CN108195532B - Method for measuring equivalent rigidity of beam structure crack - Google Patents
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Abstract
Description
技术领域technical field
本发明属机械设备故障诊断领域，具体涉及一种梁结构裂纹等效刚度的测量方法。The invention belongs to the field of mechanical equipment fault diagnosis, and particularly relates to a method for measuring the equivalent stiffness of beam structure cracks.
背景技术Background technique
随着科学技术的进步和现代工业的发展，对机械设备的维护提出了越来越高的要求，作为大型复杂结构的重要承力单元，梁类结构在工程实践中有着广泛的应用(如航空航天、机械设备、桥梁结构等)，在长期交变应力或冲击荷载的作用下，结构常常会产生裂纹。裂纹的产生和不断的扩展，常常使结构发生断裂失效，最终导致灾难性事故的发生。因此，梁结构的裂纹检测是工程项目安全的重要保证。随着裂纹的发生和扩展，裂纹等效刚度也会产生相应的变化，这种变化能够在有效地反映结构的损伤程度和特征。因此，对裂纹等效刚度进行研究，对梁结构裂纹检测具有十分重要的意义。With the advancement of science and technology and the development of modern industry, higher and higher requirements are put forward for the maintenance of mechanical equipment. As an important bearing unit of large and complex structures, beam structures are widely used in engineering practice (such as aviation Aerospace, mechanical equipment, bridge structures, etc.), under the action of long-term alternating stress or impact load, the structure often produces cracks. The generation and continuous expansion of cracks often cause the structure to fail and eventually lead to catastrophic accidents. Therefore, crack detection of beam structures is an important guarantee for the safety of engineering projects. With the occurrence and expansion of cracks, the equivalent stiffness of the cracks will also change accordingly, which can effectively reflect the damage degree and characteristics of the structure. Therefore, it is of great significance to study the crack equivalent stiffness for crack detection of beam structures.
任何结构都可以看作是由质量、阻尼与刚度矩阵组成的动力学系统，一旦结构中裂纹等效刚度发生变化，则会导致系统振动模态参数(振型、振幅、固有频率等)的改变。所以通过寻找模态参数与结构损伤的关系，可以利用模态参数的变化来识别裂纹等效刚度。在振型、振幅、固有频率等模态参数中，固有频率易于测量，且具有较高的精度。由此，本发明提出了一种利用结构的固有频率来测量梁结构裂纹等效刚度的方法。Any structure can be regarded as a dynamic system composed of mass, damping and stiffness matrices. Once the crack equivalent stiffness in the structure changes, it will lead to changes in the system vibration modal parameters (mode shape, amplitude, natural frequency, etc.) . Therefore, by looking for the relationship between modal parameters and structural damage, the change of modal parameters can be used to identify the equivalent stiffness of cracks. Among modal parameters such as mode shape, amplitude, and natural frequency, the natural frequency is easy to measure and has high accuracy. Therefore, the present invention proposes a method for measuring the equivalent stiffness of beam structure cracks by utilizing the natural frequency of the structure.
发明内容SUMMARY OF THE INVENTION
本发明的目的在于提供一种梁结构裂纹等效刚度的测量方法。该方法在裂纹位置和裂纹等效刚度的可能取值范围分别选取一系列的样本点，将这些样本点作为梁结构动力学分析的输入参数，求解裂纹梁故障数据库，进而绘制以裂纹位置和等效刚度为输入的结构前三阶固有频率影响曲面；然后对梁结构进行振动测试，采用获得的结构前三阶固有频率去截取固有频率影响曲面，绘制出前三阶固有频率影响曲线，三条固有频率影响曲线的交点可以测量出裂纹的等效刚度和相应位置。该方法适用于梁结构中不同类型和形状裂纹的等效刚度测量。The purpose of the present invention is to provide a method for measuring the equivalent stiffness of beam structure cracks. In this method, a series of sample points are respectively selected from the possible value ranges of the crack position and the equivalent stiffness of the crack, and these sample points are used as the input parameters of the dynamic analysis of the beam structure to solve the fault database of the cracked beam, and then draw the crack position and etc. The first three natural frequencies of the structure are influenced by the effective stiffness as input; then the vibration test is carried out on the beam structure, the first three natural frequencies of the structure are used to intercept the natural frequency influence surface, and the first three natural frequency influence curves are drawn. The three natural frequencies The intersection of the influence curves can measure the equivalent stiffness and corresponding location of the crack. This method is suitable for the equivalent stiffness measurement of different types and shapes of cracks in beam structures.
