Gantry crane damage detection method based on acceleration response of variable amplitude trolley

Abstract

A gantry crane damage detection method based on amplitude car acceleration response, comprising the following steps: step 1: build an amplitude car-simply supported beam gantry crane system, the amplitude car is arranged on the lifting arm of the gantry crane; Step 2: set an acceleration sensor on the amplitude car, the amplitude car moves on the lifting arm of the gantry crane at a moving speed v, the acceleration sensor collects the acceleration response data of the amplitude car in real time and transmits it to the FFT conversion module; Step 3: the FFT conversion module transforms the acceleration response data of the amplitude car to obtain an acceleration spectrum diagram; Step 4: according to the acceleration spectrum diagram, the modal parameters of the gantry crane are identified; Step 5: according to the modal parameters or acceleration response data, the damage condition of the gantry crane is detected and identified. Effect: It can realize the accurate detection of the damage result of the simply supported beam gantry crane.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gantry crane damage detection, in particular to a gantry crane damage detection method based on acceleration response of a variable-amplitude trolley. BACKGROUND

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

[0003] In reality, the modal parameters of all objects are similar to human fingerprints and are different from each other, consisting of countless unique data. The modal parameters of each structure itself usually do not change, such as natural frequency, modal shape, and structural damping, etc., but when the structure itself 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 a coordinate transformation on the data. It converts the response values in the original physical coordinates to the defined modal coordinates. Each basis vector in the modal coordinates is a characteristic vector of the vibration response in the original physical coordinates, that is, the correlation between the basis vectors in the coordinates can be used to simply describe the relationship between the response vectors.

[0004] However, the calculation modal analysis method cannot consider the coupling relationship between the response vectors, so the experimental modal analysis method is usually 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 field test or model test 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 of the structure, and then obtain the modal parameters of the structure through fast Fourier transform (FFT). However, this method has high requirements for the environment, and when measuring large machinery, a large number of test instruments such as sensors are required, the data collected by the measuring points are large, and the data processing is cumbersome. SUMMARY

[0005] The gantry crane damage detection method based on acceleration response of a variable-amplitude trolley provided by the present application can realize accurate detection of the damage result of a simply supported beam gantry crane.

[0006] To achieve the above purpose, the gantry crane damage detection method based on acceleration response of a variable-amplitude trolley provided by the present application comprises the following steps:

[0007] Step 1: Build a variable-amplitude trolley-simple beam gantry crane system, the variable-amplitude trolley is set on the lifting arm of the gantry crane, the length of the lifting arm is L, the unit length mass of the gantry crane is The material elastic modulus of the gantry crane is E, the cross-sectional moment of inertia of the gantry crane is I, and the mass of the variable-amplitude trolley is m v ;

[0008] Step 2: Set an acceleration sensor on the variable-amplitude trolley, the variable-amplitude trolley moves on the lifting arm of the gantry crane at a moving speed v, the acceleration sensor collects real-time acceleration response data of the variable-amplitude trolley and transmits it to a fast Fourier transform (FFT) conversion module;

[0009] The expression of the acceleration response data of the variable-amplitude trolley is as follows:

[0010]

[0011] Wherein, represents the acceleration response of the variable-amplitude trolley, represents the n-order acceleration response coefficient, i represents the mathematical imaginary number, ω Tn represents the n-order frequency of the simple beam system structure, t represents time, n represents the response order, 1≤n≤M, M represents the order range; v represents the variable-amplitude trolley speed, L represents the length of the gantry crane;

[0012] Step 3: The fast Fourier transform (FFT) conversion module converts the acceleration response data of the variable-amplitude trolley to obtain an acceleration frequency spectrum;

[0013] Step 4: According to the acceleration frequency spectrum, the modal parameters of the gantry crane are identified;

[0014] According to the peak value distribution of the acceleration frequency spectrum, the modal parameters of the gantry crane are obtained, the modal parameters include the natural frequency and the mode shape of the gantry crane, the natural frequency includes the left frequency and the right frequency of the gantry crane;

[0015] Step 5: According to the modal parameters or acceleration response data, the damage condition of the gantry crane is detected and identified;

[0016] The method for detecting and identifying the damage condition of the gantry crane is:

[0017] a. Damage identification method based on natural frequency change;

[0018] b. Damage identification method based on mode shape change;

[0019] c. Damage identification method based on flexibility change;

[0020] d. Damage identification method based on wavelet transform.

