Uncertainty analysis method for rotor sleeve tooth connection of chebyshev orthogonal polynomials

Abstract

The application discloses a Chebyshev orthogonal polynomial rotor sleeve tooth connecting piece uncertainty analysis method, which comprises the following steps: establishing a simplified mechanical model of the sleeve tooth connecting structure; determining key uncertainty parameters of the rotor sleeve tooth connecting structure, including a centering surface gap, a transverse load and a tightening torque; using the Chebyshev orthogonal polynomial to construct an uncertainty analysis agent model of a rotor connecting structure modal frequency; and based on the constructed uncertainty analysis agent model of the rotor connecting structure modal frequency, evaluating the influence of different parameters and combinations thereof on the modal characteristics of the rotor sleeve tooth connecting structure. The method is used for revealing the potential influence range of the uncertainty factors on the rotor modal performance, and provides a systematic analysis process and practical suggestions for design and optimization. Compared with the traditional method, the application has higher calculation efficiency and reliability in processing the rotor sleeve tooth connecting uncertainty problem, and is suitable for engineering design and decision support in the related field.

Description

TECHNICAL FIELD

[0001] The present application relates to a Chebyshev orthogonal polynomial rotor sleeve tooth connecting piece uncertainty analysis method, belonging to the technical field of change range analysis of rotor sleeve tooth connecting structure modal frequency caused by centering surface gap, transverse load and tightening torque uncertainty. BACKGROUND

[0002] Rotor sleeve tooth connecting structure is an indispensable key component in rotating machinery, and its performance directly affects the operation efficiency and safety of the machinery. Modal frequency is an important indicator for evaluating the dynamic characteristics of rotor sleeve tooth connecting structure. However, due to the uncertainty of parameters such as centering surface gap, transverse load and tightening torque, these factors will cause significant changes in modal frequency. Existing analysis methods mostly rely on linear models or empirical formulas, which cannot fully consider the complex effects caused by uncertainty, so they often cannot accurately reflect the real dynamic characteristics of the system in practical applications. This limitation makes engineers face challenges in designing and optimizing rotor sleeve tooth connecting structure, so there is an urgent need for a new analysis method to effectively quantify the influence of uncertainty on the change range of modal frequency. The present application proposes a method based on Chebyshev orthogonal polynomial surrogate model, aiming to provide a more accurate and reliable solution for uncertainty analysis of rotor sleeve tooth connecting structure, to improve the scientificity and accuracy of its design and performance evaluation. SUMMARY

[0003] The present application aims to overcome the technical defects of the prior art and proposes a Chebyshev orthogonal polynomial rotor sleeve tooth connecting piece uncertainty analysis method for analyzing the change range of rotor connecting structure modal frequency caused by centering surface gap, transverse load and tightening torque uncertainty, while ensuring analysis accuracy and improving computational efficiency.

[0004] The present application specifically adopts the following technical solutions: a Chebyshev orthogonal polynomial rotor sleeve tooth connecting piece uncertainty analysis method, comprising the following steps:

[0005] Step SS1: Establish a simplified mechanical model of the sleeve tooth connecting structure;

[0006] Step SS2: Determine the key uncertainty parameters of the rotor sleeve tooth connecting structure, including centering surface gap, transverse load and tightening torque;

[0007] Step SS3: Use Chebyshev orthogonal polynomial to construct an uncertainty analysis surrogate model of the modal frequency of the rotor connecting structure;

[0008] Step SS4: Based on the constructed uncertainty analysis surrogate model of the modal frequency of the rotor connecting structure, evaluate the influence of different parameters and their combinations on the modal characteristics of the rotor sleeve tooth connecting structure.

[0009] As a preferred embodiment, the step SS3 specifically comprises:

[0010] The Chebyshev orthogonal polynomial in the single-parameter case is constructed as follows:

[0011]

[0012] wherein T k (k) represents the Chebyshev polynomial of the first kind of order k, k is a non-negative integer, c i (i = 0, 1, …, k) are coefficients; the Gauss-Chebyshev numerical integral formula is used to calculate the coefficients c i , as follows:

[0013]

[0014] wherein q is the number of integral nodes, ξ (i) is the interpolation point of the Gauss-Chebyshev integral, w (i) is the corresponding weight.

