Edge plate damping device optimization method based on Monte Carlo and Latin hypercube

Abstract

The invention provides a marginal plate damping device optimization method based on Monte Carlo simulation and Latin hypercube design, and the method comprises the steps: selecting a certain order of vibration mode of a blade mode to carry out the structure optimization design of a damper based on the vibration mode of the blade mode, and determining the harmonic response frequency range of the blade; processing a blade group substructure by a dual-mode synthesis method, and combining an overall structure matrix through a substructure reduction matrix; obtaining a parameter matrix and a two-dimensional contact surface friction model, and constructing a dynamic equation set with dry friction nonlinearity; a dynamic equation set with dry friction nonlinearity is obtained, and an amplitude-frequency characteristic curve is solved through a harmonic balance method and an arc length continuation method; monte Carlo simulation and Latin hypercube design are carried out, a multi-parameter Monte Carlo simulation analysis program is written, and parameter optimization analysis with the optimal damping effect of the damping device as the target is completed; and obtaining an optimal parameter group to further optimize the original damping structure. The model is processed through a substructure method, and the vibration response of the blade group with dry friction damping under simple harmonic excitation can be predicted.

Description

Technical Field

[0001] This invention belongs to the field of gas turbine technology, specifically relating to an optimization method for a flange damping device based on Monte Carlo and Latin hypercube. Background Technology

[0002] Fatigue fracture caused by blade vibration is one of the core issues in the strength design of modern marine gas turbine blades. To improve the reliability and availability of gas turbines and meet the development requirements for long-life blades with wide temperature ranges, it is essential to analyze the dynamic characteristics of gas turbine blades and implement vibration reduction design. Dry friction damping has advantages such as good vibration reduction performance, simple structure, and high reliability, and is widely used in related fields.

[0003] As a key component, turbine rotor blades are exposed to high-temperature, high-pressure airflow, making their vibration a particularly prominent issue. This vibration is more likely to cause structural fatigue and fracture, thus making vibration suppression of turbine blades especially urgent. Blade damping devices, as important components widely used in turbine blade vibration reduction, place high demands on the materials and shape of the damping devices. Summary of the Invention

[0004] The purpose of this invention is to provide an optimization method for a flange damping device based on Monte Carlo and Latin hypercube principles.

[0005] An optimization method for a blade damping device based on Monte Carlo and Latin hypercube principles includes: selecting a certain vibration mode of the blade for damper optimization design; obtaining the parameters and nodal information of the analysis object; establishing a set of dynamic equations with dry friction nonlinearity; solving the blade amplitude-frequency characteristic curve; performing multi-parameter optimization analysis of the damping structure; and optimizing the original damping structure. Specifically, it includes the following steps: S1. Based on the blade mode shape, select a certain mode shape of the blade for damper structure optimization design and determine the blade harmonic response frequency range; S2, based on the dual mode synthesis method, processes the blade group substructure and combines the overall structure matrix by reducing the substructure matrix; S3, based on the parameter matrix obtained in S2 and the two-dimensional contact surface friction model, constructs a set of dynamic equations with dry friction nonlinearity; S4, based on the dynamic equations with dry friction nonlinearity obtained in S3, solves the amplitude-frequency response curve by harmonic balance method and arc length extension method; S5, based on Monte Carlo simulation and Latin hypercube design, developed a multi-parameter Monte Carlo simulation analysis program to complete parameter optimization analysis with the goal of achieving the best vibration reduction effect of the damping device; S6. Based on the optimal parameter set obtained in S4, the original damping structure is further optimized.

[0006] Furthermore, in the damper optimization design of selecting a certain vibration mode of the blade in S1, blade modal analysis is performed by establishing a single-blade finite element model.

[0007] Furthermore, in the process of obtaining the parameter matrix and node information of the analysis object, the parameter matrix includes the mass and stiffness matrices of the blades and dampers. Using finite element analysis software, finite element models of two blades and dampers are established, and the parameter matrix and node information of the substructure are exported and recombined. The finite element analysis software used is Ansys apdl.

[0008] Furthermore, in S3, the dynamic equations system with dry friction nonlinearity is established. The dynamic equations system is a differential equation system, which is mapped to a nonlinear algebraic equation system in the frequency domain through Fourier Galerkin mapping.