[0021] Through the above design, the acceleration response of the amplitude-changing trolley is calculated, and according to the expression of the acceleration response data of the amplitude-changing trolley proposed, the acceleration responses of different positions of the portal crane cross arm can be reconstructed. The reconstructed acceleration response is further converted to obtain the acceleration frequency spectrum of the amplitude-changing trolley. Through the acceleration frequency spectrum, the modal parameters such as the frequency and mode shape of the portal crane can be accurately obtained, and then the damage result of the portal crane is detected and identified. The damage result of the portal crane includes whether the portal crane is damaged, and the damage position and damage degree.

[0022] As preferred: in the step 2, the n-order frequency ω Tn The expression is as follows:

[0023]

[0024] The n-order acceleration response coefficient of the amplitude-changing trolley The expression is as follows:

[0025]

[0026] Wherein, A 1,n , A 2,n , A 3,n is the n-order response coefficient of the amplitude-changing trolley, and the expression is as follows:

[0027]

[0028] Wherein, Δ st,n is the deformation variable of the portal crane, and S n is the speed variable of the amplitude-changing trolley, and the expression is as follows:

[0029]

[0030] Wherein, g represents the acceleration of gravity, g = 9.8 m / s 2 .

[0031] As preferred: in the step 4, the left frequency ω Tn1 of the portal crane is ω Tn2 .

[0032]

[0033] The expression of the right frequency ω Tn2 of the portal crane is as follows:

[0034]

[0035] As preferred: in the step 2, the movement speed v of the luffing trolley is controlled at 25%-80% of the maximum luffing speed of the gantry crane.

[0036] As preferred: in the step 1, a hook is connected to the luffing trolley, and a hoisted object is hung on the hook, and the weight of the hoisted object is controlled at 25%-60% of the maximum hoisting weight of the gantry crane.

[0037] Since the luffing structure and the hoisting structure are used more in the operation of the gantry crane, the two parameters of the running speed of the luffing trolley and the weight of the hoisted object will affect the identification of the frequency of the gantry crane by the acceleration response of the luffing trolley. When the speed of the luffing trolley is slow, it will affect the identification rate of the frequency of the gantry crane, but when the speed is fast, the identification result will also be greatly distorted. When the speed is 25%-80% of the maximum luffing speed of the gantry crane, the identification result is the most accurate; when the hoisting weight is controlled at 25%-60% of the maximum hoisting weight of the gantry crane, the luffing trolley can identify the high-order frequency and will not cause additional vibration of the gantry crane to affect the accuracy of the identification of the frequency of the luffing trolley.

[0038] As preferred: in the step 5, the damage identification method based on the change of the natural frequency is as follows:

[0039] A luffing trolley-simple supported beam gantry crane is built. Before the damage of the gantry crane, the luffing trolley is moved on the gantry crane to obtain the acceleration response data of the luffing trolley before the damage, and the fast Fourier transform is performed to obtain the acceleration frequency spectrum diagram before the damage, and the natural frequency of the gantry crane before the damage is identified through the acceleration frequency spectrum diagram before the damage.

[0040] After the damage of the gantry crane, the luffing trolley is moved on the gantry crane to obtain the acceleration response data of the luffing trolley after the damage, and the fast Fourier transform is performed to obtain the acceleration frequency spectrum diagram after the damage, and the natural frequency of the gantry crane after the damage is identified through the acceleration frequency spectrum diagram after the damage.

[0041] The natural frequency of the gantry crane before the damage and the natural frequency of the gantry crane after the damage are compared to obtain the damage result of the gantry crane.

[0042] The natural frequency is the most easily obtained parameter among the modal parameters and has high identification accuracy. There are many methods for damage identification based on the change of the natural frequency, and the characteristics are: only the stiffness of the structure is reduced when the structure is damaged, and the change of the mass of the structure is ignored, and a modified theoretical model is established before the early damage of the structure. In theory, the ratio of the change of any two-order frequency after the damage is only a function of the damage position and is independent of the damage size.