本发明的目的是通过下述技术方案是来实现的：The object of the present invention is to be achieved through the following technical solutions:
一种梁结构裂纹等效刚度的测量方法，该方法包括下述步骤：A method for measuring the equivalent stiffness of beam structure cracks, the method comprises the following steps:
1)梁结构中裂纹可以用扭转弹簧来描述，扭转弹簧的刚度表示了裂纹等效刚度；在裂纹位置和裂纹等效刚度的可能取值范围分别选取一系列的样本点，将这些样本点代入到有限元模型中，得到裂纹梁振动的特征方程；1) The crack in the beam structure can be described by a torsion spring, and the stiffness of the torsion spring represents the equivalent stiffness of the crack; a series of sample points are selected from the crack position and the possible value range of the equivalent stiffness of the crack, and these sample points are substituted into into the finite element model to obtain the characteristic equation of the cracked beam vibration;
2)求解裂纹梁振动的特征方程，获得裂纹梁故障数据库，进而绘制以裂纹位置和裂纹等效刚度为输入的结构前三阶固有频率影响曲面；2) Solve the characteristic equation of the cracked beam vibration, obtain the cracked beam fault database, and then draw the first three-order natural frequency influence surface of the structure with the crack position and the equivalent stiffness of the crack as input;
3)通过对裂纹梁进行振动测试，提取其前三阶固有频率；3) Extract the first three natural frequencies of the cracked beam by vibration testing;
4)将实测的前三阶固有频率作为输入，截取前三阶固有频率影响曲面，获得前三阶固有频率影响曲线，利用三条影响曲线的交点测量出裂纹等效刚度。4) Using the measured first three-order natural frequencies as input, intercept the influence surface of the first three-order natural frequency, obtain the first-order natural frequency influence curve, and use the intersection of the three influence curves to measure the equivalent stiffness of the crack.
进一步，所述步骤1)中，得到裂纹梁振动的特征方程，包括下述步骤：Further, in the described step 1), the characteristic equation of the vibration of the cracked beam is obtained, including the following steps:
1)用扭转弹簧来描述梁结构中的裂纹，则结构模型可以表示为通过扭转弹簧连接起来两段无裂纹梁，扭转弹簧的刚度即为裂纹等效刚度；1) Using a torsion spring to describe the crack in the beam structure, the structural model can be expressed as two sections of crack-free beams connected by a torsion spring, and the stiffness of the torsion spring is the equivalent stiffness of the crack;
2)在裂纹位置和裂纹等效刚度的可能取值范围分别选取一系列的样本点，将这些样本点作为梁结构动力学分析的输入参数；2) Select a series of sample points in the crack position and the possible value range of the equivalent stiffness of the crack, and use these sample points as the input parameters of the dynamic analysis of the beam structure;
3)将裂纹位置和裂纹等效刚度的样本点输入到有限元模型中，得到裂纹梁振动的特征方程为：3) Input the sample points of the crack position and the equivalent stiffness of the crack into the finite element model, and obtain the characteristic equation of the crack beam vibration as:
|K(k,β)-ωi 2M|＝0|K(k,β)-ω i 2 M|=0
式中：K表示系统整体刚度矩阵，M表示系统整体质量矩阵，ωi表示圆频率，k表示裂纹等效刚度，β表示裂纹相对位置。ωi＝2πfi,i＝1,2,3，fi为系统固有频率。where K is the overall stiffness matrix of the system, M is the overall mass matrix of the system, ω i is the circular frequency, k is the equivalent stiffness of the crack, and β is the relative position of the crack. ω i =2πf i , i=1,2,3, f i is the natural frequency of the system.
进一步，所述步骤3)中，测量结构前三阶固有频率的方法如下：Further, in the described step 3), the method for measuring the first three-order natural frequencies of the structure is as follows:
1)搭建梁结构的测试实验台及测试系统，将含裂纹的梁结构夹持在实验台上；1) Build a test bench and test system for the beam structure, and clamp the cracked beam structure on the test bench;
2)对梁结构进行脉冲激励，获取振动信号，从中提取梁结构的前三阶固有频率fi,i＝1,2,3。2) Perform pulse excitation on the beam structure, obtain vibration signals, and extract the first three-order natural frequencies f i of the beam structure, i=1, 2, 3.