[0009] Furthermore, in the S4 step of solving the blade amplitude-frequency characteristic curve, the solution at the initial frequency is obtained using the harmonic balance method. The nonlinear force and Jacobian matrix are solved using a single-point two-dimensional friction model to establish the functional relationship between the normal and tangential forces on the contact surface and the relative displacement. Then, the contact surface is discretized into multiple contact elements. In actual calculations, the contact force and contact stiffness of each contact element are superimposed to obtain the overall contact force and contact stiffness. The solution at the initial frequency is then obtained using the Newton-Raphson iteration method. Finally, the amplitude-frequency characteristic curve is solved using the arc-length extension method.

[0010] Furthermore, in the multi-parameter optimization analysis, firstly, a turbine blade assembly vibration response calculation program based on the model reduction method is developed using S2-S4. Its input parameters include friction coefficient, modal damping ratio, left and right edge plate angles, contact coefficient, damping block design mass, installation radius, rotor speed, number of contact pairs, harmonic retention number in the harmonic balance method, and number of periodic sampling points. Then, combining Monte Carlo simulation and Latin hypercube design, a multi-parameter Monte Carlo simulation analysis program is developed. The multi-parameter Monte Carlo simulation analysis program is written in MATLAB.

[0011] Furthermore, in the multi-parameter optimization analysis, the design parameters of the flange damping device are the friction coefficient, the angle between the left and right flanges, the contact stiffness, and the design mass of the damping plate.

[0012] The beneficial effects of this invention are as follows: 1. This invention processes the model using the substructure method, which can efficiently and accurately predict the vibration response of blade assemblies with dry friction damping under harmonic excitation, and is generally applicable to general dry friction damping systems.

[0013] 2. This invention solves the problems of vibration response and damper structure optimization of blade assembly with dry friction damping. Therefore, this invention has practical engineering significance, can be used as a reference for engineers, and has considerable application prospects. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the analysis process of the present invention; Figure 2(a) is a model diagram of the blade of the present invention; Figure 2(b) is a model diagram of the damper of the present invention; Figure 3 This is a diagram of the first-order mode shape of the blade of the present invention; Figure 4 This is an assembly drawing of the present invention; Figure 5 This is a diagram showing the vibration pickup and excitation positions of the present invention; Figure 6(a) is a diagram showing the selection of contact pairs in this invention (left blade); Figure 6(b) is a contact pair selection diagram (damper) of the present invention; Figure 6(c) is a contact pair selection diagram of the present invention (right blade); Figure 7 This is a diagram showing the frequency response curve of the blades in this invention; Figure 8(a) is an optimized structure diagram A of the damper of the present invention; Figure 8(b) is a diagram of the optimized structure of the damper of the present invention. Detailed Implementation

[0015] The present invention will now be further described with reference to the accompanying drawings.

[0016] like Figure 1 Figure 8 shows an optimization method for a blade damping device based on Monte Carlo and Latin hypercube principles. This method includes selecting a certain vibration mode of the blade for damper optimization design, obtaining the parameters and nodal information of the analysis object, establishing a set of dynamic equations with dry friction nonlinearity, solving the blade amplitude-frequency characteristic curve, performing multi-parameter optimization analysis of the damping structure, and optimizing the original damping structure. Specifically, it includes the following steps: S1. Based on the blade mode shape, select a certain mode shape of the blade for damper structure optimization design and determine the blade harmonic response frequency range; In the damper optimization design by selecting a certain vibration mode of the blade, the blade modal analysis is carried out by establishing a single blade finite element model. S2, based on the dual mode synthesis method, processes the blade group substructure and combines the overall structure matrix by reducing the substructure matrix; In obtaining the parameter matrix and node information of the analysis object, the parameter matrix includes the mass and stiffness matrices of the blade and damper. Using finite element analysis software, finite element models of two blades and dampers are established, and the parameter matrix and node information of the substructure are exported and recombined. The finite element analysis software used is Ansys apdl. S3, based on the parameter matrix obtained in S2 and the two-dimensional contact surface friction model, constructs a set of dynamic equations with dry friction nonlinearity; In establishing the dynamic equations system with dry friction nonlinearity, the dynamic equations system is a differential equation system. The differential equation system is mapped to a nonlinear algebraic equation system in the frequency domain through Fourier Galerkin mapping. S4, based on the dynamic equations with dry friction nonlinearity obtained in S3, solves the amplitude-frequency response curve by harmonic balance method and arc length extension method; In solving the amplitude-frequency response curve of the blade in S4, the solution at the initial frequency is obtained through the harmonic balance method. The nonlinear force and Jacobian matrix are solved using a single-point two-dimensional friction model to establish the functional relationship between the normal and tangential forces on the contact surface and the relative displacement. Then, the contact surface is discretized into multiple contact elements. In actual calculations, the contact force and contact stiffness of each contact element are superimposed to obtain the overall contact force and contact stiffness. The solution at the initial frequency is obtained using the Newton-Raphson iteration method. Finally, the amplitude-frequency response curve is solved using the arc-length extension method. S5, based on Monte Carlo simulation and Latin hypercube design, developed a multi-parameter Monte Carlo simulation analysis program to complete parameter optimization analysis with the goal of achieving the best vibration reduction effect of the damping device; In the multi-parameter optimization analysis, a turbine blade assembly vibration response calculation program based on the model reduction method was first developed using S2-S4. Its input parameters included friction coefficient, modal damping ratio, left and right edge plate angles, contact coefficient, damping block design mass, installation radius, rotor speed, number of contact pairs, harmonic retention number in the harmonic balance method, and number of periodic sampling points. Then, combining Monte Carlo simulation and Latin hypercube design, a multi-parameter Monte Carlo simulation analysis program was developed. The multi-parameter Monte Carlo simulation analysis program was written in MATLAB. In the multi-parameter optimization analysis, the design parameters of the flange damping device are friction coefficient, left and right flange angle, contact stiffness, and damping plate design mass.