[0043] As preferred: in the step 5, the damage identification method based on mode shape variation is as follows:

[0044] (1) Build a variable-amplitude trolley-simple beam gantry crane, and obtain the acceleration response data of the variable-amplitude trolley by moving the variable-amplitude trolley on the gantry crane,

[0045] (2) Perform fast Fourier transform on the acceleration response data of the variable-amplitude trolley to obtain an acceleration frequency spectrum, and identify the frequency of the gantry crane;

[0046] (3) Extract the response data related to the frequency of the gantry crane from the acceleration response data by using band-pass filtering (BPS);

[0047] (4) Obtain the instantaneous amplitude of the response data by using Hilbert transform;

[0048] (5) Obtain the mode shape of the gantry crane from the instantaneous amplitude;

[0049] (6) Perform regularization processing on the mode shape of the gantry crane;

[0050] (7) Identify the damage condition of the gantry crane by using mode shape curvature method or mode shape variation pattern method.

[0051] Mode shape is a basic modal parameter, although its test accuracy is low, but it contains more information, so there are many damage identification and diagnosis techniques based on mode shape variation. (1) Mode shape curvature method, if the structure is damaged, the stiffness at the damaged part will decrease and the curvature will increase. The change of mode shape curvature increases with the increase of curvature. Therefore, the position of damage can be determined according to the change of mode shape curvature. (2) Mode shape variation pattern method, using the relative change of mode shape as the positioning parameter, that is, the ratio of the difference between the mode shape before and after damage to the mode shape before damage. When damage occurs, the relative change of mode shape on the affected degree of freedom in the damage area will have a larger value. Therefore, the position of damage can be identified by using the mode shape relative change pattern.

[0052] The damage identification method based on flexibility variation is as follows:

[0053] Under the condition that the mode satisfies the normalization, the flexibility matrix is a function of the inverse of frequency and mode shape. With the increase of frequency, the influence of the inverse of high frequency in the flexibility matrix can be ignored. In this way, only the first few low-order modal parameters and frequencies need to be measured to obtain a matrix with good accuracy. According to the difference matrix obtained from the two flexibility matrices before and after damage, the maximum element in each column of the difference matrix is found by checking the maximum element in each column, and the position of damage is found.

[0054] The damage identification method based on wavelet transform is as follows:

[0055] The acceleration response signal of the variable amplitude trolley is filtered and quadratically integrated 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.

[0056] Beneficial effects of the present invention: In previous studies, there has been no method for measuring the response of a gantry crane using the response of a luffing trolley. The present invention builds a luffing trolley-simply supported beam gantry crane system, and measures the acceleration response of the luffing trolley to accurately reflect the modal parameters of the gantry crane, thereby detecting and identifying the damage results of the gantry crane, providing a theoretical basis and methodological guidance for the subsequent realization of intelligent damage detection of structural movements similar to simply supported beams. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the process of the present invention;

[0058] Figure 2 Schematic diagram of the structure of the luffing trolley-simple-supported-beam gantry crane in the embodiment;

[0059] Figure 3 This is a comparison chart of the frequency results of the scaled model identified by finite element, theory, and experiment in the embodiment;

[0060] Figure 4 This is a frequency diagram of the gantry crane identified by the trolley response under five variable-luffing working conditions in the embodiment;

[0061] Figure 5 This is a frequency diagram of the gantry crane identified by the trolley response under five lifting weight conditions in the embodiment. DETAILED DESCRIPTION

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

[0063] like Figure 1 A gantry crane damage detection method based on the acceleration response of the luffing trolley is shown, comprising the following steps:

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

[0065] Step 2: Set an acceleration sensor on the luffing trolley, the luffing trolley moves on the lifting arm of the gantry crane at a moving speed v, the acceleration sensor collects the 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] Wherein, represents the acceleration response of the luffing trolley, represents the n-order acceleration response coefficient, i represents a mathematical imaginary number, ω Tn represents the n-order frequency of the simply supported beam system structure, t represents time, n represents the response order, 1≤n≤M, M represents the order range; v represents the luffing trolley speed, L represents the length of the gantry crane;

[0069] Step 3: The fast Fourier transform (FFT) conversion module converts the acceleration response data of the luffing trolley to obtain an acceleration frequency spectrum;

