Bolted joints can withstand large loads and can be repeatedly assembled and disassembled compared to structural joints such as riveting, welding, and cementing, so they are used in large numbers to connect detachable main bearing structures [1] . The main force parts of the aeronautical (sky), the hanging tower of the construction site, the support frame of the offshore platform, and the steel frame bridge are basically bolted. Because the pre-tightening force can improve the reliability of the bolt connection, the anti-loose ability and the fatigue strength of the bolt, and enhance the tightness and rigidity of the joint, many structures have strict requirements on the bolt pre-tightening force. Before the structure is in service, the bolts are tightened as required. However, in the long-term service process, due to various loads such as fatigue, vibration, impact, etc., the connecting bolts of the structure may gradually loosen (indicating a decrease in the tightening force of the bolt), which may cause equipment failure. The structure is completely destroyed, resulting in a serious disaster. Therefore, it is necessary to develop a non-destructive testing method to evaluate the actual state of the bolt connection online [2] .
Xu Chao et al [3] and Wang et al [4] reviewed and summarized the bolt loosening damage detection methods. The methods mentioned are summarized in four main categories: 1 based on the method of acoustic elastic effects. This method uses the phenomenon that the acoustic and elastic properties of the bolt change with the change of the bolt tightening force to detect the pre-tightening force of the bolt [5-7] . The disadvantage is that the sampling frequency of the signal acquisition device is very high (about 1Gs/s), which is not only expensive, but also high-frequency signals are susceptible to noise. 2 Piezoelectric sensor based method. The method can be further divided into a piezoelectric admittance (impedance) based method and an energy based method. The former was used by Sun et al. [8] for the loose identification of the truss structure joints, Wang Dansheng et al. [9] and Gao et al. [10] used it for the detection of bolt loose damage. The method reflects the change of the structural impedance by detecting the electrical impedance (or admittance) of the piezoelectric ceramic piece closely attached to the structure, thereby realizing the identification of the looseness of the bolt on the base structure. Wang et al. [11] studied energy-based methods. The method utilizes an active sensing technology, using a piezoelectric piece on one side of the bolted connecting member as an excitation source and a piezoelectric piece on the other side as an energy extractor, reflecting the tightness of the bolt according to the amount of energy transmitted between the two piezoelectric pieces. degree. The piezoelectric sensor-based method also utilizes high-frequency signals. In addition to the high cost and vulnerability of the device, the reliability and durability of the sensor connected to the structure to be tested also needs to be solved. 3 Methods based on nonlinear dynamics theory. Under the action of large external excitation, the bolt loosening causes the interface of the structural joint to separate, generating nonlinear dynamic response, directly utilizing the nonlinear dynamic response signal of the structure, and extracting the characteristic parameters describing the nature of the structural damage based on the nonlinear dynamics theory method. The relationship between the structural damage state and the nonlinear characteristic parameters is carried out, and then the state monitoring and identification are performed. For example, Timothy et al. [12] studied the identification problem of bolt loose state based on chaos theory. The test principle and test equipment of this type of method are very complicated and are not convenient for engineering applications. 4 Methods based on linear dynamics theory. Structural damage can cause changes in structural dynamics parameters (such as natural frequency, mode shape, damping, curvature mode, frequency response function, power spectrum, etc.), and the amount of change in these kinetic parameters can be measured to reverse the damage state of the structure. The research by Yang Zhichun et al [13-14] , Cawley et al [15] and Liang et al [16] can be classified as such methods.
Because the structural dynamics parameters are easy to test and high precision [17-18], it becomes a classic method for condition monitoring and identification. However, in the study of structural dynamics parameters to identify loose bolt damage, most of the bolts are divided into two states: "song" and "tight". The literature for quantitative detection of tightening force is still lacking. Based on the outlier analysis method based on Markov's square distance in statistics, this paper proposes a quantitative method for bolt loosening based on the Euclidean distance of the first 5 natural frequencies of the structure, and carries out experimental verification and application examples.
1 SED-based outlier analysis
In the data-driven damage detection method, if the characteristic parameters measured under the structural integrity are defined as normal data, the characteristic parameters measured under the damage condition are defined as abnormal data, and the essence of the damage detection is from the measured large amount of data. Separate the abnormal data and extract as much information as possible about the damage (degree of damage, location of damage, etc.) from the abnormal data. Due to factors such as measurement error, the measured data has a certain degree of dispersion. Even if the structure is in good condition, the measured characteristic parameter data may not be exactly the same every time, which brings difficulties to the separation of abnormal data. The outlier analysis method based on the Markov square distance is an effective method to solve this problem.
