Axial flow blade frequency optimization method, system and storage medium

Abstract

The present invention discloses a method for optimizing the frequency of axial flow blades, comprising: using a polynomial to determine the distribution of blades along the blade height; using the weighted sum of n Gaussian functions as the objective function for blade frequency optimization; calculating the objective function based on a given excitation frequency and the blade natural frequency calculated by finite element analysis; and modifying the design variables for iterative optimization, so that each order of vibration margin is greater than a set value. By repeatedly searching for the optimal distribution of blade thickness along the blade height, each order of vibration margin can meet the design requirements. This method can effectively prevent the blade natural frequency from the resonance region, thereby avoiding the occurrence of harmful blade vibration. The superiority of this method is more evident when multiple resonance margins are initially insufficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of engine blade vibration, and relates to an axial flow blade frequency optimization method, system and storage medium. Background Art

[0002] Blade vibration is a common problem in aircraft engine development. It can cause fatigue damage to the blades and lead to blade breakage. In severe cases, it can also damage the rotor and stator blades. Therefore, blade vibration has always been a concern.

[0003] The aero-engine blades designed according to aerodynamic theory are designed to meet aerodynamic performance, but often fail to meet vibration requirements. Blade vibration design requires that the blade's resonance margin be greater than a given value, as shown in the following formula:

[0004]

[0005] Where: f je is the excitation frequency (Hz); f i is the i-th order natural frequency; K b is a pre-given percentage allowable margin value, such as K 1b =10; subscripts j and i represent the jth excitation frequency and natural frequency order, respectively.

[0006] The resonance margin must be greater than a certain value, otherwise the blade may resonate and break.

[0007] There are two main types of excitation frequencies:

[0008] 1) The 1-4 node diameter exciting force caused by the uneven airflow along the circumference;

[0009] 2) The wake excitation caused by the airflow passing through the front and rear stator blades. The number of node diameters is related to the number of front and rear stator blades.

[0010] Generally, there are 3-6 or even more excitation frequencies to consider. Generally, there are 1-4 orders of blade natural frequencies to consider, or even more. When these two factors are combined, the resonance margins to consider can reach as many as a dozen. Manual adjustments are extremely difficult.

[0011] Application No. 2019105902688 discloses a frequency modulation design method for gas turbine compressor blades. First, vibration calculations are performed on compressor blades with resonance problems. Based on the calculation results and in combination with blade vibration design criteria, the risks of blade vibration are identified, and then the target frequency value of the blade is determined. Based on the qualitative relationship between blade frequency change and blade thickness adjustment, a preliminary specific thickness value of the blade is given. Vibration calculations are performed on the blades to summarize the quantitative relationship between blade frequency change and blade thickness adjustment. Referring to this relationship and based on the initially determined target frequency value, a second scheme is given. Finally, a reasonable blade adjustment scheme is found through fine-tuning. This method is mainly intended to solve the problem of first-order resonance of compressor blades within the normal operating speed range. It has a limited scope of application and cannot ensure that all vibration margins of each order meet the design requirements. Summary of the Invention

[0012] The purpose of the present invention is to provide an axial flow blade frequency optimization method, system and storage medium, which adopts a polynomial to determine the distribution of blades along the blade height, adopts the weighted sum of n Gaussian functions as the objective function of blade frequency optimization, and repeatedly searches for the optimal distribution of blade thickness along the blade height so that the vibration margins of each order can meet the design requirements.

[0013] The technical solutions for achieving the purpose of the present invention are:

[0014] A method for optimizing the frequency of an axial flow blade comprises the following steps:

[0015] S01: Use polynomial to determine the distribution of blades along the blade height;

[0016] S02: The weighted sum of n Gaussian functions is used as the objective function for blade frequency optimization;

[0017] S03: Calculate the objective function based on the given excitation frequency and the blade natural frequency calculated by finite element method;

[0018] S04: Modify the design variables and perform optimization iterations to make the vibration margins of each order greater than the set values.

[0019] In the preferred technical solution, in step S01, the blades are distributed along the blade height:

[0020]

[0021] Among them, m is the number of terms in the polynomial, j is the natural frequency order, and a j are the polynomial coefficients, and z is the normalized leaf height.

[0022] In the preferred technical solution, after S01, the following steps are further included:

[0023] First, the maximum thickness of the leaf at m normalized leaf heights is given:

[0024] h(z j ) max =h j

[0025] Substitute it into formula (1) to form m linear equations, m unknowns a j ;

[0026] Solve the linear equations to get the coefficient a j .

[0027] In the preferred technical solution, the objective function of blade frequency optimization in step S02 is:

[0028]

[0029] Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency.

