Tower crane damage detection method based on amplitude-variable trolley acceleration response

Abstract

A tower crane damage detection method based on amplitude-variable trolley acceleration response comprises the following steps that 1, an amplitude-variable trolley-cantilever beam tower crane system is built, and an amplitude-variable trolley is arranged on a cargo boom of a tower crane; 2, an acceleration sensor is arranged on the variable-amplitude trolley, the variable-amplitude trolley moves on a cargo boom of the tower crane at the moving speed v, and the acceleration sensor collects acceleration response data of the variable-amplitude trolley in real time and transmits the acceleration response data to an FFT conversion module; 3, the FFT conversion module converts the acceleration response data of the variable amplitude trolley to obtain an acceleration spectrogram; 4, according to the acceleration spectrogram, modal parameters of the tower crane are obtained through recognition; and 5, detecting and identifying the damage condition of the tower crane according to the modal parameters or the acceleration response data. The method has the effect that the damage result of the cantilever beam tower crane can be accurately detected.

Description

Technical Field

[0001] The invention relates to the technical field of tower crane damage detection, in particular to a tower crane damage detection method based on the acceleration response of a variable-luffing trolley. Background Art

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

[0003] In reality, the modal parameters of all objects are different, just like human fingerprints, and are composed of countless unique data. The modal parameters of each structure itself usually do not change, such as natural frequency, modal vibration shape, and structural damping, but when the structure itself is damaged, its modal parameters will also change. In theory, this is why damage can be identified by analyzing the modal parameters. The main content of modal analysis is actually to perform coordinate transformation on the data. It converts the response value originally in the physical coordinate to the description under the defined modal coordinate. Each basis vector under the modal coordinate is the characteristic vector of the vibration response under the original physical coordinate, that is, the correlation between the basis vectors under this coordinate can simply describe the relationship between the response vectors.

[0004] However, the computational modal analysis method cannot take into account the coupling relationship between each response vector. Therefore, the experimental modal analysis method is often used in combination with it to identify structural damage. The experimental modal analysis method, as the name implies, is to obtain the response value through field tests or model tests and then identify the actual modal parameters of the structure through numerical processing. In recent years, people usually give external excitation to the structure to pick up the vibration response value of the structure, and then obtain the modal parameters of the structure through fast Fourier transform FFT. However, this method has strict requirements on the environment, and when using this method to measure large machinery, more test instruments such as sensors are required, the amount of data collected by the measuring points is large, and data processing is more cumbersome. Summary of the invention

[0005] The present invention provides a tower crane damage detection method based on the acceleration response of the luffing trolley, which can realize accurate detection of tower crane damage results.

[0006] To achieve the above object, the present invention provides a tower crane damage detection method based on the acceleration response of the luffing trolley, the key of which is to include the following steps:

[0007] Step 1: Build a luffing trolley-cantilever tower crane system. The luffing trolley is set on the boom of the tower crane. The boom length is set to L. The unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the section inertia moment of the tower crane is I, and the mass of the luffing trolley is m v ;

[0008] Step 2: An acceleration sensor is arranged on the luffing trolley, and the luffing trolley moves on the boom of the tower crane at a moving speed v. The acceleration sensor collects acceleration response data of the luffing trolley in real time and transmits it to a fast Fourier transform (FFT) conversion module;

[0009] The expression of the acceleration response data of the luffing trolley is as follows:

[0010]

[0011] in,

[0012]

[0013] Among them, u y represents the displacement response of the variable-luffing trolley, n represents the response order, 1≤n≤M, M represents the order range; v represents the moving speed of the variable-luffing trolley, t represents time, α n represents the frequency parameter of each nth order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, and ω represents the natural frequency of the cantilever beam;

[0014] Step 3: The fast Fourier transform (FFT) conversion module transforms the acceleration response data of the variable amplitude vehicle to obtain an acceleration spectrum diagram;

[0015] Step 4: According to the acceleration spectrum diagram, the modal parameters of the tower crane are identified;

[0016] According to the peak distribution of the acceleration frequency spectrum, the modal parameters of the tower crane are obtained, wherein the modal parameters include the natural frequency and vibration mode of the tower crane, and the natural frequency includes the left frequency and the right frequency of the tower crane;

[0017] Step 5: Detecting and identifying damage of the tower crane according to the modal parameters or acceleration response data;

[0018] The method used to detect and identify damage to a tower crane is either:

[0019] a. Damage identification method based on natural frequency change;

[0020] b. Damage identification method based on vibration mode change;

[0021] c. Damage identification method based on flexibility change;

[0022] d. Damage identification method based on wavelet transform.

[0023] Through the above design, the acceleration response of the luffing trolley is obtained by calculation. According to the proposed expression of the acceleration response data of the luffing trolley, the acceleration response of the tower crane at different positions of the horizontal arm can be reconstructed, and the acceleration frequency spectrum of the luffing trolley is converted by using the reconstructed acceleration response. Through the acceleration frequency spectrum, the modal parameters such as frequency and vibration mode of the tower crane can be accurately obtained, and the damage result of the tower crane can be detected and identified. The damage result of the tower crane includes whether the tower crane is damaged, the damage location and the damage degree.

