Hong-bo PENG, Qi-qi ZHANG, Min DAN

(Aeronautical Engineering Institute, Civil Aviation University of China, Tianjin 300300, China)

Abstract: An improved model of curvature modal recognition is proposed to solve the problem that the curvature modal cannot recognize the damage of the tip and root of the structures. Blade-disc is one of the most important components of the aero-engine structure, and if it fails, it will cause a serious threat to the safe operation of the engine. The curvature modal method which is strongly sensitive to the structural faults is used to compare the changes of the blade-disc modal from different damage locations and different damage degrees, and the structure end is calculated by using the improved curvature modal method. The numerical results show that when the blade-disc is damaged, the displacement mode and structure frequency are difficult to reflect the damage position of the structure effectively, and the natural frequencies of each order mode will get decreased; the curvature modal method which can reflect the damage condition of the structure effectively gives a qualitative description of the damage degree, and the curvature changes abruptly at the damage place; the improved curvature modal recognition model can identify the damage fault at the end of the structure, which provides a theoretical basis for damage detection of aero-engine blade-disc structures.

Key words: Curvature modal, Frequency, Blade-disc structures, Improved curvature modal, Damage detection

1 Introduction

Integrated with the machinery, electricity, liquid and so on, the aero-engine is a sophisticated equipment as well as the “heart” of the aircraft while the blade-disc undertakes such major tasks as rotation and if the blade-disc fails, it will cause serious threats to the safe operation of the engine. Failures on the blade-disc are often concentrated on the blade with blade damages accounting for about 20% among the total engine failures, therefore it is one of the research priorities. Many scholars have used neural networks to identify different damage levels of various structures[1-2]. Qu yi et al extracted the characteristic difference information of blade acoustic emission signals and established a fault recognition model[3- 4]. Jiang Shaofei, Zhang Cong and other experts proposed a damage detection method for structures based on modal index and data fusion to locate the damage[5-6]. Pandey A K pointed out that the stiffness will decrease and the corresponding curvature will get increased when the structure is damaged, and the change of curvature modal will increase with the increase of damage degrees[7]. If the curvature mode shapes of the structure are regarded as the parameter of damage, the location of the damage can be well identified. The variation of the local features of the structure can be effectively reflected by the curvature modal[8], which has a good indication of the location and degree of damage. While the defect of this method is that damages cannot be identified at the end element of the structure, so an improved curvature mode recognition model(ICMRM) is proposed to solve this problem in this paper. Besides the model, the numerical analysis is carried out by taking the typical blade-disc structure as an example to verify the correctness and effectiveness of the improved model.

2 Curvature modal and improved curvature modal

2.1 Curvature modal theory

The blade-disc made of special materials is one of the most important components of the engine structure and the blades have complex twisted geometric structures. In this paper, the simplified theory is applied to regard the blade as a uniform cross section structure in spite of the torsion of the blade, which can reduce the complexity of calculation. By studying the theoretical basis of curvature mode, we can find that this theory can be applied to any type of linear structure if the blade of the blade-disk structure is treated as a beam structure in disregard of the influence of axial force[9]. Bernoulli-Euler beam[10] vibration differential equation is as follows:

(1)

Where,EI(x) is the stiffness coefficient of beam structure;V(x,t) is the lateral displacement of a point in the beam structure;M(x) andc(x) are the mass and damping atxdisplacement on the beam structure respectively，the changes in mass and damping and the load are ignored. Curvature mode is defined as the second derivative of lateral displacementv(x,t) of this point with respect to displacementx[11]. The structural curvature of a certain point is:

(2)

Where,M(x,t) is the bending moment at a displacement ofxon the structure. It can be known from Eq. (2) that the curvature of any point in the structure is inversely proportional to the stiffness of the point. When the stiffnessEI(x) changes, the curvatureq(x) also changes, and the curvature mode is more sensitive to structural damage[12]. Therefore, the curvature of the structure can be used as the basis of damage identification to determine whether the structure is damaged or not. The mode values are a series of discrete points by finite element. The curvature mode is obtained by calculating the approximate center difference[13] of the discrete point modes:

(3)

Where,φr+1,φrandφr-1are the mode shapes of the nodes atr+1,randr-1 positions, respectively, andhis the distance between adjacent nodes. And the model is the basis of the analysis that should be built firstly. Then the model is solved by dynamic equation which has been meshed and has been set by the conditions of necessary constraints. What is the most important thing is the analysis of modal. The data of displacement, frequency and curvature will be extracted. Judge whether the displacement curve is abrupt. If there is a mutation, the difference method is used to calculate the curvature. If not, the frequency should be analysed and the curvature should be calculated again to judge the recognition result. The curvature modal recognition model (CMRM) flow chart is established, as shown in Fig.1.

Fig.1 The flow chart of Curvature modal recognition

2.2 Improved curvature recognition model

The insufficiency of the curvature mode recognition model is that the end damage of the structure cannot be identified. To solve this problem, an improved curvature model recognition model(ICMRM) is proposed. The flow chart is shown in Fig.2. Firstly, the selected data are imported into four kinds of calculation models, and the data are processed by Gaussian fitting, minimum two-fit fitting, cubic polynomial fitting and BP neural network prediction models. Secondly, the corresponding function is fitted by MATLAB. The node numbers are brought into the fitting function, the calculation results are compared with the BP neural network prediction result, and the known data is used for verification, and the relative error that is minimized can be found by comparison, and finally the method is used to predict nodes outside the end portion. In order to verify the accuracy of the calculation, several sets of known data should be selected for comparison and analysis to identify the damage of the end and the failure of blade root and tip is determined.