[0017] S6. Based on the optimal parameter set obtained in S4, the original damping structure is further optimized.

[0018] For a certain type of turbine blade model and the original damper, the damper optimization design is carried out, such as... Figure 1 As shown, the damper is installed in the damper slot of one of the blades and abuts against the mating surface of the other blade. The specific assembly results are shown in Figure 2(a) and Figure 2(b). The excitation force on the blade is 20N and the working radius of the damper is 0.397m.

[0019] First, a modal characteristic analysis of the actual blade is performed. Then, the first-order blade mode shape is selected for damper optimization design, such as... Figure 3As shown, this vibration mode is a first-order bending vibration mode, and the first-order natural frequency of the blade is 1801.5Hz. This frequency can determine the range of the blade's harmonic response frequency.

[0020] A finite element model of the blade assembly and damper was established. The blade assembly and damper substructures were processed using the dual modal synthesis method. The parameter matrices and node information of the blade assembly and damper models were exported using ANSYS APDL. The substructure reduction matrices were combined with the overall structural matrix. To calculate the blade's harmonic response, the excitation location was selected at the blade tip, on the thinner side, where the first-order modal displacement response is larger. The excitation location was then selected at the middle of the blade back. Figure 4 As shown.

[0021] Based on the assembly view of the actual blades and dampers, 10 sets of contact pairs were selected in the simulation software, such as... Figure 5 As shown in Figures 6(a), 6(b), and 6(c), 10 contact points are selected on the left blade, 10 contact points on the right blade, and 20 contact points on the damper, forming 10 contact pairs for calculating dry friction damping, thus constructing a system of dynamic equations with dry friction nonlinearity. This completes the preprocessing part for solving the actual blade vibration characteristics.

[0022] A turbine blade assembly vibration response calculation program based on the model reduction method was developed. Under load condition 1.0 and an excitation force of 20 N, the left and right edge angles were set to π / 6 and π / 2, respectively, the contact pair was set to 10°, and the normal and tangential stiffness of the contact surfaces were set to 2 × 10⁻⁶. 7 With N / m, a friction coefficient set to 0.2, and a modal damping ratio set to 0.005, the left blade was excited and vibration-harvested. The amplitude-frequency response curves of the blade under different initial normal pressures were obtained, as shown below. Figure 7 As shown.

[0023] Based on a multi-parameter Monte Carlo simulation analysis program, multi-parameter optimization analysis was performed. In the design parameters, the mass was set between 1 and 10 g, the coefficient of friction between 0.1 and 0.9, the left edge angle between 15° and 75°, the right edge angle also between 15° and 75°, and the contact stiffness was set at 1×10⁻⁶. 7 ~1×10 8Between N / m. The sampling quantity was 300, the excitation force was set to 20N, the rotor speed and rotation radius were set to 9640.99 r / min and 0.397m respectively according to given values, the number of contact pairs was set to 10 according to the model preprocessing, the starting and ending frequencies were 1600Hz and 2000Hz respectively, and the calculation step size was set to 1600. Among the 300 sets of calculation results obtained under the above parameters, the design parameters that minimize the peak displacement response were: mass 1.942g, friction coefficient 0.149, left edge angle 67.1°, right edge angle 44.0°, and contact stiffness 9.4×10. 7 N / m, corresponding to a peak displacement response of 4.95 × 10 N / m. -5 m.

