness matrix of the beam element, c b is the damping matrix of the beam element; Equation (29) represents the trolley unit expression, q v is the vertical displacement generated when the luffing trolley works by itself, m v is the mass of the luffing trolley, k v is the stiffness of the luffing trolley, c v is the damping of the luffing trolley, v is the speed of the luffing trolley, is q v the first derivative, is q v the second derivative, {N} is the distribution coefficient of the vertical displacement and the rotational displacement of the force on the wheels at both ends of the nodes, g is the acceleration due to gravity, {N′} is the first derivative of {N}, and the superscript "T" represents the matrix transpose.

8. The vehicle-tower coupled twin system based on digital twin technology according to claim 7, characterized in that: The value of {N} is a Hermite interpolation polynomial. The result after cubic interpolation is: The mass matrix m of the beam element b has the following expression: The stiffness matrix k of the beam element b has the following expression: The damping matrix c of the beam element b has the following expression: c b = a0m b + a1k b (14) Among them, represents the length mass of the vehicle-tower coupling unit, EI is the elastic stiffness of the beam element, α0 and α1 represent the damping proportionality constants, the unit of α0 is s, and the unit of α1 is s -1 .

9. The vehicle-tower coupled twin system based on digital twin technology according to claim 7, characterized in that: The process of assembling n beam units and one trolley unit into the software model is as follows: According to formula (28), assemble the n beam units to obtain the beam part; on the basis of formula (28), add formula (29) to assemble the luffing trolley and the beam part; The assembly of the beam part includes the assembly of the mass matrix, the stiffness matrix, and the damping matrix. The assembly methods of the mass matrix, the stiffness matrix, and the damping matrix are the same; Among them, the assembly method of the stiffness matrix is as follows: First, according to the degree-of-freedom coding order, perform a superposition operation on the stiffness coefficients of the right node of the s-th beam unit and the left node of the s+1-th beam unit, that is, perform a superposition assembly on the stiffness coefficients at the intersection nodes of the two connected beam units to complete the process of converting from the element stiffness matrix to the global stiffness matrix; Secondly, to facilitate the assembly of the stiffness matrix of the luffing trolley, the degrees of freedom q of the luffing trolley in Equation (29) v and the degrees of freedom {u b} of the beam are reordered. After adjustment, the following equation is obtained: Among them, the vertical displacement of the luffing trolley is differentiated twice to obtain the acceleration response of the luffing trolley According to the moving position of the luffing trolley on the beam part over time, add the stiffness matrix of the luffing trolley to the element stiffness matrix of the beam unit corresponding to the position where it is located, and update the element stiffness matrix of this beam unit on the global stiffness matrix, thereby completing the update of the global stiffness matrix.

Images