[0024] Preferably, in step 2, the natural frequency ω of the tower crane is expressed as follows: The natural frequency ω of the cantilever beam structure system is expressed as follows:

[0025]

[0026] As a preference: in step 4, the left and right frequencies of the tower crane are v The expression is as follows:

[0027]

[0028] Preferably, in step 2, the movement speed v of the luffing trolley is controlled within a range of 25%-80% of the maximum luffing speed of the tower crane.

[0029] Preferably, in step 1, a hook is connected to the luffing trolley, a hanging object is hung on the hook, and the weight of the hanging object is controlled to be 25% to 60% of the maximum lifting weight of the tower crane.

[0030] Since the luffing structure and lifting structure are used more frequently in the operation of tower cranes, the two parameters of the luffing trolley, the running speed and the weight of the hoisted object, will affect the recognition of the tower crane frequency by the acceleration response of the luffing trolley. It is difficult to identify the tower crane frequency when the luffing trolley speed is slow, but the recognition result will also be greatly distorted when the speed is fast. The recognition result is most accurate when the speed is 25% to 80% of the maximum luffing speed of the tower crane; when the hoisting weight is controlled at 25% to 60% of the maximum hoisting weight of the tower crane, the luffing trolley can recognize high-order frequencies without causing additional vibrations to the tower crane, affecting the accuracy of the luffing trolley recognition frequency.

[0031] Preferably, in step 5, the damage identification method based on natural frequency change is as follows:

[0032] A luffing trolley-cantilever tower crane system is built. Before the tower crane is damaged, the luffing trolley moves on the tower crane to obtain acceleration response data of the luffing trolley before damage, and a fast Fourier transform is performed to obtain an acceleration spectrum before damage, and the natural frequency of the tower crane before damage is obtained by identifying the acceleration spectrum before damage;

[0033] After the tower crane is damaged, the luffing trolley moves on the tower crane to obtain acceleration response data of the luffing trolley after the damage, and performs fast Fourier transform to obtain an acceleration spectrum after the damage, and the natural frequency of the tower crane after the damage is identified through the acceleration spectrum after the damage;

[0034] The natural frequency of the tower crane before damage and the natural frequency of the tower crane after damage are compared to obtain the damage result of the tower crane.

[0035] The natural frequency is the easiest parameter to obtain among the modal parameters and has high identification accuracy. There are many methods for damage identification based on the change of natural frequency. Their characteristics are: when the structure is damaged, only the stiffness of the structure is reduced, while the change of the structural mass is ignored, and a modified theoretical model is established before the early damage of the structure. Theoretically, the ratio of any second-order frequency change after the damage is only a function of the damage position and has nothing to do with the size of the damage.

[0036] Preferably, in step 5, the damage identification method based on vibration mode change is as follows:

[0037] (1) Building a luffing trolley-cantilever tower crane system, obtaining acceleration response data of the luffing trolley by moving the luffing trolley on the tower crane,

[0038] (2) performing a fast Fourier transform on the acceleration response data of the luffing trolley to obtain an acceleration spectrum diagram, and identifying the frequency of the tower crane;

[0039] (3) extracting response data related to the tower crane frequency from the acceleration response data by using a bandpass filter method (BPS);

[0040] (4) obtaining the instantaneous amplitude of the response data by using Hilbert transform;

[0041] (5) obtaining a vibration mode of the tower crane from the instantaneous amplitude;

[0042] (6) performing regularization processing on the vibration mode of the tower crane;

[0043] (7) Identify the damage of the tower crane by using the mode curvature method or the mode change graph method.

[0044] The vibration mode is a basic modal parameter. Although its test accuracy is relatively low, it contains a lot of information, so there are many damage identification and diagnosis technologies based on vibration mode changes. (1) Vibration mode curvature method: If the structure is damaged, the stiffness of the damaged part will decrease and the curvature will increase. The change in vibration mode curvature increases with the increase in curvature. Therefore, the location of the damage can be determined based on the change in vibration mode curvature. (2) Vibration mode change graph method: The relative change in vibration mode is used as the positioning parameter, that is, the ratio of the difference in vibration mode before and after damage to the vibration mode before damage. When damage occurs, the relative change in vibration mode on the affected degree of freedom will appear relatively large in the damaged area. Therefore, the location of the damage can be identified using the vibration mode relative change graph.

[0045] The damage identification method based on flexibility change is as follows:

[0046] Under the condition that the mode satisfies normalization, the flexibility matrix is ​​a function of the inverse of the frequency and the vibration mode. As the frequency increases, the inverse of the high frequency in the flexibility matrix can be ignored. In this way, a matrix with good accuracy can be obtained by measuring the first few low-order modal parameters and frequencies. The maximum element in each column of the difference matrix is ​​obtained based on the difference matrix of the two flexibility matrices before and after the damage. The location of the damage can be found by checking the maximum element in each column.

[0047] The damage identification method based on wavelet transform is as follows:

[0048] The acceleration response signal of the variable amplitude trolley is filtered and integrated twice to obtain the displacement time history signal of the sampling point. Wavelet analysis is performed on the acceleration time history signal and the displacement time history signal respectively, thereby realizing the detection of structural damage.

