Complete machine imbalance response uncertainty analysis method based on sparse polynomial model

Abstract

The invention discloses a sparse polynomial model-based complete machine imbalance response uncertainty analysis method. The method comprises the following steps of SS1, dynamic modeling of rotor and stator parts; step SS2, carrying out dynamic modeling on the whole machine assembly structure; step SS3, determining the distribution interval of the connection rigidity and the supporting rigidity of the casing according to the experimental sample; step SS4, selecting a chaotic polynomial order p, and generating a chaotic polynomial expansion item; sS5, calculating the coefficient of each chaotic polynomial expansion item by adopting a regression method; sS6, determining the variation range of the imbalance response of the whole machine based on the established sparse polynomial proxy model; step SS7, if the result of the imbalance response of the whole machine is not converged, p = p + 1, executing the step SS5, and if the result is converged, outputting the result and ending. The method is used for analyzing the variation range of the whole machine imbalance response caused by the uncertainty of the connecting rigidity and the supporting rigidity of the cartridge receiver, and the calculation efficiency is improved while the analysis precision is ensured.

Description

Technical Field

[0001] The invention relates to a whole machine unbalance response uncertainty analysis method based on a sparse polynomial model, belonging to the technical field of variation range analysis of whole machine unbalance response caused by uncertainty of casing connection stiffness and support stiffness. Background Art

[0002] A turbine engine is a complex structure composed of a rotor, a support, a casing and other systems. Due to the existence of uncertain factors such as material parameters, processing tolerances, and assembly deviations, there are many uncertainties in the overall structure of the machine, which leads to uncertain changes in the dynamic characteristics and unbalanced response of the overall structure, bringing many difficulties to the turbine engine rotor dynamics design and evaluation.

[0003] In the current research work, uncertainty modeling and calculation analysis are mainly carried out based on the rotor-support system. However, the influence of the casing is ignored, and the transient response of the rotor-support-casing system cannot be fully calculated and analyzed. After considering the casing assembly, the whole machine model is more complicated, and the uncertainty problem of the whole machine structure is more complicated, but it can better reflect the reality.

[0004] Therefore, it is very necessary to carry out uncertainty analysis of the turbine engine rotor-support-casing system considering the impact of casing assembly to provide support for the engine rotor dynamics design evaluation.

[0005] In recent decades, polynomial chaos expansion has become a major technology for quantifying the uncertainty of system response. Based on the sparse polynomial proxy model method, the present invention constructs a whole machine unbalanced response dynamics analysis method considering the uncertainty of casing connection stiffness and support stiffness. Summary of the invention

[0006] The purpose of the present invention is to overcome the technical defects of the prior art, solve the above-mentioned technical problems, and propose an uncertainty analysis method for the unbalanced response of the whole machine based on a sparse polynomial model, which is used to analyze the variation range of the unbalanced response of the whole machine caused by the uncertainty of the connection stiffness and support stiffness of the casing, thereby improving the calculation efficiency while ensuring the analysis accuracy.

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

[0008] Step SS1: Dynamic modeling of the rotor and stator components;

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

[0010] Step SS3: Determine the distribution range of the casing connection stiffness and the support stiffness according to the experimental sample;

[0011] Step SS4: Select the chaotic polynomial order p and generate chaotic polynomial expansion terms;

[0012] Step SS5: Calculate the coefficients of each chaotic polynomial expansion term using a regression method;

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

[0014] Step SS7: If the result of the unbalanced response of the whole machine has not converged, then p=p+1, and the process goes to step SS5 for execution. If the result converges, the process outputs the result and ends.

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

[0016]

[0017] Among them, q∈(0,1], α is the multi-exponent of the candidate chaotic polynomial.

[0018] As a preferred embodiment, the step SS5 specifically includes: establishing a solution equation for the chaotic polynomial coefficient c:

[0019] Y=Ψc+ε (5)

[0020] Where Y is the sample data of the unbalanced response of the whole machine obtained based on the whole machine dynamics model, ε is the noise, Ψ is the matrix obtained by substituting the sample data of the uncertainty parameter into the polynomial set A, Ψ=[ψ0 ψ1 … ψ P ], P is the number of non-zero-order terms of the candidate polynomial.

[0021] As a preferred embodiment, the step SS5 specifically further includes: calculating the coefficient c using a regression method:

[0022]

[0023] As a preferred embodiment, step SS7 specifically includes: repeating steps SS4 to SS6 until the variation range of the unbalanced response is stably converged.

[0024] The beneficial effects achieved by the present invention are as follows: In the uncertainty analysis method for the unbalanced response of the whole machine based on the sparse polynomial model proposed in the present invention, the variation range of the unbalanced response of the whole machine is taken as the analysis target, a dynamic model of the rotor and stator components and a dynamic model of the assembly structure of the whole machine are established, the distribution range of the connection stiffness and the support stiffness of the casing are determined according to the experimental samples, and a sparse polynomial uncertainty analysis proxy model constructed based on the regression method is used to achieve accurate and rapid analysis of the variation range of the unbalanced response of the whole machine. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a flow chart of the uncertainty analysis method of the whole machine unbalanced response based on the sparse polynomial model of the present invention.

[0026] Figure 2 It is a schematic diagram of the whole machine dynamics model of the present invention.