[0015] As a preferred embodiment, the step SS3 specifically comprises: in the multi-parameter case, the Chebyshev orthogonal polynomial is constructed as follows:

[0016]

[0017] The coefficients c

[0018]

[0019] As a preferred embodiment, the step SS4 specifically comprises: based on the constructed uncertainty analysis surrogate model of the modal frequency of the rotor connecting structure, the propagation analysis is performed on the uncertainty parameters, the influence of different parameters and combinations thereof on the modal characteristics of the rotor toothed sleeve connecting structure is evaluated, and the variation range of the modal frequency of the rotor connecting structure is obtained.

[0020] The present application has the following beneficial effects: in the Chebyshev orthogonal polynomial-based uncertainty analysis method of the rotor toothed sleeve connecting structure proposed in the present application, the variation range of the modal frequency of the rotor connecting structure is taken as the analysis target, the key uncertainty parameters are established, including the relationship between the centering gap, the transverse load and the tightening torque and the bending stiffness of the rotor toothed sleeve, the surrogate model of the modal frequency uncertainty analysis of the rotor connecting structure is constructed based on the Chebyshev orthogonal polynomial, and the accurate and rapid analysis of the variation range of the modal frequency of the rotor connecting structure is realized. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1is a flow chart of the uncertainty analysis method of the rotor sleeve tooth connecting piece of the Chebyshev orthogonal polynomial of the application.

[0022] Figure 2 is an axial sectional view of the single-centering-face sleeve tooth structure of the application.

[0023] Figure 3 is a simplified model schematic diagram of the single-centering-face sleeve tooth structure of the application.

[0024] Figure 4 is a mechanical model schematic diagram of the single-centering-face sleeve tooth structure of the application.

[0025] Figure 5 is an equivalent shaft segment elastic modulus distribution diagram of the centering face gap uncertainty of the application.

[0026] Figure 6 is a rotor modal first-order frequency distribution diagram of the centering face gap uncertainty of the application.

[0027] Figure 7 is a rotor modal second-order frequency distribution diagram of the centering face gap uncertainty of the application.

[0028] Figure 8 is a rotor modal third-order frequency distribution diagram of the centering face gap uncertainty of the application.

[0029] Figure 9 is an equivalent shaft segment elastic modulus distribution diagram of the transverse load uncertainty of the application.

[0030] Figure 10 is a rotor modal first-order frequency distribution diagram of the transverse load uncertainty of the application.

[0031] Figure 11 is a rotor modal second-order frequency distribution diagram of the transverse load uncertainty of the application.

[0032] Figure 12 is a rotor modal third-order frequency distribution diagram of the transverse load uncertainty of the application.

[0033] Figure 13 is a thin layer elastic modulus distribution diagram of the tightening torque uncertainty of the application.

[0034] Figure 14 is a rotor modal first-order frequency distribution diagram of the tightening torque uncertainty of the application.

[0035] Figure 15 is a rotor modal second-order frequency distribution diagram of the tightening torque uncertainty of the application.

[0036] Figure 16 is a rotor modal third-order frequency distribution diagram of the tightening torque uncertainty of the application.

[0037] Figure 17 is the equivalent shaft segment elastic modulus distribution diagram of the multi-parameter uncertainty of the application.

[0038] Figure 18 is the rotor modal first-order frequency distribution diagram of the multi-parameter uncertainty of the application.

[0039] Figure 19 is the rotor modal second-order frequency distribution diagram of the multi-parameter uncertainty of the application.

[0040] Figure 20 is the rotor modal third-order frequency distribution diagram of the multi-parameter uncertainty of the application.

[0041] Figure 21 is the first-order test frequency distribution diagram in the sample frequency interval of the application.

[0042] Figure 22 is the second-order test frequency distribution diagram in the sample frequency interval of the application.

[0043] Figure 23 is the third-order test frequency distribution diagram in the sample frequency interval of the application. DETAILED DESCRIPTION

[0044] The application will be further described below in conjunction with the 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.

[0045] Example 1: As shown below, the method proposed by the application is described by taking a toothed sleeve connected rotor tester as an example. Figure 1

[0046] The rotor tester containing the toothed sleeve connection structure and the test equipment are installed, and the main test equipment includes an acceleration sensor, a force hammer, and a four-channel dynamic signal analyzer.

[0047] (1) The structural characteristics and mechanical properties of the toothed sleeve connection structure of the rotor are analyzed, and a simplified mechanical model of the toothed sleeve connection structure is established.

