Non-intrusive method for uncertainty analysis of aeroengine assembly configurations using chaotic polynomials

Abstract

The application discloses a non-invasive chaos polynomial casing assembly structure uncertainty analysis method, and belongs to the field of uncertainty analysis of casing assembly structures. The method comprises the following steps: step SS1: casing component dynamics modeling; step SS2: casing assembly structure dynamics modeling; step SS3: acquiring the probability distribution model of the fitting size and the tightening torque according to the experimental sample; step SS4: selecting the chaos polynomial order P, and generating the chaos polynomial expansion term; step SS5: calculating the coefficients of each chaos polynomial expansion term by adopting the Bayesian compressive sensing method; step SS6: determining the variation range of each order modal frequency of the casing assembly structure based on the established non-invasive chaos polynomial model; and step SS7: if the determination result does not converge, then P=P+1, and the step SS4 is executed; if the determination result converges, then the result is outputted and the method is ended. The method is used for the uncertainty analysis of each order modal frequency of the casing assembly structure, and the calculation efficiency is improved while the analysis precision is ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to a non-intrusive chaotic polynomial casing assembly structure uncertainty analysis method, belonging to the technical field of analyzing the variation range of each order mode of the casing assembly structure caused by the uncertainty of the fit size and tightening torque. BACKGROUND

[0002] The casing structure of an aero turbine engine is usually assembled by multiple casings, is the main load-bearing component in the engine, and is the key component for bearing load and containment in the aero engine. The casing is usually a thin-walled cylindrical structure, and there are many uncertainties in the machining and manufacturing process, thereby causing certain uncertainty in the dynamic characteristics of the casing structure, and finally affecting the dynamic characteristics of the rotor-support-casing whole system of the aero turbine engine. Therefore, it is necessary to establish a dynamic uncertainty analysis model of the casing assembly structure based on a small amount of test data during the design stage of the aero turbine engine, and analyze the dynamic characteristics of the casing structure.

[0003] In recent decades, polynomial chaos expansion has become a main technique for quantifying the uncertainty of system response. The PCE method is divided into intrusive and non-intrusive polynomial chaos (NIPC). The intrusive polynomial chaos expansion replaces all dependent variables and random inputs in the system control equation with their polynomial chaos expansion, constructs a polynomial chaos expansion model of the random response quantity of interest by using a certain number of integral points or sampling points, and performs uncertainty analysis on the basis, thereby quickly obtaining the statistical characteristics of the response output. The present application is based on the NIPC method, and constructs a dynamic analysis method considering the uncertainty of the casing assembly structure. SUMMARY

[0004] The present application aims to overcome the technical defects existing in the prior art, solve the above technical problems, and propose a non-intrusive chaotic polynomial casing assembly structure uncertainty analysis method for analyzing the variation range of each order mode of the casing assembly structure caused by the uncertainty of the fit size and tightening torque, thereby improving the calculation efficiency while ensuring the analysis accuracy.

[0005] The present application specifically adopts the following technical solution: a non-intrusive chaotic polynomial casing assembly structure uncertainty analysis method, comprising the following steps:

[0006] Step SS1: dynamic modeling of the casing component;

[0007] Step SS2: dynamic modeling of the casing assembly structure;

[0008] Step SS3: obtaining the probability distribution model of the fit size and tightening torque according to the experimental sample;

[0009] Step SS4: selecting a chaos polynomial order P, and generating chaos polynomial expansion terms;

[0010] Step SS5: calculating coefficients of each chaos polynomial expansion term by using Bayesian compressive sensing method;

[0011] Step SS6: determining the variation range of each order modal frequency of the casing assembly structure based on the established non-intrusive chaos polynomial model;

[0012] Step SS7: if the determination result is not convergent, then P=P+1, and the process returns to step SS4 for execution; if the determination result is convergent, then the result is outputted and the process ends.