[0070] Step 4: According to the acceleration frequency spectrum, the modal parameters of the gantry crane are identified;

[0071] According to the peak value distribution of the acceleration frequency spectrum, the modal parameters of the gantry crane are obtained, the modal parameters include the natural frequency and the vibration mode of the gantry crane, and the natural frequency includes the left frequency and the right frequency of the gantry crane;

[0072] Step 5: According to the modal parameters or the acceleration response data, the damage condition of the gantry crane is detected and identified;

[0073] The method for detecting and identifying the damage condition of the gantry crane is:

[0074] a. Damage identification method based on natural frequency change;

[0075] b. Damage identification method based on vibration mode change;

[0076] c. Damage identification method based on flexibility change;

[0077] d. Damage identification method based on wavelet transform.

[0078] As shown in the formula (1), the acceleration response of the luffing trolley is: Figure 2 The length of the gantry crane 1 is L, the mass of the luffing trolley 2 is m v , the luffing trolley 2 moves on the gantry crane 1 at a uniform speed v, the unit length mass of the gantry crane 1 is The distance of the luffing trolley 2 moving with time is xv , vertical displacement of the variable amplitude trolley 2 is u c .

[0079] For the variable amplitude trolley-simple supported gantry crane, the motion equation of the gantry crane system is:

[0080]

[0081] Wherein, u j represents the vertical displacement of the gantry crane, E is the material elastic modulus of the gantry crane, I represents the cross-sectional moment of inertia of the gantry crane, f c (t) represents the load generated by the variable amplitude trolley 2 on the gantry crane with time change; delta represents the delta function, which means that when x=vt, the value of the delta function is 1, and the value is 0 at other times; represents the derivative of the vertical displacement of the gantry crane with respect to time t, u j represents the fourth derivative of the vertical displacement of the gantry crane with respect to position x, x represents the position of the variable amplitude trolley 2 along the axis of the gantry crane from the left end point, and v is the running speed of the variable amplitude trolley 2.

[0082] For the theoretical derivation of the embodiment, according to the simplified calculation model of the gantry crane shown in Figure 2 , the modal superposition method is used to represent the vertical displacement of the gantry crane, and the solution of equation (1) is the displacement of the gantry crane u j , which can be represented by the superposition of the product of many vibration modes φ(x) and modal coordinates q Tn (t). For the gantry crane structure, the modal form that meets the boundary conditions of the simplified model is sine, and the dynamic response of the gantry crane can be represented by the following formula:

[0083]

[0084] Wherein, q Tn represents the modal coordinate of the gantry crane of a certain order, n represents the order of the vibration mode of the gantry crane, and the range is 1~M.

[0085] The relationship between the variable amplitude trolley 2 and the gantry crane 1 is embodied by the contact force between the variable amplitude trolley and the gantry crane, which can be regarded as the sum of the elastic force of the variable amplitude trolley system on the gantry crane system and the gravity of the variable amplitude trolley, since the tire of the variable amplitude trolley system is a rigid tire, the elastic force is 0, f c (t) is represented as:

[0086] f c (t)=-m v g (3)

[0087] where g is the gravity acceleration of the object, g = 9.8 m / s 2 .

[0088] In the above, the basic motion equations of the gantry crane system and the luffing trolley system have been listed. Next, the response expressions of the above two systems will be solved. The frequency ω v of the luffing trolley and the frequency ω Tn of the gantry crane are respectively:

[0089]

[0090] where k v represents the stiffness of the luffing trolley 2.

[0091] It should be noted that, since the luffing trolley is rigidly connected with the jib and there is no tire elastic force, the stiffness is not considered in the simplified model, so the frequency of the luffing trolley here will not be considered.