If the measured characteristic parameter is a univariate distribution with a mean of μ and a standard deviation of σ, the distance from the sample x to the mean can be defined in two ways; 1 x-μ, called absolute distance, 2 (x-μ)/ σ, called the relative distance. Obviously, the relative distance is a standardized distance, which not only reflects the difference between the sample and the mean, but also reflects the “position†of the sample in all samples from the perspective of the distribution probability. Expanding, for a multivariate distribution with mean μ and covariance matrix Σ, the relative distance of the sample x to the mean can be defined as Z=L -1 (x-μ), where LL T = Σ . This definition not only considers the distribution of variables, but also considers the interaction between different variables. In order to remove the square root calculation in the calculation, take the square value of the above relative distance, that is, define D=Z T Z, then
The last line is the definition of the Markov squared distance. To use the Markov square distance in damage detection, we first need to extract the multivariate characteristic parameters that can reflect the damage state from the measured data (this paper takes the vector composed of the first 5 natural frequencies of the structure as the characteristic parameter). Assuming that the measured multivariate feature parameters consist of p variables and there are n observations, it can be regarded as n points in a p-dimensional space, or as a matrix of pxn dimensions. Using the above definition, the Markov squared distance of the i-th measuring point is:
Where: D i is an outlier indicator; {f i } is the i-th measured value of the measured p-dimensional variable {f}, which is a p-dimensional vector of possible anomalies, such as a pre-structure p-order natural frequency vector obtained in different periods; {f} and Σ are the mean vector and covariance matrix of the measured n p-dimensional variables {f}, respectively. T stands for transpose operation. D i is compared with a given abnormal value threshold. If it is greater than the threshold, it is judged to be abnormal, and it can be seen from the literature [19] that the larger D i is, the farther away from the normal situation [20] . If only the distribution of the variables is considered without considering the interaction between the variables, the Mahalanobis distance can be further simplified to the standard Euclidean distance, which is defined as:
Where diag(Σ) represents the diagonal matrix of the covariance matrix Σ. The standardized Euclidean distance is because the normalized covariance matrix is ​​a diagonal matrix, and the calculation amount is much less than the Markov square distance, but it retains the good detection ability for the outliers. In actual use, if the outliers are not a priori known, the interpolation abnormal value detection is often performed, that is, the measurement vector to be detected participates in the calculation of the statistical average, including the mean and the variance; if there is a priori known Without damage data, extrapolation can be used to detect outliers for vectors that may be abnormal.
2 Bolt loosening quantitative detection method and its verification
The following is an example of a cantilever beam connected by a single bolt to introduce a quantitative detection method for the degree of looseness of the bolt.
2.1 Test device
As shown in Figure 1, the test piece is made up of two metal long beams, and the lap joint is connected through a refined stainless steel bolt (M10 (A2-70)); the right end of the test piece is fixed on the foundation, and the left end is free. A cantilever beam; measuring points and excitation points are respectively arranged on the upper and lower surfaces at a position 10 mm from the left end of the test piece.
The test piece is excited by the exciter, and the acceleration sensor is used to pick up the vibration at the measuring point, and the modal tester and the accompanying software are used to measure the first 5th-order bending natural frequency of the system. The test site is shown in Figure 2.
2.2 Test process
(1) The bolts are completely tightened (tightening torque is 24N·m), and 30 sets of the first 5 natural frequencies of the cantilever beam under tightening conditions are measured by random excitation. These data are used to calculate the mean vector {f} of the natural frequency vector in the initial state and the diagonal matrix diag(Σ) of the covariance matrix.
(2) The tightening torques of the adjusting bolts are 24N·m, 15N·m, 5N·m and hand tight, and the first 5 natural frequencies of the measuring structure are each 5 sets. Among them, except for the hand tight state, the other states are adjusted with a torque wrench. Test conditions and corresponding measurement times are shown in Table 1. This part of the data is used to find the relationship between the standard Euclidean distance of the natural frequency vector and the tightening force.
(3) The pre-tightening force of the bolts is adjusted again to be 24 N·m, 20 N·m, 15 N·m, 10 N·m, 5 N·m, and the hand tight state, and the first five natural frequencies of the measurement structure are each set of five groups. Test conditions and corresponding measurement times are shown in Table 2. This part of the data is used to analyze the relationship between the tightening force and the single mode natural frequency and the later test verification.
2.3 Relationship between SED and bolt tightening force
The 30 sets of 5-dimensional natural frequency vectors measured under tightening conditions are {f 1 }, {f 2 },...,{f 30 }, respectively, and the average vector {f} and covariance matrix of the 30 sets of vectors are calculated. The diagonal matrix diag(Σ) is then calculated according to equation (3), and the SED values ​​of the 30 sets of vectors are respectively calculated. The result is shown in Fig. 3. Obviously, the SED values ​​for each sample are randomly distributed. This calculation method is an interpolation method.
