Tower crane frequency vibration mode identification method based on vehicle-tower coupled twinborn system

Abstract

The invention discloses a tower crane frequency vibration mode identification method based on a vehicle-tower coupling twinborn system. The method is characterized by comprising the following steps: constructing an entity vehicle-tower coupling system; according to the initial parameter information of the entity vehicle-tower coupling system, a vehicle-tower coupling software model is constructed, and the entity vehicle-tower coupling system and the vehicle-tower coupling software model form a vehicle-tower coupling twinborn system and are in wireless communication connection; the sensor module collects acceleration response data and moving length data of the amplitude-variable trolley in real time and transmits the acceleration response data and the moving length data to the trolley-tower coupling software model; and the vehicle-tower coupling software model completes synchronous change with the entity vehicle-tower coupling system according to the acceleration response data and the movement length data, and calculates and outputs frequency data and vibration mode data of the tower crane in the entity vehicle-tower coupling system. The method has the effects that the dynamic change of the entity vehicle-tower coupling system can be simulated, and the frequency vibration mode data of the tower crane in the entity vehicle-tower coupling system can be output.

Description

Technical Field

[0001] The present invention relates to the technical field of tower crane damage detection, and particularly to a method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system. Background Art

[0002] At present, we usually adopt lossy and non-destructive detection methods including visual inspection, ray detection, ultrasonic detection, stress testing, magnetic particle detection, acoustic emission detection, etc. to conduct health and safety monitoring on tower cranes. The first step of most of the above-listed methods is to detect the damage location or degree of the tower crane by identifying the modal parameters of the tower crane. It can be seen that in the health and safety monitoring of tower cranes, the modal parameters of the structure are very important.

[0003] In reality, the modal parameters of all objects are similar to human fingerprints and are all different, consisting of countless unique data. The modal parameters of each structure itself usually do not change, such as natural frequency, modal vibration mode, and structural damping, etc. However, when its own structure is damaged, its modal parameters will also change. In theory, this is the reason why damage can be identified by analyzing modal parameters. The main content of modal analysis is actually to perform coordinate transformation on data. It converts the response values originally in the physical coordinates to be described in the defined modal coordinates. Each basis vector in the modal coordinates is the eigenvector of the vibration response in the original physical coordinates. That is to say, the relationship between response vectors can be simply described by using the correlation between each basis vector in this coordinate system.

[0004] However, the computational modal analysis method cannot consider the coupling relationship between each response vector. Therefore, the experimental modal analysis method is often combined with it to identify the damage of the structure. The experimental modal analysis method, as the name implies, is to obtain the response values through on-site tests or model tests and then identify the actual modal parameters of the structure through numerical processing. In recent years, people usually apply an external excitation to the structure to pick up the vibration response values of the structure, and then obtain the modal parameters of the structure through the fast Fourier transform FFT. However, this method has relatively strict environmental requirements, and when using this method to measure large machinery, a large number of test instruments such as sensors are required, the amount of data collected at the measuring points is large, and the data processing is rather cumbersome. Summary of the Invention

[0005] A method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system provided by the present invention can accurately identify the frequency and vibration mode data of the tower crane.

[0006] To achieve the above object, the key of a method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system provided by the present invention is:

[0007] Step 1: Construct an entity vehicle-tower coupling system. The entity vehicle-tower coupling system is provided with a tower crane. An amplitude-variable trolley is arranged on the boom of the tower crane, and a sensor module is arranged on the amplitude-variable trolley.

[0008] Step 2: According to the initial parameter information of the tower crane and the amplitude-variable trolley, construct a vehicle-tower coupling software model. The entity vehicle-tower coupling system and the vehicle-tower coupling software model form a vehicle-tower coupling twin system, and they are wirelessly communication-connected.

[0009] Step 3: The sensor module continuously collects the speed v, mass m v and displacement data of the amplitude-variable trolley, and transmits them to the vehicle-tower coupling software model.

[0010] Step 4: The vehicle-tower coupling software model dynamically adjusts its own data according to the collected speed v, mass m v and moving length data of the amplitude-variable trolley, completes the synchronous change with the entity vehicle-tower coupling system, and outputs the acceleration response data of the amplitude-variable trolley Then the acceleration response data is transmitted to the detection module.

[0011] Step 5: The detection module converts the acceleration response data into an acceleration spectrogram through fast Fourier transform (FFT), and outputs the frequency data and vibration mode data of the tower crane according to the acceleration spectrogram.

[0012] Through the above design, by constructing a vehicle-tower coupling twin system, mapping the real-time state of the entity vehicle-tower coupling system into the vehicle-tower coupling software model, the dynamic changes of the tower crane in the entity vehicle-tower coupling system can be intuitively understood, and according to the changes in the frequency and vibration mode data output by the vehicle-tower coupling software model, the operation plan of the entity vehicle-tower coupling system can be reasonably adjusted, thereby prolonging the service life of the tower crane and avoiding safety accidents.