[0092] From (5), we have:

[0093]

[0094] Substituting formulas (2)-(5) into formula (1) and combining the zero boundary conditions, we have:

[0095] u j (x,t)| x＝0,t＝0 = 0 (7)

[0096]

[0097] u j (x,t)| x＝L,t＝0 = 0 (9)

[0098]

[0099] The modal coordinates of the gantry crane system considering the influence of the contact force of the moving luffing trolley can be obtained as:

[0100]

[0101] Substituting formula (11) into formula (2), the dynamic response of the gantry crane can be obtained as:

[0102]

[0103] From formula (12), it is easy to see that the response of each order of the gantry crane system is:

[0104]

[0105] From equation (13), it can be concluded that the response of each order of the gantry crane simplified mathematical model is influenced by the position of the jib and the time of the trolley. A simple trigonometric analysis shows that when the selected contact observation point on the jib satisfies the following condition:

[0106]

[0107] In this case, sin(nπx / L) = 0, that is, u n (x, t) = 0, so the modal response value received by the sensor at this observation point at a certain time is zero. For example, at the midspan position of the gantry crane, x = L / 2, substituting equation (14) gives n = 2N, that is, the responses of the 2nd, 4th, 6th, etc. order modes of the gantry crane system are zero at this position. In other words, in reality, using the most common distributed accelerometers, when measuring the modal response value under external load excitation, at the above-mentioned positions, the relevant data cannot be measured theoretically because the responses of the even order modes of the gantry crane system are zero. In this way, the direct measurement method needs to consider the data loss caused by these factors when selecting the arrangement position of the sensor, which reduces the measurement efficiency to a certain extent, and also increases the work task and difficulty of the direct measurement method.

[0108] Another interesting phenomenon is that according to the above response formula, it can be found that the trolley moving to any position on the jib of the gantry crane can obtain the specific response value of the entire jib at that time, that is, the response value of the gantry crane can be obtained through the response value of the trolley, thereby deducing the frequency of the gantry crane. Because during the movement of the trolley, the position has the following time, speed and position relationship:

[0109] x c = vt, u c = u j (x, t)| x＝vt (15)

[0110] u c = u j (x, t)| x＝vt (16)

[0111] where u c represents the vertical displacement value of the trolley.

[0112] Substituting equations (15) and (16) into equation (12) gives the response of the trolley of the gantry crane system as:

[0113]

[0114] The response of the luffing trolley can be obtained by expanding the above formula:

[0115]

[0116] That is, it can be expressed as:

[0117]

[0118] Each coefficient is expressed as:

[0119]

[0120] In the above formula, Δ st,n is approximately equal to the deformation of the gantry crane caused by the luffing trolley acting on the jib when it is stationary, because the luffing trolley is relatively light, and the deformation of the gantry crane jib caused by the luffing trolley when it is stationary is small, and the deformations at different positions cannot be reasonably represented in full, S n is a velocity variable, and they are respectively:

[0121]

[0122] The acceleration response formula of the luffing trolley can be obtained by twice differentiating (19):

[0123]

[0124] That is, it can be expressed as:

[0125]

[0126] Each coefficient is expressed as:

[0127]

[0128] From equation (26), it can be obviously judged that the response of the trolley is composed of two parts. One part is due to the change of its own motion state, which brings the trolley frequency part. The frequency of this part is related to the speed and time of the trolley, which is nπvt / L. Secondly, when the trolley moves on the boom of the gantry crane, the vibration of the gantry crane also changes with the modal of the trolley, which is nπx / L. When the trolley is working, it causes the vertical vibration of the boom, and the vibration wave is transmitted along the x-axis direction of the boom to form an extra frequency component, which is called the trolley frequency. It can be found that the reason for this frequency component is that the trolley acts on the boom, and the boom transmits the action back to the trolley, and the two interact with each other. Therefore, if the trolley does not work on the luffing mechanism, the frequency component will not be formed on the boom. The other part is the offset frequency of the gantry crane itself. The left frequency of the gantry crane is and the right frequency of the gantry crane is Obviously, the frequency of the gantry crane is related to its own properties and only related to the speed of the trolley. In the simplified mathematical calculation model of the embodiment, the frequency component of the trolley response is the same as the frequency component of the gantry crane, but if other simplified calculation models considering the stiffness of the trolley are considered, the trolley response will also contain the natural frequency of the trolley itself, the trolley frequency and the specific expression of the gantry crane frequency are as follows:

[0129]

[0130] From equations (30)-(32), it can be seen that the left and right frequencies of the gantry crane are based on the square of the natural frequency of the gantry crane ω Tn plus or minus a square of the amplitude nπv / L. The reason for this phenomenon is that the spatial position relationship between the trolley and the boom changes with time, and the vibration wave The source and the receiver also produce relative motion. When the wavelength is compressed, the frequency will increase, which is the right frequency of the gantry crane. When the wavelength is lengthened, the frequency will decrease, which is the left frequency of the gantry crane. This phenomenon is called the Doppler effect. In the simplified mathematical calculation model of the gantry crane assumed in this paper, the frequency component contained in the response of the trolley is almost the same as the frequency component contained in the response of the gantry crane itself, which provides a theoretical basis and method guidance for realizing the intelligent detection of the gantry crane movement.