[0049] The beneficial effects of the present invention are as follows: the modal parameter identification method of the tower crane is simplified, the accuracy and reliability of the modal parameter identification of the tower crane are improved, a new detection direction is opened up for the damage result detection of the tower crane, the complexity of the damage detection process of the tower crane is reduced, and the detection cost is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the process of the present invention;

[0051] Figure 2 It is a structural schematic diagram of a luffing trolley-cantilever beam tower crane in the embodiment;

[0052] Figure 3 This is a comparison diagram of the acceleration response of the variable-luffing trolley in the embodiment;

[0053] Figure 4 It is a comparison diagram of the acceleration response of the flat-top tower crane in the embodiment;

[0054] Figure 5 This is the acceleration response spectrum of the flat-top tower crane;

[0055] Figure 6 It is the acceleration response spectrum of the variable-luffel trolley;

[0056] Figure 7 The vibration diagram of the tower crane identified by assuming the car body response using the modal method;

[0057] Figure 8 The vibration diagram of the tower crane identified by analytical method;

[0058] Fig. 9 The vibration shape diagram of the tower crane identified by the Rayleigh-Ritz method car body response;

[0059] Fig.10 Comparison chart of frequency results of scaled model identification for theoretical derivation, numerical simulation, and experimental testing;

[0060] Fig.11 The tower crane frequency diagram identified by the trolley response under five variable-luffing conditions;

[0061] Fig.12 This is the tower crane frequency diagram identified by the car body response under five lifting weight conditions. DETAILED DESCRIPTION

[0062] The present invention is further described in detail below in conjunction with the accompanying drawings and specific examples. The following examples or drawings are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0063] like Figure 1 As shown: A tower crane damage detection method based on the acceleration response of the variable-luffing trolley comprises the following steps:

[0064] Step 1: Build a luffing trolley-cantilever tower crane system. The luffing trolley is set on the boom of the tower crane. The boom length is set to L. The unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the section inertia moment of the tower crane is I, and the mass of the luffing trolley is m v ;

[0065] Step 2: An acceleration sensor is arranged on the luffing trolley, and the luffing trolley moves on the boom of the tower crane at a moving speed v. The acceleration sensor collects acceleration response data of the luffing trolley in real time and transmits it to a fast Fourier transform (FFT) conversion module;

[0066] The expression of the acceleration response data of the luffing trolley is as follows:

[0067]

[0068] in,

[0069]

[0070] Among them, u y represents the displacement response of the variable-luffing trolley, n represents the response order, 1≤n≤M, M represents the order range; v represents the moving speed of the variable-luffing trolley, t represents time, α n represents the frequency parameter of each nth order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, and ω represents the natural frequency of the cantilever beam;

[0071] Step 3: The fast Fourier transform (FFT) conversion module transforms the acceleration response data of the variable amplitude vehicle to obtain an acceleration spectrum diagram;

[0072] Step 4: According to the acceleration spectrum diagram, the modal parameters of the tower crane are identified;

[0073] According to the peak distribution of the acceleration frequency spectrum, the modal parameters of the tower crane are obtained, wherein the modal parameters include the natural frequency and vibration mode of the tower crane, and the natural frequency includes the left frequency and the right frequency of the tower crane;

[0074] Step 5: Detecting and identifying damage of the tower crane according to the modal parameters or acceleration response data;

[0075] The method used to detect and identify damage to a tower crane is either:

[0076] a. Damage identification method based on natural frequency change;

[0077] b. Damage identification method based on vibration mode change;

[0078] c. Damage identification method based on flexibility change;

[0079] d. Damage identification method based on wavelet transform.

[0080] In this example, various parameters of different parts of the luffing trolley-tower crane model are shown in Table 1 below:

[0081] Table 1

[0082]

[0083] According to the above parameter settings, the acceleration response of the luffing trolley for obtaining the modal parameters of the tower crane was verified through theoretical derivation, numerical simulation and experimental test.

[0084] Theoretical derivation By building a luffing trolley-cantilever tower crane model, a theoretical formula for identifying the modal parameters of the tower crane based on the luffing trolley response is derived. The frequency parts contained in the luffing trolley acceleration response and the tower crane response are the same, both of which are the driving frequency of the luffing trolley and the left and right frequencies of the tower crane. Since the modal response of the tower crane is directly measured by sensors in traditional technology, and the sensors cannot identify the corresponding odd-order modal responses at certain observation points of the crane, the acceleration response of the luffing trolley is measured by sensors without considering whether the measurement point position can pick up the vibration acceleration response of the tower crane. This is a major advantage of the luffing trolley method compared to the traditional method of measuring modal parameters, which indirectly verifies that it is more accurate and faster to identify the frequency of the tower crane from the acceleration spectrum of the luffing trolley.

[0085] like Figure 2 As shown in the figure, for the simplified cantilever beam model, the motion equation of the tower crane's boom system can be expressed as:

[0086]

[0087] for Figure 2 The simplified mathematical calculation model of the cantilever beam shown in the figure can be used to deal with the free vibration problem of this model. The free vibration processing method of the discrete model can be used to consider it. When the cantilever beam is in free vibration, the amplitude of the displacement shape of the beam will change with time, but the displacement shape itself will generally not change significantly with time. Therefore, the modal superposition method is used to calculate the boom displacement u x It can be expressed as the vibration mode function φ(x) and the modal coordinate q n (t) are superimposed, that is:

[0088]

[0089] Among them, α represents the frequency parameter of each order.