进一步，所述步骤4)中，利用固有频率影响曲线的交点测量出裂纹等效刚度的步骤如下：Further, in the step 4), the step of measuring the equivalent stiffness of the crack by the intersection of the natural frequency influence curve is as follows:
1)以实测得到的梁结构前三阶固有频率作为输入，去截取构造的前三阶固有频率影响曲面，绘制出前三阶固有频率影响曲线；1) Using the measured first three-order natural frequencies of the beam structure as the input, to intercept the first three-order natural frequency influence surface of the structure, and draw the first three-order natural frequency influence curve;
2)将前三阶固有频率影响曲线绘制在同一坐标系中，利用三条固有频率影响曲线的交点可以测量出裂纹等效刚度。2) The first three natural frequency influence curves are drawn in the same coordinate system, and the equivalent stiffness of the crack can be measured by the intersection of the three natural frequency influence curves.
本发明采用了有限元建模及振动测试技术，具有下列特点：The present invention adopts finite element modeling and vibration testing technology, and has the following characteristics:
1.本发明只需对整体结构或局部结构进行测试，不需预先知道裂纹的位置就可以确定裂纹等效刚度的大小；1. The present invention only needs to test the overall structure or local structure, and the equivalent stiffness of the crack can be determined without knowing the position of the crack in advance;
2.本发明适用于梁结构中不同类型和形状裂纹的等效刚度测量；2. The present invention is suitable for the equivalent stiffness measurement of cracks of different types and shapes in beam structures;
3.本发明可以用于不同截面形状梁结构中裂纹的等效刚度测量，如矩形梁、圆截面梁、空心梁等。3. The present invention can be used to measure the equivalent stiffness of cracks in beam structures with different cross-sectional shapes, such as rectangular beams, circular cross-section beams, hollow beams, and the like.
附图说明Description of drawings
图1(a)、1(b)分别为是矩形裂纹梁结构和裂纹横截面；Figures 1(a) and 1(b) are the rectangular crack beam structure and the crack cross section, respectively;
图2是裂纹梁的扭转弹簧模型；Figure 2 is the torsion spring model of the cracked beam;
图3(a)、3(b)、3(c)分别为矩形梁结构的前三阶固有频率影响曲面；Figures 3(a), 3(b), and 3(c) are the influence surfaces of the first three natural frequencies of the rectangular beam structure;
图4(a)、4(b)分别为两种工况下的裂纹等效刚度测量的频率影响曲线图。Figures 4(a) and 4(b) are the frequency influence curves of the crack equivalent stiffness measurement under two working conditions, respectively.
具体实施方式Detailed ways
附图用于辅助说明本发明的具体实施例。本发明可以用于不同截面形状梁结构中裂纹的等效刚度测量，如矩形梁、圆截面梁、空心梁等。下面以矩形梁为例，结合附图对本发明的内容作进一步详细说明。The accompanying drawings are used to assist in explaining specific embodiments of the present invention. The invention can be used for the equivalent stiffness measurement of cracks in beam structures with different cross-sectional shapes, such as rectangular beams, circular-section beams, hollow beams, and the like. The content of the present invention will be further described in detail below with reference to the accompanying drawings, taking a rectangular beam as an example.
参照图1(a)、1(b)所示，为矩形裂纹梁模型。图1(a)为矩形裂纹梁结构，图 1(b)为裂纹横截面，x、y、z为三个方向的直角坐标，a为裂纹深度，b为梁的宽度，h为梁的高度。Referring to Figures 1(a) and 1(b), it is a rectangular crack beam model. Figure 1(a) is a rectangular crack beam structure, Figure 1(b) is a crack cross-section, x, y, z are rectangular coordinates in three directions, a is the crack depth, b is the width of the beam, and h is the height of the beam .
参照图2所示，为裂纹梁的扭转弹簧模型。用扭转弹簧来描述梁结构中的裂纹，则结构模型可以表示为通过扭转弹簧连接起来两段无裂纹梁，扭转弹簧的刚度即为裂纹等效刚度。Referring to Figure 2, it is the torsion spring model of the cracked beam. If a torsion spring is used to describe the crack in the beam structure, the structural model can be expressed as two sections of crack-free beams connected by a torsion spring, and the stiffness of the torsion spring is the equivalent stiffness of the crack.
参照图3(a)、3(b)、3(c)所示，为矩形梁结构的前三阶固有频率影响曲面。图3(a)、3(b)、3(c)分别表示第一、二、三阶的固有频率曲面，图中β表示裂纹相对位置，k表示裂纹等效刚度，f1、f2、f3为结构前三阶固有频率。Referring to Figures 3(a), 3(b), and 3(c), it is the first three-order natural frequency influence surface of the rectangular beam structure. Figures 3(a), 3(b), and 3(c) represent the first , second , and third order natural frequency surfaces, respectively. f 3 is the first three order natural frequency of the structure.