[0131] In the past research, there is no method to measure the response of gantry crane by the response of trolley, the present application builds a trolley-simple beam gantry crane, by measuring the acceleration response of trolley, accurately reflects the frequency of gantry crane, and then detects and identifies the damage result of gantry crane, which provides a theoretical basis and method guidance for realizing intelligent damage detection of similar simple beam structure.

[0132] Next, the influence of the trolley speed and the weight of the hoisted object on the identification of the frequency of the gantry crane based on the trolley signal is analyzed, the trolley speed parameter is studied by model test, and the weight of the hoisted object parameter is studied by finite element simulation method. If the model test is used to study the weight of the hoisted object, the test scheme has little difference and cannot clearly reflect the influence of the parameters on the method. In this embodiment, the influence of five trolley speed conditions and five hoisted object weight conditions on the method is studied, and the specific conditions are shown in Table 1:

[0133] Table 1 Parameter analysis condition table

[0134]

[0135] The selection of the above conditions depends on the maximum trolley speed and the maximum hoisted weight that can be achieved under the normal working condition of the real gantry crane. The trolley speed is converted from the motor rotation speed based on the motion speed of the trolley of the real gantry crane, and the hoisted weight is valued according to the maximum hoisted weight decreased by about 20%.

[0136] Before carrying out the parameter research test, the accuracy of the theoretical principle, finite element simulation and field test needs to be compared and analyzed. By using finite element simulation, theoretical derivation and field test to identify the frequency of the gantry crane based on the response of the trolley of the same scale model, the comparison result of the smoothed frequency is shown in Figure 3 , it can be clearly seen in Figure 3 that the finite element numerical simulation result is basically consistent with the test result, and the result obtained by theoretical derivation is slightly different. The reason for the different energy at the same frequency is that the coupling effect between the trolley and the tower is not considered in the motion equation, so the energy is smaller than the energy values obtained by the other two methods. At the same time, since the theoretical derivation adopts a simplified mathematical model of simple beam, the effect of identifying the frequency is not as good as the finite element and model test.

[0137] After completing the mutual verification of the accuracy of the theory, finite element and model test, the trolley speed research of this paper is first carried out. Figure 4 The results of identifying the frequency of the gantry crane by the response of the trolley under different trolley speed conditions are shown. When the trolley speed is 3.16x10 -3m / s (Case 1), which is a very low uniform motion state, the body response can identify the first order frequency of the gantry crane, but it is difficult to identify the second order frequency. Unlike this, when the trolley speed is 9.50 x 10 -3 m / s (Case 3), the body response can well identify the first and second order frequencies of the gantry crane. However, when the trolley speed exceeds the upper limit control, for example, 2.1 x 10 -2 m / s (Case 5), the identified frequency will be severely distorted, which can be because when the trolley moves faster, the acceleration sensor installed on the trolley receives a larger deviation value in the same time, thereby affecting the accuracy of data reception. In addition, when the trolley speed is faster, the acceleration sensor identifies the signal distortion, which will cause the spectrum leakage to be more serious when the FFT is transformed, thereby causing incorrect numerical analysis and affecting the accuracy of frequency spectrum identification. Based on the above analysis, it is considered that within the range of trolley speed that the gantry crane can accept, when identifying the frequency of the gantry crane, 25% to 80% of the maximum trolley speed that the gantry crane can reach in the normal working state should be used for modal identification of the gantry crane, otherwise the inaccuracy of the measured results is high.

