Whole machine unbalance response uncertainty analysis method based on sparse polynomial model

Abstract

The application discloses a whole machine unbalance response uncertainty analysis method based on a sparse polynomial model, and comprises the following steps: step SS1, rotor-stator component dynamics modeling; step SS2, whole machine assembly structure dynamics modeling; step SS3, determining the distribution interval of casing connecting stiffness and supporting stiffness according to experimental samples; step SS4, selecting a chaotic polynomial order p, and generating a chaotic polynomial expansion term; step SS5, calculating the coefficient of each chaotic polynomial expansion term by using a regression method; step SS6, determining the change range of the whole machine unbalance response based on the established sparse polynomial proxy model; step SS7, if the result of the whole machine unbalance response does not converge, then p=p+1, and the step SS5 is executed, and if the result converges, the result is outputted and the method ends. The application is used for analyzing the change range of the whole machine unbalance response caused by the uncertainty of the casing connecting stiffness and the supporting stiffness, and can improve the calculation efficiency while ensuring the analysis precision.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of whole machine unbalance response uncertainty analysis method based on sparse polynomial model, belong to the change range analysis technical field of whole machine unbalance response caused by casing connection stiffness, supporting stiffness uncertainty. BACKGROUND

[0002] Turbine engine is the complex structure of rotor, support, casing and other systems, due to the existence of material parameters, machining tolerance, assembly deviation and other uncertain factors, there are many uncertain factors in the whole machine structure, which leads to the uncertainty of the dynamic characteristics and unbalance response of the whole machine structure, which brings many difficulties to the design and evaluation of turbine rotor dynamics.

[0003] In the current research work, mainly based on rotor-support system to carry out uncertainty modeling, calculation and analysis.But it ignores the influence of casing, and cannot completely calculate and analyze the transient response of rotor-support-casing whole machine system.Considering the assembly of casing, the whole machine model is more complex, and the uncertainty problem of the whole machine structure is more complex, but it can better reflect the actual situation.

[0004] Therefore, considering the influence of casing assembly, it is necessary to carry out whole machine uncertainty analysis of turbine rotor-support-casing system, which provides support for the design and evaluation of engine rotor dynamics.

[0005] In recent decades, polynomial chaos expansion has become a main technology for quantifying the uncertainty of system response.The present application is based on sparse polynomial surrogate model method, and constructs a whole machine unbalance response dynamics analysis method considering the uncertainty of casing connection stiffness and supporting stiffness. SUMMARY

[0006] The present application aims to overcome the technical defects of the prior art, solve the above technical problems, and propose a whole machine unbalance response uncertainty analysis method based on sparse polynomial model, for analyzing the change range of whole machine unbalance response caused by casing connection stiffness and supporting stiffness uncertainty, while ensuring the analysis accuracy and improving the calculation efficiency.

[0007] The present application specifically adopts the following technical solutions: a whole machine unbalance response uncertainty analysis method based on sparse polynomial model, comprising the following steps:

[0008] Step SS1: rotor-stator component dynamics modeling;

[0009] Step SS2: whole machine assembly structure dynamics modeling;

[0010] Step SS3: determine the distribution interval of casing connection stiffness and supporting stiffness according to experimental samples;

[0011] Step SS4: selecting a chaotic polynomial order p, generating chaotic polynomial expansion terms;

[0012] Step SS5: calculating coefficients of each chaotic polynomial expansion term by using regression method;

[0013] Step SS6: determining a variation range of the whole machine unbalance response based on the established sparse polynomial surrogate model;

[0014] Step SS7: if the result of the whole machine unbalance response does not converge, then p = p + 1, and turning to Step SS5 for execution, if the result converges, outputting the result and ending.

[0015] As a preferred embodiment, the Step SS4 specifically comprises: selecting a chaotic polynomial order p, generating a candidate chaotic polynomial set A by using hyperbolic truncation method according to the distribution interval of the casing connection stiffness and the support stiffness, and combining the sparsity of the chaotic polynomial coefficients:

[0016]

[0017] wherein q ∈ (0, 1], and a is a multi-index of the candidate chaotic polynomial.

[0018] As a preferred embodiment, the Step SS5 specifically comprises: establishing a solving equation of the chaotic polynomial coefficients c:

[0019] Y = Ψc + ε (5)

[0020] wherein Y is sample data of the whole machine unbalance response obtained based on the whole machine dynamics model, ε is noise, Ψ is a matrix obtained by substituting the sample data of the uncertain parameters into the polynomial set A, Ψ = [ψ0 ψ1 … ψ P ], and P is the number of non-zero terms of the candidate polynomial.