[0030] In the preferred technical solution, in step S02, the maximum thickness of the blade at m normalized blade heights is selected as the design variable H = [h1 ... h m ] T ;

[0031] The constraints are as follows:

[0032] H U -H≥{0}

[0033] HH L ≥{0}

[0034] Wherein: subscript U represents the upper limit of H, and L represents the lower limit.

[0035] In a preferred technical solution, the method for calculating the blade natural frequency in step S03 includes:

[0036] S31: generating parameters required for blade shaping, wherein the parameters include a maximum blade thickness;

[0037] S32: Perform blade shaping using an existing blade shaping program to obtain blade profile data;

[0038] S33: Divide the blade finite element mesh according to the blade profile data;

[0039] S34: Use the finite element method to perform geometric nonlinear analysis on the blade at a given speed, obtain the stress distribution of the blade, and calculate the blade's natural frequency.

[0040] The present invention also discloses a computer storage medium on which a computer program is stored. When the computer program is executed, the axial flow blade frequency optimization method is implemented.

[0041] The present invention further discloses an axial flow blade frequency optimization system, comprising:

[0042] The blade height distribution module is constructed, and a polynomial is used to determine the blade height distribution;

[0043] The objective function construction module adopts the weighted sum of n Gaussian functions as the objective function of blade frequency optimization;

[0044] The calculation module calculates the objective function based on the given excitation frequency and the blade natural frequency calculated by finite element method;

[0045] The optimization iteration module modifies the design variables and performs optimization iteration to make the vibration margin of each order greater than the set value.

[0046] In a preferred technical solution, the blade distribution along the blade height constructed by the blade distribution construction module is:

[0047]

[0048] Among them, m is the number of terms in the polynomial, j is the natural frequency order, and a j are the polynomial coefficients, and z is the normalized leaf height.

[0049] In the preferred technical solution, the objective function for blade frequency optimization constructed by the objective function construction module is:

[0050]

[0051] Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency.

[0052] Compared with the prior art, the present invention has the following significant advantages:

[0053] This method uses a polynomial to determine the distribution of blade thickness along the blade height and a weighted sum of n Gaussian functions as the objective function for blade frequency optimization. By repeatedly searching for the optimal distribution of blade thickness along the blade height, the vibration margins of all orders meet the design requirements. This method effectively avoids the resonant region of the blade's natural frequency, preventing harmful vibrations. The advantages of this method are particularly evident when multiple resonance margins are initially insufficient. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flow chart of an axial flow blade frequency optimization method according to an embodiment;

[0055] Figure 2 is a principle block diagram of an axial flow blade frequency optimization system according to an embodiment;

[0056] Figure 3 A schematic diagram of control parameters of the blade profile of a preferred embodiment;

[0057] Figure 4 Schematic diagram of blade profiles of various cross sections of a blade in a preferred embodiment;

[0058] Figure 5 Schematic diagram of the objective function-blade natural frequency curve of the embodiment;

[0059] Figure 6 An optimization flow chart of the axial flow blade frequency optimization system of an embodiment;

[0060] Figure 7 A schematic diagram of leaf profile data points of an embodiment;

[0061] Figure 8 A finite element mesh diagram of an axial flow blade of an embodiment;

[0062] Figure 9 1 is a comparison diagram of the blade points and finite element nodes of the embodiment. DETAILED DESCRIPTION

[0063] The principle of the present invention is: using a polynomial to determine the distribution of blades along the blade height, using the weighted sum of n Gaussian functions as the objective function of blade frequency optimization, and repeatedly searching for the optimal distribution of blade thickness along the blade height so that the vibration margins of each order can meet the design requirements.

[0064] Example 1:

[0065] like Figure 1 As shown, a method for optimizing the frequency of an axial flow blade comprises the following steps:

[0066] S01: Use polynomial to determine the distribution of blades along the blade height;

[0067] S02: The weighted sum of n Gaussian functions is used as the objective function for blade frequency optimization;

[0068] S03: Calculate the objective function based on the given excitation frequency and the blade natural frequency calculated by finite element method;

[0069] S04: Modify the design variables and perform optimization iterations to make the vibration margins of each order greater than the set values.

[0070] In a preferred implementation, in step S01, the blades are distributed along the blade height:

[0071]

[0072] Among them, m is the number of terms in the polynomial, j is the natural frequency order, and a j are the polynomial coefficients, and z is the normalized leaf height.

[0073] In a preferred implementation, S01 and subsequent steps further include:

[0074] First, the maximum thickness of the leaf at m normalized leaf heights is given:

[0075] h(z j ) max =h j

[0076] Substitute it into formula (1) to form m linear equations, m unknowns a j ;

[0077] Solve the linear equations to get the coefficient a j .

[0078] In a preferred implementation, the objective function of blade frequency optimization in step S02 is:

[0079]

[0080] Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency.