Substituting the five sets of measurement results corresponding to the 24N·m operating conditions in Table 1 into equation (3), respectively, obtaining five SED values ​​(the five data points are the results of extrapolation calculation), and the same as the 30 of FIG. The SED values ​​are plotted together, as shown in Figure 4. As can be seen from Fig. 4, the five data obtained by extrapolation cannot be separated from the data obtained by the previous 30 interpolation methods. This is sensible because the conditions they represent are 24 N·m tightening torque.
Then, using the extrapolation method, the SED values ​​corresponding to the other working conditions in Table 1 are obtained, and the results are plotted in Fig. 5 together with the data obtained in the previous period. It can be seen from Fig. 5 that the distinction between the SEDs corresponding to the four tightening torque states is obvious, and no confusion occurs; 2 the SEDs corresponding to the same tightening torque state have little difference with each other; 3 the SED decreases with the tightening torque Increase monotonically. In order to further find the quantitative relationship between the SED and the tightening torque, the 20 SED values ​​corresponding to the working conditions of Table 1 and the tightening torque values ​​were fitted by Matlab software to obtain an exponential curve as shown in FIG. The curve visually reveals the quantitative relationship between the SED and the tightening torque, and can be used as a predictive curve of the bolt tightening torque, that is, a reference curve for bolt looseness damage detection.
2.4 Method for assessing the degree of looseness of bolts using SED
According to the above analysis, the method of estimating the looseness of bolts using the first 5 natural frequencies of the structure is summarized as follows:
(1) Test several sets of natural frequencies of the tightening state to form a natural frequency vector matrix, and calculate the average vector and covariance matrix of the matrix. The number of samples must be no less than the dimension of the vector.
(2) Test the natural frequency vector of a limited number of tightening conditions, and calculate the SED value between each vector to the above average vector by extrapolation method, and fit the relationship between the SED value and the tightening force obtained in each working condition. As a reference curve for damage degree detection.
(3) Test the natural frequency vector of the structure under test, calculate the SED value between it and the above average vector, and then compare the obtained result with the reference curve to give an estimated bolt tightening force in the state to be tested. The first two steps are basic work and need to be carried out before the formal service of the structure.
2.5 Test verification
A total of 30 sets of measurement data in the six working conditions in Table 2 are substituted into equation (3), and the corresponding 30 SED values ​​are obtained by extrapolation method, and are drawn together with 30 SEDs obtained by interpolation in the tightening condition. In Figure 8. Comparing Fig. 7 with Fig. 5, Fig. 7 reflects the same rule as Fig. 5. The 30 SED values ​​corresponding to the six operating conditions in Table 2 are plotted together with the reference curves in Figure 6 (see Figure 8). It can be seen from Fig. 8 that the total of 30 data of the six groups used for verification agree well with the reference curve (the maximum error occurs at 10 N·m and the absolute error is about 4 N'm), which proves the rationality of the method.
3 Application examples
In order to explore the effectiveness of the above method in the case of multi-bolt connection, it is applied to the quantitative detection of bolt loosening in the physical model of a satellite solar panel.
3.1 Test device
The satellite solar panels are fixed to the foundation by clamps (see Figures 9 and 10). The solar panels and clamps are connected by four M6 bolts, and the tightening torque of the bolt design working state is 12 N·m.
3.2 Test reference curve
The test of the reference curve is carried out during the assembly of the solar panel model. First, tighten the four bolts evenly by hand. Then, use a torque wrench to adjust the tightening torque of each bolt to 3N·m. The adjustment method is carried out according to the method in [21] to ensure that the tightening torque of each bolt is equal, and the natural frequency of the test structure is 5 sets. Then, the same method was used to test the natural frequencies of each group under 4N·m and 8N·m conditions, and the natural frequencies were 35 sets under the condition of 12N·m. Finally, the SED value of each working condition is calculated by the foregoing method and the reference curve is fitted (see Fig. 11).
3.3 Detection effect
The detection effect of the multi-bolt structure is selected by the method proposed in the three working conditions test.
Working condition 1: four bolts are loose to 10N·m;
Working condition 2: four bolts are loose to 6N·m;
Working condition 3: The bolts on both sides are loose to 4N·m, and the middle two bolts are kept 6N·m.
In each state test structure, the natural frequency of each group is 5 groups, and the SED index is calculated by using equation (3), and compared with the curve, the tightening torque evaluation result is obtained. (Because there are 5 sets of data for each state, 5 evaluation results are obtained. ). The comparison between the evaluation results and the actual tightening torque is shown in Table 3.
It can be seen from Table 3 that the maximum error is -0.78 N·m when working condition 1, and the error is -0.19 N·m if the average value of 5 measurements is used; the maximum error is 0.96 N·m when working condition 2 If the average value of the five measurements is used, the error is 0.65 N·m; although the curve does not have the ability to detect the condition 3, the average of the condition 3 is the corresponding pre-tightening torque value (4.91 N·m) on the reference curve. Between 6N·m and 4N·m, it embodies an “equivalent damage†degree.