[0090] The mechanical relationship between the luffing trolley and the boom is expressed by the contact force between the luffing trolley and the boom. Similarly, the contact force between the trolley and the boom can be regarded as the weight of the luffing trolley itself, ignoring the elastic force of the luffing trolley itself, that is:

[0091] f c (t) = -m v g (3)

[0092] The basic motion equations of the cantilever beam and the moving mass block are obtained in formula (1) and formula (3). Next, we will solve the response formulas of the above two parts. Since the variable-length carriage is simplified to a moving mass block, its own natural frequency is not considered, and only the natural frequency of the cantilever beam is considered. The expression is:

[0093]

[0094] It should be noted here that the cantilever beam vibration frequency α L The value of is solved according to the transcendental equation listed by the cantilever beam boundary condition. The approximate solutions of the first three orders are given here: (αL)1=1.875, (αL)2=4.694, (αL)3=7.855. The approximate solutions of the fourth order and above are determined according to the following formula:

[0095]

[0096] Taking the derivative of formula (2) twice with respect to time yields:

[0097]

[0098] Taking the fourth derivative of formula (2) with respect to position, we get:

[0099]

[0100] At the same time, according to the cantilever beam frequency formula (4), we can get:

[0101]

[0102] Substituting formula (6) and formula (7) into the motion equation (1) of the cantilever beam, we can obtain:

[0103]

[0104] Since the modal function is orthogonal, the trigonometric function is simplified by multiplying both sides of equation (9) by the following formula:

[0105]

[0106] Then, the product is integrated along the length of the cantilever beam to obtain:

[0107]

[0108] In formula (11), when j≠n, the integral result is zero. The integral is meaningful only when j=n. Substituting formula (8) into the above formula, the above formula can be rewritten as:

[0109]

[0110] Next, replace j with n in the above equation and simplify the result to a second-order nonlinear differential equation with constant coefficients, as shown below:

[0111]

[0112] Next, we first solve the right side of the equation according to formula (13). Due to the selectivity of the delta function, we get:

[0113]

[0114] Therefore, the integral result of the numerator on the right side of formula (13) is:

[0115]

[0116] Correspondingly, the integral result of the denominator on the right side of formula (13) is:

[0117]

[0118] When the moving mass block performs variable amplitude motion on the simplified cantilever beam model, the position of the moving mass block has the following relationship:

[0119]

[0120] Among them, x y Indicates the position of the luffing trolley on the cantilever beam, u y Represents the vertical displacement of the luffing trolley under the cantilever beam structure.

[0121] Substituting formula (15), formula (16) and formula (3) into formula (13) yields:

[0122]

[0123] In real life, the overall weight of the luffing mechanism is about 6 to 8 tons, and the overall weight of the tower crane is about 89 tons, accounting for 9%. Therefore, the m v , here the mass of the hook is also incorporated into the mass of the luffing trolley. In addition, it should be noted that different beams have different boundary conditions. The boundary conditions of common beams are given below:

[0124] (1) Fixed end: vertical displacement, lateral displacement and rotation angle are all 0, that is,

[0125] u(x,t)=0 (20)

[0126] u′(x,t)=0 (21)

[0127] Hinge end: vertical displacement, lateral displacement and bending moment are all 0, that is,

[0128] u(x,t)=0 (22)

[0129] EIu″(x,t)=0 (23)

[0130] Free end: bending moment and shear force are both 0, that is,

[0131] EIu″(x,t)=0 (24)

[0132] EIu″″(x,t)=0 (25)

[0133] The boundary condition of the cantilever beam structure is that one end is fixed and the other end is free. Considering that the tower crane is not excited before the luffing trolley moves, its initial condition needs to be assumed as:

[0134] u x (x=0)=0 (26)

[0135] u x ′(x=0)=0 (27)

[0136] EIu″(x=L)=0 (28)

[0137] EIu″″(x=L)=0 (29)

[0138] This maps to u x In the expression, the initial condition is expressed as:

[0139] q Tn (t)| t＝0 =0 (30)

[0140]

[0141] Formula (19) is a typical second-order non-homogeneous linear differential equation with constant coefficients. Therefore, it can be solved according to the characteristics of the equation to obtain the modal coordinate response of the tower crane:

[0142]

[0143] It should be noted that due to the complex vibration mode function of the cantilever beam itself, the solution of the non-homogeneous linear differential equation is relatively complicated. Therefore, only part of the results are released in the main text. Most of the omitted parts are the deformation of the crane when the luffing trolley acts on the flat-top tower crane when it is stationary and the speed variable when the luffing trolley is moving. The overall results A, B, C, D are as follows:

[0144]

[0145]

[0146] Substituting formula (34) into formula (2), the response of the flat-top tower crane can be obtained as follows:

[0147]

[0148] It can be clearly seen from formula (35) that the response of each order of the flat-top tower crane is:

[0149]

[0150] Although the results are relatively complex, it can still be seen that each order response of the flat-top tower crane is affected by both time and space. If the position point of the observed flat-top tower crane boom meets the following conditions:

[0151]

[0152] In the above formula, n is the response order, N is a positive real number, and when the sensor measurement point position meets the above conditions, the response value received by the sensor is zero. For example, at the mid-span position of the crane arm, that is, the sensor is arranged at x=L / 2, the corresponding 1st, 3rd, 5th and other odd-order modal responses received by the sensor are zero. Compared with the modal response expression calculated by the simplified mathematical calculation model of the simply supported beam in the previous section, it can be seen that it is difficult to extract the response values ​​of different orders at the same position. For the direct measurement of the modal parameters of the flat-top tower crane with multiple sensors in reality, in theory, no response will be measured when the position is at the observation point. Therefore, in order to solve this problem, sensors are arranged at intervals throughout the flat-top tower crane in reality, which greatly increases the economic burden, practicality and safety. At the same time, when arranging the sensor position, the parameters of the flat-top tower crane to be measured are unclear before measurement, which will result in the data efficiency of some sensor measurement points not being guaranteed to be accurate.