[0081] In a preferred implementation, in step S02, the maximum blade thickness values at m normalized blade heights are selected as the design variable H = [h1 ... h m ] T ;

[0082] The constraints are as follows:

[0083] H U -H≥{0}

[0084] HH L ≥{0}

[0085] Among them: H U Indicates the upper limit of H, H L is the lower limit of H.

[0086] In a preferred implementation, the method for calculating the blade natural frequency in step S03 includes:

[0087] S31: generating parameters required for blade shaping, wherein the parameters include a maximum blade thickness;

[0088] S32: Perform blade shaping using an existing blade shaping program to obtain blade profile data;

[0089] S33: Divide the blade finite element mesh according to the blade profile data;

[0090] S34: Use the finite element method to perform geometric nonlinear analysis on the blade at a given speed, obtain the stress distribution of the blade, and calculate the blade's natural frequency.

[0091] In another embodiment, this embodiment further discloses a computer storage medium having a computer program stored thereon, and when the computer program is executed, the axial flow blade frequency optimization method is implemented.

[0092] In another embodiment, Figure 2 As shown, this embodiment further discloses an axial flow blade frequency optimization system, comprising:

[0093] The blade height distribution construction module 10 uses a polynomial to determine the blade height distribution;

[0094] The objective function construction module 20 adopts the weighted sum of n Gaussian functions as the objective function of blade frequency optimization;

[0095] The calculation module 30 calculates the target function according to the given excitation frequency and the blade natural frequency calculated by finite element method;

[0096] The optimization iteration module 40 modifies the design variables and performs optimization iteration so that the vibration margins of each order are greater than the set values.

[0097] Specifically:

[0098] 1) Propose to use polynomial to determine the distribution of blade height

[0099] like Figure 3 As shown, the blade profile can be determined by multiple control parameters, among which the maximum thickness H max It can be used to modify the thickness of the blade. Other parameters are not within the scope of the present invention and will not be described here.

[0100] like Figure 4 As shown, a 3D blade is composed of a series of stacked blade profiles. Modifying the blade thickness generally requires modifying the maximum thickness of each section. Because a blade has many sections, modifying the maximum thickness of each section individually increases the computational complexity and can easily result in unevenness along the blade height.

[0101] This embodiment proposes to use a polynomial to determine the distribution of blade height along the blade:

[0102]

[0103] Where: m is the number of terms in the polynomial (usually 3-6), a j are the polynomial coefficients, and z is the normalized leaf height.

[0104] First, the maximum thickness of the leaf at m normalized leaf heights is given:

[0105] h(z j ) max =h j ,(j=1,…,m)

[0106] Substitute into (1) to form a system of m linear equations, where the m unknowns are a j (j=0,…,m-1).

[0107] Solving the linear equations yields the coefficient a in equation (1): j In this way, the maximum thickness of all sections can be controlled by m parameters hj.

[0108] 2) Propose a mathematical model for blade frequency optimization

[0109] The optimization algorithm is used to select the maximum thickness value of each cross-section blade, and the blade modeling, blade finite element mesh generation, finite element blade dynamic frequency calculation, and resonance margin calculation are performed respectively, so that the resonance margin of the considered blade is all greater than the set value.

[0110] The optimization mathematical model includes three contents:

[0111] Design variables

[0112] Select the above m parameters H=[h1 … h m ] T is the design variable.

[0113] Constraints

[0114] The constraints are as follows:

[0115] H U -H≥{0}

[0116] HH L ≥{0}

[0117] Wherein: the subscript "U" represents the upper limit of H, and "L" represents the lower limit.

[0118] Objective function

[0119] It is proposed to use the weighted sum of n Gaussian functions as the objective function:

[0120]

[0121] Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency.

[0122] The objective function F(f(H)) is a function of the blade natural frequency f(H), and the blade natural frequency f(H) is a function of the design variable H. Therefore, the objective function is ultimately a function of the design variable H.

[0123] Figure 5 The following is a schematic diagram of the objective function-blade natural frequency curve. As can be seen from the figure, the objective function increases sharply as the blade approaches the excitation frequency. These large intervals of the objective function correspond to the blade resonance range. The optimization iteration seeks the minimum value, thereby avoiding these resonance ranges.

[0124] Optimization mathematical model

[0125] Search for:

[0126] H=[h1 … h m ] T

[0127] Among them, R represents a real number, n represents n-dimensional space;

[0128] satisfy:

[0129]

[0130] Minimize:

[0131]

[0132] Optimization algorithms (such as genetic algorithms and composite methods) are used to solve the optimization mathematical model established above. Solving the optimization mathematical model requires repeatedly modifying the design variables and subsequently calculating the objective function. The specific optimization strategy employed by the optimization algorithm determines how the design variables are modified.

