CN108195532B - Method for measuring equivalent rigidity of beam structure crack - Google Patents
Method for measuring equivalent rigidity of beam structure crack Download PDFInfo
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- CN108195532B CN108195532B CN201711331415.7A CN201711331415A CN108195532B CN 108195532 B CN108195532 B CN 108195532B CN 201711331415 A CN201711331415 A CN 201711331415A CN 108195532 B CN108195532 B CN 108195532B
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Abstract
The invention discloses a method for measuring equivalent rigidity of a beam structure crack. Respectively selecting a series of sample points in the possible value ranges of the crack position and the crack equivalent stiffness, taking the sample points as input parameters of beam structure dynamics analysis, solving a crack beam fault database, and further drawing a structural front three-order natural frequency influence curved surface taking the crack position and the equivalent stiffness as input; and then, carrying out vibration test on the beam structure, intercepting the natural frequency influence curved surface by adopting the obtained front three-order natural frequency of the structure, drawing a front three-order natural frequency influence curve, and measuring the equivalent rigidity and the corresponding position of the crack by the intersection point of the three natural frequency influence curves. The method is suitable for equivalent rigidity measurement of different types and shapes of cracks in the beam structure.
Description
Technical Field
The invention belongs to the field of fault diagnosis of mechanical equipment, and particularly relates to a method for measuring equivalent rigidity of a beam structure crack.
Background
With the progress of scientific technology and the development of modern industry, higher and higher requirements are put forward on the maintenance of mechanical equipment, and as an important bearing unit of a large-scale complex structure, a beam structure is widely applied in engineering practice (such as aerospace, mechanical equipment, bridge structures and the like), and the structure often cracks under the action of long-term alternating stress or impact load. The generation and continued propagation of cracks often results in structural failure, ultimately leading to catastrophic failure. Therefore, crack detection of beam structures is an important guarantee of engineering project safety. As the crack occurs and propagates, the equivalent stiffness of the crack changes correspondingly, and the change can effectively reflect the damage degree and characteristics of the structure. Therefore, the method has very important significance for detecting the cracks of the beam structure by researching the equivalent rigidity of the cracks.
Any structure can be regarded as a dynamic system consisting of a mass, damping and rigidity matrix, and once the equivalent rigidity of a crack in the structure changes, the vibration mode parameters (vibration mode, amplitude, natural frequency and the like) of the system can be changed. Therefore, by searching the relation between the modal parameters and the structural damage, the crack equivalent stiffness can be identified by using the change of the modal parameters. Among modal parameters such as mode shape, amplitude, natural frequency and the like, the natural frequency is easy to measure and has higher precision. Therefore, the invention provides a method for measuring the equivalent rigidity of the beam structure crack by using the natural frequency of the structure.
Disclosure of Invention
The invention aims to provide a method for measuring equivalent rigidity of a beam structure crack. Respectively selecting a series of sample points in the possible value ranges of the crack position and the crack equivalent stiffness, taking the sample points as input parameters of beam structure dynamics analysis, solving a crack beam fault database, and further drawing a structural front three-order natural frequency influence curved surface taking the crack position and the equivalent stiffness as input; and then, carrying out vibration test on the beam structure, intercepting the natural frequency influence curved surface by adopting the obtained front three-order natural frequency of the structure, drawing a front three-order natural frequency influence curve, and measuring the equivalent rigidity and the corresponding position of the crack by the intersection point of the three natural frequency influence curves. The method is suitable for equivalent rigidity measurement of different types and shapes of cracks in the beam structure.
The purpose of the invention is realized by the following technical scheme:
a method for measuring the equivalent rigidity of a beam structure crack comprises the following steps:
1) the cracks in the beam structure can be described by torsion springs, and the stiffness of the torsion springs represents the equivalent stiffness of the cracks; respectively selecting a series of sample points in the possible value ranges of the crack position and the crack equivalent stiffness, and substituting the sample points into a finite element model to obtain a characteristic equation of the crack beam vibration;
2) solving a characteristic equation of the vibration of the crack beam to obtain a crack beam fault database, and further drawing a structural first three-order natural frequency influence curved surface taking the crack position and the crack equivalent stiffness as input;
3) extracting the first three-order natural frequency of the crack beam by performing vibration test on the crack beam;
4) and taking the actually measured front third-order natural frequency as input, intercepting the front third-order natural frequency influence curved surface to obtain a front third-order natural frequency influence curve, and measuring the equivalent rigidity of the crack by using the intersection point of the three influence curves.