[0013] Meanwhile, by continuously collecting the speed v, mass m v and displacement data of the entity vehicle-tower coupling system, and then outputting the acceleration response data of the amplitude-variable trolley through the vehicle-tower coupling software model, compared with the method of directly collecting the acceleration response data of the amplitude-variable trolley through an acceleration sensor, the situation of inaccurate acceleration detection caused by the vibration of the boom due to the movement of the amplitude-variable trolley is effectively avoided, and the adverse impact of the boom vibration on the frequency and vibration mode detection of the tower crane is eliminated.

[0014] Preferably, in the step 1, the sensor module includes a speed sensor, a weighing sensor, and a displacement sensor;

[0015] Among them, the speed sensor is arranged on the driving wheel of the luffing drive motor, and is used for collecting the speed response data of the luffing trolley in real time and transmitting it to the vehicle-tower coupling software model;

[0016] The displacement sensor is arranged on the wheel of the luffing trolley, and is used for collecting the moving length data of the luffing trolley in real time. The displacement sensor is a rotary encoder wheel.

[0017] By collecting the moving length data of the luffing trolley in real time through the displacement sensor, not only can the specific position of the luffing trolley on the boom be accurately detected, but also the problem of cumulative error in calculating the displacement length by multiplying speed and time can be effectively avoided, thereby improving the accuracy of the displacement length data.

[0018] The speed sensor and the displacement sensor ensure the real-time collection of the dynamic data of the physical vehicle-tower coupling system, provide a real and reliable data source for the vehicle-tower coupling software model, realize the twin synchronization of the vehicle-tower coupling twin system, and ensure the accuracy and reliability of the output frequency and vibration mode data.

[0019] Preferably, a hook is arranged on the luffing trolley, a heavy object is hung on the hook, and a weighing sensor is also arranged on the hook. The weighing sensor collects the heavy object mass data and transmits it to the vehicle-tower coupling software model.

[0020] The vehicle-tower coupling software model calculates and updates the mass m of the luffing trolley in real time according to the heavy object mass data v .

[0021] Preferably, in the step 2, the initial parameter information includes the boom length l of the tower crane, the mass per unit length elastic modulus E and moment of inertia I of the cross section, as well as the mass m of the luffing trolley v , stiffness k v , speed v;

[0022] Among them, the mass m of the luffing trolley v is the sum of the self-mass of the luffing trolley, the mass of the hook and the mass of the heavy object.

[0023] Preferably, the vehicle-tower coupling software model is provided with a vehicle-tower coupling unit. The vehicle-tower coupling unit includes a beam unit and a trolley unit. The vehicle-tower coupling software model is composed of n beam units and one trolley unit;

[0024] n beam elements are assembled to form the beam part of the vehicle-tower coupling software model, and the beam part corresponds to the boom structure of the tower crane in the physical vehicle-tower coupling system. The trolley element corresponds to the luffing trolley structure in the physical vehicle-tower coupling system.

[0025] The vehicle-tower coupling element well simulates the coupling effect between the vehicle and the tower.

[0026] The vehicle-tower coupling element 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 element, the vertical displacement u B and the rotational displacement θ B of the right end node of the beam element, and the vertical displacement q v of the luffing trolley.

[0027] Preferably, the expression of the vehicle-tower coupling element is as follows:

[0028]

[0029] Rewrite formula (26) as:

[0030]

[0031] 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 , θ A represent the degrees of freedom of the left end node of the beam element, and u B , 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, c b is the damping matrix of the beam element;

[0032] Formula (29) represents the trolley element 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, and v is the speed of the luffing trolley. is q v The first derivative is is q v The second derivative. {N} is the distribution coefficient of the vertical displacement and rotational displacement of the force on the wheel at both ends of the node, g is the acceleration due to gravity, {N'} is the first derivative of {N}, and the superscript "T" represents the matrix transpose.

[0033] Preferably: The value of {N} is the Hermite interpolation polynomial, and the result after cubic interpolation is:

[0034]

[0035] The mass matrix m of the beam element b has the following expression:

[0036]

[0037] The stiffness matrix k of the beam element b has the following expression:

[0038]

[0039] The damping matrix c of the beam element b has the following expression:

[0040] c b = a0m b + a1k b

[0041] where 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 .

[0042] Preferably: The process of assembling n beam elements and a trolley element into the vehicle-tower coupling software model is as follows:

[0043] According to the formula (28), assemble n beam elements to obtain the beam part; on the basis of the formula (28), add the formula (29) to assemble the luffing trolley and the beam part.

[0044] The vehicle-tower coupling software model consists of two parts, one part is the beam part, and the other part is the luffing trolley. Therefore, when assembling the vehicle-tower coupling software model, first assemble the two parts, and then assemble the luffing trolley on the beam part to complete the overall assembly.