Fig.2 The flow chart of improving curvature modal

3 Numerical analysis

In the calculation of finite element simulation, the damage of the structure can generally be simulated by the reduction of mass or stiffness.In this paper, the reduction of stiffness of structural elements is realized through the reduction of elastic modulus by which different damage conditions of structures are determined. A large-scale analysis software of finite element is used to establish the model as shown in Fig.3.

Fig.3 The whole blade-disc structure model

If the whole blade-disc model is used for analysis, a very large amount of mesh will be generated and the computing demand will be huge. The blade-disc structure belongs to a periodic symmetrical structure (circular symmetric structure). Therefore, the principle of modal reduction is adopted in this paper and a single sector model is selected (as shown in Fig.4) for calculation, which can reduce the scale of analysis and the amount of calculation. The full-constrained boundary conditions are set for each node at the end of the axle hole of the sector model, and the periodic boundary conditions are used for both sides of the sector model, and the movement ofYandZdirections are restricted to carry out modal analysis. The basic parameters are: elastic modulusE=110 GPa, material densityρ=4 540 kg/m3, Poisson’s ratioμ=0.3, inner diameterr1=33 mm, outer diameterr2=80 mm, blade lengthl=90 mm, widthn=26 mm, thicknessd=0.5 mm, and SOLID185 is used to divide the grid for blade-disc model, a total of 4 554 grids and 6 480 nodes are generated. Three kinds of damage cases are assumed, as shown in Table 1.

Fig.4 Damage points of single sector

Table 1 Damage cases of the blade-disc structure

The first four modes of the blade-disc are obtained by numerical simulation in finite element software ANSYS. According to the modal analysis, the blade is bent in the first, third and fourth order modal. The torsion happened to the blade in the second order modal, which will affect the curvature calculation. Therefore, the displacement modes of containing damage is extracted without considering this situation.

The vibration modes of the structure are basically smooth curves by fitting the displacement of each discrete node, which cannot determine where the damage happens. Then, the frequency of the blade-disc structure will be analyzed.

Table 2 Frequency comparison of different cases of damage Hz

From the frequencies of the model, it can be concluded that as the numbers and degree of damage gets increased, the frequency gets decreased slightly. This is because the reduction of stiffness happened in the blade-disc structure, however, the fault location of the structure cannot be determined here, which indicates that the frequency is not sensitive to the damage. According to the curvature mode theory, when the structure is damaged at a certain local position, the curvature modal has a corresponding mutation near the damage position. However, the characteristic of the element is that an element is composed of nodes on both sides, and damage of element causes its nodes to change accordingly. Therefore, the element damages of one, two, and three locations are simulated separately, and the recognition model will be used for judgment.

Fig.5 The diagram of displacement vibration of blade-disc structure

Fig.6 is the recognition effect graphs of one damage, two damages and three damages, respectively. At the pre-set damage, the curvature of them changes abruptly, which shows that the curvature modal is sensitive to the structural damage. In order to avoid the contingency of the damage location identification, the correctness of the method is verified by selecting the data of the one-sided part of the damage for calculation. The data between node 1 159 and 1 186 and so on among which the nodes that could not be calculated at the end are eliminated are selected for calculation and different degrees of damage are identified for blade body, leading edge and trailing edge.

Fig.6 Diagram of recognition effect of damage case

According to the analysis, it can be concluded that different data selected can also meet the calculation requirements and the effect of identifying multiple damages is achieved[14]. Therefore, the identification model is universally applicable. Through the identification model calculation, the curvature of one, two and three damaged places has changed obviously, and with the increase of damage degree, the curvature mutation also gets increased correspondingly. According to the characteristics of the structure, the damage of an element will cause corresponding changes to the nodes on both sides of the element, which is consistent with the effective graphics of simulation visualization. However, the limitation of the curvature recognition model is that the damage of the end cannot be calculated. If the nodes that do not exist outside the end are virtualized and then it is substituted into the curvature recognition model, this problem can be solved. Due to space limitations, the predicted curves of the neural network are only presented, as shown in Fig.8.

Fig.7 Diagram of different degrees of damage

Fig.8 The diagram of node prediction effect

The relative errors of each method are calculated by the fitting function, as shown in Table 3. Finally, the relative errors of neural network prediction result are the smallest, Gauss quadratic fitting errors are the second, and the errors of least squares fitting and the cubic polynomial fitting are greater than those of the former two methods. Therefore, the neural network model is selected to calculate the errors. The calculated results are normalized, and the effect as shown in Fig.9 can be obtained from the calculation of the improved curvature mode recognition model.

Table 3 Comparison of prediction results of the calculation model

Fig.9 Diagram of effect of improved curvature recognition model

Although the tip and root of the aero-engine blade are the places where the frequency of failure is very high, the limitations of end damage identification are effectively avoided by the improved curvature mode method. The obvious recognition results are obtained at the positions of the tip and root. It can be concluded that the curvature has changed at the end of the structure.The identification model can effectively identify the damage location, which provides a good theoretical reference for practical engineering detection.

4 Conclusion

The modal values cannot identify characteristics the damages, and the curvature modal method is more sensitive to the structural damage, but the improved curvature modal identification model can effectively avoid the shortcomings of the curvature modal. In this paper, the effectiveness of this method is verified by taking typical blade-disc structures as the object of the study and the numerical simulation is implemented through large commercial finite element software to analyze the location of single damage, multiple damages and different damage degrees. Therefore, the following conclusions can be drawn:

(1) The curvature modal recognition model can identify the locations of single damage and multiple damages of the blade-disc structure.

(2) As the degree of damage gets increased, the amplitude at the failure point of the modal curvature curve will be changed correspondingly. It is indicated that the method can identify the damage degree of blade-disc.

(3) The improved curvature recognition model is used to predict the end nodes of the blade-disk structure. The damage of the tip and the end of the blade can be detected and a good recognition effect is obtained.