[0133] like Figure 6 As shown in Figure 2, the process of modifying design variables and calculating the objective function must be automatically implemented on a computer. The specific steps are as follows:

[0134] 1) Start

[0135] 2) Original parameter input

[0136] Including the excitation frequency, the number of design variables, the upper and lower limits of the design variables, the blade height z corresponding to each design variable, etc.

[0137] 3) Assign initial values to design variables

[0138] For m parameters H=[h1 … h m ] T Set the initial value within the respective upper and lower limits.

[0139] 4) Automatically generate blade shape input data

[0140] The parameters required for blade shaping are shown in Figure 3 , which includes the maximum thickness of the blade.

[0141] 5) Blade shape

[0142] Use the existing blade modeling program to model the blade and obtain the blade profile data. Figure 7 .

[0143] 6) Divide the blade finite element mesh according to the blade profile data

[0144] like Figure 8 Shown is the finite element mesh diagram of an axial flow blade generated based on blade profile data.

[0145] The coordinates of the finite element mesh nodes are obtained by interpolating the coordinates of the blade points. Figure 9 Comparison diagram of blade points and finite element nodes.

[0146] 7) Blade natural frequency calculation

[0147] First, the finite element method is used to perform a geometrically nonlinear analysis of the blade at a given speed (under centrifugal force) to obtain the blade's stress distribution. The blade's natural frequency is then calculated, taking into account the stress generated by the centrifugal force, thereby obtaining the so-called "dynamic frequency."

[0148] 8) Objective function calculation

[0149] The objective function in equation (3) is calculated based on the given excitation frequency and the blade natural frequency calculated by finite element method.

[0150] 9) Modify design variables

[0151] Compare the obtained objective functions and modify the design variables according to the optimization algorithm criteria within the upper and lower limit intervals of the design variables;

[0152] 10) Has the optimization requirement been met? If yes, go to step 11; if no, go to step 4.

[0153] 11) Output optimization results;

[0154] 12) Stop.

[0155] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A method for optimizing the frequency of an axial flow blade, characterized in that: The following steps are involved: S01: Using a polynomial to determine the distribution of blades along the leaf height; the distribution of blades along the leaf height is: Among them, m is the number of terms in the polynomial, j is the natural frequency order, and a j are the polynomial coefficients, z is the normalized leaf height; S02: Using the weighted sum of n Gaussian functions as the objective function for blade frequency optimization; the objective function for blade frequency optimization is: Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency; S03: Calculate the objective function based on the given excitation frequency and the blade natural frequency calculated by finite element method; S04: Modify the design variables and perform optimization iterations to make the vibration margins of each order greater than the set values.

2. The axial flow blade frequency optimization method according to claim 1, characterized in that: The S01 further includes: First, the maximum thickness of the leaf at m normalized leaf heights is given: h(z j ) max =h j Substitute it into formula (1) to form m linear equations, m unknowns a j ; Solve the linear equations to get the coefficient a j .

3. The axial flow blade frequency optimization method according to claim 1, characterized in that: In step S02, the maximum blade thickness values at m normalized blade heights are selected as the design variable H=[h1…h m ] T ; The constraints are as follows: H U -H≥{0} H-H L ≥{0} Among them, H U is the upper limit of H, H L is the lower limit of H.

4. The axial flow blade frequency optimization method according to claim 1, characterized in that: The blade natural frequency calculation method in step S03 includes: S31: generating parameters required for blade shaping, wherein the parameters include a maximum blade thickness; S32: Perform blade shaping using an existing blade shaping program to obtain blade profile data; S33: Divide the blade finite element mesh according to the blade profile data; S34: Use the finite element method to perform geometric nonlinear analysis on the blade at a given speed, obtain the stress distribution of the blade, and calculate the blade's natural frequency.

5. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the axial flow blade frequency optimization method according to any one of claims 1 to 4 is implemented.

6. An axial flow blade frequency optimization system, characterized in that: include: The blade height distribution construction module adopts a polynomial to determine the blade height distribution along the blade; the blade height distribution along the blade height constructed by the blade height distribution construction module is: Among them, m is the number of terms in the polynomial, j is the natural frequency order, and a j are the polynomial coefficients, z is the normalized leaf height; The objective function construction module adopts the weighted sum of n Gaussian functions as the objective function of blade frequency optimization; the objective function of blade frequency optimization constructed by the objective function construction module is: Where: n is the number of resonance margins to be considered, w i is the weighting coefficient, σ k is the variance of the resonance frequency forbidden zone corresponding to the kth excitation frequency, f kj is the jth natural frequency of the node diameter corresponding to the kth excitation frequency, f ek is the kth excitation frequency; The calculation module calculates the objective function based on the given excitation frequency and the blade natural frequency calculated by finite element method; The optimization iteration module modifies the design variables and performs optimization iteration to make the vibration margin of each order greater than the set value.

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