[0045] Preferably, 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;

[0046] Among them, the assembly method of the stiffness matrix is as follows:

[0047] 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 element and the left node of the (s + 1)-th beam element, that is, perform superposition assembly on the stiffness coefficients at the intersection node of the two connected beam elements, and complete the process of converting from the element stiffness matrix to the global stiffness matrix;

[0048] Secondly, in order to facilitate the assembly of the stiffness matrix of the luffing trolley, swap the order of the degrees of freedom q v of the luffing trolley and the degrees of freedom {u b} of the beam in formula (29). After adjustment, the following formula is obtained:

[0049]

[0050] Among them, by taking the second derivative of the vertical displacement of the luffing trolley, the acceleration response of the luffing trolley can be obtained

[0051] 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 global stiffness matrix, thereby completing the update of the global stiffness matrix.

[0052] Preferably, in step 4, the output process of the mode data is as follows:

[0053] (1) Calculate the frequency data of the tower crane through the corresponding frequency expression of the tower crane;

[0054] (2) Adopt the band-pass filtering method (BPS) to extract the response data related to the frequency data of the tower crane from the acceleration response information;

[0055] (3) Use the Hilbert transform to obtain the instantaneous amplitude of the response data;

[0056] (4) Obtain the mode data of the tower crane from the instantaneous amplitude.

[0057] The beneficial effects of the present invention are: by constructing a vehicle-tower coupled twin system, the dynamic changes of the physical vehicle-tower coupled system can be simulated, and the frequency and mode data of the tower crane in the physical vehicle-tower coupled system can be output, and the damage identification of the tower crane can be carried out according to the frequency and mode data of the tower crane. Description of the Drawings

[0058] Figure 1 is a schematic flow diagram of the present invention;

[0059] Figure 2 is a schematic diagram of the structure of the vehicle-tower coupling unit in the embodiment;

[0060] Figure 3 is a schematic diagram of a rigid wheel in the embodiment;

[0061] Figure 4 is a schematic diagram of the degree-of-freedom coding of the first part of the vehicle-tower coupling software model in the embodiment;

[0062] Figure 5 is a schematic diagram of the degree-of-freedom coding of the second part of the vehicle-tower coupling software model in the embodiment;

[0063] Figure 6 is a schematic diagram of the assembly of a common beam in the first stage of the embodiment;

[0064] Figure 7 is a schematic diagram of the assembly of a luffing trolley in the second stage of the embodiment;

[0065] Figure 8 is a comparison diagram of the acceleration response of the luffing trolley in the embodiment;

[0066] Figure 9 is a comparison diagram of the acceleration response of a flat-top tower crane in the embodiment;

[0067] Figure 10 is a frequency spectrum diagram of the acceleration response of a flat-top tower crane;

[0068] Figure 11 is a frequency spectrum diagram of the acceleration response of the luffing trolley;

[0069] Figure 12 is a vibration mode diagram of the tower crane recognized by the vehicle body response of the assumed mode method;

[0070] Figure 13 is a vibration mode diagram of the tower crane recognized by the vehicle body response of the analytical method;

[0071] Figure 14 is a vibration mode diagram of the tower crane recognized by the vehicle body response of the Rayleigh-Ritz method. Detailed Description of the Invention

[0072] The present invention will be further described in detail below with reference to the drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but not to limit the scope of the present invention.

[0073] As Figure 1 shown: A method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupling twin system includes the following steps:

[0074] Step 1: Construct an entity vehicle-tower coupling system, which is provided with a tower crane. A luffing trolley is arranged on the boom of the tower crane, and a sensor module is arranged on the luffing trolley;

[0075] Step 2: According to the initial parameter information of the tower crane and the luffing trolley, construct a vehicle-tower coupling software model. The entity vehicle-tower coupling system and the vehicle-tower coupling software model form a vehicle-tower coupling twin system, and they are wirelessly communication-connected;

[0076] Step 3: The sensor module continuously collects the speed v, mass m v and displacement data of the luffing trolley, and transmits them to the vehicle-tower coupling software model;

[0077] Step 4: The vehicle-tower coupling software model dynamically adjusts its own data according to the collected speed v, mass m v and moving length data of the luffing trolley, completes the synchronous change with the entity vehicle-tower coupling system, and outputs the acceleration response data of the luffing trolley Then the acceleration response data is transmitted to the detection module;

[0078] Step 5: The detection module converts the acceleration response data into an acceleration spectrogram through fast Fourier transform (FFT), and outputs the frequency data and vibration mode data of the tower crane according to the acceleration spectrogram.

[0079] In the Step 1, the sensor module includes a speed sensor, a weighing sensor and a displacement sensor;

[0080] Among them, the speed sensor is arranged on the driving wheel of the luffing drive motor, and is used to continuously collect the speed response data of the luffing trolley and transmit it to the vehicle-tower coupling software model;

[0081] The displacement sensor is arranged on the wheel of the luffing trolley, and is used to continuously collect the moving length data of the luffing trolley. The displacement sensor is a rotary encoder wheel.