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

[0028] Figure 4 It is the distribution diagram of the test results of 10 groups of whole machine uncertainty tests.

[0029] Figure 5 This is a comparison chart of the unbalanced response boundaries of the whole machine predicted by the sparse polynomial model and the traditional Monte Carlo method. DETAILED DESCRIPTION

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

[0031] Example 1: Figure 1 As shown, in the uncertainty analysis method of the unbalanced response of the whole machine based on the sparse polynomial model proposed in the present invention, the variation range of the unbalanced response of the whole machine is taken as the analysis target, the dynamic model of the rotor and stator components and the dynamic model of the whole machine assembly structure are established, the distribution range of the casing connection stiffness and the support stiffness is determined according to the experimental samples, and the sparse polynomial uncertainty analysis proxy model constructed by the regression method is used to realize the accurate and rapid analysis of the variation range of the unbalanced response of the whole machine.

[0032] Taking a turbine engine complete machine tester as an example, the method proposed in the present invention is described. The rotor tester 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 acquisition system.

[0033] (1) Whole machine dynamics modeling

[0034] Considering the nonlinearity of the rotor sleeve gear connection, the uncertainty of the casing assembly and the uncertainty of the rotor support, the nonlinear uncertainty model of the whole machine of the turbine engine whole machine tester is established. Figure 2 shown.

[0035] (2) Determine the distribution range of the casing connection stiffness and support stiffness based on the experimental samples

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

[0037] (3) The order p of the chaotic polynomial is selected. According to the distribution range of the casing connection stiffness and the support stiffness and the sparsity of the chaotic polynomial coefficients, the hyperbolic truncation method is used to generate the candidate chaotic polynomial set A:

[0038]

[0039] Among them, q∈(0,1], α is the multi-exponent of the candidate chaotic polynomial.

[0040] Establish the solution equation of the chaotic polynomial coefficient c:

[0041] Y=Ψc+ε (8)

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

[0043] The coefficient c is calculated using the regression method:

[0044]

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

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

[0047] (5) Whole machine test verification

[0048] The 10 groups (critical speed, maximum response) obtained from the 5 sets of whole machine tests with casing assembly and support structure uncertainty are all within the range of the unbalanced response calculated by this method. The results are as follows Figure 4 As shown, the effectiveness of the method is verified. Figure 4 The critical speed is in the range of [21900, 24500] rpm, the maximum vibration response is in the range of [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 uncertainty analysis method of the whole machine unbalance response based on the sparse polynomial proxy model proposed in this invention, the variation of the casing connection stiffness and the support stiffness is considered, and the variation range of the whole machine unbalance response is analyzed, and only 5 groups of test samples are needed. Compared with the 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. The comparison of the measurement results of the two is as follows: Figure 5 As shown in the figure, the blue and red dotted lines respectively give the minimum and maximum boundaries (envelopes) of the unbalanced response obtained based on the method of the present invention, and the green one is the simulation result of the traditional Monte Carlo method. Figure 5 It can be seen that the accuracy of the method of the present invention is consistent with the result of the traditional Monte Carlo method, which shows the superiority of the method of the present invention.

[0050] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0051] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. The uncertainty analysis method of the whole machine unbalanced response based on the sparse polynomial model is characterized by: The steps include: Step SS1: Dynamic modeling of the rotor and stator components; Step SS2: whole machine assembly structural dynamics modeling; Step SS3: Determine the distribution range of the casing connection stiffness and the support stiffness according to the experimental sample; Step SS4: Select the chaotic polynomial order p and generate chaotic polynomial expansion terms; Step SS5: Calculate the coefficients of each chaotic polynomial expansion term using a regression method; Step SS6: determining a variation range of the whole machine unbalance response based on the established sparse polynomial proxy model; Step SS7: If the result of the unbalanced response of the whole machine has not converged, then p=p+1, and the process goes to step SS5 for execution. If the result converges, the process outputs the result and ends.

2. The uncertainty analysis method for whole machine unbalanced response based on sparse polynomial model according to claim 1 is characterized in that: The step SS4 specifically includes: selecting the chaotic polynomial order p, and generating a candidate chaotic polynomial set A by using a hyperbolic truncation method according to the distribution interval of the casing connection stiffness and the support stiffness and the sparsity of the chaotic polynomial coefficients: Among them, q∈(0,1], α is the multi-exponent of the candidate chaotic polynomial.

3. The uncertainty analysis method for whole machine unbalanced response based on sparse polynomial model according to claim 1 is characterized in that: The step SS5 specifically includes: establishing a solution equation for the chaotic polynomial coefficient c: Y=Ψc+ε (2) Where Y is the sample data of the unbalanced response of the whole machine obtained based on the whole machine dynamics model, ε is the noise, Ψ is the matrix obtained by substituting the sample data of the uncertainty parameter into the polynomial set A, Ψ=[ψ0 ψ1 … ψ P ], P is the number of non-zero-order terms of the candidate polynomial.

4. The uncertainty analysis method for unbalanced response of a whole machine based on a sparse polynomial model according to claim 3 is characterized in that: The step SS5 specifically further includes: using a regression method to calculate the coefficient c:

5. The uncertainty analysis method for whole machine unbalanced response based on sparse polynomial model according to claim 1 is characterized in that: The step SS7 specifically includes: repeating the steps SS4 to SS6 until the variation range of the unbalanced response is stably converged.

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