[0021] As a preferred embodiment, the Step SS5 specifically further comprises: calculating the coefficients c by using regression method.

[0022]

[0023] As a preferred embodiment, the Step SS7 specifically comprises: repeating the Step SS4-Step SS6 until the variation range of the unbalance response stably converges.

[0024] The beneficial effects achieved by this invention are as follows: In the uncertainty analysis method for overall machine unbalance response based on sparse polynomial model proposed in this invention, the variation range of overall machine unbalance response is taken as the analysis target. Dynamic models of rotor-stator components and overall machine assembly structure are established. The distribution range of casing connection stiffness and support stiffness is determined according to experimental samples. Based on the sparse polynomial uncertainty analysis proxy model constructed by regression method, accurate and rapid analysis of the variation range of overall machine unbalance response is achieved. Attached Figure Description

[0025] Figure 1 This is a flowchart of the uncertainty analysis method for overall system imbalance response based on a sparse polynomial model according to the present invention.

[0026] Figure 2 This is a schematic diagram of the overall dynamics model of the present invention.

[0027] Figure 3 This is a schematic diagram of the critical speed and maximum response boundary predicted by the nonlinear uncertainty model of the whole machine according to the present invention.

[0028] Figure 4 This is a distribution chart of the test results from 10 sets of whole-machine uncertainty tests.

[0029] Figure 5 This is a comparison chart of the overall system imbalance response boundary predicted by the sparse polynomial model and the traditional Monte Carlo method. Detailed Implementation

[0030] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0031] Example 1: As Figure 1 As shown, in the uncertainty analysis method for overall machine unbalanced response based on sparse polynomial model proposed in this invention, the range of variation of overall machine unbalanced response is taken as the analysis target. Dynamic models of rotor-stator components and overall machine assembly structure are established. The distribution range of casing connection stiffness and support stiffness is determined according to experimental samples. A sparse polynomial uncertainty analysis proxy model is constructed using regression method to achieve accurate and rapid analysis of the range of variation of overall machine unbalanced response.

[0032] Taking a turbine engine complete engine test apparatus as an example, the method proposed in this invention is illustrated. The rotor test apparatus includes a main body and an auxiliary system. The auxiliary system includes a drive system, a lubricating oil supply and return device, and a test data acquisition system, etc.

[0033] (1) Overall dynamics modeling

[0034] A nonlinear uncertain model of the turbo-engine test rig is established, considering the nonlinear connection between the rotor and the casing, the assembly uncertainty of the casing, and the bearing uncertainty of the rotor. Figure 2

[0035] (2) Determine the distribution interval of the casing connection stiffness and the bearing stiffness according to the experimental samples

[0036] Five compressor casings and front bearing bushings with different fit sizes are designed and processed. The distribution interval of the five casing fit sizes is [-0.04 0.03] mm. The five bearing fit clearances are 10 microns, 6 microns, transition fit (2 microns), 8 microns, and 11 microns, i.e. [-0.01, 0.011] mm, and the corresponding front bearing stiffness is [8.1, 9.6] MN / m.

[0037] (3) Select the chaotic polynomial order p, and according to the distribution interval of the casing connection stiffness and the bearing stiffness, combined with the sparsity of the chaotic polynomial coefficients, use the hyperbolic truncation method to generate a candidate chaotic polynomial set A:

[0038]

[0039] where q ∈ (0, 1], and α is the multi-index of the candidate chaotic polynomial.

[0040] Establish the equation for solving the chaotic polynomial coefficients c:

[0041] Y = Ψc + ε (8)

[0042] where Y is the sample data of the unbalance response of the whole machine based on the whole machine dynamics model, ε is the noise, Ψ is the matrix obtained by substituting the sample data of the uncertain parameters into the polynomial set A. Ψ = [ψ0 ψ1 … ψ P ], and P is the number of non-zero terms of the candidate polynomial.

[0043] Use the regression method to calculate the coefficients c:

[0044]

[0045] (4) Simulation prediction of the unbalance response of the whole machine

[0046] The constructed sparse polynomial surrogate model is used to calculate the variation range of the unbalance response of the whole machine. The uncertainty parameters are sampled 13 × 11 = 143 groups, and the calculated unbalance response is shown in Figure 3 . Figure 3 The upper and lower red lines respectively give the maximum and minimum boundaries (envelops) of the unbalance response.