[0013] As a preferred embodiment, the chaos polynomial expansion terms in step SS4 are Ψ=[ψ0 ψ1 …ψP-1]T, and P is the number of polynomial expansion terms. P

[0014] As a preferred embodiment, the coefficients of each chaos polynomial expansion term in step SS5 are c, wherein,

[0015] As a preferred embodiment, step SS5 specifically comprises:

[0016] Step SS51: selecting a base function ψ i ;

[0017] Step SS52: updating γ i in the following formula (2);

[0018]

[0019] Step SS53: updating μ and Σ by using the following formula (3);

[0020]

[0021] Step SS54: updating s i and q i by using the following formula (4);

[0022]

[0023] Step SS55: updating λ by using the following formula (5);

[0024]

[0025] Step SS56: establishing a chaos polynomial model of the uncertainty of the casing assembly structure:

[0026] Y=Ψc\*MERGEFORMAT(6) ​

[0027] Y is the modal frequency of the casing assembly structure.

[0028] As a preferred embodiment, the step SS6 specifically comprises: calculating the variation range of the modal frequency of the casing assembly structure based on formula (6).

[0029] As a preferred embodiment, the step SS7 specifically comprises: repeating the steps SS4-SS6 until the variation range of the modal frequency converges.

[0030] The present application has the following beneficial effects: in the non-invasive chaos polynomial-based casing assembly structure uncertainty analysis method provided by the present application, the variation range of the modal frequency of the casing assembly structure is taken as the analysis target, the casing component dynamics model and the casing assembly structure dynamics model are established, the probability distribution model of the fit size and the tightening torque is obtained according to the experimental sample, the uncertainty analysis proxy model of the target quantity is constructed based on the non-invasive chaos polynomial, and the accurate and rapid analysis of the variation range of the modal frequency of the casing assembly structure is realized. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 is a flowchart of the non-invasive chaos polynomial-based casing assembly structure uncertainty analysis method of the present application.

[0032] Figure 2 is a fan-compressor connecting casing test model diagram.

[0033] Figure 3 is a fan-compressor connecting casing modal test frequency response function diagram.

[0034] Figure 4 is a fan-compressor connecting casing test model diagram.

[0035] Figure 5 is a fan-compressor connecting casing test model diagram.

[0036] Figure 6 is a fit size normal distribution curve diagram.

[0037] Figure 7 is a fan-compressor connecting casing test model diagram.

[0038] Figure 8 is a connecting stiffness normal distribution curve diagram.

[0039] Figure 9 is a normal distribution curve diagram of the elastic modulus.

[0040] Figure 10is the histogram of the first four modal frequencies of the connecting case under 1000 sample spaces.

[0041] Figure 11 is the distribution diagram of the second order test frequency in the sample frequency interval.

[0042] Figure 12 is the distribution diagram of the fourth order test frequency in the sample frequency interval. DETAILED DESCRIPTION

[0043] The application will be further described below in conjunction with the accompanying drawings. The following examples are only used to more clearly illustrate the technical solutions of the application, and cannot be used to limit the protection scope of the application.

[0044] In the method for analyzing the uncertainty of the connecting case assembly structure based on the non-invasive chaotic polynomial provided in the application, the variation range of the modal frequencies of the connecting case assembly structure is taken as the analysis target, the dynamic model of the connecting case components and the dynamic model of the connecting case assembly structure are established, the probability distribution model of the fitting size and the tightening torque is obtained according to the experimental samples, the uncertainty analysis proxy model of the target quantity is constructed based on the non-invasive chaotic polynomial, and the accurate and rapid analysis of the variation range of the modal frequencies of the connecting case assembly structure is realized.

[0045] The following takes the fan and compressor connecting case assembly structure of an engine as an example to describe the method for analyzing the uncertainty of the connecting case assembly structure based on the chaotic polynomial provided in the application.

[0046] The finite element model and the geometric model of the fan and compressor connecting case are shown in Figure 5 and Figure 7 The fan case and the compressor case are connected through bolts, and there are 20 bolts at the connecting position, and the bolt specification is M4.

[0047] (1) The modal test of the fan and compressor connecting case is performed, and the test is shown in Figure 2 The test point layout is consistent with the single component test, and three acceleration sensors are arranged to identify the possible heavy modal characteristics. The frequency response function obtained by the test of the fan and compressor connecting case is shown in Figure 3 The frequency range of the test is 0-2000Hz. The modal frequency and mode shape of the test before 2000Hz are shown in Figure 4 The thin layer is used to replace the bolt, and the finite element model of the fan and compressor connecting case is shown in Figure 5 The connecting stiffness is 4.91e9N / m, and the thin layer elastic modulus is 6.53e9Pa by the theoretical calculation formula of the thin layer unit elastic modulus. The finite element model of the fan and compressor connecting case is established, and the modal frequency and mode shape before 2000Hz are calculated.