[0138] In order to analyze the influence of the hoisted weight on the identification of the frequency of the gantry crane during the trolley amplitude motion, the working speed of the trolley is 0.6 m / s. The influence of the hoisted weight on the identification of the frequency of the gantry crane during the trolley amplitude motion is analyzed by MATLAB simulation, and the results are shown in Figure 5 From Figure 5 it can be clearly seen that when the amount of the weight hung on the trolley is larger, the response value of the trolley can better identify the frequency of the gantry crane. Figure 5From the static state to the start of motion, it is found that the greater the weight of the hoisted load, the greater the energy generated by the luffing trolley during operation. This is because the trolley does not generate any additional vibration when it is stationary, and when the trolley starts to move at a constant speed, the vertical deformation of the trolley changes, which causes vertical vibration. When the suspended load is heavier, the deformation of the trolley is greater, and the additional vibration response is greater, and the energy value of the identification frequency is greater. By carefully observing the first-order frequency in the figure, it can be found that under the conditions of 160 kg (Case 1), 480 kg (Case 2), and 800 kg (Case 3), the left and right frequencies of the gantry crane at this order cannot be seen. The specific reasons have been analyzed above. According to the formula for the distance between left and right frequencies, it can be known that the distance between left and right frequencies decreases with the decrease of order. Here, the second reason is embodied. When the hoisted load is heavy, the load will sway when the trolley moves left and right, which will cause additional vibration of the gantry crane, resulting in a significant change in the left and right frequencies. Therefore, the hoisted load should be controlled within 25% to 60% of the maximum hoisted load that the real gantry crane can achieve under normal working conditions, so that the luffing trolley can identify high-order frequencies and will not cause additional vibration of the gantry crane to affect the accuracy of the luffing trolley identification frequency. It should also be noted that when the mass is too large, the luffing trolley at the free end of the cantilever will cause geometric nonlinearity, which is related to the size of the mass. The greater the weight, the greater the influence of geometric nonlinearity on the identification frequency. Since geometric nonlinearity is different from the linear assumption of the identification method in this paper, it will affect the effect of identifying the whole from the point, so geometric nonlinearity is not considered in this embodiment. This is also a part that needs to be improved in the later stage.

[0139] In summary, since the luffing trolley and the gantry crane are rigidly connected, the trolley body frequency of the luffing trolley is a high-order frequency and does not affect the identification of the gantry crane frequency. The frequency of the gantry crane can be well identified from the response of the moving trolley body. The frequency of the gantry crane is identified through theoretical derivation, finite element simulation, and field test of the same gantry crane scale model. The identification results are consistent with each other, indicating that the feasibility of identifying the frequency of the gantry crane based on the response of the luffing trolley is excellent. The influence of different parameters, luffing speed, and hoisted load on the identification frequency of this method is analyzed. It is found that it is difficult to identify the frequency of the gantry crane when the luffing trolley speed is slow, but the identification result will also be greatly distorted when the speed is fast. When the speed is 25% to 80% of the maximum luffing speed of the real gantry crane, the identification result is the most accurate. When the hoisted load is controlled within 25% to 60% of the maximum hoisted load of the real gantry crane, the luffing trolley can identify high-order frequencies and will not cause additional vibration of the gantry crane to affect the accuracy of the luffing trolley identification frequency.

[0140] The above merely provides the preferred embodiments of the present application, and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modifications, equivalent replacements, improvements, etc. made within the principles and technical scope of the present application shall fall into the scope of the present application.

Claims

1. A method for detecting damage of a gantry crane based on an acceleration response of a trolley, characterized in that, The method comprises the following steps: Step 1: build a variable-amplitude trolley-simple beam gantry crane system, the variable-amplitude trolley is arranged on the lifting arm of the gantry crane, the length of the lifting arm is L, the unit length mass of the gantry crane is The material elastic modulus of the gantry crane is E, the cross-sectional moment of inertia of the gantry crane is I, and the mass of the variable-amplitude trolley is m v ; Step 2: An acceleration sensor is arranged on the luffing trolley, the luffing trolley moves on the lifting arm of the gantry crane at a moving speed v, the acceleration sensor collects acceleration response data of the luffing trolley in real time and transmits the data to a fast Fourier transform (FFT) conversion module; The expression of the acceleration response data of the luffing trolley is as follows: wherein, denotes the acceleration response of the trolley, denotes the n-th order acceleration response coefficient, i denotes the mathematical imaginary number, ω Tn denotes the n-th order frequency of the simply supported beam system structure, t denotes time, n denotes the order of response, 1 ≤ n ≤ M, M denotes the range of orders; v denotes the trolley speed, L denotes the length of the gantry crane; Step 3: The fast Fourier transform (FFT) conversion module converts the acceleration response data of the luffing trolley to obtain an acceleration frequency spectrum; Step 4: The modal parameters of the gantry crane are identified according to the acceleration frequency spectrum; The modal parameters of the gantry crane are obtained according to the peak value distribution of the acceleration frequency spectrum, the modal parameters include the natural frequency and the mode shape of the gantry crane, and the natural frequency includes the left frequency and the right frequency of the gantry crane; Step 5: The damage condition of the gantry crane is detected and identified according to the modal parameters or the acceleration response data; The method for detecting and identifying the damage condition of the gantry crane is: a. a damage identification method based on natural frequency change; b. a damage identification method based on mode shape change; c. a damage identification method based on flexibility change; d. a damage identification method based on wavelet transform.