[0024] The optimized parameter set obtained based on the multi-parameter Monte Carlo simulation analysis program is shown in Figure 8(a) and Figure 8(b) according to the obtained flange angle. The material density and mass can be adjusted to remove material from the non-contact surface of the bottom. The friction coefficient is greatly affected by the roughness of the contact surface, and some studies have shown that the contact stiffness is closely related to the contact surface area.

[0025] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An optimization method for a flange damping device based on Monte Carlo and Latin hypercube principles, characterized in that, This includes selecting a certain vibration mode of the blade for damper optimization design, obtaining the parameters and node information of the analysis object, establishing a set of dynamic equations with dry friction nonlinearity, solving the blade amplitude-frequency characteristic curve, multi-parameter optimization analysis of the damping structure, and optimizing the original damping structure. Specifically, the following steps are included: S1. Based on the blade mode shape, select a certain mode shape of the blade for damper structure optimization design and determine the blade harmonic response frequency range; S2, based on the dual mode synthesis method, processes the blade group substructure and combines the overall structure matrix by reducing the substructure matrix; S3, based on the parameter matrix obtained in S2 and the two-dimensional contact surface friction model, constructs a set of dynamic equations with dry friction nonlinearity; S4, based on the dynamic equations with dry friction nonlinearity obtained in S3, solves the amplitude-frequency response curve by harmonic balance method and arc length extension method; S5, based on Monte Carlo simulation and Latin hypercube design, developed a multi-parameter Monte Carlo simulation analysis program to complete parameter optimization analysis with the goal of achieving the best vibration reduction effect of the damping device; S6. Based on the optimal parameter set obtained in S4, the original damping structure is further optimized.

2. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, In the S1 section, a certain vibration mode of the blade is selected for damper optimization design. The blade modal analysis is performed by establishing a single-blade finite element model.

3. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, The parameter matrix and node information of the analysis object are obtained. The parameter matrix includes the mass and stiffness matrices of the blades and dampers. Finite element analysis software is used to establish finite element models of two blades and dampers, export the parameter matrix and node information of the substructure and reassemble them. Ansys apdl is used as the finite element analysis software.

4. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, In the S3, a set of dynamic equations with dry friction nonlinearity is established. The set of dynamic equations is a set of differential equations. The differential equations are mapped to a set of nonlinear algebraic equations in the frequency domain through Fourier Galerkin mapping.

5. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, In the S4 method for solving the blade amplitude-frequency response curve, the solution at the initial frequency is obtained using the harmonic balance method. The nonlinear force and Jacobian matrix are solved using a single-point two-dimensional friction model to establish the functional relationship between the normal and tangential forces on the contact surface and the relative displacement. Then, the contact surface is discretized into multiple contact elements. In actual calculations, the contact force and contact stiffness of each contact element are superimposed to obtain the overall contact force and contact stiffness. The solution at the initial frequency is then obtained using the Newton-Raphson iteration method. Finally, the amplitude-frequency response curve is solved using the arc-length extension method.

6. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, In the multi-parameter optimization analysis, firstly, a turbine blade assembly vibration response calculation program based on the model reduction method was developed using S2-S4. Its input parameters include friction coefficient, modal damping ratio, left and right edge plate angles, contact coefficient, damping block design mass, installation radius, rotor speed, number of contact pairs, harmonic retention number in the harmonic balance method, and number of periodic sampling points. Then, combining Monte Carlo simulation and Latin hypercube design, a multi-parameter Monte Carlo simulation analysis program was developed. The multi-parameter Monte Carlo simulation analysis program was written in MATLAB.

7. The optimization method for a flange damping device based on Monte Carlo and Latin hypercube according to claim 1, characterized in that, In the multi-parameter optimization analysis, the design parameters of the flange damping device are friction coefficient, left and right flange angle, contact stiffness, and damping plate design mass.

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