参照图4(a)、4(b)所示，为裂纹等效刚度测量的频率影响曲线图。图4(a)、 4(b)分别为两种工况下裂纹等效刚度测量图，三条频率影响曲线图的交点指示了测量的裂纹等效刚度以及其所对应的裂纹位置。图中β表示裂纹相对位置，K表示裂纹等效刚度。Referring to Figures 4(a) and 4(b), it is a graph showing the influence of frequency of crack equivalent stiffness measurement. Figures 4(a) and 4(b) are the measurement diagrams of the equivalent crack stiffness under two working conditions, respectively. The intersection of the three frequency influence curves indicates the measured equivalent stiffness of the crack and its corresponding crack position. In the figure, β represents the relative position of the crack, and K represents the equivalent stiffness of the crack.
本发明按以下步骤实施:The present invention is implemented according to the following steps:
步骤1.将梁结构中的裂纹用扭转弹簧来描述，获得裂纹梁振动的特征方程。具体为：
1)矩形裂纹梁结构和裂纹横截面如图1(a)、1(b)所示。用扭转弹簧来描述梁结构中的裂纹，则结构模型可以表示为通过扭转弹簧连接起来两段无裂纹梁，扭转弹簧的刚度即为裂纹等效刚度。裂纹梁的扭转弹簧模型如图2所示。1) The structure of the rectangular crack beam and the crack cross section are shown in Figures 1(a) and 1(b). If a torsion spring is used to describe the crack in the beam structure, the structural model can be expressed as two sections of crack-free beams connected by a torsion spring, and the stiffness of the torsion spring is the equivalent stiffness of the crack. The torsion spring model of the cracked beam is shown in Figure 2.
2)在裂纹位置和裂纹等效刚度的可能取值范围分别选取一系列的样本点，将这些样本点作为梁结构动力学分析的输入参数。2) Select a series of sample points in the crack position and the possible value range of the equivalent stiffness of the crack, and use these sample points as the input parameters of the dynamic analysis of the beam structure.
3)将裂纹位置和裂纹等效刚度的样本点输入到有限元模型中，得到裂纹梁振动的特征方程为：3) Input the sample points of the crack position and the equivalent stiffness of the crack into the finite element model, and obtain the characteristic equation of the crack beam vibration as:
|K(k,β)-ωi 2M|＝0|K(k,β)-ω i 2 M|=0
式中：K表示系统整体刚度矩阵，M表示系统整体质量矩阵，ωi表示圆频率， k表示裂纹等效刚度，β表示裂纹相对位置。ωi＝2πfi,i＝1,2,3，fi为系统固有频率。where K is the overall stiffness matrix of the system, M is the overall mass matrix of the system, ω i is the circular frequency, k is the equivalent stiffness of the crack, and β is the relative position of the crack. ω i =2πf i , i=1,2,3, f i is the natural frequency of the system.
步骤2.根据裂纹梁故障数据库绘制结构前三阶固有频率影响曲面，如图 3(a)、3(b)、3(c)所示。具体为：
1)求解裂纹梁振动的特征方程，获得裂纹梁故障数据库；1) Solve the characteristic equation of the cracked beam vibration and obtain the cracked beam fault database;
2)绘制以裂纹位置和等效刚度为输入的结构前三阶固有频率影响曲面。2) Draw the first three-order natural frequency influence surface of the structure with the crack position and equivalent stiffness as input.
步骤3.通过对裂纹梁进行振动测试，测量结构前三阶固有频率。具体为：
1)搭建梁结构的测试实验台及测试系统，将含裂纹的梁结构夹持在实验台上；1) Build a test bench and test system for the beam structure, and clamp the cracked beam structure on the test bench;
2)对梁结构进行脉冲激励，获取振动信号，从中提取梁结构的前三阶固有频率fi,i＝1,2,3。2) Perform pulse excitation on the beam structure, obtain vibration signals, and extract the first three-order natural frequencies f i of the beam structure, i=1, 2, 3.