[0082] A hook is arranged on the luffing trolley, a heavy object is hung on the hook, and a weighing sensor is also arranged on the hook. The weighing sensor collects the mass data of the heavy object and transmits it to the vehicle-tower coupling software model.

[0083] In the Step 2, the initial parameter information includes the boom length l, unit length mass elastic modulus E and section moment of inertia I of the tower crane, and the mass m of the luffing trolley v, stiffness k v , velocity v;

[0084] Among them, the mass m of the luffing trolley v is the sum of the self - mass of the luffing trolley, the mass of the hook and the mass of the heavy object.

[0085] The vehicle - tower coupling software model is provided with a vehicle - tower coupling unit. The vehicle - tower coupling unit includes a beam unit and a trolley unit. The vehicle - tower coupling software model is composed of n beam units and one trolley unit;

[0086] The n beam units are assembled to form the beam part of the vehicle - tower coupling software model. The beam part corresponds to the boom structure of the tower crane in the physical vehicle - tower coupling system. The trolley unit corresponds to the luffing trolley structure in the physical vehicle - tower coupling system.

[0087] In order to analyze the modal parameters of the whole tower crane more accurately, the tower crane is discretized into multiple units, and it is assumed that the luffing trolley only acts on one unit. In order to simulate the coupling situation between the tower crane and the luffing trolley in reality more realistically, the stiffness and damping of the luffing trolley are considered. Since the luffing trolley and the boom are in contact through steel wheels in real life, the stiffness of the luffing trolley will be taken as approaching infinity.

[0088] The vehicle - tower coupling unit well reflects the coupling relationship between the luffing trolley and the boom. For the convenience of subsequent finite - element simulation, the beam part of the vehicle - tower coupling unit is assumed to be a beam unit. The degrees of freedom of the whole vehicle - tower coupling unit can be Figure 2 seen 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 two nodes. At the same time, the luffing trolley also belongs to a separate structural part, and its uniform motion will also cause vertical displacements of itself and the boom, which is the 5th degree of freedom.

[0089] As Figure 2 shown: The vehicle - tower coupling unit is composed of a luffing trolley and a beam unit. The luffing trolley is simplified into a calculation model with a mass of m v , a stiffness of k v , a damping of c v , and a wheel mass of m w . The position where the luffing trolley contacts the beam unit is at a distance x c from the left end of the beam unit. 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:

[0090]

[0091] Among them, q vis the vertical displacement generated by the luffing trolley during its own operation. 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;

[0092] In reality, the luffing trolley and the tower crane are connected and move through steel wheels. The contact surface is a point contact, which is simulated as a schematic diagram of a rigid wheel as shown in Figure 3 . Since the wheel is rigid, there is no elastic restoring force between the top of the wheel and the luffing trolley, and only the damping force F1 acts on it. At the same time, due to the interaction between the boom and the luffing trolley, the wheel will also receive the reaction force p1 from the boom. Then, the motion equation expression of the wheel of the luffing trolley is:

[0093]

[0094] Among them, F1 can be expressed as:

[0095] The motion equation of the car-tower coupling unit is as follows:

[0096]

[0097] Among them, m b represents the consistent mass matrix of the beam element, c b represents the damping matrix of the beam element, k b represents the stiffness matrix of the beam element, {u b} represents the displacement column matrix of the ordinary element beam, and its value is:

[0098] {u b} = {u A θ A u B θ B} (5)

[0099] Among them, u A , θ A represent the left node degrees of freedom of the ordinary element beam, and u B , θ B represent the right node degrees of freedom of the ordinary element beam.

[0100] The value of {N} is the Hermite interpolation polynomial, and the result after cubic interpolation is:

[0101]

[0102] Here, {N} is the distribution coefficient of the force on the wheel at the vertical displacement and rotational displacement of the two end nodes, and is related to the position x cand related to the length L of the beam element;

[0103] For the vehicle-tower coupling element, its consistent mass matrix can be obtained in the following way:

[0104] Assume that the left end of the ordinary beam is subjected to a unit angular acceleration The acceleration distribution along the beam length is:

[0105]

[0106] where ψ(x) is the displacement shape function at the nodes of the ordinary beam. According to D'Alembert's principle, the calculated result of the inertial force resisting this acceleration is:

[0107]

[0108] The nodal inertial force generated by this acceleration is calculated from the distributed inertial force in formula (8) through the principle of virtual displacement, which is called the mass influence coefficient associated with the acceleration. Introduce a vertical virtual displacement, and let the work done by the nodal external force p a be equal to the work done by the distributed inertial force f I (x), that is, use the following formula:

[0109]

[0110] 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:

[0111]

[0112] where m ij is any one of the mass influence coefficients of any beam segment, i is the number of the beam segment, and j represents the jth displacement degree of freedom at the beam end node.