Further, in the step 1), obtaining a characteristic equation of the vibration of the crack beam includes the following steps:
1) describing cracks in the beam structure by using the torsion spring, wherein the structural model can be expressed as two crack-free beams which are connected by the torsion spring, and the rigidity of the torsion spring is the equivalent rigidity of the cracks;
2) respectively selecting a series of sample points at the crack position and in the possible value range of the crack equivalent stiffness, and taking the sample points as input parameters of the beam structure dynamics analysis;
3) inputting the crack position and the sample point of the crack equivalent stiffness into a finite element model, and obtaining a characteristic equation of the crack beam vibration as follows:
|K(k,β)-ωi 2M|＝0
in the formula: k represents the overall stiffness matrix of the system, M represents the overall mass matrix of the system, omegaiDenotes the circular frequency, k denotes the crack equivalent stiffness, β denotes the crack relative position ωi＝2πfi,i＝1,2,3，fiIs the system natural frequency.
Further, in the step 3), the method for measuring the natural frequency of the first third order of the structure is as follows:
1) building a test experiment table and a test system of the beam structure, and clamping the beam structure containing the cracks on the experiment table;
2) carrying out pulse excitation on the beam structure to obtain a vibration signal, and extracting the first three-order natural frequency f of the beam structure from the vibration signali,i＝1,2,3。
Further, in the step 4), the step of measuring the crack equivalent stiffness by using the intersection point of the natural frequency influence curve includes:
1) taking the first three-order natural frequency of the beam structure obtained through actual measurement as input, intercepting the structural first three-order natural frequency influence curved surface, and drawing a first three-order natural frequency influence curve;
2) and drawing the first three-order natural frequency influence curves in the same coordinate system, and measuring the equivalent rigidity of the crack by using the intersection points of the three natural frequency influence curves.
The invention adopts finite element modeling and vibration testing technology, and has the following characteristics:
1. the method can determine the equivalent rigidity of the crack only by testing the whole structure or the local structure without knowing the position of the crack in advance;
2. the method is suitable for measuring the equivalent stiffness of different types and shapes of cracks in the beam structure;
3. the method can be used for measuring the equivalent rigidity of cracks in beam structures with different section shapes, such as rectangular beams, circular section beams, hollow beams and the like.
Drawings
FIGS. 1(a), 1(b) are respectively a rectangular crack beam structure and a crack cross section;
FIG. 2 is a torsion spring model of a crack beam;
fig. 3(a), 3(b), and 3(c) are the first three-order natural frequency influencing curved surfaces of the rectangular beam structure, respectively;
fig. 4(a) and 4(b) are frequency influence graphs of crack equivalent stiffness measurement under two working conditions respectively.
Detailed Description
The accompanying drawings are included to provide a further understanding of the invention. The method can be used for measuring the equivalent rigidity of cracks in beam structures with different section shapes, such as rectangular beams, circular section beams, hollow beams and the like. The present invention will be further described in detail below with reference to the attached drawings by taking a rectangular beam as an example.
Referring to fig. 1(a) and 1(b), a rectangular crack beam model is shown. Fig. 1(a) is a rectangular crack beam structure, fig. 1(b) is a crack cross section, x, y and z are rectangular coordinates in three directions, a is a crack depth, b is a beam width, and h is a beam height.
Referring to fig. 2, a torsion spring model of a crack beam is shown. And describing cracks in the beam structure by using the torsion spring, wherein the structural model can be expressed as two crack-free beams which are connected by the torsion spring, and the rigidity of the torsion spring is the equivalent rigidity of the cracks.