[0048] (2) In the assembly connection modeling of the casing, thin layer elements are often used instead of bolt connections to simplify the model and reduce the difficulty of calculation. When there is a difference in the fitting size between the fan and the compressor casing, it will cause different connection surfaces between the fan casing and the compressor casing, resulting in uncertainty in the stiffness of the casing connection, and the equivalent thin layer element connection stiffness is also uncertain. The gap sizes of the five different fitting sizes of the compressor are 0.014 mm, 0.0064 mm, -0.0096 mm, -0.0189 mm and -0.0034 mm. The modal frequencies of the five compressor and fan connection casings within 2000 Hz are tested, the distribution of the modal frequencies under the uncertainty of different fitting sizes is analyzed, the casing connection stiffness and the elastic modulus of the thin layer element are identified through the modal frequencies, and whether the frequencies meet the normal distribution under different fitting sizes is determined. The different fitting sizes are shown in Table 1.

[0049] Table 1 Distribution parameters of different fitting sizes

[0050]

[0051] The modal frequencies of the first five different fitting size compressor and fan connection casings within 2000 Hz are shown in Table 2.

[0052] Table 2 Modal frequencies of the five different fitting size compressor and fan connection casings within 2000 Hz

[0053]

[0054] (3) Assuming that the fitting size follows a normal distribution, the five fitting sizes meet the normal distribution, the mean is -0.0023 mm, and the variance is 0.0001378 mm. 1000 times of sampling are performed on the fitting size, the normal distribution curve of the fitting size is shown in Figure 6 , and the fitting size distribution interval is [-0.04 0.03] mm.

[0055] A geometric model of the fan and compressor connection casing containing solid thin layer elements is established, the thickness of the thin layer is 1 mm, and the geometric model is shown in Figure 7 . Based on the theory of connection stiffness and thin layer element elastic modulus, the initial connection stiffness of the casing is calculated to be 4.91×10 9 N / m, and the elastic modulus is 6.53×10 9 Pa. The modal frequencies of the connection casing within 2000 Hz are calculated based on the thin layer elastic modulus, and are shown in Table 3.

[0056] Table 3 Modal frequencies of the fan and compressor connection casing finite element model within 2000 Hz

[0057] Order 1 2 3 4 Frequency (Hz) 815.55 816.3 1564.1 1564.1

[0058] The first order and the second order of the fan compressor connecting casing are heavy modes, and the third order and the fourth order are heavy modes, the second order mode frequency obtained by test is used to identify the casing connecting stiffness and the thin layer elastic modulus, and the identified casing connecting stiffness and the thin layer unit elastic modulus are shown in Table 4.

[0059] Table 4 Casing connecting stiffness and thin layer elastic modulus of different matching sizes

[0060] No. 1 No. 2 No. 3 No. 4 No. 5 Mean Variance Elastic modulus x 10 9 Pa]] 5.34 7.38 3.64 4.35 6.69 5.48 2.439 Connection stiffness x 10 9 N / m 4.02 5.04 2.73 3.27 4.78 3.97 0.958

[0061] The fan compressor casing connecting stiffness and the thin layer unit elastic modulus are in normal distribution, the normal distribution curves of the connecting stiffness and the thin layer elastic modulus are shown in Figure 8 and Figure 9 The distribution interval of the connecting stiffness is [1.175 6.966]×10 9 N / m, and the distribution interval of the thin layer elastic modulus is [0.793 10.22]×10 9 Pa.

[0062] (4) The order of the chaotic polynomial is selected, and the chaotic polynomial expansion term Ψ=[ψ0 ψ1 … ψ P ] is generated according to the probability distribution of the matching size and the tightening torque, and P is the number of polynomial expansion terms:

[0063] (5) The coefficients c of each chaotic polynomial expansion term are calculated by using the Bayesian compressed sensing method;

[0064]

[0065] This step includes the following sub-steps:

[0066] a) Select the base function ψ i (initially corresponding to the constant regression quantity);

[0067] b) Update γ i in the following formula;

[0068]

[0069] c) Update μ and Σ by using the following formula;

[0070]

[0071] d) Update s i and q i by using the following formula;

[0072]

[0073] e) Update λ by using the following formula:

[0074]

[0075] Chaotic polynomial model for establishing uncertainty of casing assembly structure

[0076] Y = Ψc (6)

[0077] Y is each order modal frequency of the casing assembly structure.