[0113] Since the vehicle-tower coupling element is a homogeneous ordinary beam structure, its consistent mass matrix is:

[0114]

[0115] where represents the mass per unit length of the vehicle-tower coupling element;

[0116] The stiffness matrix k b of the beam element is calculated by a method similar to that for analyzing the element mass coefficient. Any stiffness coefficient corresponding to the beam bending can be expressed by the following formula:

[0117]

[0118] Among them, ψ″(x) represents the imaginary curvature, EI is the elastic stiffness of the beam element. Then, through the interpolation function, the stiffness matrix of the vehicle-tower coupling element is obtained:

[0119]

[0120] Assuming that the damping is proportional to the combination of the consistent mass matrix and the stiffness matrix, a simple damping matrix formula can be obtained. This method is called Rayleigh damping. Using this method to calculate the damping matrix c of the beam element b :

[0121] c = a0m + a1k (14)

[0122] The two coefficients in the above formula are obtained by solving a pair of simultaneous equations:

[0123]

[0124] Among them, ω m and ω n are two specific frequencies of the tower crane that are known, 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:

[0125]

[0126] 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, that is, ξ m = ξ n = ξ. Formula (15) is simplified to the following expression:

[0127]

[0128] In the vehicle-tower coupling element, the luffing trolley will not accidentally fall outside the boom 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:

[0129] q w = u c = {N} T {u b}} (18)

[0130] Taking the first derivative of the above formula can obtain:

[0131]

[0132] Taking the second derivative can obtain:

[0133]

[0134] In the differentiation of the above two equations, the following relationships are utilized:

[0135]

[0136] Substituting formulas (19) and (20) into formula (1), the motion equation of the car body can be obtained and expressed as follows:

[0137]

[0138] Then, substituting formulas (3), (19), (20), and (22) into formula (2), the contact force between the luffing trolley and the tower crane can be obtained as:

[0139]

[0140] Next, substituting formula (23) into formula (4), the motion equation of the car-tower coupling unit can be expressed as:

[0141]

[0142] Combining formula (22) and formula (24) into a matrix, the expression of the car-tower coupling unit is as follows:

[0143]

[0144] The above car-tower coupling unit can be used for subsequent research on the damage mode 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 mass of the wheels 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 as:

[0145]

[0146] It can be seen from the above formula (26) that the expression of the car-tower coupling unit includes two parts, and all five degrees of freedom of the car-tower coupling unit are considered. 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 car-tower coupling unit well simulates the coupling effect between the car and the tower.

[0147] The expression of the above-mentioned car-tower coupling unit has been derived. Next, the MATLAB software will be used to achieve the overall simulation of the car-tower coupling software model by combining multiple car-tower coupling units, so as to identify the modal parameters of the tower crane.

[0148] Since a series of programming is required for MATLAB software, in order to more simply implement the simulation of the vehicle-tower coupling software model, especially the simulation of the luffing trolley moving at a constant speed, 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:

[0149]

[0150] Or the expression of the vehicle-tower coupling unit can also be directly rewritten as two units:

[0151]

[0152] 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 boom is expressed through the expression of the luffing trolley in this embodiment.

[0153] In the above text, the result of the expression of a single vehicle-tower coupling unit is derived. Next, the overall model assembly of the vehicle-tower coupling software model will be carried out. But before assembly, the degree-of-freedom encoding of the entire model needs to be listed as a whole. The degree-of-freedom encoding required in this article is divided into two major parts. The first part is to first consider that the vehicle-tower coupling software model is 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 vehicle-tower coupling 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 encoding is, firstly, that 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 be able to more quickly and accurately encode the overall structure.

[0154] As Figure 5 shown, it is a schematic diagram of the change in the overall degree of freedom after considering the boundary conditions of the vehicle-tower coupling software model. This is the second part of the degree-of-freedom encoding. Since it is a cantilever beam structure, the two ends are respectively a fixed end and a free end. The degree of freedom of the fixed end is 0, and the degree of freedom of the free end is 3. And because the lateral displacement degree of freedom is not considered, the degree of freedom of the free end is 2, and the degrees of freedom of each intermediate node do not change and are still 2. Then the total number of degrees of freedom of the beam element is 2N, plus one degree of freedom carried by the luffing trolley, and 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 implementing the assembly of the vehicle-tower coupling system through MATLAB in the following text.

[0155] Next, it is the most important step in implementing the 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 complexity of the assembly process, in order not to cause confusion in understanding, the entire assembly process will be divided into two stages, and the assembly of the vehicle-tower coupling software model will be completed step by step. First, like the degree-of-freedom coding, 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.