[0153] In the above part, the displacement response formula of the boom part of the flat-top tower crane is derived. Next, the modal parameters of the variable-length trolley that change with time are theoretically derived to obtain the relationship between the cantilever beam frequency formula and the acceleration response formula.

[0154] Next, by substituting formula (17) and formula (18) into formula (35), the displacement response of the variable-luffing trolley can be obtained as follows:

[0155]

[0156] By taking the derivative of equation (38) twice, we can get the acceleration response of the variable-luffing trolley:

[0157]

[0158] in,

[0159]

[0160]

[0161] From the results of some formulas (39), one part is the driving frequency response caused by the operation of the luffing trolley on the boom. The meaning of the driving frequency of the VTI structure is the same as that of the simplified system model of the simply supported beam. Both can be interpreted as the luffing trolley operating on the boom causes the boom to vibrate, and the vibration of the boom causes the luffing trolley to produce relative vibration. Therefore, the vibration generated by the luffing trolley has an impact on the boom mode. From the above explanation, it can be seen that the driving frequency in this article is different from the previous classic definition. It is only related to the motion state of the trolley and has nothing to do with periodic motion. The other part is the response controlled by the left and right frequencies of the flat-top tower crane. The response frequency component of the simplified cantilever beam model does not have the natural frequency of the car body. The specific driving frequency ω T Formula and tower crane left and right frequency ω v The formula is as follows:

[0162]

[0163] Another point that needs to be explained is that this paper converts the displacement response of the variable-luffing trolley into the acceleration response of the variable-luffing trolley for theoretical analysis. This is mainly because in field tests or model tests, the sensor is easier to measure the acceleration response value of the variable-luffing trolley. As long as an acceleration sensor is installed on the variable-luffing trolley, the acceleration response value can be measured. The displacement of the variable-luffing trolley is a relative displacement, which is difficult to measure in real life and the displacement value measured is not accurate. It will be disturbed by various external factors. Another main reason is that the body frequency is a major peak in the acceleration spectrum of the variable-luffing trolley. It is difficult for researchers to identify the frequency peak of the tower crane, especially when the frequencies of the two are close and the peaks are difficult to distinguish. However, since the variable-luffing trolley is simplified as a moving mass block in this paper, its natural frequency is difficult to show in the body acceleration spectrum, so there is no such trouble. Therefore, referring to the simplified calculation model of the cantilever beam, the acceleration response of the variable-luffing trolley is used to obtain the parameters of the flat-top tower crane, which can better identify the frequency value.

[0164] In the numerical simulation, the MATLAB programming software was used to simulate the car-tower coupling, and the frequency of the tower crane was successfully identified using the response of the variable-luffing trolley. The car body acceleration response values ​​obtained by theoretical derivation and numerical simulation were compared with the acceleration response values ​​of the flat-top tower crane. Figure 3 , Figure 4 shown.

[0165] like Figure 3As shown in the figure, it includes the acceleration response value of the variable-luffing trolley derived from theoretical derivation and the acceleration response value of the variable-luffing trolley obtained through numerical simulation. Figure 3 It can be clearly seen that there is a small difference between the theoretical value and the numerical simulation value: the peak value of the response value is roughly equal, the overall vibration period and vibration waveform are relatively consistent, but there is a slight deviation in the response value at the underestimated position of the vibration waveform. The main reason for the deviation described above may be that many external factors in reality are ignored during the theoretical derivation process, including the damping of the luffing trolley itself. At the same time, in the theoretical derivation, this paper considers the stiffness of the luffing trolley to be 0, while in the numerical simulation, the stiffness of the luffing trolley is 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.

[0166] like Figure 4 As shown in Figure 1, it includes the tower crane acceleration response value derived from theoretical derivation and the tower crane response value obtained through numerical simulation. Figure 4 It can be clearly seen that the vibration mode and period between the two are roughly the same, but compared with the acceleration response comparison chart of the variable-leverage trolley, there is a deviation in the response value between the simulation value and the theoretical value. Whether in the trough or peak of the response value vibration waveform, the response value size differs by a certain value, and the difference between the two continues to increase with time.

[0167] Figure 3 and Figure 4 The accuracy between the theoretical derivation and the numerical simulation was verified by comparing the simulation values ​​with the theoretical values. In addition to the difference in the values ​​of the variable-length trolley stiffness, another reason for the above-mentioned difference is the difference in the methods used. In the theoretical derivation, the modal superposition method was used to represent the displacement response value, while the Hermite interpolation method was used in the numerical simulation to obtain the displacement response value distribution coefficient at the node of the unit beam. It can be seen that the difference between the theoretical value and the simulation value is inevitable, and the difference is small and can be ignored. Figure 3 and Figure 4 It can be seen that the acceleration response of the luffing trolley is more oscillating than that of the flat-top tower crane. This is because the luffing trolley directly absorbs the vibration generated by energy, and is secondly affected by the vibration wave, which makes the amplitude of the high-frequency component of the acceleration of the luffing trolley larger.