[0078] (6) Based on the constructed chaotic polynomial, the modal frequency of the fan compressor connecting casing within 2000 Hz is analyzed under 1000 thin layer elastic modulus sample intervals.

[0079] (7) Steps (4)-(6) are repeated until the analysis result converges. Figure 10 The first order modal frequency distribution interval is [808.981 6.15] Hz, the second order modal frequency distribution interval is [809.678 16.91] Hz, the third order modal frequency distribution interval is [1551.091 565.6] Hz, and the fourth order modal frequency distribution interval is [1551.091 565.6] Hz. Figure 10 It can be seen from the above table that under 1000 sample spaces, the first four order modal frequencies of the fan compressor connecting casing are left skewed distribution.

[0080] In the casing assembly structure uncertainty analysis method based on non-invasive chaotic polynomial, the change of the matching size and the tightening torque is considered, the change range of the modal frequency of the casing assembly structure is analyzed, and only 5 groups of tests are needed. Compared with the 100 times of tests required by the traditional Monte Carlo method, the analysis time is shortened by 95%, and the analysis efficiency is greatly improved. As shown in Figure 11 and 12 The accuracy of the method is basically consistent with the results of the traditional Monte Carlo method, and the superiority of the method is obvious.

[0081] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in the form of a computer program product implemented on one or more computer usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0082] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks. Figure 1 one or more flow or flows and / or block diagram block or blocks. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart or flows and / or block diagram block or blocks.

[0083] Finally, it should be noted that the above-mentioned embodiments are merely intended for describing the technical solutions of the present application, but not for limiting it. Although the present application has been described in detail with reference to the above-mentioned embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalent replaced without departing from the spirit and scope of the present application, and any modification or equivalent replacement should be covered in the protection scope of the claims of the present application.

Claims

1. A method for analyzing the uncertainty of a non-intrusive assembly of a chaotic polynomial, characterized in that, The method comprises the following steps: Step SS1: modeling of the dynamics of the casing component; Step SS2: modeling of the dynamics of the casing assembly structure; Step SS3: obtaining a probability distribution model of the mating size and the tightening torque according to an experimental sample; Step SS4: selecting a chaotic polynomial order P and generating a chaotic polynomial expansion term; Step SS5: calculating coefficients of each chaotic polynomial expansion term by using a Bayesian compressive sensing method; the coefficients of each chaotic polynomial expansion term in the step SS5 are c, wherein, ; The step SS5 specifically comprises: Step SS51: Selecting basis functions ; Step SS52: update γ in the following equation (2) i ; ； Step SS53: update the value of the variable "a" using the following equation (3) and ; ； Step SS54: Update s using the following equation (4) i and q i ; ； Step SS55: updating λ by using the following formula (5); ； Step SS56: establishing a chaotic polynomial model of the uncertainty of the casing assembly structure: ； wherein, is the modal frequency of each order of the gearbox assembly structure; Step SS6: determining the variation range of each order modal frequency of the casing assembly structure based on the established non-intrusive chaotic polynomial model; Step SS7: if the determination result does not converge, P=P+1, and the step SS4 is executed, if the determination result converges, the result is outputted and the process is ended.

2. The method of claim 1, wherein, The chaotic polynomial expansion term in the step SS4 is P is the number of polynomial expansion terms.

3. The method of claim 1, wherein the non-intrusive chaotic polynomial response surface method is a method of analyzing a cabin assembly uncertainty. The step SS6 specifically comprises: calculating the variation range of each order modal frequency of the casing assembly structure based on the formula (6).

4. The method of claim 3, wherein the non-intrusive chaotic polynomial response surface method is a method of analyzing a cabin assembly uncertainty. The step SS7 specifically comprises: repeating the steps SS4-SS6 until the variation range result of each order modal frequency converges.

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