Referring to FIGS. 3(a) and 3(b)b) FIGS. 3(a), 3(b), and 3(c) show the first, second, and third order natural frequency curves, respectively, in which β shows the relative position of a crack, k shows the crack equivalent stiffness, and f shows the crack equivalent stiffness1、f2、f3The first three natural frequencies of the structure.
Referring to fig. 4(a) and 4(b), frequency influence graphs of crack equivalent stiffness measurements are shown. Fig. 4(a) and 4(b) are crack equivalent stiffness measurement diagrams under two working conditions respectively, and the intersection points of the three frequency influence graphs indicate the measured crack equivalent stiffness and the corresponding crack positions. In the figure, β represents the relative position of the crack, and K represents the crack equivalent stiffness.
The invention is implemented according to the following steps:
1) the rectangular crack beam structure and the crack cross section are shown in fig. 1(a) and 1 (b). And describing cracks in the beam structure by using the torsion spring, wherein the structural model can be expressed as two crack-free beams which are connected by the torsion spring, and the rigidity of the torsion spring is the equivalent rigidity of the cracks. The torsion spring model of the crack beam is shown in fig. 2.
2) And respectively selecting a series of sample points from the crack position and the possible value range of the crack equivalent stiffness, and taking the sample points as input parameters of the beam structure dynamics analysis.
3) Inputting the crack position and the sample point of the crack equivalent stiffness into a finite element model, and obtaining a characteristic equation of the crack beam vibration as follows:
|K(k,β)-ωi 2M|＝0
in the formula: k represents the overall stiffness matrix of the system, M represents the overall mass matrix of the system, omegaiDenotes the circular frequency, k denotes the crack equivalent stiffness, β denotes the crack relative position ωi＝2πfi,i＝1,2,3，fiIs the system natural frequency.
And 2, drawing the first three-order natural frequency influence curved surface of the structure according to the crack beam fault database, as shown in fig. 3(a), 3(b) and 3 (c). The method specifically comprises the following steps:
1) solving a characteristic equation of the vibration of the crack beam to obtain a crack beam fault database;
2) and drawing a structural front third-order natural frequency influence curved surface taking the crack position and the equivalent stiffness as input.
And 3, measuring the inherent frequency of the first three orders of the structure by performing vibration test on the crack beam. The method specifically comprises the following steps:
1) building a test experiment table and a test system of the beam structure, and clamping the beam structure containing the cracks on the experiment table;
2) carrying out pulse excitation on the beam structure to obtain a vibration signal, and extracting the first three-order natural frequency f of the beam structure from the vibration signali,i＝1,2,3。
And 4, measuring the equivalent rigidity of the crack by using the intersection point of the natural frequency influence curve, as shown in the figures 4(a) and 4 (b). The method specifically comprises the following steps:
1) taking the first three-order natural frequency of the beam structure obtained through actual measurement as input, intercepting the structural first three-order natural frequency influence curved surface, and drawing a first three-order natural frequency influence curve;
2) and drawing the first three-order natural frequency influence curves in the same coordinate system, and measuring the equivalent rigidity of the crack by using the intersection points of the three natural frequency influence curves.
The invention is further illustrated in detail by the following specific examples:
example 1:
the length L is 0.4m, the width b is 0.012m, the height h is 0.02m, and the young's modulus E is 1.7381 × 1011N/m2Density rho of 7384.9kg/m3Poisson's ratio v ═ 0.3, β, and k indicate the relative position of the crack and the equivalent stiffness, respectively.
In the embodiment, a series of sample points are respectively selected from the crack position and the possible value range of the crack equivalent stiffness, the sample points are used as input parameters of beam structure dynamics analysis, a crack beam fault database is solved, and the crack position is drawnAnd the first three-order natural frequency influence curved surface of the structure with the equivalent stiffness as the input, as shown in fig. 3(a), 3(b) and 3(c), and fig. 3(a), 3(b) and 3(c) respectively show the first, second and third-order natural frequency curved surfaces. Then, the beam structure is subjected to vibration test, and the first three-order natural frequency f obtained under two working conditions1、f2、f3As shown in table 1.