[0048] The toothed sleeve connection structure of the rotor is a single-centering surface toothed sleeve structure, mainly connected by a single cylindrical surface centering through the compressor shaft and the turbine shaft. The characteristics of the toothed sleeve connection structure of the rotor are that in the working process, the connection structure bears the axial tension of the compressor shaft and the turbine shaft and transmits the torque, and the centering surface bears the bending moment acting on the shaft. In addition, due to the discontinuity of the connection structure, the definition of bending stiffness needs to consider the macro deflection after stress deformation.

[0049] ​During working, the connection structure bears axial tension of compressor shaft and turbine shaft, the spline structure transmits torque, and the centering surface bears bending moment. Figure 2 The axial section view of single centering surface spline structure is shown, and how each part interacts with each other under the force state is illustrated.

[0050] Establish Figure 3 The simplified model shown is subjected to force analysis, and the right end of the rotor is subjected to transverse load and axial load. During engine operation, the shaft section also bears huge forward and backward aerodynamic load, so the left end of the spline compressor shaft end can be considered as fixed. Since there is only one centering surface, the spline will produce contact when subjected to transverse bending load, thereby providing bending stiffness, that is, it will affect the stiffness of the connection structure. Therefore, when the turbine shaft is subjected to transverse load, the contact state of the centering surface and the spline will change. Therefore, the spline surface and the centering surface need to consider the influence of nonlinear mechanics. The transverse load applied by the compression bolt will change the contact state of the left end of the spline turbine shaft and the compression surface of the compressor shaft, and its influence also needs to be considered. The rest of the positions are not in contact.

[0051] Through the analysis of the spline simplified model, the mechanical model shown in Figure 4 is obtained.

[0052] (2) According to the key uncertainty parameters of the rotor spline connection structure, including the centering surface gap, the transverse load and the tightening torque;

[0053] (3) The Chebyshev orthogonal polynomial is used to construct the uncertainty analysis proxy model of the modal frequency of the rotor spline connection structure. In the single parameter case, the Chebyshev orthogonal polynomial is constructed as follows:

[0054]

[0055] Where, T k (k,ξ) represents the first kind of Chebyshev polynomial of order k, k is a non-negative integer, c i (i=0,1,…,k) is the coefficient; the Gauss-Chebyshev numerical integral formula is used to calculate the coefficient c i in the formula as follows:

[0056]

[0057] Where, q is the number of integral nodes, ξ (i) is the interpolation point (integral node) of Gauss-Chebyshev integral, w (i) is the corresponding weight.

[0058] In the multi-parameter case, the Chebyshev orthogonal polynomial is constructed as follows:

[0059]

[0060] The coefficients in the formula are calculated by the following numerical integration formula

[0061]

[0062] (4) Based on the constructed surrogate model, the propagation analysis of the uncertain parameters is carried out, the influence of different parameters and their combinations on the modal characteristics of the rotor toothed connection structure is evaluated, the variation range of the modal frequency of the rotor connection structure is obtained, and the results are as follows:

[0063] a) Uncertainty of the centering surface gap

[0064] The centering surface gap is selected as the uncertain parameter for analysis. Based on the constructed Chebyshev orthogonal polynomial model, the elastic modulus E of the equivalent shaft section is obtained d The distribution diagram is shown in Figure 5 . Further, the elastic modulus of each group of equivalent shaft sections is respectively brought into the rotor simplified model, and the first three order modal frequencies are calculated, and the distribution is shown in 6, Figure 7 and Figure 8 .

[0065] b) Uncertainty of the transverse load

[0066] The transverse load is selected as the uncertain parameter for analysis. Based on the constructed Chebyshev orthogonal polynomial model, the elastic modulus E of the equivalent shaft section is obtained d The distribution is shown in Figure 9 . The elastic modulus of each group of equivalent shaft sections is respectively brought into the rotor simplified model, and the first three order modal frequencies are calculated, and the distribution is shown in Figure 10 , 11 and 12.

[0067] c) Uncertainty of the tightening torque

[0068] Figure 13 is the thin layer elastic modulus distribution diagram of the tightening torque uncertainty, the tightening torque is selected as the uncertain parameter for analysis. Based on the constructed Chebyshev orthogonal polynomial model, the first three order modal frequencies of the rotor toothed connection structure are calculated, and the distribution is shown in Figure 14 , Figure 15 and Figure 16 .