[0047] ​(5) Whole machine test verification

[0048] 5 sets of whole machine test including assembly of the casing and uncertainty of the supporting structure, 10 groups of (critical speed, maximum response) obtained are within the variation range of the unbalance response calculated by the method, and the results are shown in Figure 4 , which verifies the effectiveness of the method. Figure 4 The critical speed is located in the interval [21900, 24500] rpm, the maximum vibration response is located in the interval [72, 265] μm, and the quadrilateral formed by the red solid line gives the boundary of the (critical speed, maximum vibration response) distribution.

[0049] In the whole machine unbalance response uncertainty analysis method based on the sparse polynomial surrogate model provided in the application, the variation of the casing connection stiffness and the supporting stiffness is considered, and the variation range of the whole machine unbalance response is analyzed, only 5 sets of test samples are needed. Compared with 100 tests required by the traditional Monte Carlo method, the analysis time is shortened by more than 90%, and the analysis efficiency is greatly improved. As shown in Figure 5 , the blue and red dotted lines in the figure respectively give the minimum and maximum boundaries (envelops) of the unbalance response obtained based on the method of the application, and the green color is the simulation result of the traditional Monte Carlo method, from Figure 5 It can be seen that the accuracy of the method described in the application is consistent with the result of the traditional Monte Carlo method, and thus the superiority of the method described in the application is obvious.

[0050] Those skilled in the art should understand that the embodiments of the application can be provided as a method, a system, or a computer program product. Therefore, the application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0051] The application is described with reference to flowcharts and / or block diagrams according to the method, device (system), and computer program product of the embodiments of the application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a method for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 one flow or multiple flows and / or blocks Figure 1apparatuses that implement the functions specified in the flowchart or flowchart blocks. These computer program instructions can also be loaded onto a computer or other programmable data processing devices to cause a series of operational steps to be performed on the computer or other programmable data processing devices to produce a computer implemented process such that the instructions that are executed on the computer or other programmable data processing devices provide steps for implementing the functions specified in the flowchart or flowchart blocks. Figure 1 flowchart or flowchart blocks. Figure 1 apparatuses that implement the functions specified in the flowchart or flowchart blocks. These computer program instructions can also be loaded onto a computer or other programmable data processing devices to cause a series of operational steps to be performed on the computer or other programmable data processing devices to produce a computer implemented process such that the instructions that are executed on the computer or other programmable data processing devices provide steps for implementing the functions specified in the flowchart or flowchart blocks. Figure 1 flowchart or flowchart blocks. Figure 1 flowchart or flowchart blocks.

[0052] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application rather than limiting it, although the present application has been described in detail with reference to the above examples, those skilled in the art should understand that: the specific embodiments of the present application can still be modified or replaced by the equivalent, without departing from the spirit and scope of the present application, any modification or equivalent replacement of the present application should be covered within the protection scope of the claims of the present application.

Claims

1. A method for analyzing the uncertainty of the response of a machine to unbalance based on a sparse polynomial model, characterized in that, The method comprises the following steps: Step SS1: modeling of the dynamics of the rotor-stator component; Step SS2: modeling of the dynamics of the overall assembly structure; Step SS3: determining the distribution intervals of the casing connection stiffness and the support stiffness according to experimental samples; Step SS4: selecting the order p of the chaotic polynomial and generating the chaotic polynomial expansion term; the step SS4 specifically comprises: selecting the order p of the chaotic polynomial, generating a candidate chaotic polynomial set A according to the distribution intervals of the casing connection stiffness and the support stiffness, and combining the sparsity of the chaotic polynomial coefficients and using a hyperbolic truncation method; A p,q = {a: ||a q ≤ p} (1); wherein q∈(0, 1], and a is a multi-index of the candidate chaotic polynomial; Step SS5: calculating the coefficients of each chaotic polynomial expansion term by using a regression method; the step SS5 specifically comprises: establishing a solving equation of the chaotic polynomial coefficients c: Y=Ψc+ε (2); Wherein, Y is the sampling sample data of the whole machine unbalance response based on the whole machine dynamics model, ε is noise, Ψ is the matrix obtained by substituting the sampling sample data of the uncertainty parameter into the polynomial set A, Ψ=[ψ0 ψ1 … ψ P ], P is the number of candidate polynomial non-zero terms; the step SS5 specifically further comprises: calculating the coefficients c by using a regression method: Step SS6: determining the variation range of the overall unbalance response based on the established sparse polynomial proxy model; Step SS7: if the result of the overall unbalance response does not converge, then p=p+1, and the step SS5 is executed, and if the result converges, the result is output and the method ends.

2. The method of claim 1, wherein the sparse polynomial model-based machine imbalance response uncertainty analysis method is characterized by, the step SS7 specifically comprises: repeating the steps SS4-SS6 until the variation range of the unbalance response stably converges.

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