[0156] Next, the specific processes of the two assembly stages will be described in detail in combination with the charts. First, the first assembly stage is relatively simple, which is to assemble N individual identical beam elements. For beam elements, the overall mass matrix, overall stiffness matrix, and overall damping matrix all adopt the same assembly method. 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 degree-of-freedom stiffness coefficients of the left and right nodes of this beam element are shown in Table 1:

[0157] Table 1

[0158]

[0159] As Figure 6 shown, it is a simple schematic diagram of the first assembly stage. The horizontal and vertical coordinates of the entire figure are the numbers of the first block of degree-of-freedom coding. The square blocks are used to represent the ordinary beam structure. Since the number of degrees of freedom of the ordinary beam is 4, the side length of this block is also 4×4, that is, the degree-of-freedom coding of the ordinary unit beam with n = 1 is 1, 2, 3, 4, where 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 pairwise intersection nodes of the ordinary beams to complete the process of converting from the element stiffness matrix to the overall stiffness matrix. Through Figure 6 it can be seen that the rows and columns of the overall stiffness matrix formed after the completion of the entire first-stage assembly are both 2N + 2. The assembly of the luffing trolley will be carried out in the second stage.

[0160] First, before the second-stage 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 of the luffing trolley qv and the degrees of freedom of the beam {u b}, and after adjustment, the following formula can be obtained:

[0161]

[0162] For the example given in the first stage, the luffing trolley unit 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 trolley-tower coupling software model is complete. It should be noted that N and N′ in formula (30) change with the position x of the luffing trolley c moving. For the trolley-tower coupling unit proposed in the present invention, how to realize the movement of the luffing trolley unit on the beam element is the most crucial step, as Figure 7 shown. First, the position where the luffing trolley unit is located needs to be obtained, and then the element matrix of this beam element will be superimposed with the element matrix of the luffing trolley. Since there is an 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, and the latest element matrix is obtained by recalculation. Finally, the element matrix is superimposed on the overall matrix obtained in the first stage.

[0163] The above text describes how to superimpose the luffing trolley unit on the beam element. Next, how to achieve real-time luffing trolley superposition will be described. Assume that the luffing trolley is moving at a constant speed. Therefore, the {N} of the ordinary beam also changes with time, and {N} needs to be updated in real time according to the time transformation. Assume that the update rate is the same as the trolley moving speed, and the value is Δt. Next, the second-stage luffing trolley matrix assembly path will continue to be described using the example above. When the luffing trolley runs to the beam element with n = 2, at this time, the element matrices with degrees of freedom numbered 3, 4, 5, and 6 of this beam element need to be updated. At the same time, the degree of freedom 2N + 3 of the luffing trolley is added to the element matrix of the original beam element along with the corresponding element matrix, and the results are shown in Table 2. At the same time, the degrees of freedom of all other beam elements do not change. When the luffing trolley moves to the next element, 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.

[0164] Table 2

[0165]

[0166] Finally, the matrix of the trolley-tower coupling software model is obtained by using each step of 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 matrix of the trolley-tower coupling software model. Next, it is in accordance with Figure 5As shown in the figure, considering the boundary conditions, that is, the degrees of freedom of the beam element when n = 1 are only the vertical and rotational degrees of freedom of the right - hand node, and the degrees of freedom of the beam element when n = N are 4 degrees of freedom. Therefore, the degrees of freedom of the entire vehicle - tower coupling 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, by using appropriate numerical solution methods, the response of any degree of freedom of the entire system at any time can be obtained. Commonly used numerical solution methods include the central difference method, fourth - order R - k method, and Newmark - β. In this paper, the commonly used Newmark - β method is adopted to solve the VTI system. In the Newmark - β method, the calculation of integral constants is required, as shown below:

[0167] a0 = 1 / (β×dt 2 ) (31)

[0168] a1 = γ / (β×dt) (32)

[0169] a2 = 1 / (β×dt) (33)

[0170] a3 = 1 / (2×β)-1 (34)

[0171] a4 = γ / β-1 (35)

[0172] a5 = dt / 2(γ / β - 2) (36)

[0173] a6 = dt×(1 - γ) (37)

[0174] a7 = γ×dt (38)

[0175] Among them, γ represents the coefficient of the linear variation weight between the influence of the initial and final accelerations 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 calculation integral constants, and dt represents the time variation.

[0176] Next, the various parameters of different parts of the vehicle - tower coupling software model adopted are as shown in Table 3 below:

[0177] Table 3

[0178]

[0179] According to the above parameter settings, the acceleration response of the luffing trolley is used to verify the modal parameters of the tower crane through two schemes: theoretical derivation and numerical simulation.

[0180] In numerical simulation, the MATLAB programming software was used to realize the assembly of the vehicle-tower coupling software model. The frequency of the tower crane was successfully identified by using the response of the luffing trolley. The acceleration response values of the vehicle body obtained from theoretical derivation and numerical simulation were compared with those of the flat-top tower crane, as Figure 8 , Figure 9 shown.