[0168] Frequency identification of flat-top tower crane: Figure 3 , Figure 4 The acceleration response of the medium-luffing trolley and the topless tower crane is subjected to fast Fourier transform FFT to obtain the acceleration spectrum of the topless tower crane and the luffing trolley, as shown in Figure 5 , Figure 6 shown.

[0169] like Figure 5 , Figure 6 As shown in the two figures, it can be clearly seen that the driving frequency ω caused by the operation of the variable-length trolley v From the peak value of the driving frequency in the figure, it can be seen that it is most obvious when the luffing trolley changes its motion state. This may be the result of the huge kinetic energy generated at the moment when the luffing trolley changes from a stationary state to a uniform motion state.

[0170] Secondly, Figure 5 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 reason for the left and right frequencies is mainly due to the movement of the variable-length trolley, which causes the Doppler phenomenon. This also indirectly verifies the reliability of the theoretical derivation. As the frequency order increases, it can be found that the distance between the left and right frequencies is also getting larger. This is mainly because the difference between the left and right frequencies of the flat-top tower crane will also increase with the increase of the frequency order n. From Figure 6 It can also be found that the left and right frequencies of the first and second order frequencies cannot be clearly seen. This is because the value of n is small in the low frequency stage, that is, the difference between the two is originally small, and the FFT method also has spectrum leakage. The above two reasons make it difficult to see the left and right frequencies of the first and second order frequencies of the flat-top tower crane. In order to solve the problem of the large difference between the left and right frequencies of the tower crane, the use of the present invention can solve the problem of unclear recognition of the low-order frequencies of the tower crane, and at the same time can ensure the recognition of the high-order frequencies of the tower crane, such as Figure 6 shown.

[0171] from Figure 5 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 the amplitude is small and difficult to see clearly in the figure. Figure 6 The first four frequencies of the flat-top tower crane can be clearly identified, including the driving frequency of the luffing trolley itself. The amplitude of these four frequencies does not decrease as quickly as the amplitude in the tower crane acceleration spectrum, that is, the amplitude does 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 identification frequency is more stable.

[0172] In summary, it can be seen that using the acceleration response of the variable-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.

[0173] Identification of vibration modes of flat-top tower cranes: The vibration modes of tower cranes are important parameters in the modal parameters of tower cranes, and are also the main reference structural parameters in the health and safety detection of tower cranes. Since the tower crane is simplified into a cantilever beam structure, only the first three vibration modes of the cantilever beam are given below. In order to verify the feasibility of identifying the vibration modes of tower cranes based on the amplitude-changing trolley signal, three methods of solving vibration modes will be used to verify each other, namely, the hypothetical modal method, the analytical method, and the Rayleigh-Ritz method. At the same time, since the coupling between the car and the tower must be considered, the method proposed by Yang et al. in 2014 is cited here. The specific steps are as follows:

[0174] (1) Establish the trolley-tower coupling finite element and obtain the response of the luffing trolley and the tower crane through MATLAB;

[0175] (2) Perform FFT transformation on the acquired luffing trolley response to obtain the luffing trolley spectrum diagram, and then perform FFT transformation on the tower crane response to obtain the tower crane spectrum diagram. The two are compared to verify the accuracy of the spectrum diagram, such as Figure 5 and Figure 6 As shown;

[0176] (3) The driving response and high-order modal components in the acceleration response of the variable amplitude vehicle are eliminated by bandpass filtering (BPS);

[0177] (4) Using Hilbert Transform (HT) to obtain the instantaneous amplitude of the response after filtering;

[0178] (5) Reconstruct the vibration mode of the tower crane.

[0179] Figure 7 , Figure 8 as well as Fig. 9 The first three vibration modes of the simplified tower crane model are obtained based on the response of the variable-length trolley using the modal method, analytical method and Rayleigh-Ritz method. By comparison, it can be seen that the first three vibration modes of the simplified tower crane model identified by the modal method and the Rayleigh-Ritz method are similar, while the first three amplitudes obtained by the analytical method have a large difference. However, all three methods can obtain the vibration modes of the simplified model through the response of the variable-length trolley, which verifies the feasibility of the method proposed in the present invention.

[0180] Next, the accuracy of theoretical derivation, numerical simulation and experimental test is compared and analyzed. The same scaled model is used to identify the tower crane frequency based on the response of the variable-length trolley by using finite element simulation, theoretical derivation and field test. The smoothed frequency comparison results are shown in Fig.10 As shown in Fig.10It can be clearly seen that the finite element numerical simulation results are basically consistent with the test results, while the results obtained by theoretical derivation are slightly different. The reason for the different energy generated at the same frequency may be that the motion equation does not take the coupling effect between the vehicle and the tower into account, so the energy generated is smaller than the energy values ​​obtained by the other two methods. At the same time, since the theoretical derivation uses a simplified mathematical model of the cantilever beam, the effect of identifying the frequency is not as good as the finite element numerical simulation and model test.