[0069] d) Combined influence of multiple parameters

[0070] Figure 17is an equivalent axis segment elastic modulus distribution diagram of multi-parameter uncertainty of the application, considering that multiple uncertainty parameters exist simultaneously, that is, carrying out calculation and analysis on the influence of two-parameter uncertainty of the dynamic modal characteristics of the rotor, namely the centering surface gap and the transverse load. Based on the constructed Chebyshev orthogonal polynomial model, the first three order modal frequencies of the rotor gear connection structure are calculated, and the distribution is shown in Figure 18 、 Figure 19 and Figure 20 .

[0071] (5) Test verification

[0072] Figure 21 、 Figure 22 and Figure 23 indicate the distribution of the first three order test modal frequencies (red circles) of the rotor gear connection structure under different tightening torques in the simulation calculation frequency (red circles) interval. As can be seen from Figure 21 、 Figure 22 and Figure 23 , the first three order frequencies of the test test points are all within the frequency interval obtained by using the method for analysis and evaluation of the application, indicating the correctness and effectiveness of the method of the application.

[0073] 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 take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the application can take the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program code.

[0074] The application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products 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 implemented 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 device that implements the functions specified in the flow Figure 1 flow or multiple flows and / or blocks Figure 1 The computer program instructions can also be stored in a computer readable storage medium capable of causing a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable storage medium produce a manufactured product including instruction devices that implement the functions specified in the flow Figure 1 flow or multiple flows and / or blocksFigure 1 the functions specified in the flow or flows and / or blocks. Such computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable devices to generate computer-implemented processes in order to achieve the functions specified in the flow or flows and / or blocks. Figure 1 the functions specified in the flow or flows and / or blocks. Such computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable devices to generate computer-implemented processes in order to achieve the functions specified in the flow or flows and / or blocks. Figure 1 the functions specified in the flow or flows and / or blocks. Such computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable devices to generate computer-implemented processes in order to achieve the functions specified in the flow or flows and / or blocks.

[0075] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application rather than limit the same, and although the present application has been described in detail with reference to the above examples, those of ordinary skill in the art should understand that the specific embodiments of the present application can be modified or replaced equivalently without departing from the spirit and scope of the present application, and any modifications or equivalent replacements thereof should be covered within the protection scope of the claims of the present application.

Claims

1. A method for uncertainty analysis of rotor sleeve gear connectors using Chebyshev orthogonal polynomials, characterized in that, Includes the following steps: Step SS1: Establish a simplified mechanical model of the toothed connection structure; Step SS2: Determine the key uncertainty parameters based on the rotor sleeve tooth connection structure, including centering surface clearance, lateral load, and tightening torque; Step SS3: Construct a surrogate model for uncertainty analysis of the modal frequencies of the rotor connection structure using Chebyshev orthogonal polynomials; Step SS4: Based on the uncertainty analysis surrogate model of the constructed rotor connection structure modal frequencies, evaluate the influence of different parameters and their combinations on the modal characteristics of the rotor sleeve tooth connection structure.

2. The uncertainty analysis method for rotor sleeve gear connectors using Chebyshev orthogonal polynomials according to claim 1, characterized in that, Step SS3 specifically includes: The Chebyshev orthogonal polynomials are constructed in the case of one parameter as follows: Among them, T k (ξ) denotes a Chebyshev polynomial of the first kind with order k, where k is a non-negative integer, and c i (i = 0, 1, ..., k) are coefficients; the coefficients c in equation (1) are calculated using the Gauss-Chebyshev numerical integration formula. i ,as follows: Where q is the number of integration nodes, ξ (i) w is the interpolation point for the Gauss-Chebyshev integral. (i) These are the corresponding weights.

3. The uncertainty analysis method for rotor sleeve gear connectors using Chebyshev orthogonal polynomials according to claim 2, characterized in that, Step SS3 specifically includes: In the case of multiple parameters, constructing the Chebyshev orthogonal polynomials as follows: The coefficients in equation (3) are calculated using the following numerical integration formula.

4. The uncertainty analysis method for rotor sleeve gear connectors using Chebyshev orthogonal polynomials according to claim 1, characterized in that, Step SS4 specifically includes: based on the constructed uncertainty analysis proxy model of the rotor connection structure modal frequency, performing propagation analysis on the uncertainty parameters, evaluating the influence of different parameters and their combinations on the modal characteristics of the rotor sleeve tooth connection structure, and obtaining the variation range of the rotor connection structure modal frequency.

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