[0181] As Figure 8 shown, it includes the acceleration response value of the luffing trolley obtained from 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, and the overall vibration period and vibration waveform are relatively consistent. However, there are slight deviations in the response values generated at the underestimated part of the vibration waveform. The main reason for the above-mentioned 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 was considered to be 0, while in the numerical simulation, the stiffness of the luffing trolley was considered to be close to infinity. The numerical simulation is closer to the coupling effect between the tower crane and the luffing trolley in reality.

[0182] As Figure 9 shown, it includes the acceleration response value of the tower crane obtained from theoretical derivation and the response value 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 it is at the trough or peak of the vibration waveform of the response value, there is a certain difference in the response value, and the difference between the two is still increasing with the increase of time.

[0183] Figure 8 and Figure 9 both verified the accuracy between theoretical derivation and numerical simulation through the comparison of simulation values and theoretical values. 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. In 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 displacement response value distribution coefficient at the node of the unit beam. 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. 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.

[0184] Frequency identification of flat-top tower crane: For Figure 8 , Figure 9 the acceleration response of the luffing trolley and the acceleration response of the flat-top tower crane, perform fast Fourier transform (FFT) to obtain the acceleration spectrograms of the flat-top tower crane and the luffing trolley, as shown in Figure 10 , Figure 11 .

[0185] As shown in Figure 10 , Figure 11 , it can be clearly seen from both figures the driving frequency ω v of the luffing trolley. It can be seen from the peak of the driving frequency in the figure that it is most obvious at the moment when the luffing trolley changes its motion state. This may be because a huge kinetic energy is generated when the luffing trolley changes from a stationary state to a uniform motion state.

[0186] Secondly, Figure 10 the frequency of the flat-top tower crane can be identified, and the frequency of each order of the flat-top tower crane is not a single peak. It can be found that most frequencies can clearly see two peaks, that is, the left frequency and the right frequency of the flat-top tower crane. The main reason for the generation of the left frequency and the right frequency is that the motion of the luffing trolley leads to the occurrence of the Doppler effect, which also verifies the reliability of the theoretical derivation from the side. As the order of the frequency increases, it can be found that the distance between the left and right frequencies also becomes larger and larger. This is mainly because the difference between the left and right frequencies of the flat-top tower crane will also increase as the frequency order n increases. It can also be found from Figure 11 that the left and right frequencies of the first and second order frequencies cannot be clearly seen. This is because at the low frequency stage, the value of n is small, that is, the difference between the two is relatively small, and there is also spectral leakage in the FFT method. Due to the above two reasons, it is difficult to see the left and right frequencies of the first and second order frequencies of the flat-top tower crane. To solve the problem of the increasing difference between the left and right frequencies of the tower crane, using the present invention can solve the problem of unclear identification of the low-order frequencies of the tower crane, and at the same time can ensure the identification of the high-order frequencies of the tower crane, as shown in Figure 11 .

[0187] From Figure 10 , it can be seen that only three frequencies are identified, namely the driving frequency of the luffing trolley, the first-order frequency of the flat-top tower crane, and the second-order frequency of the flat-top tower crane, and their amplitudes are relatively small and difficult to see clearly in the figure. Different from this, in the spectrum Figure 11 of the luffing trolley, the first four-order frequencies of the flat-top tower crane can be clearly and distinctly identified, of course, including the driving frequency of the luffing trolley itself. The amplitudes of these four-order frequencies do not decrease rapidly like the amplitudes in the acceleration spectrum of the tower crane, that is, they do not decrease rapidly with the increase of the order. The above phenomenon shows that the luffing trolley method can continuously identify more tower crane frequencies, and the identified frequencies are more stable.

[0188] In summary, it can be seen that using the acceleration response of the luffing trolley to obtain the frequency value of the flat-top tower crane is a more accurate method, especially for identifying the high-order frequencies of the tower crane.

[0189] Modal identification of flat-top tower crane: The mode shape of the tower crane is an important parameter among the modal parameters of the tower crane and is also the main structural parameter referred to in the health and safety inspection of the tower crane. Since the tower crane is simplified to a cantilever beam structure, only the first three-order mode shapes of the cantilever beam are given below. To verify the feasibility of identifying the tower crane mode shape based on the luffing trolley signal, three methods for solving the mode shape will be used to verify each other, namely the assumed mode method, the analytical method, and the Rayleigh-Ritz method. The specific usage steps are as follows:

[0190] (1) Establish a vehicle-tower coupled finite element, and obtain the luffing trolley response and the tower crane response through MATLAB;

[0191] (2) Perform FFT transformation on the obtained luffing trolley response to obtain the luffing trolley frequency spectrum diagram, and then perform FFT transformation on the tower crane response to obtain the tower crane frequency spectrum diagram. Compare the two to verify the accuracy of the frequency spectrum diagram, as Figure 10 and Figure 11 shown;

[0192] (3) Remove the driving response and high-order modal components in the luffing trolley acceleration response through the band-pass filtering method (BPS);

[0193] (4) Use the Hilbert transform (HT) to obtain the instantaneous amplitude of the filtered response;

[0194] (5) Reconstruct the tower crane mode shape.