[0181] Next, the influence of the two parameters, the luffing speed and the weight of the hanging object, on the frequency identification of the tower crane based on the luffing trolley signal is analyzed. The luffing speed parameter is studied by model test, and the hanging weight parameter is studied by finite element simulation. If the model test is used to study the hanging weight, the difference in the selected values ​​of the test scheme is not large, and the influence of the parameters on the method cannot be clearly reflected. This embodiment will study the influence of five luffing trolley speed conditions and five hanging weight conditions on the method. The specific conditions are shown in Table 1:

[0182] Table 1 Parameter analysis working condition table

[0183]

[0184] The selection of the above working conditions depends on the investigation of the maximum luffing speed and the maximum lifting weight that can be achieved under the normal working state of the actual tower crane. The luffing speed is based on the motor rotation speed converted from the movement speed of the luffing trolley of the actual tower crane, and the lifting weight is taken as the value reduced by about 20% according to the maximum lifting weight.

[0185] Before conducting this parameter research test, it is necessary to compare and analyze the accuracy of theoretical principles, finite element simulation and field tests. By using finite element simulation, theoretical derivation and field tests to identify the tower crane frequency based on the response of the variable-length trolley on the same scale model, the smoothed frequency comparison results are Fig.11 As shown. Fig.11 It can be clearly seen that the finite element numerical simulation results are basically consistent with the test results, while the results obtained by theoretical derivation are slightly different. The reason for the different energy generated at the same frequency may be that the motion equation does not take the coupling effect between the vehicle and the tower into account, so the energy generated is smaller than the energy values ​​obtained by the other two methods. At the same time, since the theoretical derivation uses a simplified mathematical model of the cantilever beam, the effect of identifying the frequency is not as good as that of the finite element and model test.

[0186] After completing the mutual verification of the accuracy of the three methods of theory, finite element and model test, this paper first carried out the study of the variable-length trolley speed. Fig.12 The results of the tower crane frequency identification by the luffing trolley response under different luffing speed conditions are shown.-3 m / s (Case 1), it is a very low uniform motion state. The car body response can identify the first-order frequency of the tower crane, but the second-order frequency is difficult to identify. -3 m / s (Case 3), the body response can well identify the first and second order frequencies of the tower crane. However, when the amplitude change speed exceeds the upper limit control, for example 2.1×10 -2 m / s (Case 5), the identified frequency will be seriously distorted. This may be because when the luffing trolley moves faster, the acceleration sensor installed on the luffing trolley will receive a larger deviation value in the same time, thus affecting the accuracy of data reception. In addition, when the luffing speed is faster, the acceleration sensor will recognize the signal distortion, which will cause more serious spectrum leakage during FFT transformation, resulting in incorrect numerical analysis and affecting the accuracy of spectrum recognition. Based on the above analysis, it is believed that within the range of luffing trolley speeds that the tower crane can accept, when identifying the tower crane frequency based on it, 25% to 80% of the maximum luffing speed that can be achieved under normal working conditions of the actual tower crane should be used for modal recognition of the tower crane, otherwise the measured results will be highly inaccurate.

[0187] In order to analyze the influence of the hoisting weight on the identification frequency of the tower crane during the luffing movement of the trolley, the study was carried out at the actual luffing trolley working speed of 0.6m / s. The influence of the hoisting weight on the identification frequency of the tower crane during the luffing movement was analyzed through MATLAB simulation. The results are as follows: Fig.12 As shown. Fig.12 It can be clearly seen that when the weight hung on the luffing trolley is greater, the response value of the luffing trolley can better identify the frequency of the tower crane. Fig.12When the medium-length variable-length trolley moves from static to starting to move, it is obvious that the greater the lifting weight, the greater the energy generated by the variable-length trolley when it is working. This is because the trolley does not generate any additional vibration when it is static. When the trolley starts to move at a uniform speed, the vertical deformation of the trolley changes, and then vertical vibration is generated. When the hanging weight is heavier, the deformation of the trolley is greater, the additional vibration response is greater, and the energy value of the identification frequency is greater. Carefully observing the first-order frequency in the figure, it can be found that under the working conditions of 160kg (Case1), 480kg (Case2) and 800kg (Case3), the left and right frequencies of the tower crane at this order cannot be seen. The specific reasons have been analyzed above. According to the spacing formula of the left and right frequencies, it can be known that the left and right frequency spacing decreases with the decrease of the order. This reflects the second reason. When the lifting weight is heavy, the weight moves left and right with the trolley, which will cause the weight to swing, causing additional vibration of the tower crane, resulting in obvious left and right frequency changes. Therefore, the hoisting weight must be controlled within 25% to 60% of the maximum hoisting weight that can be achieved under normal working conditions of the actual tower crane, so that the luffing trolley can identify high-order frequencies without causing additional vibrations in the tower crane that affect the accuracy of the recognition frequency of the luffing trolley. It should also be noted that when the mass is too large, the luffing trolley will cause geometric nonlinearity at the free end of the cantilever, and the degree of geometric nonlinearity is related to the mass size. The greater the weight, the greater the influence of the degree of geometric nonlinearity on the recognition frequency. Since geometric nonlinearity is different from the linear assumption of the recognition method in this article, it will affect the overall effect of point recognition. Therefore, this embodiment does not consider geometric nonlinearity, which is also a part of the recognition method that needs to be improved later.