4 Conclusion
In this paper, a method for quantitative evaluation of bolt tightening force using SED with the first 5 natural frequencies of the structure is proposed. Through the above research, the following conclusions can be drawn:
(1) The SED value of the 5th natural frequency of the structure is exponentially related to the bolt tightening torque;
(2) The method proposed in the paper is not only applicable to the single bolt connection structure, but also has a certain detection capability for the multi-bolt connection structure. In addition, the relevant issues are discussed as follows:
(1) It can be found from the test results of the solar panel model that in the same state, the natural frequencies obtained by multiple measurements are separately identified, and the results have a certain degree of dispersion, so the average value can be taken as the final evaluation result.
(2) At present, the method has a good quantitative evaluation effect on the same tightening torque of each bolt; in addition, through the detection of the condition of solar sail condition 3, there is also a certain "equivalent damage" detection for different pre-tightening conditions. Capabilities; but for more complex situations and higher detection requirements, further research is needed, and combining with other local detection methods is a direction of exploration.
(3) The natural frequency reflects the overall characteristics of the structure, and the looseness of the bolt is the local performance change of the structure. It is necessary to check the looseness of the bolt from the natural frequency change to a certain condition—the local performance change affects the overall characteristics of the structure. . It can be seen from the reference curve that when the bolt looseness is not large, the influence on the overall characteristics of the structure is small, so the curve is very gentle. At this time, the detection accuracy of the method is generally low; when the bolt is loose to a certain extent, it will be The overall characteristics of the structure have a large impact, corresponding to the relatively steep part of the curve, at which point the method can obtain more accurate results.
(4) If quantitative evaluation is not required, but simple trend monitoring, no reference curve is needed, and any state is used as the starting state, and the SED value of the characteristic parameter vector measured by each time node is calculated by equation (3), and Perform time-based trend analysis. This can extend the scope of application of the method.
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Chinese Aeronautical Establishment. Composite Structures Design Manual [M]. Beijing: Aviation Industry Press, 2001.
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XU Chao, ZHOU Bang-you, LIU Xin-en, et al. A review of vibration-based condition monitoring and identification for mechanical bolted joints [J]. Structure & Environment Engineering, 2009,36(2):29-36.
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Characteristics and Advantages
(1) Intelligent control design: adjustable main parameter and secondary parameter automatically according to the weight of door leaves;
(2) Low noise: Special static sound track, integration of motor, worm-gear and retarder.
(3) Anti-clamping function: automatically reverse when meeting barriers;
(4) Unique electronic motor lock: the motor will lock up when the door is forced to open.(controlled by remote or switch)
(5) Tighten force: seal door when closed, power consumption approximately 10W under standby;
(6) Advanced brushless motor(36V,100W) can automatically adopt different heavy door leaves;
(7) Bi-doors inter-locking: one of the door leaves always remains closing;
(8)Safety sensor terminal: sensor stops working when door closed;
(9)Unique coating technology: never rusty;
(10)Easy and convenient to install;
(11)Working Process: when the door leaf closes to the right place, the door leaf will slightly shift to the door frame and the ground. The rubbers on the four sides of the door leaf will completely combine with door frame and ground, which ensures air tightness. When the door is open, the rubbers will separate from door frame and ground, which avoids contraction on the ground.
Technical Specification
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Specification |
Light Duty |
Heavy Duty |
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Rang of the Door |
Single-Leaf |
Double-Leaf |
Single-Leaf |
Double-Leaf |
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Door leaf max weight |
100kg |
100kg x 2 |
200kg |
200kg x 2 |
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Mounting Method |
Surface mounting or built-in mounting |
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Open Width |
700-2000mm |
650-2000mm |
750-2000mm |
650-2000mm |
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Power Supply |
AC 220v ± 10%, 50-60 Hz |
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Opening Speed |
300-500mm/s (adjustable) |
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Closing Speed |
250-550mm/s (adjustable) |
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Creep speed |
30-100mm/s (adjustable) |
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Hold-open time |
0.5-20s (adjustable) |
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Airproof Force (Max.) |
>70N |
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Manual Pushing Force |
<100N |
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Electronic Lock Force |
>800N |
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Power consumption |
150W |
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Ambient temperature |
-20+50 C |
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Technical Details:
(1) Rubber lining sealing technology combined with V groove on the guide rail enables the door completely sealed when the door closed;
(2)Special door body location technology. Semicircular surface beam on the ground matches with the V style groove at the bottom of door leaf, which stop the door from swing and make sure it moves stable and smooth;
(3) The door body decorated with matte stainless steel or spray surface, and on the middle and both sides with sealing stripes to ensure the hermetic effect.
(4)Feet sensor switch applied to avoid contagion;
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