[0195] Figure 12 , Figure 13 and Figure 14 are the first three-order mode shapes of the simplified tower crane model obtained by the modal method, the analytical method, and the Rayleigh-Ritz method based on the luffing trolley response, respectively. It can be seen from the comparison that the first three-order mode shapes of the simplified tower crane model identified by the assumed mode method and the Rayleigh-Ritz method are similar, while the differences in the first three-order amplitudes obtained by the analytical method are larger. However, all three methods can obtain the mode shape of the simplified model through the response of the luffing trolley, verifying the feasibility of the method proposed in the present invention.

[0196] 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 method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system, characterized in that: It includes the following steps: Step 1: Construct an entity vehicle-tower coupling system. The entity vehicle-tower coupling system is provided with a tower crane. A luffing trolley is arranged on the boom of the tower crane, and a sensor module is arranged on the luffing trolley; Step 2: According to the initial parameter information of the tower crane and the luffing trolley, construct a vehicle-tower coupling software model. The entity vehicle-tower coupling system and the vehicle-tower coupling software model form a vehicle-tower coupling twin system, and they are wirelessly communicatively connected; Step 3: The sensor module collects the speed v, mass m v and displacement data of the luffing trolley in real time and transmits them to the vehicle-tower coupling software model; Step 4: The vehicle-tower coupling software model dynamically adjusts its own data according to the collected speed v, mass m of the luffing trolley v and the moving length data, completes the synchronous change with the physical vehicle-tower coupling system, and outputs the acceleration response data of the luffing trolley Then the acceleration response data is transmitted to the detection module; Step 5: The detection module converts the acceleration response data through fast Fourier transform (FFT) into an acceleration spectrogram, and outputs the frequency data and vibration mode data of the tower crane according to the acceleration spectrogram.

2. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 1, wherein: In the said Step 1, the sensor module includes a speed sensor, a weighing sensor and a displacement sensor; Among them, the speed sensor is arranged on the driving wheel of the luffing drive motor, and is used to collect the speed response data of the luffing trolley in real time and transmit it to the vehicle-tower coupling software model; The displacement sensor is arranged on the wheel of the luffing trolley, and is used to collect the moving length data of the luffing trolley in real time. This displacement sensor is a rotary encoder wheel.

3. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 2, wherein: A hook is arranged on the luffing trolley, a heavy object is hung on the hook, and a weighing sensor is also arranged on the hook. This weighing sensor collects the heavy object mass data and transmits it to the vehicle-tower coupling software model.

4. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 3, wherein: In the step 2, the initial parameter information includes the boom length l of the tower crane, the mass per unit length elastic modulus E, moment of inertia I of the cross section, and the mass m of the luffing trolley v , stiffness k v , and speed v; Among them, the mass \(m\) of the luffing trolley v is the sum of the self - mass of the luffing trolley, the mass of the hook and the mass of the heavy object.

5. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 1, wherein: The vehicle-tower coupling software model is provided with a vehicle-tower coupling unit. The vehicle-tower coupling unit includes a beam unit and a trolley unit. The vehicle-tower coupling software model is composed of n beam units and one trolley unit; The n beam units are assembled to form the beam part of the vehicle-tower coupling software model. The beam part corresponds to the boom structure of the tower crane in the entity vehicle-tower coupling system, and the trolley unit corresponds to the luffing trolley structure in the entity vehicle-tower coupling system.

6. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 5, 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, and {u b} is the displacement array of the beam element, {u b} = {u A θ A u B θ B}, where u A and θ A represent the degrees of freedom of the left node of the beam element, and 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, and 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 wheel at both ends of the node, g is the acceleration due to gravity, {N′} is the first derivative of {N}, and the superscript "T" represents the matrix transpose.

7. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 6, characterized in that: The value of {N} is a Hermite interpolation polynomial, and 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 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 proportional constants, the unit of α0 is s, and the unit of α1 is s -1 .

8. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 6, wherein: The process of assembling n beam units and one trolley unit into the vehicle-tower coupling software model is as follows: According to the said 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.

9. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 8, characterized in that: The assembly of the beam part includes the assembly of the mass matrix, the assembly of the stiffness matrix and the assembly of 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 formula (29) v and the degrees of freedom {u b} of the beam are swapped in order, and the following formula is obtained after adjustment: 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.

10. The method for identifying the frequency and vibration mode of a tower crane based on a vehicle-tower coupled twin system according to claim 1, wherein: In the said Step 4, the output process of the vibration mode data is as follows: (1) Calculate the frequency data of the tower crane through the corresponding frequency expression of the tower crane; (2) Adopt the band-pass filtering method (BPS) to extract the response data related to the frequency data of the tower crane from the acceleration response information; (3) Obtain the instantaneous amplitude of the response data by using the Hilbert transform; (4) Obtain the vibration mode data of the tower crane from the instantaneous amplitude.

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