[0188] In summary, since the luffing trolley is rigidly connected to the tower crane, the body frequency of the luffing trolley is a high-order frequency and will not affect the identification of the tower crane frequency. The frequency of the tower crane can be well identified from the body response of the mobile luffing trolley. The tower crane frequency is identified by theoretical derivation, finite element simulation and field test on the same tower crane scale model. The identification results are consistent with each other, indicating that the feasibility of identifying the tower crane frequency based on the response of the luffing trolley is excellent. The influence of different parameters, luffing speed and hoisting weight on the frequency identification of this method is analyzed. It is found that when the luffing trolley speed is slow, it is difficult to identify the tower crane frequency, but when the speed is fast, the identification result will also be greatly distorted. When the speed is 25% to 80% of the maximum luffing speed of the actual tower crane, the identification result is the most accurate; when the hoisting weight is controlled at 25% to 60% of the maximum hoisting weight of the actual tower crane, the luffing trolley can identify the high-order frequency without causing additional vibration of the tower crane to affect the accuracy of the luffing trolley identification frequency.

[0189] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A tower crane damage detection method based on the acceleration response of the luffing trolley, characterized in that: The following steps are involved: Step 1: Build a luffing trolley-cantilever tower crane system. The luffing trolley is set on the boom of the tower crane. The boom length is set to L. The unit length mass of the tower crane is The material elastic modulus of the tower crane is E, the section inertia moment of the tower crane is I, and the mass of the luffing trolley is m v ; Step 2: An acceleration sensor is arranged on the luffing trolley, and the luffing trolley moves on the boom of the tower crane at a moving speed v. The acceleration sensor collects acceleration response data of the luffing trolley in real time and transmits it to a fast Fourier transform (FFT) conversion module; The expression of the acceleration response data of the luffing trolley is as follows: in, Among them, u y represents the displacement response of the variable-luffing trolley, n represents the response order, 1≤n≤M, M represents the order range; v represents the moving speed of the variable-luffing trolley, t represents time, α n represents the frequency parameter of each nth order, L represents the length of the cantilever beam, i represents a mathematical imaginary number, and ω represents the natural frequency of the cantilever beam; Step 3: The fast Fourier transform (FFT) conversion module transforms the acceleration response data of the variable amplitude vehicle to obtain an acceleration spectrum diagram; Step 4: According to the acceleration spectrum diagram, the modal parameters of the tower crane are identified; According to the peak distribution of the acceleration frequency spectrum, the modal parameters of the tower crane are obtained, wherein the modal parameters include the natural frequency and vibration mode of the tower crane, and the natural frequency includes the left frequency and the right frequency of the tower crane; Step 5: Detecting and identifying damage of the tower crane according to the modal parameters or acceleration response data; The method used to detect and identify damage to a tower crane is either: a. Damage identification method based on natural frequency change; b. Damage identification method based on vibration mode change; c. Damage identification method based on flexibility change; d. Damage identification method based on wavelet transform.

2. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In step 2, the natural frequency ω of the tower crane is expressed as follows: The natural frequency ω of the cantilever beam structure system is expressed as follows:

3. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In step 4, the left and right frequencies of the tower crane are v The expression is as follows:

4. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In step 2, the movement speed v of the luffing trolley is controlled within a range of 25% to 80% of the maximum luffing speed of the tower crane.

5. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In the step 1, a hook is connected to the luffing trolley, and a hanging object is hung on the hook. The weight of the hanging object is controlled to be 25% to 60% of the maximum lifting weight of the tower crane.

6. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In step 5, the damage identification method based on natural frequency change is as follows: A luffing trolley-cantilever tower crane system is built. Before the tower crane is damaged, the luffing trolley moves on the tower crane to obtain acceleration response data of the luffing trolley before damage, and a fast Fourier transform is performed to obtain an acceleration spectrum before damage, and the natural frequency of the tower crane before damage is obtained by identifying the acceleration spectrum before damage; After the tower crane is damaged, the luffing trolley moves on the tower crane to obtain acceleration response data of the luffing trolley after the damage, and performs fast Fourier transform to obtain an acceleration spectrum after the damage, and the natural frequency of the tower crane after the damage is identified through the acceleration spectrum after the damage; The natural frequency of the tower crane before damage and the natural frequency of the tower crane after damage are compared to obtain the damage result of the tower crane.

7. The tower crane damage detection method based on the acceleration response of the luffing trolley according to claim 1 is characterized in that: In step 5, the damage identification method based on vibration mode change is as follows: (1) Building a luffing trolley-cantilever tower crane system, obtaining acceleration response data of the luffing trolley by moving the luffing trolley on the tower crane, (2) performing a fast Fourier transform on the acceleration response data of the luffing trolley to obtain an acceleration spectrum diagram, and identifying the frequency of the tower crane; (3) extracting response data related to the tower crane frequency from the acceleration response data by using a bandpass filter method (BPS); (4) obtaining the instantaneous amplitude of the response data by using Hilbert transform; (5) obtaining a vibration mode of the tower crane from the instantaneous amplitude; (6) performing regularization processing on the vibration mode of the tower crane; (7) Identify the damage of the tower crane by using the mode curvature method or the mode change graph method.

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