步骤4.利用固有频率影响曲线的交点测量出裂纹等效刚度，如图4(a)、4(b)、所示。具体为：
1)以实测得到的梁结构前三阶固有频率作为输入，去截取构造的前三阶固有频率影响曲面，绘制出前三阶固有频率影响曲线；1) Using the measured first three-order natural frequencies of the beam structure as the input, to intercept the first three-order natural frequency influence surface of the structure, and draw the first three-order natural frequency influence curve;
2)将前三阶固有频率影响曲线绘制在同一坐标系中，利用三条固有频率影响曲线的交点可以测量出裂纹等效刚度。2) The first three natural frequency influence curves are drawn in the same coordinate system, and the equivalent stiffness of the crack can be measured by the intersection of the three natural frequency influence curves.
下面通过具体实施例对本发明做进一步详细说明：The present invention is described in further detail below by specific embodiments:
实施例1：Example 1:
本实施例以矩形梁为例，主要为了说明梁结构裂纹等效刚度的测量方法。矩形梁两端简支，长度L＝0.4m，宽度b＝0.012m，高度h＝0.02m，杨氏弹性模量 E＝1.7381×1011N/m2，密度ρ＝7384.9kg/m3，泊松比v＝0.3。β和k分别表示裂纹的相对位置和等效刚度。This embodiment takes a rectangular beam as an example, mainly to illustrate the method for measuring the equivalent stiffness of beam structure cracks. The two ends of the rectangular beam are simply supported, the length L=0.4m, the width b=0.012m, the height h=0.02m, the Young’s modulus of elasticity E=1.7381×10 11 N/m 2 , the density ρ=7384.9kg/m 3 , Poisson's ratio v=0.3. β and k represent the relative position and equivalent stiffness of the crack, respectively.
本实施例通过在裂纹位置和裂纹等效刚度的可能取值范围分别选取一系列的样本点，将这些样本点作为梁结构动力学分析的输入参数，求解裂纹梁故障数据库，进而绘制以裂纹位置和等效刚度为输入的结构前三阶固有频率影响曲面，如图3(a) 、 3(b) 、 3(c)所示，图3(a)、3(b)、3(c)分别表示第一、二、三阶固有频率曲面。然后对梁结构进行振动测试，在两种工况下获得的前三阶固有频率f1、f2、f3如表1所示。In this embodiment, a series of sample points are respectively selected from the possible value ranges of the crack position and the equivalent stiffness of the crack, and these sample points are used as input parameters for the dynamic analysis of the beam structure to solve the cracked beam fault database, and then draw the crack position with the crack position. The first three natural frequencies of the structure with the equivalent stiffness as the input affect the surface, as shown in Fig. 3(a), 3(b), 3(c), Fig. 3(a), 3(b), 3(c) represent the first, second, and third order natural frequency surfaces, respectively. Then the vibration test of the beam structure is carried out, and the first three order natural frequencies f 1 , f 2 and f 3 obtained under the two working conditions are shown in Table 1.
表1结构固有频率和裂纹等效刚度测量结果Table 1. Measurement results of structural natural frequency and crack equivalent stiffness
采用表1中两种工况下的结构前三阶固有频率去截取固有频率影响曲面，可以绘制出前三阶固有频率影响曲线。将前三阶固有频率影响曲线绘制在同一个坐标系中，其交点可以测量出裂纹等效刚度k及相应的裂纹位置β，如图4(a) 、 4(b) 所示。图4(a)为在工况I的频率影响曲线图，图4(b)为工况II的频率影响曲线图。从图4(a)和图4(b)中得到的测量结果如表1所示，结果验证了梁结构裂纹等效刚度测量方法的有效性。Using the first three natural frequencies of the structure under the two working conditions in Table 1 to intercept the natural frequency influence surface, the first three natural frequency influence curves can be drawn. The first three-order natural frequency influence curves are drawn in the same coordinate system, and the intersection point can measure the crack equivalent stiffness k and the corresponding crack position β, as shown in Figures 4(a) and 4(b). Fig. 4(a) is a graph of frequency influence in working condition I, and Fig. 4(b) is a graph of frequency influence in working condition II. The measurement results obtained from Fig. 4(a) and Fig. 4(b) are shown in Table 1, and the results verify the validity of the method for measuring the equivalent stiffness of beam structure cracks.
虽然本发明以上述实施例对本发明做出了详细的描述，但上述实施例并不用于限定本发明。在不脱离本发明技术方案所给出的技术特征和结构范围的情况下，对技术特征所作的增加、变形或以本领域同样内容的替换，均应属本发明的保护范围。Although the present invention has been described in detail with the above embodiments, the above embodiments are not intended to limit the present invention. Without departing from the technical features and structural scope given by the technical solution of the present invention, any additions, modifications to the technical features or replacements with the same content in the field shall fall within the protection scope of the present invention.
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