TABLE 1 measurement of the natural frequency and equivalent stiffness of the structure
The inherent frequency influence curve of the first three orders can be drawn by intercepting the inherent frequency influence curve by adopting the inherent frequencies of the first three orders under the two working conditions in the table 1. The first three-order natural frequency influence curves are drawn in the same coordinate system, and the crack equivalent stiffness k and the corresponding crack position beta can be measured at the intersection point, as shown in fig. 4(a) and 4 (b). Fig. 4(a) is a frequency influence graph in the operating condition I, and fig. 4(b) is a frequency influence graph in the operating condition II. The measurement results obtained from fig. 4(a) and 4(b) are shown in table 1, and the results verify the effectiveness of the beam structure crack equivalent stiffness measurement method.
Although the present invention has been described in detail with reference to the above embodiments, the above embodiments are not intended to limit the present invention. The technical features of the invention can be added, changed or substituted by the same content in the field without departing from the technical features and the structural scope of the invention.
Claims (3)
1. A method for measuring equivalent rigidity of beam structure cracks is characterized by comprising the following steps: the method comprises the following steps:
1) the cracks in the beam structure can be described by torsion springs, and the stiffness of the torsion springs represents the equivalent stiffness of the cracks; respectively selecting a series of sample points in the possible value ranges of the crack position and the crack equivalent stiffness, and substituting the sample points into a finite element model to obtain a characteristic equation of the crack beam vibration;
in the step 1), obtaining a characteristic equation of the vibration of the crack beam comprises the following steps:
(1) describing cracks in the beam structure by using the torsion spring, wherein the structural model can be expressed as two crack-free beams which are connected by the torsion spring, and the rigidity of the torsion spring is the equivalent rigidity of the cracks;
(2) respectively selecting a series of sample points at the crack position and in the possible value range of the crack equivalent stiffness, and taking the sample points as input parameters of the beam structure dynamics analysis;
(3) inputting the crack position and the sample point of the crack equivalent stiffness into a finite element model, and obtaining a characteristic equation of the crack beam vibration as follows:
|K(k,β)-ωi 2M|＝0
in the formula, K represents a system overall rigidity matrix, M represents a system overall mass matrix, K represents crack equivalent rigidity, β represents the relative position of the crack, and omega represents the relative position of the crackiRepresenting the circular frequency, ωi＝2πfi,i＝1,2,3，fiExtracting the first three inherent frequencies of the beam structure;
2) solving a characteristic equation of the vibration of the crack beam to obtain a crack beam fault database, and further drawing a structural first three-order natural frequency influence curved surface taking the crack position and the crack equivalent stiffness as input;
3) extracting the first three-order natural frequency of the crack beam by performing vibration test on the crack beam;
4) and taking the actually measured front third-order natural frequency as input, intercepting the front third-order natural frequency influence curved surface to obtain a front third-order natural frequency influence curve, and measuring the equivalent rigidity of the crack by using the intersection point of the three influence curves.
2. The method for measuring the equivalent rigidity of the beam structure crack as claimed in claim 1, wherein in the step 3), the method for measuring the natural frequency of the first three orders of the structure is as follows:
(1) building a test experiment table and a test system of the beam structure, and clamping the beam structure containing the cracks on the experiment table;
(2) pulse excitation of beam structuresObtaining vibration signal, and extracting the first three-order natural frequency f of the beam structure from the vibration signali,i＝1,2,3。
3. The method for measuring the equivalent rigidity of the beam structure crack as claimed in claim 1, wherein in the step 4), the step of measuring the equivalent rigidity of the crack by using the intersection points of the three influence curves comprises the following steps:
(1) taking the first three-order natural frequency of the beam structure obtained through actual measurement as input, intercepting the structural first three-order natural frequency influence curved surface, and drawing a first three-order natural frequency influence curve;
(2) and drawing the first three-order natural frequency influence curves in the same coordinate system, and measuring the equivalent rigidity of the crack by using the intersection points of the three natural frequency influence curves.
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| 基于无网格法梁结构多裂纹定量识别;罗志钢 等;《振动与冲击》;20160715;第35卷(第13期);第207-208页第2节 * |
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