2. A method of gantry crane damage detection based on response of the trolley acceleration according to claim 1, characterized in that: In the step 2, the n-th frequency ω Tn The expression is as follows: The n-th order acceleration response coefficient of the variable amplitude trolley The expression is as follows: where A 1,n , A 2,n , A 3,n are the n-th order response coefficients of the amplitude car, and the expression is as follows: where Δ st,n is the deformation variable of the gantry crane, S n is the speed variable of the variable amplitude trolley, and the expression is as follows: where g represents the acceleration of gravity, g = 9.8 m / s 2 .

3. The variable amplitude trolley acceleration response based gantry crane damage detection method of claim 1, wherein: In the step 4, the left frequency ω Tn1 The expression is as follows: The right frequency ω of the portal crane Tn2 The expression is as follows:

4. The variable amplitude trolley acceleration response based gantry crane damage detection method of claim 1, wherein: In the step 2, the moving speed v of the luffing trolley is controlled at 25%-80% of the maximum luffing speed of the gantry crane.

5. The variable amplitude trolley acceleration response based gantry crane damage detection method of claim 1, wherein: In the step 1, a hook is connected to the luffing trolley, and a hoisted object is hung on the hook, and the weight of the hoisted object is controlled at 25%-60% of the maximum hoisting weight of the gantry crane.

6. The variable amplitude trolley acceleration response based gantry crane damage detection method of claim 1, wherein: In the step 5, the damage identification method based on natural frequency change is as follows: A luffing trolley-simple supported beam gantry crane is built, before the damage of the gantry crane occurs, the luffing trolley moves on the gantry crane to obtain the acceleration response data of the luffing trolley before the damage, and the fast Fourier transform is performed to obtain the acceleration frequency spectrum before the damage, and the natural frequency of the gantry crane before the damage is identified through the acceleration frequency spectrum before the damage; After the damage of the gantry crane occurs, the luffing trolley moves on the gantry crane to obtain the acceleration response data of the luffing trolley after the damage, and the fast Fourier transform is performed to obtain the acceleration frequency spectrum after the damage, and the natural frequency of the gantry crane after the damage is identified through the acceleration frequency spectrum after the damage; The natural frequency of the gantry crane before the damage and the natural frequency of the gantry crane after the damage are compared to obtain the damage result of the gantry crane.

7. The variable amplitude trolley acceleration response based gantry crane damage detection method of claim 1, wherein: In the step 5, the damage identification method based on mode shape change is as follows: (1) A luffing trolley-simple supported beam gantry crane is built, and the luffing trolley moves on the gantry crane to obtain the acceleration response data of the luffing trolley, (2) The fast Fourier transform is performed on the acceleration response data of the luffing trolley to obtain the acceleration frequency spectrum, and the frequency of the gantry crane is identified; (3) The band-pass filtering method (BPS) is used to extract the response data related to the frequency of the gantry crane in the acceleration response data; (4) The instantaneous amplitude of the response data is obtained by using Hilbert transform. (5) obtaining the vibration mode of the gantry crane from the instantaneous amplitude; (6) performing regularization processing on the vibration mode of the gantry crane; (7) identifying the damage condition of the gantry crane through the vibration mode curvature method or the vibration mode change pattern method.

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